hedge fund strategies -phd thesis
TRANSCRIPT
Electronic copy available at: http://ssrn.com/abstract=1008319
An Analysis of Hedge Fund Strategies
Daniel P.J. CAPOCCI HEC-ULG Management School – University of Liège (Belgium) PhD Thesis in Management
Electronic copy available at: http://ssrn.com/abstract=1008319
A mon petit Louis
Electronic copy available at: http://ssrn.com/abstract=1008319
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An Analysis of Hedge Fund Strategies
by Daniel P.J. CAPOCCI
Senior Portfolio Manager – Kredietbank Luxembourgeoise S.A.
HEC-ULG Management School – University of Liège (Belgium)
Luxembourg School of Finance – University of Luxembourg
EDHEC Risk and Asset Management Research Center
An Analysis of Hedge Fund Strategies – Table of Contents
Acknowledgements .............................................................................................. i
An Analysis of Hedge Fund Strategies - Abstract .................................................. i
Preface................................................................................................................ ii
Introduction and Purpose .................................................................................... 1
Analysis of Hedge Fund Performance ................................................................ 45
Hedge Fund Performance and Persistence in Bull and Bear Markets ................ 120
The Sustainability of Hedge Fund Performance: New Insights ......................... 190
The Neutrality of Market Neutral Funds ........................................................... 273
Diversifying using Hedge Funds: A Utility-Based Approach.............................. 339
General Conclusion ......................................................................................... 405
An Analysis of Hedge Fund Strategies – Table of Contents
References ...................................................................................................... 410
An Analysis of Hedge Fund Strategies – List of Figures ................................... 424
An Analysis of Hedge Fund Strategies – List of Figures ................................... 425
An Analysis of Hedge Fund Strategies – List of Tables..................................... 426
An Analysis of Hedge Fund Strategies – Detailed Table of Contents ................ 431
An Analysis of Hedge Fund Strategies – Detailed Table of Contents ................ 431
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Acknowledgements
I would like to thank sincerely everyone that helped me directly and indirectly
during my work on this thesis. I will start by thanking my parents, Christine Wenders and
Nazzareno Capocci for their constant support.
I would also like to thank my boss, Patrick Vander Eecken, my sweetheart Renata
Vitórica as well as all the authors, anonymous referees and conference participants
(European Investment Review – 2003 and 2004, Global Finance Conference – 2005,
Institutional Fund Management – 2006) for their constructive and helpful comments on
my work. In particular, I would like to thank Vikas Agarwal, Naratip Balajiva, Jean-Marc
Brisy, David Capocci, Mark Carhart, Gabriel Catherin, Kenneth French, Greg N.
Gregoriou, David Hsieh, Bing Liang, Loistl Otto, Narayan Naik, Roger Otten, Magali
Thelen and Dee Weber. I would also like to thank Frédéric Duquenne for using his
impressive programming capabilities to help me finalise my final study.
Last but certainly not least, I would like to thank the members of my doctoral
committee and particularly my co-supervisors Georges Hübner, who worked with me on
several studies and who showed me the way on several occasions, as well as Albert
Corhay who provided constructive remarks on my papers.
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An Analysis of Hedge Fund Strategies - Abstract
This PhD thesis analyses hedge fund strategies in detail by decomposing hedge
fund performance figures. Our aim is to present hedge funds, to understand what
managers expect to do and to understand how they make or destroy value over time. In
order to achieve this objective, we develop a multi-factor performance analysis model,
use it over several time periods and improve it over time. This model aims to determine
both whether hedge funds create pure alpha over time (alpha over classical markets) and
whether there is persistence in hedge fund returns over time. Following this, I analyse
another specific aspect of hedge funds, their neutrality relative to equity markets in order
to validate hedge fund managers’ claims that they are market neutral. Finally, we
develop new efficient frontier measures, which not only include returns and volatility, but
also skewness and kurtosis in order to determine whether hedge funds are really
beneficial to investors.
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Preface
I discovered the term hedge fund at the library of the University of Liège in
September 1999 while reading the abstract of a paper by William Fung and David Hsieh.
This paper was published in the Review of Financial Studies and was called Empirical
Characteristics of Dynamic Trading Strategies: the Case of Hedge Funds. At this time,
hedge funds were somewhat unknown investment vehicles providing very limited
information. Since then, the finance industry and the world of hedge funds in particular
have changed dramatically. Today, hedge funds are present almost everywhere. They
have been studied for years by dozens of academicians and professionals, who have tried
to understand the funds themselves, how hedge fund managers make money, the real
risks underlying alternative strategies, the use of hedge funds as diversification tools and
how they are really different from other investment products.
At the heart of my thesis are the performance figures of hedge fund managers. My
entire thesis is based on performance figures and their use as a way to understand hedge
fund strategies. The thesis is classified in three parts:
Part 1: The Persistence in Hedge Fund Performance
- Analysis of Hedge Fund Performance
- Hedge Fund Performance and Persistence in Bull and Bear Markets
- Sustainability in Hedge Fund Performance: New Insights
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Part 2: An Analysis of Hedge Fund’s Market Exposure
- The Neutrality of Market Neutral Funds
Part 3: Hedge Funds as Diversification Tools
- Diversifying Using Hedge Funds: A Utility-Based Approach
The thesis starts with an extended multi-factor model and a new way of
classifying funds that enables us to identify alpha creators following a persistence
analysis (part one). Part two, on market neutral funds, looks at this prominent hedge
fund strategy. The third and final study is on the inclusion of hedge funds in a portfolio.
My first study on hedge funds performed prior to my PhD uses “spanning” as a
way of determining whether hedge funds enable investors to improve significantly the
risk-return profile of their portfolio, thereby allowing them to reach a higher efficient
frontier. Interestingly, the last study of my doctoral thesis attempts to determine
whether an investor can reach a higher level of utility by including hedge funds in his
portfolio of stock and bond mutual funds. The main difference between this and my first
research on the subject is that both are based on the same underlying idea. The
difference is that in the final study I define and estimate an adapted efficient frontier that
takes into consideration not only volatility, as measured by the standard deviation, but
also higher moments into account when determining the impact of hedge fund insertion
in a classical portfolio (the hypothesis of normality is no longer needed).
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In coming to the end of this thesis, I believe that I have not only learned a great
deal, but have also developed new ideas encouraging me to continue to work on the
subject. I have really enjoyed exploring the world of hedge funds and this thesis is only a
start, since the world of hedge funds is continuously evolving in terms of the number of
funds, assets under management as well as the strategies employed.
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Introduction and Purpose
Hedge funds are private investment vehicles that can take long and short
positions in various markets, using various investment strategies and these funds are
accessible to large investors only. On the one hand, this definition is precise; on the
other, it is very broad. This is clear and focused. From another point of view, the funds
may use various kinds of securities on various markets. This part of the definition is
much more open and allows almost anyone to classify his fund as a hedge fund as long
as it is long and short…
Since the early 1990s, when around 2,000 hedge funds were managing assets
totalling ca. $60 billion, the subsequent growth in the number and asset base of hedge
funds has never really been refuted. The industry only suffered from a relative slowdown
in 1998, but since then has enjoyed a renewed vitality with an estimated total of 10,000
funds managing more than a trillion US dollars by the end of 2006. The growing trend of
the sector remained remarkably sustained during the stock market collapse that started
in March 2000, when the NASDAQ Composite Index reached an all-time high of 5,132,
and finished three years later with a floor level of 1,253. In the meantime, the global net
asset value (NAV) of hedge funds continued to grow at a steady rate of 10.6% (Van
Hedge Funds Advisors International, 2002), contrasting with a decrease of 2.7% in the
worldwide mutual fund industry (Investment Company Institute, 2003). More recently, in
2001, Capocci & Hübner (2004) estimated that there were 6.000 HF managing around
$400b. In 2007, Capocci, Duquenne & Hübner (2007) estimate that there are 10.000 HF
managing around $1trillion. This is a growth of 11% in the number of funds and 26% in
assets over six years.
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The purpose of this doctoral thesis is clearly established: to understand hedge
fund strategies by looking at the performance numbers produced. Our first objective of
the studies is to understand clearly hedge fund managers and to explain how they create
alpha over time. This involves developing, testing and improving a performance analysis
model to understand hedge fund performance, while developing and adapting a
methodology to determine whether there is any persistence in hedge fund returns on the
other. I achieve this objective in three complementary studies grouped in Part 1
(Analysis of Hedge Fund Performance, Hedge Fund Performance and Persistence in Bull
and Bear Markets and Sustainability in Hedge Fund Performance: New Insights).
The second objective of the thesis is clearly linked to the first. Since the purpose
is to understand hedge fund strategies in detail, I perform a specific analysis on the most
represented and the most interesting, market neutral funds. By definition, market neutral
funds must a limited exposure to the market. I check for this neutrality and analyse what
kind of funds consistently outperform over time: the pure market neutral funds, market
timers or funds with a more directional bias (see Part two: An Analysis of Hedge Fund’s
Market Exposure).
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Finally, the third complementary objective for the thesis is to determine whether
hedge fund strategies should be included in a classical portfolio of stocks and bonds. In
Part three, Diversifying Using Hedge Funds: A Utility-Based Approach, we analyse the
inclusion of hedge funds in a portfolio of stocks and bonds. The main originality of this
study centres upon the development of a new efficient frontier, based not only on
volatility but also on higher moments (skewness and kurtosis) and on a utility function
that more closely corresponds to that of the investor without normality or other strong
assumption. The specificities and main objectives of each study are reported in Table 1.
In the remainder of this introduction I present a global literature review. Then, I
present the data issue before disserting on investing in hedge funds for the final
investors. Finally, we present the three parts of the Thesis in detail.
Table 1: Studies Specificities and Objectives
Specificity Objective 1 Objective 2
An Analysis of Hedge Fund Performance
- Introduction of the extended multi-factor model
- Analysis based on performance
- Determine if HF strategies sign. outperform classical markets
- Determine if HF strategies sign. and persis. outperform classical markets
Hedge Fund Performance and
Persistence in Bull and Bear Markets
- Consider various market conditions & adpated model (high yield & mortgage
factors) - Analysis based on performance
- Determine if HF strategies sign. outperform classical markets in bull
and/or bear market conditions
- Determine if HF strategies sign. and persis. outperform classical markets in
bull and/or bear market conditions
The Sustainability of Hedge Fund Performance
- Adapted model (option factors) - Adapted meth. based on performance
& other risk-adj. measures
- Determine if HF strategies sign. outperform classical markets using
several risk-adjusted measures
- Find a systematic way of buying HF in order to sign. and persis. outperform
classical markets
The Neutrality of Market Neutral
Funds
- Focus on market neutral funds (28% of the industry)
- Focused on LT and ST periods and various market conditions
- Determine the market exposure of market neutral funds
- Determine if high/low beta market neutral funds outperform their hig/low
beta peers
Diversifying using Hedge Funds
- Analyse the impact of inserting HF in a classical portfolio taking abnormality
into account - Distinguish between dir. undir HF and
FoF
- Develop a methodology to determine if a portfolio can be diversified with
securities displaying abnormal return dist. charact.
- Determine if bond and/or equity investors should include HF in their
portfolio
This Table reports the specificities and the objectives of the studies grouped in this PhD Thesis. Part 1: The Persistence in Hedge Fund Performance contains three studies (An Analysis of Hedge Fund Performance, Hedge Fund Performance and Persistence in Bull and Bear Markets and the Sustainability of Hedge Fund Performance: new insights). Part 2: An Analysis of Hedge Fund’s Market Exposure contains one study (The Neutrality of Market Neutral Funds). Part 3: Hedge Funds as Diversification Tools contains one study (Diversifying Using Hedge Funds: A Utility-Based Approach). For each Part we report the main specificity of the study and its first and second objective.
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Global Literature Review
There have been many studies on hedge funds covering many different aspects of
the industry. In each of the specific studies reported in the heart of the thesis, we
perform literature reviews including studies whose results are directly linked to the
subject under analysis. In this introduction, we provide a global literature review on
hedge fund studies.
As illustrated in Figure 1, hedge fund academic studies can be classified into four
global categories: 1. Hedge fund performance, 2. Hedge fund investment style, 3.
Correlation analysis and diversification power and 4. Other studies. In the first global
category, we report studies that are focused on hedge fund performance. There are three
fields within this first category of hedge fund performance analysis. The first of these
fields includes studies that compare the performance of hedge funds with equity and
other indices (see for example Ackermann, McEnally and Ravenscraft, 1999; Brown,
Goetzmann and Ibbotson, 1999; Liang, 1999; Amin and Kat, 2001; Liang, 2001; Barès,
Gibson and Gyger, 2002; Liang, 2003; Agarwal and Naik, 2004). Results of such studies
are mitigated. Some authors (Brown et al, 1999; Liang, 1999; Capocci et al., 2005)
conclude that hedge funds have been able to outperform these indices, while others
(Ackermann et al., 1999; Agarwal and Naik, 2004) are more cautious in their conclusion.
Hübner and Papageorgiou (2006) find that there are three kinds of persistence in hedge
fund returns. Firstly, that there is statistical evidence of positive persistence based on
alphas for non-directional portfolios in the bullish period. Secondly, there is statistical
evidence of negative persistence for directional portfolios in both the bullish and the
bearish periods. Finally, the authors find statistical evidence of progressive positive
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persistence based on alphas for funds of funds in both the bullish and the bearish
periods.
The second field of hedge fund performance analysis compares the performance of
hedge funds with mutual funds. In this context, Ackermann, McEnally and Ravenscraft
(1999) and Liang (1999) find that hedge funds consistently achieve better performance
than mutual funds, although they are lower and more volatile than the reference market
indices considered.
The third field of hedge fund performance analysis includes the study of the
persistence of hedge fund returns. Persistence is particularly important in the case of
hedge funds because, as suggested by Brown, Goetzmann and Ibbotson (1999) and
Liang (2000, 2001), the hedge fund industry has a higher attrition rate than is the case
in mutual funds (see Brown, Goetzmann and Ibbotson, 1999). They prove that offshore
hedge funds have positive risk adjusted returns, but they attribute this result to style
effect and conclude that there is no proof of any particular alpha-generating capacity of
some fund managers. Agarwal and Naik (2000) analyse the presence of persistence in
hedge fund returns using a one-year moving average period. They find that there is proof
of persistence in hedge fund performance, particularly for poorly performing funds that
continue to underperform.
Figure 1: Four global categories of hedge fund academic studies
HEDGE FUND PERFORMANCEHEDGE FUND INVESTMENT
STYLECORRELATION ANALYSIS and
DIVERSIFICATION POWEROTHER STUDIES
- Risks (Schneeweis and Spurgin, 1999; Jorion, 2000; Amenc et al., 2002a; Amenc et al., 2002b, Berényi, 2002).
- Bias analysis (Liang, 2000; Fung and Hsieh, 2000.
- Comparison with mutual funds (Ackermann et al., 1999 and Liang, 1999).
- Rolling regression (McGuire, Remolona and Tsatsaronis, 2005)
- Diversification power (Amin and Kat, 2001; Amenc and Martellini, 2002).
- Hedge fund indices (Brooks and Kat, 2001; Amenc and Martellini, 2002; Fung and Hsieh, 2002b).
- Persistence in performance (Agarwal and Naik, 2000; Brown et al., 1999; Hübner and Papagergiou, 2006; Liang 2001; Liang, 2000).
- Dynamic model (Swinkels and Van der Sluis, 2001; Posthuma and Van der Sluis)
- CTAs (see for example Edwards and Park, 1996; Fung and Hsieh, 2001; Gregoriou and Rouah, 2003; Liang, 2003; Spurgin and Georgiev, 2001).
Figure 1 reports four global categories of hedge fund academic studies. We group studies on hedge fund performance, hedge fund investment style, correlation analysis, diversification power and finally the other studies.
- Comparison with classical markets (Ackermann et al., 1999; Brown et al., 1999; Liang, 1999; Amin and Kat, 2001; Liang, 2001; Barès et al., 2002; Liang, 2003; Agarwal and Naik, 2004).
- Sharpe style analysis (Fung and Hsieh, 1997; Brown et al., 1998; Brealy and Kaplanis, 2001, Brown and Goetzmann, 2001, Liang 2001; Ben Dor and Jagannathan, 2002; Liang 2003).
- Correlation analysis (Fung and Hsieh, 1997; Schneeweis and Spurgin, 1997; Liang, 1999; Agarwal and Naik, 1999).
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The vast majority of performance studies on hedge funds have not focused solely
on the behaviour under different market conditions. The periods under review do not
favour this exercise, as periods of downward trending stock markets were rare and
discontinuous between 1994 and March 2000. For the period 1990-1998, Edwards and
Caglayan (2000) found that only three types of hedge fund strategies (Market Neutral,
Event Driven and Macro) provided protection to investors when stock markets decline.
More recently, Ennis and Sebastian (2003) contend that, in general, hedge funds did not
provide investor protection after the market downturn of March 2000; rather, their
superior performance was mostly due to the good market timing of their managers.
The second global category of hedge fund academic studies includes authors
that try to analyse and describe hedge fund investment style and who explain these
features with style models (see for example, Fung and Hsieh, 1997; Brown, Goetzmann
and Park, 1998; Brealy and Kaplanis, 2001; Brown et al., 2001; Liang 2001; Ben Dor and
Jagannathan, 2002 and Liang 2003). In this context, Fung and Hsieh (1997) apply
Sharpe's style analysis (see Sharpe, 1992) to a large sample of hedge funds and
commodity trading advisors (CTAs). They assume that fund returns are linearly related to
the returns through a number of factors and measure those factors through eight
mimicking portfolios. They find that the regressions had little explanatory power and
consequently suggest that the resulting low adjusted r-square is due to the funds’ trading
strategy. Ben Dor and Jagannathan (2002) stress the importance of selecting the right
style benchmarks and emphasise how the use of inappropriate style benchmarks may
lead to the wrong conclusion. A particular aspect that has been taken into account more
recenthly is the style drift in hedge fund returns. This effect comes from the fact that
hedge fund managers are opportunity driven and therefore change style over time.
Brown, Goetzmann and Park (1998) analyse hedge fund returns during the 1997-98
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Asian crisis using rolling regression to take the style drift into consideration. The
methodology consists in realizing a set of linear regressions and moving the estimation
period of each of them by one observation. This simple technique enables one to observe
style variation of a manager over time. This methodology has one major drawback: the
choice of a number of observations used for the estimation. McGuire, Remolona and
Tsatsaronis (2005) apply the same methodology. To handle this issue, Posthuma and Van
der Sluis (2005) propose to use a dynamic style model in which beta can vary over time
developed by Swinkels et Van der Sluis (2001). This technique is adaptive in the sense
that changes in the style exposures are priced up automatically from the data. Unlike the
ad hoc rolling regression approach, the time variation in the exposures is explicitly
modelled. No restrictions are imposed on the betas. As stressed by Posthuma and Van
der Sluis, this model is a state-space model and can be estimated by using standard
Kalman filter techniques1. No window size and ad hoc chosen length need to be used.
The Kalman filter procedure chooses the optimal weighting scheme directly from the
data. The filter is an adaptive system based on the measurement and updating
equations.
The third global category of hedge fund academic studies focuses on the
correlation of hedge funds with other investment products and analyses the power of the
diversification properties of hedge funds. Fung and Hsieh (1997) and Schneeweis and
Spurgin (1998) prove that the insertion of hedge funds into a portfolio can significantly
improve its risk-return profile, thanks to the weak correlation to the funds with other
financial securities. This low correlation is also emphasised by Liang (1999) as well as by
Agarwal and Naik (2004). Amin and Kat (2001) find that stand-alone investment hedge
funds do not offer a superior risk-return profile, but that a great majority of funds
1 See Pollock (1999) for a detailed presentation of the Kalman filtering and space-state models.
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classified as inefficient on a stand-alone basis are able to produce an efficient payoff
profile when mixed with the S&P 500. They obtained the best results when 10-20% of
the portfolio value is invested in hedge funds. Kooli (2007) analyzes the power of hedge
funds as an efficient frontier enhancer. He finds that hedge funds as an asset class
imprive the mean-variance frontier of sets of benchmarks portfolios but that investors
who already hold a diversified portfolio do not improve their statistics using hedge funds.
The author finds however that funds of hedge funds do bring diversification for mean-
variance investors. Taking all these results into consideration, hedge funds are seen as
good investment tool. Amenc and Martellini (2002) prove on the basis of ex-post
estimations that the inclusion of hedge funds in a portfolio can lead to a significant
decrease in the volatility of the portfolio without leading to a significant change in the
returns. This implies that a stronger risk control does not necessarily correspond to a
decrease in return.
In the fourth global category of hedge fund academic studies, “Other studies”,
other authors have analysed various other aspects of the hedge fund industry.
Schneeweis and Spurgin (2000), Jorion (2000), Amenc, Curtis and Martellini (2002),
Amenc, Martellini and Vaissié (2002) and Berényi (2002) study the risks involved in
hedge fund investments. Schneeweis and Spurgin (1999) as well as Amenc, Martellini
and Vaissié (2002) prove that hedge fund returns are not only exposed to the market
risk, but that other risks such as volatility risk, default risk or liquidity risk have to be
considered. Liang (2000) analyse the presence of survivorship bias in hedge fund data
and Fung and Hsieh (2000) include other biases in their analysis. Ackermann, McEnally
and Ravenscraft (1998) emphasise that stricter legal limitations for mutual funds rather
than for hedge funds hinder their performance. Some authors alos studied hedge fund
indices (see Brooks and Kat, 2001; and Amenc and Martellini, 2003). There are many
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different hedge fund index providers such as EACM, HFR, CSFB/Tremont, Zurich Capital,
Van Hedge, the Hennessee Group, Hedgefund.net, LJH Global Investment, Mar, Altvest
and Magnum. Fung and Hsieh (2002b) looked at the natural biases present in hedge fund
indices.
Commodity trading advisors (CTAs) are a particular category in the hedge fund
world. Unlike hedge funds, which first appeared an academic journal in 1997, CTAs have
been studied for a longer period of time. Many studies were published in the late 80s and
in the early 90s (see for example, Elton et al., 1987, 1989, 1990, or Edwards and Ma,
1988). Since 1997, some authors have considered CTAs as part of the hedge fund world
(Fung and Hsieh, 1997; Schneeweis and Spurgin, 2000), whereas others have studied
them either by separating them from hedge funds (Liang, 2003) or on a stand-alone
basis (Fung and Hsieh, 2001; Gregoriou and Rouah, 2003 and Capocci, 2004b). Research
on CTAs is very sparse and it is difficult to present a complete literature review. However,
Billingsley and Chance (1996) and Edwards and Park (1996) demonstrate that CTAs can
add diversification to stocks and bonds in a mean-variance framework. Schneeweis,
Savanayana and McCarthy (1991) and Schneeweis (1996) stated that the benefits of
CTAs are similar to those of hedge funds, in that they improve upon and can offer a
superior risk-adjusted return trade-off to stock and bond indices while acting as
diversifiers in investment portfolios.
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Fung and Hsieh (1997) prove that a constructed CTA style factor has a persistent
positive return when the S&P 500 has a negative return. According to Schneeweis,
Spurgin and Georgiev (2001), CTAs are known regularly to short stock markets. Fung
and Hsieh (2001) analyse CTAs and conclude that they are similar to a look-back call and
a look-back put. Gregoriou and Rouah (2003) examine whether the percentage changes
in the NAVs of CTAs follow random walks. They prove that all classifications (except the
diversified sub-index) behave in the same way as a random walk. The effectiveness of
CTAs in enhancing risk-return characteristics of portfolios could be compromised when
pure random walk behaviour is identified. Kat (2002) finds that allocating to managed
futures allows investors to achieve a very substantial degree of overall risk reduction at
limited cost. Managed futures appear to be more efficient diversifiers than hedge funds.
Regarding performance, the results are mitigated even though Edwards and
Caglayan (2001) conclude that, during bear markets, CTAs provide greater downside
protection than hedge funds, and have higher returns along with a negative correlation
with stock returns in bear markets. Schneeweis and Georgiev (2002) conclude that
careful inclusion of CTA managers in an investment portfolio can enhance its return
characteristics, especially during severe bear markets. Schneeweis, Spurgin and
McCarthy (1996) observe that performance persistence is virtually non-existent between
1987 and 1995. There is little information on the long-term diligence of these funds
(Edwards and Ma, 1998, Irwin, Zulauf and Ward, 1994, Kazemi, 1996). In his book
Managed Trading: Myths and Truths, Jack Schwager reviews the literature on whether
CTAs exhibit performance persistence and conducts his own analysis. He concludes that
there is little evidence that the top performing funds can be predicted. According to
Worthington (2001), between 1990 and 1998, the correlation of managed futures to the
S&P 500 during its best 30 months was 0.33 and that it was –0.25 during the worst 30
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months. Georgiev (2001) underlines, however, that one of the drawbacks of CTAs is that,
during bull markets, their performance is generally inferior to that of hedge funds.
Brorsen and Townsend (2002) have shown that a minimal amount of performance
persistence is found in CTAs and that some advantages might exist in selecting CTAs
based on past performance, when a long time series of data is available and accurate
methods are used. Finally, Capocci (2004b) proves that there is persistence in CTA
returns for badly performing funds, which tend to continue to significantly underperform
their peers.
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The Data Issue
The main issue with hedge fund analysis is access to databases and the quality of
data2. There are several hedge fund databases available but only three of them have
more than ten years of actual data collection experience: the Centre for International
Securities and Derivatives Markets (CISDM) at the University of Massachusetts in
Amherst, Hedge Fund Research (HFR) in Chicago, and Lipper TASS (TASS). As of
December 2004, TASS had 4,130 funds (2,431 live and 1,699 defunct), HFR had 5,158
funds (2,939 live and 2,219 defunct), and CISDM had 3,246 funds (1,315 live and 1,931
defunct). There are four other entrants to this field – The Barclay Group (Barclays),
Morgan Stanley Capital International (MSCI), Eureka Hedge, and Standard and Poors
(S&P). Because of their late entry to this field, their data were largely from reconstructed
history rather than real-time collection of hedge fund performance.
As stated by Liang (2000) and Fung and Hsieh (2006) many hedge funds report to
only a single database. Only few of them report to more than one database. Liang (2000)
reports that not only most funds do not report to the two databases he compared but
moreover that there are significant differences in returns, inception date, net assets
value, incentive fee, management fee, and investment styles across the two databases.
2 See for example Fung & Hsieh (2002b).
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In Figure 2, Fung and Hsieh (2006) compare the HFR, TASS and CISDM
databases. The Venn diagram divides the global hedge fund universe composed of five of
the main hedge fund databases. As shown in Figure 2, the overlap between the
databases is very low. This indicates that results obtained when performing an analysis
based on a specific database may be different if another database is used. Moreover,
generalization based on a single database may not be true for the entire hedge fund
industry since any database only represent part of the industry.
In this Thesis we use HFR, CISDM and Barclays (together and/or individually). Since
most funds do not report to all the existing databases it in interesting to apply the same
methodology to different databases in order to be sure that the results obtained do not
depend on the particular database used. We have done for our extended multi-factor
performance decomposition model. We first apply it to a combination of the HFR and
CISDM databases. Then, we apply the adapted version to CISDM alone before using a
combination of the CISDM and the Barclay databases. Our results remain consistent
independently of the database used. The databases used and their characteristics are
reported in Table 2.
Table 2 indicates that we use between 634 and 4476 individual funds over the five
studies of this Thesis and between 347 and 2011 fund of funds. The period covered goes
from 1994/2000 for the shorter one to 1993/2003 for the longest (without considering
sub-period analysis).
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The second important aspect regarding the quality of hedge fund data is the
presence of biases in databases. First, hedge funds report their performance to hedge
fund database providers on a voluntary basis and a result in statistical sampling theory is
that voluntary participation can lead to sampling biases. Voluntary participation means
that only a portion of the universe of hedge funds is observable. This means that funds
tend to report to databases only when their performance have been good and may stop
reporting once the performance becomes less attractive. This effect leads to a bias in
database that is called instant return history bias or the backfill bias.
The backfill bias on equity market data is commonly calculated by an indirect
approach. As stated by Posthuma and van der Sluis (2003), this indirect approach is
eliminating the first two years of reported data; see e.g. Fama & French (1993). Brown,
Goetzmann & Park (1998) use the method of Park to estimate an instant history of 15
months for the TASS database. Ackermann et al. (1999), Fung & Hsieh (2000), and
Edwards & Caglayan (2001) addressed the backfill bias for hedge funds in different
periods for different databases, and all used indirect approaches. Ackermann et al.
(1999) eliminate two years and find an average annual bias of 0.5% for MAR and HFR
database funds with different sample periods ending in 1995. Fung & Hsieh (2000)
calculate the backfill bias for the TASS database over the period 1994 to 1998. They
eliminate the first 12 months of returns, because they find a median 343 day incubation
period. The lasting mean performance was 1.4% lower over the period 1994–1998,
leading to a backfill bias of 1.4% for the TASS database over the period 1994–1998.
Edwards & Caglayan (2001) use the same indirect approach of eliminating 12 months of
returns from the MAR database and find that the average annual returns of hedge funds
in the first year are 1.17% higher than the annual returns in subsequent years. We
estimate it by calculating the mean return of a portfolio investing in all funds and then we
17
make the same estimation by leaving the first 12, 24, 36 & 60 first returns of each fund.
We then compare the difference in performance.
Figure 2: Hedge fund database universe repartition
Source: Fung & Hsieh (2006)
Table 2: Database Comparison
Data providerNumber of strategies
Hedge fundsPercentage dissolved
Funds of funds
Percentage dissolved
Analysis period
An Analysis of Hedge Fund Performance
HFR/ CISDM 28 2449 28% 347 34% 1994/2000
Hedge Fund Performance and Persistence in Bull
and Bear MarketsCISDM 16 2247 47% 647 33% 1994/2002
The Sustainability of Hedge Fund Performance
CISDM/ Barclays
16 3060 60% 907 72% 1994/2002
The Neutrality of Market Neutral Funds
CISDM 4 634 37% n/a n/a 1993/2002
Diversifying using Hedge Funds
CISDM 16 4476 46% 2011 40% 1993/2003
This Table reports the comparison of the databases used over this PhD Thesis. HFR = Hedge Fund Research, Inc, CISDM = Center for International Securities Derivatives Markets. Nb of strat = number of strategies used, Hedge funds = number of individual hedge funds, Percentage dissolved = percentage of funds in the database that stop reporting to it before the end of the period under review. Funds of funds = funds of hedge funds and analysis period = period under review for the corresponding study.
19
Another very important bias is the survivorship bias. Funds disappearing from
database tend to have poorer performance than existing funds. Not taking these funds
into account leads to survivorship bias. Survivorship bias is calculated as the
performance difference between surviving funds and all funds in the dataset.
Survivorship is an issue in hedge fund analysis and this bias is estimated between 1.5%
(Fung & Hsieh, 1998) & 3% (Liang, 2001). We estimate these biases for our databases
and the results are reported in Table 3.
Our estimation of backfill bias lies between 1.2% and 1.3% when the 12 first
months of existence of each fund is removed to estimations between 2% and 2.2% when
more months are removed. The results indicate that funds outperform over their first
months of existence. Our estimations are in line with those of other studies even if
Posthuma and van der Sluis (2003) recently estimate that the magnitude of the overall
backfill bias is about 4% per annum on average. The difference can have several
reasons. First, they decide to eliminate the last month of existence of any fund by 50%,
this rule will clearly impact estimation. Second, the period they analyse starts in 1996
whereas ours (and many others estimations) is based on data starting in 1993 or 1994.
Third, since most hedge funds still report to one database only, there may be differences
in statistics of the different databases used. We use together or separately HFR, CISDM
and Barclays whereas Posthuma and van der Sluis (2003) has access to TASS. Finally,
Posthuma and van der Sluis (2003) use a direct method of examining the backfill bias.
Instead of eliminating the same average or median incubation period for all funds, the
direct method eliminates the individual incubation period per fund. The information that
they use is information from TASS and it is mainly based on qualitative information from
TASS employee.
20
Table 3: Backfill bias and survivorship bias estimation
Survivorship biasBackfill bias
(12m)Backfill bias
(24m)Backfill bias
(36m)
Analysis of HF Perf. 1.22% 1.2% 1.6% 2.0%
HF Perf. and Pers. in B&B Mkt
1.51% 1.3% 1.8% 2.2%
Sustainability of HF Perf.
1.08% n/a n/a n/a
Neutrality of Mkt Ntl Funds
1.68% n/a n/a n/a
This table reports the estimated survivorship bias and instant return history bias as estimated in four of our studies. Survivorship bias comes from the fact that funds disappearing from database tend to have a worse performance than existing funds. Not taking these funds into account lead to a survivorship bias. Instant return history bias comes from the fact that hedge funds report their performance to hedge fund database providers on a voluntary basis and a result in statistical sampling theory is that voluntary participation can lead to sampling biases.
Without considering what methodology is the best, the differences between
Posthuma and van der Sluis (2003) methodology and ours explain the difference in
estimations. Througout this Thesis, we prefer to use the indirect approach with no
qualitative influence.
21
A last element to stress is that a fund can be accessible to investors even if its
returns are not reported in any database. There are still good managers building a track
record before actively marketing the fund but that will be open to new investors in case
of demand. The use of data is to try to represent the hedge fund industry as closely to
the reality as possible but the hedge fund industry is not limited to funds reporting to
databases. The fact that many funds still report their performance to one database only
comforts us in this idea.
We are convinced that this bias may be quite low. Several authors (see Ackermann et
al, 1999; Fung and Hsieh, 2002b) argue that this bias can be counterbalanced by good
managers that stop reporting to databases when they close the funds to new investors.
Selection bias manifests itself in two basic ways. Hedge funds may enter a database on a
voluntary basis. On the one hand, presumably, only those funds that have good
performance and are looking to attract new investors want to be included in a database.
Therefore, hedge funds in a database tend to have better performance than those that
are excluded. On the other hand, hedge funds may not be participating in a database
because they are not looking to attract new investors. These self-excluded funds may
have better performance than the average hedge fund. Thus, the net effect of selection
bias on the returns of hedge funds in a database is ambiguous. Practically, there is no
way to mitigate this bias and we have to keep in mind that this bias may be present.
22
Our estimation of survivorship bias lies between 1.22% and 1.68%. Such values
are in the lower end of recent estimation. Brown et al. (1999) report a bias of 3% for
offshore hedge funds per year. Fung & Hsieh (2000) use the TASS database and
calculate the annual survivorship bias to be 3% with a 15% drop out rate. Liang (2000)
examines this survivorship bias in hedge fund returns by comparing the TASS and the
HFR database. He finds that the survivorship bias exceeds 2% per year in the TASS
database, while the HFR database survivorship bias equals 0.6%, which is consistent with
the higher drop out rate in the TASS database. Ackermann, McEnally & Ravenscraft
(1999) suggest that two biases, the survivorship bias and the self-selection bias, offset
each other. The difference can be explained by several factors. First, most of our studies
analyses period ending by the end of 2002. Until recently, only the best managers
managed hedge funds. Since the demand for hedge funds exploded after the internet
bubble starting in 2000, more and more players entered the industry. The best managers
continue to launch funds, but less experienced individual are also attracted by the high
fee levels. As any other these funds get listed in databases but as they do not offer
attractive returns, most of them are dissolved after two or three years of data. This
element could explain an increase in the percentage of dissolved funds and a higher
survivorship bias after 2002 or 2003.
Finally, the three parts of this Thesis are based on individual hedge fund data;
several other researchers have used and/or looked at hedge fund indices (see Brooks and
Kat, 2001; Amenc and Martellini, 2003). The use of indices to analyse the hedge fund
world may also lead to measurement problems. There are many hedge fund indices
providers and most of them are reported in Table 4 with their main characteristics.
23
The literature on the subject report five main potential problems with using hedge
fund indices3. First, since the quality of hedge fund data is poor, constructing indices
based on hedge fund data will result in biases in the index. As a result the returns of
hedge fund indices may not be meaningful. Second, some of the best hedge fund
managers do not disclose fund information to the public. If the assets held by these
managers make up a large portion of the assets in the hedge fund universe, then hedge
fund indices will under-represent the returns of the universe. Third, there is a debate on
how indices should be constructed, i.e. equally weighted or asset weighted. Some hedge
fund indices use dollars under management as the weighting for the individual
components.
3 See Liew (2003) and Amenc and Martellini (2003) for more information on the subject.
24
Table 4: Hedge Fund Indices Comparison
ProvidersNb of
StrategiesLaunch Nb of Funds Website
EACM 13 1996 100 eacmalternative.com
HFR 15 1994 1,1 hfr.com
CSFB/Tremont 9 1999 340 hedgeindex.com
Zürich Capital 5 2001 60 zcmgroup.com
Van Hedge 12 1995 750 vanhedge.com
Hennessee Group 22 1992 450 hedgefnd.com
Hedgefund.net 33 1979 1,8 hedgefund.net
LJH Global Investments 16 1992 800 ljh.com
MAR 15 1990 1,3 marhedge.com
Altvest 13 2000 1,4 altvest.com
Magnum 8 1994 NA magnum.com
This Table reports a comparison between the major hedge fund indices available. Nb of strategies = number of strategies as defined by the index provider. Launch = launch date of the indices for the corresponding index provider. Nb of funds = estimated num
In practice this Figure 2 is difficult to determine, since many hedge fund managers
have managed accounts and on/off-shore vehicles. Moreover, hedge funds may have
different levels of leverage and may vary their leverage employed through time.
Standardizing for leverage is problematic in index construction. Fourth, indices, suffer
from the problem that they overweight markets that have had strong historical
performance. Fifth, as shown by Amenc an Martellini (2003), there are significant
differences in return distribution for the same strategies4.
4 Amenc and Martellini (2003) analysed the largest differences between the same indices of the hedge
fund indices providers on a monthly basis and found differences up to 22% for a single month.
25
All these aspects mentioned above mean that the real hedge fund world can be
different from the one analysed in academic papers and that general conclusion cannot
always be applied to particular hedge fund strategies or individual managers.
26
Investing in Hedge Funds
Despite the growing interest in hedge funds, it is difficult for many individual and
institutional investors to participate in this area of the market. Several reasons can
explain this effect: high minimum wealth levels, sophisticated investor requirements or
complexity of the strategy applied. Funds of funds have several advantages in
comparison to individual hedge funds. They provide investors with diversification across
manager styles and professional oversight of fund operations that can provide the
necessary degree of due diligence. In addition, many funds of funds hold shares in hedge
funds closed to new investment allowing smaller investors the access to those managers.
Because of these, funds of funds constitute the only way of investing in hedge funds for
many investors.
There is however, one major drawback: the additional fees. The additional fees
has two main impacts. First, the return distribution of fund of funds will be complex
because strongly impacted by the level of fees and more importantly by the distribution
of these fees. When some underlying funds will offer positive returns, other may be down
leading to a complex distribution of returns for the fund of funds. In addition, the fund of
funds fee structure over the underlying fund one generally cut the profits by a
performance fee once they reach a certain level (LIBOR for example) cutting the upside
of the portfolio while on the downside there is no performance fees. The second and
obvious element is that the additional fee will lower the performance of the fund of funds
that can only be as attractive as the one of the hedge fund industry as a whole if the
fund of funds managers make a good selection of underlying managers. In case of bad
27
choice, the final outcome for investors will be less attractive than stated in academic
studies.
Several studies analyse the impact of fees in funds of funds. Brown et al. (2005)
concluded that funds of funds offered a relatively poor historical performance relative to
the hedge funds in which they invest. They explain the poor performance of funds of
funds by the performance fees charges by underlying funds when they offer a positive
performance even if the fund of funds as a whole is negative. Gregoriou et al. (2005)
compare the performance of funds of funds with the one of portfolio constructed on the
basis of alpha, Sharpe ratio and information ratio and find that a portion of the fund of
funds available can be beaten through a simple selection strategy based on simple
statistics.
These elements stress out that there is a difference between conclusion of
academic paper and the reality for final investors. Care has to be given when trying to
profit from academic conclusion based on individual hedge funds and these cannot
always be applicable for funds of hedge funds.
29
Abstract Part One: The Persistence in Hedge Fund Performance
As stated in the first part of the introduction, the first objective of this Thesis is to
understand hedge fund managers and to explain how they create alpha over time. This
involve developing, testing and improving a performance analysis model in order to
understand hedge fund performance on the one hand, while on the other developing and
adapting a methodology to determine whether there is any persistence in hedge fund
returns. We achieved this objective in three complementary studies (Analysis of Hedge
Fund Performance, Hedge Fund Performance and Persistence in Bull and Bear Markets
and Sustainability in Hedge Fund Performance: New Insights).
The basis of Part 1 is study 1 that aims at answering to one question: What
factors might explain hedge fund returns? We base our multi-factor performance
decomposition model on models that are used in the mutual fund literature for years,
Fama and French (1993)5 and Carhart (1997)6 models. Even if hedge funds are different
from mutual funds by the strategy they apply, the securities they use and the freedom
they have in their management, they remain investment funds. As such, we saw a model
coming from the mutual fund literature as a good basis to build a new performance
decomposition model specific to hedge funds.
5 Fama and French’s (1993) model includes the following: a size factor that takes into account the
difference in performance between small and large companies; a style factor that takes into account
the difference in performance between growth and value players
6 Carhart (1997) extension added a momentum factor that takes into account the fact that certain
managers favour previously well performing stocks in their portfolio.
30
Since hedge funds do invest not only in US equities, we add several factors that
take into account the fact that hedge funds invest in non-US equities and in bonds
(government, corporate, high yield and default), as well as commodities. Our model
evolves over time for several reasons. First, some factors didn’t help explaining hedge
fund performance. Second, in some cases, the correlation between factors increased
leading to a risk of multicolinearity. Finally, some factors were added as they seem to
help decomposing the performance. The models we developed over the three studies are
described in Table 5.
As stated in Table 5, the first model has 11 factors, the second 10 and the one
used in the last part of the analysis 10 and 14. From model 1 to model 2, we re-adjust
the factor used in the model to integrate a high yield factor and a mortgage backed
securities factor to take into consideration the significant increase in the number of funds
exposed to the high yield market and to determine if the exposure of fixed income funds
to the mortgage was high or not7. The high yield factor finally helps but the mortgage
factor does not.
As we will see in the papers, the model with the stronger power of explanation is
model 3 that has a relatively limited number of factors but that covers almost all the
aspects of hedge fund investing and that enable us to reach very high R².
7 There has been a major move in the mortgage market in September 2002 and several hedge funds
have faced strong losses.
31
Table 5: Multi-factor Performance Decomposition Model
Model 1 Model 2 Model 3 Model 4
Capocci & Hübner (2004)
Capocci, Corhay & Hübner (2005)
Capocci (2006)-1
Capocci (2006)-2
Alpha X X X X
US Stock Market X X X X
Size X X X X
Style X X X X
International Style X n/a n/a n/a
Momentum X X X X
Non-US Stock Market X X X X
US Bond X n/a n/a n/a
Wd Gov Bond X X X X
EMBI X X X X
Lehman BAA X n/a n/a n/a
High Yield n/a X X X
Mortgage n/a X n/a n/a
GSCI X X X X
Currency n/a n/a X X
Option Factors n/a n/a n/a X
Number of factors 11 10 10 14
This Table reports a comparison of the multi-factor performance models used in this Thesis. Size = the size market risk premium of Fama and French (1993), style = the style market risk premium of Fama and French (1993), international style = the international style market risk premium of Fama and French (1996), momentum = Carhart’s (1997) "momentum" factor, non-US stock market = MSCI World excluding US, US bonds = the Lehman Aggregate US Bond Index, Wd Gov Bond = JPMorgan world government bond index, EMBI = JP Morgan Emerging Market Bond Index, Lehman BAA = the Lehman BAA Corporate Bond Index, High yield = Lehman High Yield Bond Index, Mortgage = Lehman Mortgage-Backed Securities Index, Salomon World Government Bond Index, GSCI = Goldman Sach Commodity Index, Currency = the Federal Reserve Bank Trade Weighted Dollar Index, Option factors = Agarwal and Naik (2004) at-the-money (ATMC), out-of-the money (OTMC) European call option factors, and at-the-money (ATMP) and out-of-the money (OTMP) European put option factors.
32
Over our three studies on the persistence in hedge fund performance, the
objective is to explain long term hedge fund performance in order to determine whether
some hedge fund strategies significantly outperform classical markets over time. Our
results indicate that most hedge fund strategies do offer significant alpha over a long
period of time. These results were not due to the lack of power of the model since, in all
cases, the adjusted r-squared were very high. The next logical step was to perform the
same analysis under various market conditions and we did that in our second study. More
precisely, we analyse hedge fund performance and persistence in performance over bull
market conditions, bear market conditions and over a full cycle. Our results indicate that
hedge funds tend to outperform during bull market conditions but that this out-
performance is no longer significant under bear market conditions. The only exception
was market neutral strategies, which needed further analysis that is reported later in this
Thesis.
Once we discussed that hedge fund strategies do significantly outperform classical
markets over time, we analysed the persistence of this performance, that is, we looked
at whether there was a repetitive way to isolate it over time. At this level, we reach the
second important basic concept also used in the second study: the decile classification of
Carhart (1997). As we state in the study:
“Active hedge fund selection strategies could increase the expected return
on a portfolio if hedge fund performance is predictable. The hypothesis that
hedge funds with a superior average return in this period will also have a
superior average return in the next period is called the hypothesis of
persistence in performance.”
33
Carhart’s methodology is relatively straightforward to understand. Each year, all
funds are ranked in 10 equally weighted portfolios based on their previous year’s return.
The portfolios are held until the following January and then rebalanced again. The
combination of our multi-factor model with this methodology enables us to determine
whether there is persistence in hedge fund returns.
Our results indicate that there is some proofs of persistence for low volatility funds
that tend neither to be the best performers, nor the worst, but that offer relatively
consistent returns over time. This result was the first important conclusion of our thesis.
It needs deeper analysis over a shorter period of time, which was done in the second
study. Persistence analysis indicates that most of the predictability of superior
performance is found in bull market conditions (prior to March 2000). Our results confirm
several previous studies that found that persistence, if any, is mostly located among
medium performers. In bear market conditions, only negative persistence can be found
among the past losers, suggesting that bad performance has probably been the decisive
factor for hedge funds mortality.
In both studies, low volatility funds were the ones offering significant alpha. The
only issue is that these funds tend to be classified in the middle decile portfolios. This led
us to the conclusion that we needed another way of classifying hedge funds in the
persistence analysis in order to be able to clearly identify the funds that significantly and
consistently outperformed. This is exactly what we did in our third study. We tested
several ways of classifying funds on the basis of their past performance: returns,
volatility, Sharpe ratio, alpha, beta, skewness and kurtosis. Our results clearly indicates
that measures incorporating volatility display a very strong ability to assist investors in
creating alpha and in consistently and significantly outperforming classical indices. We
checked the robustness of our results by performing the same analysis over sub-periods,
34
during bull and bear market conditions (defined as the up and down months of the S&P
500 and as consecutive bull and bear market periods) and by changing the month of
classification (June instead of January). We found a consistent, systematic way of
creating pure alpha using a simple classification methodology based on basic statistics:
risk-return trade-off measures (Sharpe score), pure volatility measures (standard
deviation) and, to a lesser extent, beta exposure, which appear to be better and more
stable ways of classifying hedge funds in order to detect persistency in the returns. Funds
offering stable returns, with limited volatility and/or with limited exposure to the equity
market consistently and significantly outperformed equity and bond markets.
We report the specificity, objectives and main conclusions of each study of Part 1
in Table 6.
Table 6: Persistence Analysis Studies Specificities, Objectives and Conclusions
Objective 1 Conclusion 1 Objective 2 Conclusion 2
An Analysis of Hedge Fund Performance
- Determine if hedge fund strategies significantly outperform classical markets
- Most hedge fund strategies do offer significant alpha over the long term despite a high R²
- Determine if hedge fund strategies significantly and persistently outperform classical markets
- There is no proof of persistence for hedge funds but low volatile funds that tend to neither be the best performers nor the worst
Hedge Fund Performance and Persistence in Bull
and Bear Markets
- Determine if hedge fund strategies significantly outperform classical markets in bull and/or bear market conditions
- Hedge funds tend to outperform during bull market conditions (not significantly in bear markets)
- Determine if hedge fund strategies significantly and persistently outperform classical markets in bull and/or bear market conditions
- No significant outperformance in bear market conditions but for market neutral funds
The Sustainability of Hedge Fund Performance
- Determine if hedge fund strategies significantly outperform classical markets using several risk-adjusted measures
- Most hedge fund strategies do offer significant alpha over the long term despite a high R²
- Find a systematic way of buying hedge funds in order to significantly and persistently outperform classical markets
- Systematic outperformance of hedge fund portfolios invested in previous year' low volatile funds (measured by Sharpe score, standard deviation)
This Table reports the specificities, objectives and conclusion of the studies grouped in Part 1: The Persistence in Hedge Fund Performance. Part 1 countains three studies (An Analysis of Hedge Fund Performance, Hedge Fund Performance and Persistence in Bull and Bear Markets and the Sustainability of Hedge Fund Performance: new insights). For each study we report the main specificities of the study aalong with its first and second objective and conclusions.
36
Abstract Part Two: The Neutrality of Market Neutral Funds
Self-defined market neutral funds significantly and consistently outperformed the
classical market over time. This result requires further analysis. The objective of this
second part is clear: to analyse the exposure to the equity market of market neutral
funds and to explore how to isolate funds that consistently outperform. The study
analyses a complete cycle as well as sub-periods (bull and bear market conditions).
Market neutral funds represent a large part of the industry, around 28% of our database
used in the second Study of Part 1: Hedge Fund Performance and Persistence in Bull and
Bear Markets.
Our results confirm that the betas obtained were low in absolute terms even
though they were all significantly positive. The decile analysis indicates that the more
volatile funds (top and worst performing funds) have the highest market exposure,
confirming that low volatility funds emerge over time. At the individual fund level, one
third of the funds are significantly positively exposed to the market, while two thirds of
the alphas are significantly positive. We perform an analysis at the individual fund level
in order to obtain this result because market neutral index analysis lead to controversial
results. This result also stresses the importance of considering individual funds when
performing an empirical analysis. This can be explained by two reasons. First, the
aggregation of funds in indices leads to an increase in exposure to the equity market.
Second, the funds that are significantly exposed can bias the results because a) the bulk
of the funds are not significantly exposed to the market; only one third of the funds
were, and b) only five percent of the funds are significantly negatively exposed to the
market.
37
Table 7: Neutrality of Market Neutral Fund Specificities,
Objectives and Conclusions
Objective 1 Conclusion 1 Objective 2 Conclusion 2
Neutrality of Mkt Ntl Funds
- Determine the market exposure of
market neutral funds
- Market neutral funds tend to be
significantly exposed to the equity market
(low in absolute terms)
- Determine if high/low beta market
neutral funds outperform their
hig/low beta peers
- Real market neutral funds outperform dirty market neutral funds
This Table reports the specificities, objectives and conclusion of the study of Part 2: An Analysis of Hedge Fund’s Market Exposure. Part 2 countains one study (The Neutrality of Market Neutral Funds). We report the main specificities of the study and its
The sub-period analysis also reports two interesting results. First, during the bear
market, most poor performing market neutral funds out-performed the equity market
without being significantly exposed to the market, but the best performing funds
significantly out-perform the equity market and offer significantly positive returns.
Second, during the bullish period, no index is significantly exposed to the market.
However, during the bearish period, all but the best performing deciles are significantly
exposed to the market, but they all (except the best performing funds) created
significant alpha.
Our analysis leads to the conclusion that most market neutral funds are not
significantly exposed to the equity market, but tend to be more exposed during bear
markets than during bull markets without being negatively impacted. We report the
specificity, objectives and main conclusions of part 2 in Table 7.
38
Abstract Part Three: Hedge Funds as Diversification Tools
Hedge fund performance decomposition and strategy analysis were the first two
aims of this doctoral thesis. In order to complete these analyses, we analysed in our third
and final part the impact of inserting hedge funds into a classical portfolio of stock and
bond mutual funds. Hedge funds exhibit abnormal returns. This is the basic reason why
traditional tools like the mean-variance efficient frontier analysis should not be used for
their analysis. In this paper we develop the idea of an adapted capital market line in an
extended risk-return framework that includes not only volatility as a measure of risk but
also higher moments.
Our methodology is based on the Taylor’s extension of the linex utility function
developed by Bell (1988). We decompose this function and take into account the mean
return, the volatility, the asymmetry of the return distribution (skewness) and the
presence of fat tails (kurtosis). This decomposition enables us to define a new and
extended risk measures that we use in a classical risk-return framework. The only
difference is that the risk factor is no more only defined by the standard deviation of the
returns. This new tool has the same underlying idea as the classical efficient frontier and
can be illustrated the same way while taking into account more sophisticated statistics.
Our results indicate that directional hedge funds should be considered separately
from undirectional hedge funds and fund of hedge funds. Adding a small allocation to
directional hedge funds does not significantly change the risk-return profile offered by
the global portfolio. When more than 20% is allocated to directional hedge funds, there is
a significant improvement for diversified portfolios (20 to 80% allocated to the risky
39
asset). Over a allocation of 50% to directional hedge funds offers significantly more
attractive returnsin every case.
However, adding undirectional hedge funds or fund of funds to a classical portfolio
enables investors to reach higher levels of returns for low and medium risk levels for
allocation as low as 10% to hedge funds. For high allocation to the risky asset,
undirectional strategies do not help diversifying and reaching higher return levels. Our
results confirm that undirectional strategies and funds of funds are diversificating low risk
profile investments and should be used as such.
The new adapted efficient frontier opens new doors for asset allocators. Based on
the clients’ objective and the market conditions, it determines if hedge funds must be
added to the existing portfolio. Moreover it helps to determine what hedge fund strategy
should be favoured.
We report the specificity, objectives and main conclusions of part 3 in Table 8.
Table 8: Hedge Funds as Diversification Tools: Specificities, Objectives and Conclusions
Objective 1 Conclusion 1 Objective 2 Conclusion 2
Diversifying using hedge funds
- Develop a methodology to determine if a portfolio can be
diversified with securities displaying abnormal return distribution characteristics
- Taylor's expansion of Bell's utility function enables us to take skewness and kurtosis
into account - The adapted Capital Market Line and new efficient frontier
complete the development
- Determine if bond and/or equity investors should
include hedge funds in their portfolio
- High allocation to directional hedge funds do significantly
improve the profile - Adding small allocation of
undirecitonal hedge funds and funds of hedge funds
significantly improve the profile
This Table reports the specificities, objectives and conclusion of the study of Part 3: Hedge Funds as Diversification Tools. Part 3 countains one study (Diversifying using Hedge Funds: a utility based approach). We report the main specificities of the study and its first and second objective and conclusions.
Part One: The Persistence in Hedge Fund Performance
Analysis of Hedge Fund Performance
Daniel P.J. CAPOCCI
HEC-ULG Management School – University of Liège (Belgium)
Georges HÜBNER
HEC-University of Liège, Limburg Institute of Financial Economics,
Maastricht University, and Luxembourg School of Finance, University of
Luxembourg.
Capocci, Daniel and Georges Hübner, January 2004, Analysis of Hedge Fund
Performance, Journal Empirical of Finance 11/1, 55-89
45
Analysis of Hedge Fund Performance
Abstract
Using one of the largest hedge fund databases ever used (2796 individual funds
including 801 dissolved), we investigate hedge fund performance using various asset
pricing models, including an extension of Carhart’s (1997) specification combined with
the Fama and French (1998) and Agarwal and Naik (2004) models and a new factor that
takes into account the fact that some hedge funds invest in emerging bond markets. This
addition is particularly suitable for more than half of the hedge fund categories, and for
all funds in general. The performance of hedge funds for several individual strategies and
different sub-periods, including the Asian Crisis period, indicates limited evidence of
persistence in performance but not for extreme performers.
46
Analysis of Hedge Fund Performance
I Introduction
With almost 6.000 funds managing around $400 billion in capital, hedge funds
justify an increased attention in financial press as well as in the academic world. These
funds, that have been existing for more than fifty years, are not legally defined but share
some common characteristics: they use a broad range of instruments like short selling,
derivatives, leverage or arbitrage on different markets. Hedge funds require high
minimum investments and their access is limited to individual investors or to institutions
with large financial resources. Currently, about 90% of hedge fund managers are based
in the US, 9% in Europe, and 1% in Asia and elsewhere. While the number of funds has
more than doubled since the mid-nineties, around 80% of hedge funds are smaller than
$100 million, and around 50% are smaller than $12 million. This reflects the high
number of recent entries.
Scientific literature on performance-evaluation yields controversial results. This
lack of consensus on the « right » model puts researchers in a quandary (Metrick, 1999).
This study investigate hedge funds performance levels and persistence using various
asset-pricing models, including an extension of Carhart’s (1997) model, combined with
the models of Fama and French (1998) and Agarwal and Naik (2004) and with a factor,
never previously used in this context, accounting for the fact that some hedge funds
invest in emerging bond markets. This analysis is carried out for different sub-periods
including the Asian Crisis period and for several individual hedge funds strategies.
47
The rest of the study is organised as follow. Section 2 reviews some of the major
mutual and hedge funds performance studies with a focus on the evolution in the models
used. Section 3 sets out the performance models we will use. The next Section provides
a thorough description of our database. Section 5 brings some insights on hedge fund
performance. Section 6 reports the performance of hedge funds. Section 7 documents
and explains the persistence in hedge fund returns. Section 8 concludes the study.
II Literature Review
2.1 Performance Studies
Despite the increasing interest that hedge funds have originated due to their
recent development, few performance studies have been carried out on hedge funds
comparing to other investment tools like mutual funds. This can partly be explained by
their private characteristics and the difficulties encountered to have access to individual
funds data. Therefore, it is interesting to succinctly consider the results obtained in the
main performance studies of mutual funds before introducing results of studies on hedge
funds.
In general, performance studies can mainly be classified in two categories,
depending on whether they conclude or deny that mutual funds have significantly higher
realized returns that those obtained by following passive strategies8, inducing that
managers of mutual funds have access to sufficient information to recover their costs.
8 See a.o. Lehmann and Modest (1987), Ippolito (1989), and Grinblatt and Titman (1989, 1992) for
contenders of superior performance of hedge funds, and Jensen (1969), Malkiel (1995), Gruber (1996)
and Carhart (1997) for studies reaching the opposite conclusion.
48
Among studies finding superior mutual funds performance, numerous studies
investigate further its persistence. On the one hand, Hendricks et al. (1993), Goetzmann
and Ibbotson (1994), Brown and Goetzmann (1995), and Wermers (1996) show
persistence in mutual funds performance for a short period (1 to 3 years), and attribute
it to hot hands9 or to common investment strategies. It is worth noting that Carhart
(1997) and Daniel and al. (1997) demonstrate that the momentum effect in the share’s
returns explain the hot hands effect detected by Hendricks, et al. (1993). On the other
hand, Ippolito (1989), Grinblatt and Titman (1989, 1992), Elton et al. (1993), Elton et al.
(1996), Sirri and Tufano (1998), and Zheng (1999) report a predictability in the mutual
funds returns over a longer period of time.
Considering the recent interest for this sector, studies on hedge funds persistence
in performance are less frequent. Nevertheless, Agarwal and Naik (2000) sustain that
persistence in hedge funds performance exists. This issue of persistence in performance
is particularly important in the case of hedge funds because, as emphasised by Brown
and al. (1999, 2001) and Liang (1999), hedge funds experience an attrition rate much
higher than mutual funds. Brown and al. (1999) prove that offshore hedge funds display
positive returns adjusted for risk but they attribute this performance to style effect and
conclude that there is hardly any evidence of the existence of differential manager skills.
Ackermann and al. (1999) and Liang (1999) who compare the performance of
hedge funds to mutual funds and several indices find that hedge funds constantly obtain
better performance than mutual funds, although lower than the market indices
considered. They also indicate that the returns in hedge funds are more volatile than
both the returns of mutual funds and those of market indices. Ackermann and
9 This effect means that the securities held by funds that had better performance one year realize
superior returns than other funds the following year.
49
Ravenscraft (1998) emphasise that the stronger legal limitations for mutual funds than
for hedge funds hinder their performance. According to Brown and al. (2001), hedge
funds showing good performance in the first part of the year reduce the volatility of their
portfolio in the second half of the year.
Fung and Hsieh (1997) and Schneeweis and Spurgin (1998) prove that the
insertion of hedge funds in a portfolio can significantly improve its risk-return profile
thanks to their weak correlation with other financial securities. This low correlation is also
emphasised by Liang (1999) and Agarwal and Naik (2000). Amin and Kat (2001) find
that stand-alone investment hedge funds do not offer a superior risk-return profile, but
that a great majority of funds classified as inefficient on a stand-alone basis are able to
produce an efficient payoff profile when mixed with the S&P 500. They obtain the best
results when 10-20% of the portfolio value is invested in hedge funds. Taking all these
results into account, hedge funds seem a good investment tool.
2.2 Evolution in Performance Measurement
In the eighties, performance measures based on the CAPM, like Jensen’s alpha
(1968) and their extensions were commonly used in performance evaluation. The recent
interest in multi-factor models primarily comes from the literature on the cross-sectional
variations in stock return. Several studies10 report that the cross-section of average
returns on U.S. common stocks shows little relation to the betas of the Sharpe (1964)-
Lintner (1965) CAPM or the Breeden (1979) ICAPM. Instead, these authors identify other
factors like the size of the company (Banz, 1981), leverage (Bhetari, 1988),
earnings/price (Basu, 1983), book-to-market (Rosenberg et al. 1985; Fama and French,
10 See e.g. Reinganum (1981), Breeden, Gibbons, and Litzenberger (1989), Fama and French (1996)
and Chan, Jegadeesh and Lakonishok (1996).
50
1992), dividend yield (Litzenberger and Ramaswamy, 1979, 1982) and more recently the
momentum effect (Jegadeesh and Titman, 1993; Carhart, 1995) that have reliable power
to explain the cross-section of average returns.
Subsequent multi-factor models include the 8-factor model developed by Grinblatt
and Titman (1994), the asset class factor model from Sharpe (1992), the 3-factor model
from Fama and French (1993), the 4-factor model from Carhart (1997), and the
international model of Fama and French (1998).11
However, recent studies have cast doubt on the usefulness of these new models.
Kothari and Warner (2001) show that the Fama and French (1993) 3-factor model
provides better results than the classical CAPM, but document that it detects significant
abnormal results (including timing) when none really exists. In addition, Carhart (1997)
develops his own 4-factor model that proves to be superior to the classical CAPM, the
Grinblatt and Titman (1989) 8-factor model and the Fama and French (1993) 3-factor
model.
In hedge funds literature, different models have also been used in performance
evaluation. In an early study, Fung and Hsieh (1997) extend Sharpe’s (1992) asset class
factor model and find five dominant investment styles in hedge funds. Schneeweis and
Spurgin (1998) also use style analysis based on a multi-factor approach. Brown and al.
(1999) and Ackermann and al. (1999) use a single factor model and focus only on total
risk. Agarwal and Naik (2000) use regression-based (parametric) and contingency-table-
based (non-parametric) methods. Their parametric method regresses alphas (or
appraisal ratios) on their lags. For the non-parametric method, they construct a
contingency table of winners and losers depending on the alpha. Liang (1999) uses the
11 See Allen and Soucik (2000) for a description of the major models used in mutual funds
performance studies.
51
extension of Fung and Hsieh (1997) model, regressions based on fund characteristics,
and classical measure like the Sharpe ratio. Agarwal and Naik (2004) propose a general
asset class factor model comprising of excess returns on passive option-based strategies
and on buy-and-hold strategies to benchmark the performance of hedge funds. Agarwal
(2001) uses a model consisting of trading strategy factors and location factors to explain
the variation in hedge funds returns over time.
These results suggest that it is necessary to realize performance studies based on
multi-factor models, rather than simply use the CAPM, but there exists no unanimously
accepted model. Therefore, it is preferable to use several specifications in order to
compare the results obtained.
52
III Performance Measurement Models
For comparison purposes, our study of hedge funds performance starts with the
CAPM. The basic multi-factor specifications are the Fama and French (1993) 3-factor
model and its international version of 1998 (Fama and French, 1998) and the Carhart
(1997) model because they are not dominated by any other model in the mutual funds
performance literature.12 Finally, we construct a multifactor model that extends the
Carhart (1997) model by combining it with factors proposed in Fama and French (1998)
model and Agarwal and Naik (2000) and by adding an additional factor.
3.1 The Capital Asset Pricing Model
The first performance model we use is a single index model based on the classical
CAPM developed by Sharpe (1964) and Lintner (1965). Its equation to estimate is the
following:
( ) TtRRRR PtFtMtPPFtPt ,...,2,1 =+−+=− εβα (1)
where RPt = return of fund P in month t; RFt = risk-free return on month t; RMt =
return of the market portfolio on month t; εPt = error term; αP and βP are the intercept
and the slope of the regression, respectively.
12 Following Bams and Otten (2002) we do not consider the Sharpe’s (1992) asset class factor model
which is an asset allocation model and not an asset evaluation model.
53
The intercept of this equation, αp commonly called Jensen’s alpha (1968) is
usually interpreted as a measure of out- or under-performance relative to the market
proxy used.
3.2 The 3-factor Model of Fama and French (1993) and its international version of Fama
and French (1998)
The Fama and French (1993) 3-factor model is estimated from an expected form
of the CAPM regression. It takes the size and the book-to-market ratio of the firms into
account. It is estimated from the following extension of the CAPM regression:
( ) TtHMLSMBRRRR PttPtPFtMtPPFtPt ,...,2,1 321 =+++−+=− εβββα (2)
where SMBt = the factor-mimicking portfolio for size (‘small minus big’) and HMLt
= the factor-mimicking portfolio for book-to-market equity (‘high minus low’).13 These
factors aim at isolating the firm-specific components of returns.
In the international version of the model, Fama and French (1998) consider twelve
major EAFE (Europe, Australia, and Far East) countries and several emerging markets
and propose an international factor mimicking for book-to-market equity (HML). The
formula is the following:
13 See Fama and French (1993) for a precise description of the construction of SMBt and HMLt.
54
( ) TtIHMLRRRR PttPFtMtPPFtPt ,...,2,1 21 =++−+=− εββα (3)
where IHMLt = an international version of HMLt.
According to Fama and French (1998), the international CAPM cannot explain the
value premium in international returns, but a one-state-variable international ICAPM that
explains returns with the global market return and a risk factor for relative distress
captures the value premium in country and global returns.
3.3 The 4-Factor Model of Carhart (1997)
Carhart’s (1997) 4-factor model is an extension of the Fama and French (1993)
factor model. It takes into account size and book-to-market ratio, but also an additional
factor for the momentum effect. Grinblatt, Titman and Wermers (1995) define this effect
as buying stocks that were past winners and selling past losers. This model is estimated
with the following regression:
( ) TtYRPRHMLSMBRRRR PttPtPtPFtMtPPFtPt ,...,2,1 14321 =++++−+=− εββββα (4)
Where PR1YRt = the factor-mimicking portfolio for the momentum effect.14
14 For a description of the construction of PR1YR see Carhart (1997).
55
As stressed by Daniel et al. (1997), this model assumes that, in the absence of
stock selection or timing abilities, the coefficients of four zero investment factor
mimicking portfolios are appropriate measures of multidimensional systematic risk. It
identifies a matching passive portfolio return for each fund return.
3.4 An Extended Multi-Factor Model
In order to take into account the different characteristics of the hedge fund
industry, we implement a combination and an extension of Carhart’s (1997) 4-factor
model, the international model of Fama and French (1998), and the model used by
Agarwal and Naik (2004) and Agarwal (2001).
This model contains the zero investment strategies representing Fama and
French’s (1993) size and value, Fama and French (1998) international value and
Carhart’s (1997) momentum factor, a default factor (Lehman BAA corporate bond index)
as introduced by Agarwal and Naik (2004), a factor for non-US equities investing funds
(MSCI World excluding US), three factors to take into account the fact that hedge funds
invest in US and foreign bond indices (Lehman US aggregate bond index, Salomon world
government bond index, and JP Morgan Emerging Market Bond Index) and finally a
commodity factor (GSCI Commodity Index). Beyond the combination of existing models,
the originality of this model is to feature a factor that takes into account the fact that
hedge funds may invest in bonds on emerging markets.
In order account for the fact that hedge funds invest in a wide range of equities
including small and large companies, the market proxy used is the Russel 3000 that
represents over 95% of investable US equity market.
56
Note that Agarwal and Naik (2004) and Agarwal (2001) take several additional
factors such as the MSCI Emerging Markets, the Salomon Brothers Government and
Corporate Bond Index, and the Lehman High Yield Bond Index. Their high colinearity with
other factors lead us not to test these indices further.
Following Agarwal (2001) we choose the Goldman Sachs Commodity index instead
of a Gold index used by Fung and Hsieh (1997) as the former indicates better exposure
of hedge funds in commodities especially considering the fact that hedge funds may not
be investing solely in gold among commodities. Its components are weighted according
to their impact on production in the world economy.
( )( ) ( ) ( )( ) ( ) ( ) PtFttPFttPFttP
FttPFttPFttP
tPtPtPtPFtMtPPFtPt
RGSCIRLEHBAARJPMEMBI
RSWGBIRLAUSBIRMSWXUS
YRPRIHMLHMLSMBRRRR
εβββ
βββ
βββββα
+−+−+−+
−+−+−+
++++−+=−
11109
875
44321 1
(5)
where RMt = return on the Russel 3000 index; MSWXUSt = return of the MSCI World
Index excluding US; LAUSBIt = return on the Lehman Aggregate US Bond Index;
SWGBIt = return on the Salomon World Government Bond Index; JPMEMBIt = return of
the JP Morgan emerging market Bond Index; LEHBAAt = return of the Lehman BAA
Corporate Bond Index; GSCIt = return of the Goldman Sachs Commodity Index.
57
IV Data
4.1 Data Providers
First, it is important to stress all information on hedge funds is available
exclusively on a voluntary basis, for ‘allowed’ persons depending on the country in which
the fund wants to find investors. Fortunately, many hedge funds release monthly
information to inform existing investors or to attract new ones. Some data collectors
make them, in turn, available to the qualifying public. As stressed by Amin and Kat
(2001), there are three main hedge fund database providers in the world. These are
‘Managed Account Reports’ (MAR, 1500 funds), ‘Hedge Fund Research, Inc.’ (HFR, 1400
funds), and ‘TASS Management’ (TASS, 2200 funds). These databases are the most used
in academic and commercial hedge fund studies. The MAR database is used, among
others, by Fung and Hsieh (1997), Schneeweis and Spurgin (1998), and Amin and Kat
(2001). HFR is used by Schneeweis and Spurgin (1998), Liang (1999), Agarwal and Naik
(2000, 2002), and Agarwal (2001). The TASS database is used in Brown et al. (2001),
Fung and Hsieh (2000, 2001), and Brown and Goetzmann (2001). The three databases
have never been used together in a study, but Ackermann et al. (1999) and Ackermann
and Ravenscraft (1998) used a combination of HFR and MAR. Liang (2000) uses a
combination of TASS and HFR.
Data vendors do not only collect performance data. For a majority of funds, they
record other useful information such as company name, start and ending date, strategy
followed, assets under management, management and incentive fees, managers’ name
etc. There is no consensus on the definition of the strategy followed but there are
similarities. MAR defines 9 strategies along with 15 sub-strategies. HFR defines sixteen
58
different strategies in two categories, 12 non-directional and 5 directional strategies, plus
the Funds of Funds and the Sector categories. Finally, TASS defines 15 strategies.
4.2 Hedge Funds
We use hedge fund data from HFR and MAR, similarly to Ackermann et al. (1999),
whose database ranges from 1988 to 1995. Both databases give monthly net-of-fee
individual returns and other information on individual funds and group them in indices.
The HFR database provides 198 monthly returns on 1811 individual hedge funds plus 48
HFR indices (16 investment styles with 3 indices for each investment style: onshore,
offshore and a combined index), and the MAR database gives 2354 individual hedge
funds plus 23 indices between January 1984 and June 2000. Then, in each database, we
remove funds that appear twice15 and funds with quarterly returns. This leaves us with
1639 individual hedge funds in the HFR database and 2014 hedge funds in the MAR
database. For the 857 funds present in both databases, we use the database presenting
more observations.
This leaves a total of 2796 individual hedge funds. This is one of the greatest
database ever used in hedge funds performance studies. These funds include 1995
(71%) survived funds and 801 (29%) dissolved funds.
15 This happened in three cases: when the same fund (same name, company, and returns) appeared
twice in the database; when the same fund (same name, and returns) appeared twice in the database
with two different company names; and when the same fund (same company, and returns) appeared
twice in the database with two different fund names.
59
4.3 Risk-free Return and Market Performance
As underlined by Agarwal (2001), a fundamental challenge in a risk-adjusted
analysis of hedge funds is the identification of a meaningful benchmark. Fung and Hsieh
(1997), Schneeweis and Spurgin (1998) and Liang (1999) use style analysis based multi-
factor approach, while Brown et al. (1999) address this issue by employing a Generalised
Stylistic Classification (GSC) algorithm and grouping the managers on the basis of their
realized returns.
We have to choose a market performance index. The alternative is the value-
weighted portfolio of all NYSE, Amex and NASDAQ stocks usually used in mutual funds
performance studies (see for example Fama and French, 1993, 1996, 2000; Carhart,
1997) or the Russel 3000 used in Agarwal and Naik (2004) and Agarwal (2001). The
comparison of descriptive statistics of the two proxies suggests that both market proxies
are very similar.16 The results of the study should not be influenced by the market proxy
chosen.
We take the value-weighted portfolio of all NYSE, Amex and NASDAQ stocks
market proxy, and the one-month T-bill from Ibbotson Associates as the risk-free rate.
16 The comparison is available upon request.
60
4.4 Biases in Hedge Funds Data
Survivorship bias is an important issue in mutual funds performance studies (see
Carhart and al., 2000). In response to this concern, data vendors do backfill fund’s
performance history when a new fund is added to the database. This allows them to
provide data that go back before the starting date of the database itself (usually 1993).
These providers do not eliminate defunct funds and should normally not suffer
from survivorship bias for the years after the start of the databases. However, as pointed
out in several other studies (see Brown et al., 2001), survivorship bias is very likely to be
present and not negligible, although hardly measurable, for the period before 1994. This
bias may severely hinder statistical inference (Hendricks et al., 1997; Carhart et al.,
2000).
Moreover, according to Ackermann et al. (1999) and to Fung and Hsieh (2000),
two upward biases exist in the specific case of hedge funds because, since they are not
allowed to advertise, they consider inclusion in a database primarily as a marketing tool.
The first one is called the self-selection bias is present because funds that realize good
performance have less incentive to report their performance to data providers in order to
attract new investors, because they might be considered by the SEC as making illegal
advertising. The second bias called instant history bias or backfilled bias (Fung and Hsieh
2000) occurs because a fund’s performance history is backfilled after inclusion. This may
cause an upward bias because funds with a poor track record are less likely to apply for
inclusion than funds with good performance history. Nevertheless, to avoid polemics, we
take all funds (both living and dissolved) into account.
61
V Data analysis
We will first discuss evidence of biases before and after 1994 in our database, as
evidence of a serious difference in these two sub-periods would cast doubt on the
reliability of the global analysis for the 1984-2000 period.
5.1 Survivorship bias
Survivorship bias has received considerable attention in the academic literature.
Two definitions of this bias are commonly used in studies: the performance difference
between surviving funds and dissolved funds (e.g. Ackermann et al., 1999) and the
performance difference between living funds and all funds (e.g. Liang, 2000). We report
the bias using both definitions for the whole period and for 2 sub-periods 1984-1993 and
1994-2000.
In Panel A of Table 9, we report a monthly survivorship bias of 0.36% (or 4.45%
per annum) for the whole period using the first formula and in Panel B a bias of 0.07%
per month (0.9% per annum) using the second formula. A look at sub-period biases
indicates that survivorship bias is much higher after 1994.
The particularly low estimate for the bias in the 1984-1993 period is due to the
extremely low attrition rate of hedge funds in the database. As our sample does not
report data on dissolved funds prior to 1994 for MAR and prior to 1993 for HFR, one is
automatically left with funds that survived this period and thus survivorship is indeed
qualitatively maximal. This indicates the lack of reliability of the database for this period.
Ackerman et al. (1999) use the same combination of databases as we do and the
first definition of survivorship bias. Their value (0.16% per year) is lower than the value
we obtain for the whole period and for the second sub-period (respectively 0.9% and
62
4.45% per year) and closer to the one we obtain for the first sub-period (0.6% per year).
This difference can mostly be explained by the different time period analysed. Ackermann
et al. (1999) study the 1988-1995 period, i.e. the greatest part of their time window
does not encompass funds that disappeared during the period. The issue of their
suspiciously low survivorship bias has been extensively discussed by Fung and Hsieh
(2000) and Liang (2000).
The value reported using the second definition for period 1994-2000 (1.2%) is
very close to the percentage of 1.5% from Fung and Hsieh (1998). It is however lower
than the 0.30% monthly bias found by Fung and Hsieh (2000), the 3% bias found by
Liang (2001) and the industry consensus bias of 3% stressed by Amin and Kat (2001).17
Liang (2000) compares the survivorship bias in HFR and TASS database and finds
significant differences between them. He finds out that they are mostly non-overlapping,
but the TASS database is probably more complete as it covers a larger number of
dissolved funds. Our relatively low survivorship is in line with Liang’s (2000) claim that
the HFR and MAR databases taken together do not fully resolve the survivorship issue,
even though our sample covers a larger time period.
17 We find this consensus value quite high when compared to the 0.8-1.5 bias reported by Malkiel
(1995) and Brown and Goetzmann (1995) for US mutual funds.
Table 9: Survivorship Bias in Hedge Funds
Year Return St. Dev. Obs. Return Std. Dev. Obs. Return Std. Dev. Obs.
1984 1,08 3,26 348 0,97 1,57 248 1,36 7,6 76
1985 2,55 1,44 501 2,83 1,61 356 1,87 1,34 121
1986 1,8 1,58 716 1,99 1,55 497 1,58 2,33 195
1987 1,5 4,16 1069 1,4 4,26 782 1,64 5,39 263
1988 1,72 1,54 1376 1,83 1,73 1020 1,44 1,03 332
1989 1,52 0,79 1931 1,65 0,87 1444 1,13 0,76 463
1990 0,74 1,16 2792 0,77 1,22 2063 0,61 1,32 705
1991 2,08 1,67 3880 2,07 1,96 2826 2,12 1,4 1030
1992 1,23 0,61 5280 1,24 0,74 3860 1,2 0,64 1396
1993 1,95 0,47 7245 1,91 0,48 5140 2,07 0,66 2081
1994 0,16 0,69 9856 0,16 0,79 6931 0,15 0,73 2901
1995 1,62 0,86 13528 1,68 1,14 9298 1,48 0,58 4206
1996 1,69 0,75 17654 1,66 0,77 11942 1,75 0,97 5688
1997 1,51 0,81 22454 1,6 0,75 15122 1,35 1,3 7308
1998 0,46 10,08 25735 0,78 11,94 18440 -0,36 3,72 7271
1999 2,46 2,12 25826 2,58 2,09 21712 1,79 2,92 4090
2000 1,15 2,23 12421 1,22 2,23 11880 -1 3,3 529
Mean 84-93 1.62 1.67 1.50
Mean 94-00 1.29 1.38 0.74
Mean 84-00 1.48 1.55 1.19
All Funds Surviving Funds Dissolved Funds
64
Bias 84-93 0,16 per Month Bias 84-93 0,05 per Month
1,96 per Year 0,6 per Year
Bias 94-00 0,65 per Month Bias 94-00 0,09 per Month
7,79 per Year 1,22 per Year
Bias 84-00 0,36 per Month Bias 84-00 0,07 per Month
4,45 per Year 0,89 per Year
Panel B: Living Funds - All FundsPanel A: Living Funds - Dead Funds
This Table reports the survivorship bias of calculated from our database. Our combined HFR/TASS database contains 2796 hedge funds, including 1995 survived funds and 801 dissolved funds as of June 2000. In Panel A survivorship bias is calculated as the performance difference between surviving funds and dissolved funds. In Panel B survivorship bias is calculated as the performance difference between surviving funds and all funds. All returns are net of fees and on a monthly basis. Numbers in the table are monthly percentage.
These biases suggest that poor performance could be the main reason for
disappearance. Figure 3 plots returns of the dissolved funds in our database over the 24-
month period before their exit dates. It shows a declining return pattern towards the date
of exit, indicating inferior performance: it corresponds to a decrease of the mean return of
almost 3.5% in two years.
65
Figure 3: Monthly returns for dead funds towards the
dissolution date
-1,5
-1
-0,5
0
0,5
1
1,5
2
24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
Months to dissolution
Ret
urns
Monthly returns are computed on the MAR/HFR database over the 24-months period
before their exit dates. Data are obtained on 801 individual hedge funds between January
1984 and June 2000.
66
5.2 Instant Return History Bias
When new funds are added into a database, historical returns are backfilled. This
corresponds to a demand by fund managers who market themselves if they have good
track records, i.e. after compiling good performance. Fung and Hsieh (2000) estimate this
bias using a 12 month incubation period. They find a 1.4% per year difference in returns
for the 1994-1998 period.
Following Park (1995), Brown et al. (1997) and Fung and Hsieh (2000), we
estimate this bias for our hedge fund database in two steps. On the one hand, we
estimate the average monthly return using the portfolio which invests in all funds from our
database each month (we called this portfolio the observable one). On the other, we
estimate the average monthly return from investing in all these funds after deleting the
first 12, 24, 36 and 60 months of returns (we called this portfolio the adjusted observable
one). The bias is estimated for the whole period and splitting the time period in two in
order to compare our results with those obtained by Fung and Hsieh (2000). Results are
reported in Table 10.
For the 1/84-6/00 period, the observable monthly return averaged 1.49%, while
the adjusted observable one was 1.42% (when deleting the 12 first months), 1.26% (24
months), 1.20% (36 months), and 1.15% (36 months). This gives an estimate of
approximately 0.9% per year, lower than the 1.4% found by Fung and Hsieh (2000) for
the instant history bias. For the 1/94-6/00 period, the bias of 1.2% per year is closer to
the one of Fung and Hsieh (2000). The remaining difference can be explained by the
difference in time period covered and in the database used. Interestingly, our results
indicate that the longer the estimation period, the bigger the bias.
67
Contrarily to the results reported for the survivorship bias, Table 10 yields a
consistently greater estimate of the instant history bias for the pre-1994 than the post-
1994 period when 24 months or more are deleted.
Based on these pieces of evidence regarding the presence of biases, the rest of this
study will focus on performance level and persistence for the 1994-2000 sub-period, and
only consider the 1984-1993 sub-period in isolation in order to compare the consistency of
the results obtained and relate them to the presence of the biases of the database.
Results for the whole 1984-2000 period are not reported because we may not soundly
claim that the pre- and post-1994 time windows exhibit the same biases with the same
severity.
68
5.3 Basic Performance
Before going in the heart of our work, panel A of Table 10 contains descriptive
statistics of the funds in our database, including living and dead funds. Given that MAR
and HFR classify differently the individual hedge funds, we combine the data for strategies
that exist across both databases (sometimes under different names) and we add the
strategies or sub-strategies present in only one database.18 We contrast hedge funds data
against the descriptive statistics of the market proxy, the MSCI World excluding US, Fama
and French’s (1993) SML and HML, Fama and French’s (1998) international IHML,
Carhart’s (1997) momentum factor, Lehman US aggregate bond index, Salomon World
government bond index, JP Morgan Emerging Market Bond Index, Lehman BAA corporate
bond index (default spread), and Goldman Sachs Commodity Index. These statistics are
reported in panel B of Table 10.
Panel A shows that the highest mean return was achieved by the US Opportunistic
Small Caps (2.58%) followed by the US Opportunistic Growth (2.15%) and by the Sector
(1.91%). Strategies that offer the lowest mean return are Foreign Exchange (0.64%),
Short Sellers (0.71%) and Funds of Funds (0.78%), whereas the mean return of the
whole database is 1.29%. The results are similar for mean excess returns.
18 The description of these strategies is available upon request.
69
Table 10: Estimation of Instant Return History Bias
Mean Annual Return
DifferenceAv. Nb of Fds per
Month
All 1,49% 768
Without 12M 1,42% 0,08% 644
Without 24M 1,26% 0,23% 527
Without 36M 1,20% 0,29% 425
Without 60M 1,15% 0,35% 269
Mean Annual Return
DifferenceAv. Nb of Fds per
Month
All 1,62% 207
Without 12M 1,58% 0,04% 147
Without 24M 1,35% 0,28% 103
Without 36M 1,27% 0,35% 71
Without 60M 1,21% 0,41% 32
Mean Annual Return
DifferenceAv. Nb of Fds per
Month
All 1,29% 1631
Without 12M 1,19% 0,10% 1308
Without 24M 1,16% 0,13% 1017
Without 36M 1,13% 0,16% 773
Without 60M 1,10% 0,19% 426
1/94-6/00
1/84-12/93
1/84-6/00
This Table reports the Instant History Bias calculated from our database. Our combined database contains 2796 hedge funds, including 1995 survived funds and 801 dissolved funds as of June 2000. Instant history bias is calculated as the performance difference between the average monthly return using the portfolio which invests in all funds each month (the observable portfolio) and the average monthly return from investing in these funds after deleting the first 12, 24, 36 and 60 months of returns (the adjusted observable portfolio). All returns are net of fees and on a monthly basis. Numbers in the table are monthly percentage.
70
When standard deviation is taken into account through the Sharpe measure (the
ratio of excess return and standard deviation), results are somewhat different. Funds
offering the best trade-off between risk and return are the US Opportunistic Small Caps
(0.3814), followed by the Market Neutral Convertible Arbitrage (0.3633) and the Market
Neutral Relative Value Arbitrage (0.2766). The worst Sharpe ratio is obtained by the Short
Sellers (0.0465), which are also in the worst performing funds when risk is not taken into
account.
A look at the t-stats indicates that mean returns are significantly different from 0 at
the 5% significance level for all funds but the Short Sellers and that the mean excess
returns are significantly different from 0 at the 1% in a majority of cases..
Panel B of Table 11 shows that the mean excess return of the Market Proxy is
1.26% per month (about 16% per year) and statistically different from zero. This large
value indicates that the period under review is unambiguously bullish. The mean excess
premium of the MSCI World excluding US is an insignificant 0.43% per month. The
average SMB and HML returns are insignificant, unlike the results obtained by Fama and
French (1993) and Carhart (1997).19 The international HML and the momentum factor give
more interesting values. They respectively produced an average premium of 0.28% and
1.15% per month, the latter being economically as well as statistically significant.
19 The differences in SMB and HML can be explained by the different periods covered by our studies.
Their high variance suggests a very unstable behavior.
71
Table 11: Descriptive Statistics of Hedge Funds Strategies and
Passive Investment Strategies
No of Fds Sub-strategy
Living Funds
Dead Funds
Mean Return
t(mean) = 0 Std. Dev.
Event Driven 108 100% 56 52 1,25 3,49 5,06
Distressed Securities 49 45,4% 25 24 0,98 3,34 4,12
Risk Arbitrage 50 46,3% 27 23 1,49 3,76 5,59
No sub-strategy 9 8,3% 4 5 1,08 5,53 2,76
Global 349 100% 184 165 1,02 2,2 6,5
International 62 17,8% 27 35 1,02 2,26 6,35
Emerging 203 58,2% 123 80 0,94 1,98 6,69
Regional Established 84 24,1% 34 50 1,36 4,2 4,56
Global Macro 319 259 60 1,68 4,11 5,75
Market Neutral 711 100% 522 189 1,06 3,78 3,95
Long/short 150 21,1% 83 67 1,31 4,2 4,41
Convertible Arbitrage 44 6,2% 38 6 0,89 9,4 1,33
Fixed Income 61 8,6% 50 11 0,79 2,5 4,43
Stock Arbitrage 392 55,1% 309 83 1,08 3,98 3,81
Mortgage-Backed Sec. 56 7,9% 42 14 0,84 3,78 3,11
Relative Value Arb. 8 1,1% 0 8 1,2 5,94 2,84
Short Sellers 24 9 15 0,71 1,52 6,57
US Opportunistic 212 100% 139 73 1,87 4,29 6,14
Growth 88 41,5% 67 21 2,15 4,49 6,75
Value 110 51,9% 61 49 1,61 4,21 5,38
Small Caps 14 6,6% 11 3 2,58 6,36 5,71
Long Only Leveraged 27 16 11 1,73 3,31 7,33
Market Timing 49 40 9 1,1 3,29 4,69
Equity non-Hedge 120 86 34 1,68 3,53 6,7
Foreign Exchange 9 9 0 0,64 9,29 0,97
Sector 186 132 54 1,91 4,34 6,2
Funds of Funds 347 229 118 0,78 3,55 3,09
Non classified 335 314 21 1,42 3,75 5,33
All funds 2796 1995 801 1,29 3,27 5,56
Panel A: Hedge Funds strategies
72
Median Min Max Mean exc. return
t(mean exc.) =0
Sharpe ratio
Event Driven 0,94 -8,62 6,71 0,85 2,36 0,17
Distressed Securities 0,86 -9,75 6,37 0,57 1,96 0,14
Risk Arbitrage 1,02 -7,97 10,47 1,05 2,65 0,19
No sub-strategy 1,32 -8,79 6,47 0,68 3,47 0,25
Global 0,86 -17,46 10,94 0,61 1,32 0,09
International 0,88 -12,66 9,83 0,62 1,37 0,10
Emerging 0,75 -20,01 11,56 0,54 1,13 0,08
Regional Established 1,12 -8,97 9,54 0,96 2,96 0,21
Global Macro 1,36 -6,27 9,93 1,27 3,12 0,22
Market Neutral 0,92 -3,36 5,29 0,66 2,34 0,17
Long/short 0,98 -1,7 6,54 0,91 2,91 0,21
Convertible Arbitrage 0,84 -1,79 2,31 0,48 5,11 0,36
Fixed Income 0,65 -5,62 7,99 0,38 1,22 0,09
Stock Arbitrage 0,97 -4,59 6,1 0,67 2,49 0,18
Mortgage-Backed Sec. 0,75 -4,31 3,09 0,43 1,96 0,14
Relative Value Arb. 1,24 -5,82 6,62 0,79 3,89 0,28
Short Sellers 0,81 -10,4 10,96 0,31 0,65 0,05
US Opportunistic 1,6 -11,75 13,71 1,47 3,36 0,24
Growth 1,85 -12,41 17,52 1,75 3,65 0,26
Value 1,27 -11,74 10,2 1,2 3,15 0,22
Small Caps 2,41 -7,92 17,53 2,18 5,37 0,38
Long Only Leveraged 1,24 -14,47 15,64 1,32 2,54 0,18
Market Timing 0,77 -2,47 10,38 0,69 2,08 0,15
Equity non-Hedge 1,41 -14,535 11,2 1,28 2,68 0,19
Foreign Exchange 0,61 -5,46 3,05 0,23 3,42 0,24
Sector 1,47 -12,54 12,32 1,51 3,42 0,24
Funds of Funds 0,8 -8,7 6,83 0,38 1,71 0,12
Non classified 1,04 -2,91 6,71 1,02 2,69 0,19
All funds 1,01 -7,88 7,87 0,89 2,25 0,16
Panel A (continued): Hedge Funds strategies
Panel B: Passive Strategies
Mean Return t(mean) = 0 Std. Dev. Median Min Max
Mean excess return
t(excess mean) = 0 Sharpe ratio
Equity
Market Proxy 1,64 5,75 4 2,34 -15,31 7,84 1,26 4,44 0,315
MSCI World Excluding US 0,97 3,18 4,28 1,32 -13,61 12,9 0,43 1,41 0,100
F&F SMB Factor -0,16 -0,48 4,74 -0,45 -16,69 21,49 -0,61 -1,82 -0,129
F&F HML Factor 0 -0,02 3,61 0,1 -9,05 12,03 -0,41 -1,61 -0,115
F&F HML International Factor 0,28 1,28 3,04 0,12 -12,75 7,92 -0,19 -0,87 -0,062
Momentum Factor 1,15 3,7 4,39 1,03 -10,93 13,88 0,81 2,58 0,184
Bond
Lehman US Aggregate -0,12 -1,41 1,19 -0,02 -2,73 3,87 -0,54 -6,32 -0,449
Salomon World Government 0,45 3,64 1,72 0,27 -3,43 5,94 0,05 0,38 0,027
JPM Emerging Market Bond Index 0,97 2,64 5,15 1,68 -21,98 10,55 0,52 1,41 0,100
Lehman BAA Corp. 0,52 4,86 1,51 0,55 -3,12 4,8 0,13 1,18 0,084
Commodity
Goldman Sachs Commodity 0,75 2,06 5,14 0,95 -12,28 15,79 0,26 0,71 0,050
This table shows the inception date, mean returns, t-stat for mean = 0, standard deviation, medians, minimum, maximum, mean excess returns, t-stat for mean excess return = 0, and Sharpe ratios for the individual hedge funds in our combined MAR/HFR database following 12 strategies and 15 sub-strategies, and for 11 passive investment strategies for the 1/1994 and 6/2000 period. Sharpe ratio is the ratio of excess return and standard deviation. In panel A, No of Fds represent the number of funds following a particular strategy (or sub-strategy), Living Funds and Dead Funds represents the number of surviving and dead funds (in June 2000, without considering the new funds established in 6/2000). We calculate the Mean Excess Return and the Sharpe ratio considering Ibbotson Associates one-month T-bills. Numbers in the table are monthly percentage.
74
The highest mean return was obtained by the Market Proxy for equity, and by the
JP Morgan Emerging Market Bond Index for the bond. The Sharpe ratios bring the same
results, with the only difference that the Lehman BAA Corporate (0.0842) has a Sharpe
ratio very close to the one obtained by the JP Morgan Emerging Market Bond Index (0.1).
The Sharpe ratio obtained by our whole hedge fund database (0.1596) is lower
than the one for the Market Proxy (0.3154), and higher than for the MSCI World Excluding
US (0.0999).
5.4 Correlation
Fung and Hsieh (1997), Schneeweis and Spurgin (1998), Liang (1999) and Amin
and Kat (2001) report a weak correlation between hedge funds and other securities.
Hence, the addition of hedge funds to a traditional portfolio should improve its risk-return
trade-off.
Table 12 reports correlation coefficients among and between hedge funds and
passive investment strategies.
Panel A reports correlations among hedge funds strategies. There is a high
variability between different strategies, ranging from 0.97 (between Equity non-Hedge
and US Opportunistic) to –0.80 (between Short Selling and US Opportunistic). 39
correlation coefficients (40%) are greater than 0.80 and 14 (14%) are negative. In
particular, Short Sellers are negatively correlated with all the other hedge fund strategies.
75
Panel B reports correlation coefficients between hedge funds and equity, bond and
commodity indices. The range is narrower than in the previous case (from –0.65 to 0.86).
Correlation coefficients between hedge funds strategies and the Market Proxy are, in
almost all cases, greater than 0.5 whereas they are always smaller than 0.3 with the MSCI
World excluding US and than 0.5 with bond indices (except for the default factor). These
results confirm that hedge funds strategies are weakly correlated with traditional
investment tools.20
Panel C displays correlations among Passive Investment strategies. All coefficients
are below 0.46 (and higher than –0.53) and almost 90% of them are below 0.3, too low to
raise serious multi-colinearity concerns.
20 Except with the market proxy, but this result can easily be understood since the market proxy
contains almost all the American market.
76
VI Hedge Funds Performance
The aim of this section is to determine whether or not hedge funds as a whole and
depending on the strategy followed have out-performed the market. We compute all
estimations by using Newey-West (1987) standard errors to adjust for any autocorrelation
in the returns.
Following the discussion of the previous section, the discussion of performance
models will be performed on the 1994-2000 period, when the database can be considered
as fully reliable.
6.1 Performance Measurement using the CAPM
The first performance model used is the CAPM based single index model. Panel A of
Table 13 reports the results for the strategies, sub-strategies and for the All Funds
category. We use equally weighted portfolio excess returns for each investment style and
for the All Funds category, and we estimate the model for each fund individually.21 The
last columns give the distribution of individually estimated alphas per strategy, with the
percentage of significantly positive, insignificant and negative alphas at the 5% level. This
approach enables us to analyse hedge funds performance in more details.
21 To make individual estimation, we require all funds to have consecutive monthly return history for at
least 24 months, so that relatively accurate risk measures can be estimated.
Table 12: Correlation between Hedge Funds and Passive Investment Strategies
EVT GLB MAC MKN SHS OPP LOL MKT ENH FEX SEC FOF NCL ALL
EVT 1
GLB 0,74 1
MAC 0,85 0,74 1
MKN 0,83 0,82 0,89 1
SHS -0,7 -0,46 -0,73 -0,60 1
OPP 0,85 0,74 0,95 0,84 -0,8 1
LOL 0,85 0,78 0,91 0,87 -0,71 0,91 1
MKT 0,27 0,17 0,44 0,31 -0,22 0,39 0,31 1
ENH 0,86 0,76 0,94 0,83 -0,78 0,97 0,88 0,43 1
FEX 0,77 0,69 0,61 0,71 -0,51 0,62 0,65 0,15 0,65 1
SEC 0,87 0,77 0,94 0,85 -0,78 0,95 0,90 0,42 0,95 0,66 1
FOF 0,83 0,92 0,88 0,95 -0,58 0,84 0,89 0,26 0,83 0,72 0,86 1
NCL 0,1 0,13 0,38 0,35 -0,30 0,35 0,29 0,27 0,26 -0,15 0,30 0,25 1
ALL 0,89 0,87 0,96 0,94 -0,71 0,95 0,93 0,38 0,94 0,71 0,95 0,95 0,32 1
Panel A: Correlation between Hedge Funds strategies
EVT GLB MAC MKN SHS OPP LOL MKT ENH FEX SEC FOF NCL ALL
MKT 0,69 0,64 0,72 0,58 -0,54 0,77 0,67 0,39 0,82 0,58 0,71 0,65 0,10 0,73
WXU 0,13 0,29 0,10 0,25 0,04 0,06 0,18 -0,19 0,05 0,26 0,06 0,27 -0,07 0,16
SMB 0,54 0,36 0,57 0,55 -0,65 0,57 0,58 0,20 0,52 0,31 0,63 0,47 0,27 0,56
HML -0,32 -0,31 -0,45 -0,31 0,49 -0,48 -0,41 -0,30 -0,53 -0,32 -0,48 -0,32 0,00 -0,43
IHML -0,14 -0,05 -0,31 -0,26 0,34 -0,31 -0,30 -0,17 -0,21 -0,02 -0,30 -0,17 -0,29 -0,24
MOM 0,14 0,05 0,29 0,24 -0,35 0,25 0,29 0,28 0,18 0,03 0,26 0,18 0,20 0,23
LUS 0,09 -0,05 0,06 -0,03 -0,06 0,06 0,09 0,05 0,06 0,02 0,04 -0,01 0,02 0,02
SWG 0,02 -0,23 0,00 -0,12 -0,12 0,05 0,00 0,20 0,08 -0,10 0,04 -0,19 0,01 -0,06
MEM 0,20 0,31 0,16 0,24 -0,01 0,11 0,25 -0,18 0,09 0,35 0,08 0,30 -0,16 0,20
BAA 0,66 0,55 0,49 0,58 -0,40 0,51 0,56 0,19 0,54 0,86 0,53 0,57 -0,13 0,58
GSC 0,35 0,18 0,31 0,32 -0,27 0,28 0,34 0,15 0,31 0,39 0,31 0,25 0,03 0,30
Panel B: Correlation between Hedge Funds strategies and Passive Investments strategies
MKT WXU SMB HML IHML MOM LUS SWG MEM BAA
MKT 1
WXU -0,1 1
SMB 0,02 0,09 1
HML -0,43 0,02 -0,28 1
IHML -0,05 0,23 -0,38 0,08 1
MOM 0,08 -0,23 0,31 -0,14 -0,52 1
LUS 0,13 0,04 -0,04 0,06 -0,06 0,04 1
SWG 0,13 -0,30 -0,10 -0,07 0,03 0,14 0,38 1
MEM -0,01 0,46 0,06 0,06 0,15 -0,12 0,24 -0,15 1
BAA 0,45 0,19 0,20 -0,27 0,00 -0,01 0,15 0,04 0,23 1
GSC 0,44 -0,03 -0,03 -0,06 -0,1 0,22 0,19 0,38 -0,01 0,43
This Table reports the correlation coefficient between hedge funds strategies (Panel A), between hedge funds strategies and passive investment strategies (Panel B) and between passive investment strategies for the January 1994-June 2000 period. EVT = Event Driven, GLB = Global, MAC = Global Macro, MKN = Market Neutral, SHS = Short Selling, OPP = US Opportunistic, LOL = Long only Leveraged, MKT = Market Timing, ENH = Equity non-Hedge, FEX = Foreign Exchange, SEC = Sector, FOF = Funds of Funds, NCL = Non Classified, ALL = All hedge funds, MKT = Market Proxy, WXU = World excluding US, IHML = International HML, MOM = Momentum, LUS = Lehman US Aggregate Bond Index, SWG = Salomon World Government Bond Index, MEM = JP Morgan Emerging Market Bond Index, BAA = Lehman BAA Corporate Bond Index and GSC = Goldman Sachs Commodity Index.
Panel C: Correlation between Passive Investment strategies
80
The betas estimated in Panel A are rather low, except for US Opportunistic Growth
and the Long Only Leveraged, suggesting the need to use a more detailed model. Overall,
two thirds of the strategies produce significantly positive alphas. The All Funds category
also significantly out-performs the market at the 1% level. In almost all out-performing
strategies, more than 30% of the alphas are significant. Surprisingly, for some strategies
(e.g. Equity non-Hedge or the Non Classified funds), more than 80% of the individual
funds do not significantly out-perform the market, inducing that the best funds must have
obtained extremely high returns.22
6.2 Performance Measurement using Multi-Factor Models
It is presumably better to use a multi-factor model to account for all possible
investment strategies. In Panel B of Table 13, we report the results for Carhart’s 4-factor
model and in Panel C the results for our combined model applied to hedge funds.23
Panels B and C reveal that the premium on the SMB factor is, in almost all cases,
significantly positive. However, in the Short Sellers strategy, the premium is significantly
negative. Panel C shows that the HML (respectively IHML) factor seems to add less
explanatory power as only one third (respectively one seventh) of the factors is
significantly positive at the 5% level. The momentum factor does not prove to be a strong
indicator of hedge funds behaviour. Only 6 out of 28 investment styles exhibit significant
momentum loadings (at the 10% level). Moreover, the sign of the coefficient is in 3 cases
negative, indicating momentum contrarian strategies.
22 These results are remarkably similar to the 1984-1994 period (data available upon request).
23 The Fama and French (1993) model produces results very similar to the Carhart model.
81
Panel C also indicates that the World excluding US, US Bond, Default, World
Government Bond and Commodity factors add explanatory power in 20 to 33% of the
cases. The default factor has, as we can expect, a negative impact in half of the cases.
The Emerging Bond factor adds explanatory power in 16 of the strategies and sub-
strategies. It is highly significant (at the 1% level) in more than half of the strategies, as
well as for the All Funds category.
These results provide some insight into the preferences of hedge funds managers
depending on the strategy followed:
Almost all managers seem to prefer smaller stocks;
Most Event Driven, Market Neutral and US Opportunistic managers prefer stocks with
high book-to-market ratios;
Some Event Driven and Market Neutral managers follow a momentum strategy and
others are momentum contrarian;
More than half of the managers invest in emerging bond markets.
82
Table 13: Performance Measurement using the CAPM,
Carhart’s 4-factor model and the combined model.
R² adj No Fds
Event Driven 0,35% ** 0,42 *** 0,57 84 25% 73% 2%
Distressed Sec. 0,10% 0,39 *** 0,43 37 11% 89% 0%
Risk Arbitrage 0,55% *** 0,45 *** 0,53 38 42% 53% 5%
No sub-strategy 0,18% 0,42 *** 0,4 9 11% 89% 0%
Global -0,13% 0,62 *** 0,45 258 12% 86% 3%
International -0,03% 0,54 *** 0,54 50 10% 90% 0%
Emerging -0,26% 0,67 *** 0,38 151 9% 87% 4%
Regional Est. 0,43% ** 0,44 *** 0,53 57 19% 79% 2%
Global Macro 0,62% *** 0,55 *** 0,62 252 23% 75% 2%
Market Neutral 0,40% *** 0,21 *** 0,42 553 33% 66% 1%
Long/short 0,72% *** 0,16 *** 0,26 102 34% 64% 2%
Convertible Arb. 0,41% *** 0,06 *** 0,08 39 74% 26% 0%
Fixed Income -0,08% 0,39 *** 0,43 48 10% 88% 2%
Stock Arbitrage 0,38% *** 0,24 *** 0,38 310 31% 68% 1%
Mortgage-Back. 0,35% *** 0,07 *** 0,06 46 28% 70% 2%
Alpha Distribution + / 0 / -Alpha Mkt
83
Panel A (continued): Single index model
R² adj No Fds
Rel. Value Arb. 0,51% ** 0,2 *** 0,19 8 50% 50% 0%
Short Sellers 0,86% *** -0,48 *** 0,39 18 28% 72% 0%
US Opport. 0,50% *** 0,8 *** 0,7 180 19% 81% 1%
Growth 0,60% *** 0,96 *** 0,65 68 24% 76% 0%
Value 0,36% ** 0,7 *** 0,74 100 14% 85% 1%
Small Caps 1,39% *** 0,66 *** 0,35 12 33% 67% 0%
Long Only Lev. 0,17% 0,96 *** 0,54 18 11% 83% 6%
Market Timing 0,47% *** 0,18 *** 0,14 34 26% 74% 0%
Equity non-Hed. 0,24% 0,86 *** 0,77 112 9% 89% 2%
Foreign Exch. 0,01% 0,19 *** 0,37 9 0% 67% 33%
Sector 0,68% *** 0,69 *** 0,62 128 30% 67% 2%
Funds of Funds -0,07% 0,37 *** 0,49 278 13% 83% 4%
Non classified 4,83% *** 0,08 0,01 230 13% 86% 0%
All funds 0,36% ** 0,44 *** 0,64 2154 24% 74% 2%
Mean R²adj 0,44 Mean 23% 74% 3%
Alpha Distribution + / 0 / -Alpha Mkt
84
Event Driven 0,43% *** 0,44 *** 0,24 *** 0,11 ***
Distressed Sec. 0,24% 0,42 *** 0,29 *** 0,14 ***
Risk Arbitrage 0,62% *** 0,46 *** 0,22 *** 0,09 ***
No sub-strategy 0,08% 0,41 *** 0,14 *** 0,08
Global 0,03% 0,63 *** 0,26 *** 0,10
International 0,10% 0,54 *** 0,21 *** 0,06
Emerging -0,07% 0,68 *** 0,29 *** 0,09
Regional Est. 0,53% *** 0,44 *** 0,21 *** 0,07
Global Macro 0,67% *** 0,51 *** 0,27 *** 0,03
Market Neutral 0,42% *** 0,21 *** 0,14 *** 0,05 *
Long/short 0,71% *** 0,17 *** 0,15 *** 0,10 ***
Convertible Arb. 0,45% *** 0,08 *** 0,06 *** 0,06 ***
Fixed Income 0,02% 0,33 *** 0,16 *** -0,08
Stock Arbitrage 0,41% *** 0,24 *** 0,17 *** 0,06 *
Mortgage-Back. 0,29% *** 0,08 *** 0,01 0,04
Alpha Mkt SMB HML
85
R² adj No Fds
Event Driven -0,06 *** 0,78 84 27% 69% 4%
Distressed Sec. -0,11 *** 0,70 37 14% 81% 5%
Risk Arbitrage -0,04 * 0,68 38 42% 55% 3%
No sub-strategy 0,11 *** 0,50 9 22% 78% 0%
Global -0,12 ** 0,53 258 14% 84% 3%
International -0,09 *** 0,63 50 10% 88% 2%
Emerging -0,14 * 0,45 151 11% 87% 3%
Regional Est. -0,06 * 0,66 57 25% 72% 4%
Global Macro 0,03 0,83 252 31% 68% 2%
Market Neutral 0,00 0,64 553 37% 62% 1%
Long/short 0,01 0,59 102 36% 63% 1%
Convertible Arb. -0,04 *** 0,20 39 77% 23% 0%
Fixed Income -0,01 0,53 48 8% 92% 0%
Stock Arbitrage 0,00 0,59 310 38% 61% 1%
Mortgage-Back. 0,04 ** 0,07 46 30% 67% 2%
Panel B (continued): Carhart's 4-factor model
Alpha Distribution + / 0 / -PR1YR
86
Mortgage-Back. 0,29% *** 0,08 *** 0,01 0,04
Rel. Value Arb. 0,59% *** 0,24 *** 0,12 * 0,15 **
Short Sellers 0,77% *** -0,38 *** -0,35 *** 0,07
US Opport. 0,63% *** 0,75 *** 0,38 *** 0,02
Growth 0,78% *** 0,83 *** 0,43 *** -0,11
Value 0,46% *** 0,7 *** 0,29 *** 0,11 ***
Small Caps 1,57% *** 0,64 *** 0,55 *** 0,14 *
Long Only Lev. 0,25% 0,9 *** 0,54 *** 0,11
Market Timing 0,43% *** 0,14 *** 0,03 -0,06
Equity non-Hed. 0,44% *** 0,8 *** 0,35 *** -0,03
Foreign Exch. 0,07% 0,19 *** 0,08 *** 0,01
Sector 0,82% *** 0,63 *** 0,4 *** 0,01
Funds of Funds -0,02% 0,37 *** 0,19 *** 0,08 *
Non classified 4,76% *** 0,09 0,12 0,10
All funds 0,43% *** 0,42 *** 0,23 *** 0,04
Panel B (continued 2x): Carhart's 4-factor model
Alpha Mkt SMB HML
87
R² adj No Fds
Rel. Value Arb. -0,05 0,21 8 50% 50% 0%
Short Sellers -0,07 * 0,72 18 17% 83% 0%
US Opport. 0,00 0,90 180 31% 68% 2%
Growth 0,04 0,86 68 38% 60% 1%
Value -0,05 * 0,88 100 24% 74% 2%
Small Caps -0,06 0,64 12 42% 58% 0%
Long Only Lev. 0,06 0,77 18 17% 78% 6%
Market Timing 0,09 * 0,18 34 18% 82% 0%
Equity non-Hed. -0,06 *** 0,93 112 19% 80% 1%
Foreign Exch. -0,04 *** 0,42 9 11% 89% 0%
Sector 0,00 0,89 128 41% 59% 0%
Funds of Funds -0,02 0,63 278 20% 77% 3%
Non classified 0,06 0,06 230 43% 55% 2%
All funds -0,01 0,84 2154 30% 69% 2%
Mean R²adj 0,60 Mean 0,28 70% 2%
Panel B (continued 3x): Carhart's 4-factor model
Alpha Distribution + / 0 / -PR1YR
88
Event Driven 0,34% * 0,42 *** 0,01 0,25 *** 0,10 *** 0,05
Distressed Sec. 0,09% 0,40 *** 0,06 0,27 *** 0,12 *** 0,04
Risk Arbitrage 0,60% *** 0,44 *** -0,03 0,24 *** 0,08 *** 0,07
No sub-strategy -0,05% 0,43 *** 0,00 0,16 *** 0,10 0,05
Global -0,50% 0,68 *** 0,12 * 0,16 *** 0,07 0,04
International -0,21% 0,56 *** 0,13 ** 0,13 *** 0,03 -0,05
Emerging -0,71% 0,73 *** 0,13 * 0,17 *** 0,06 0,06
Regional Est. 0,27% 0,50 *** 0,10 ** 0,18 *** 0,09 * -0,02
Global Macro 0,56% *** 0,53 *** 0,06 * 0,25 *** 0,04 -0,09 *
Market Neutral 0,28% *** 0,21 *** 0,07 *** 0,11 *** 0,04 ** -0,04
Long/short 0,67% *** 0,16 *** 0,01 0,13 *** 0,08 *** -0,07 ***
Convertible Arb. 0,42% *** 0,05 *** 0,05 ** 0,05 *** 0,04 ** 0,02
Fixed Income -0,26% 0,36 *** 0,09 * 0,13 *** -0,07 * 0,04
Stock Arbitrage 0,22% * 0,25 *** 0,09 *** 0,13 *** 0,06 ** -0,05
Mortgage-Back. 0,23% 0,02 0,02 0,02 0,01 0,01
SMB HML I HML
Panel C: The combined model
Alpha Mkt Wd x US
89
R² adj
Event Driven -0,03 -0,04 -0,01 0,06 *** 0,11 * 0,00 0,79
Distressed Sec. -0,08 ** -0,08 -0,03 0,07 ** 0,16 ** 0,00 0,74
Risk Arbitrage -0,02 0,01 -0,09 0,05 * 0,13 -0,01 0,66
No sub-strategy 0,12 *** -0,10 0,39 *** 0,06 -0,16 0,00 0,51
Global 0,01 -0,33 * -0,41 *** 0,13 *** -0,12 0,09 ** 0,67
International -0,02 -0,17 -0,21 * 0,06 * -0,05 0,08 *** 0,72
Emerging 0,02 -0,38 * -0,48 *** 0,16 *** -0,17 0,12 ** 0,6
Regional Est. -0,03 -0,22 ** -0,09 0,03 -0,16 * -0,03 0,71
Global Macro 0,03 -0,11 0,01 0,06 *** -0,06 -0,02 0,85
Market Neutral 0,02 -0,15 *** -0,06 0,03 0,07 0,01 0,72
Long/short 0,00 -0,12 * -0,05 0,02 0,10 * 0,02 * 0,61
Convertible Arb. -0,02 * 0,06 -0,11 *** 0,03 * 0,16 *** 0,00 0,49
Fixed Income 0,05 * -0,17 -0,02 0,04 -0,09 0,02 0,55
Stock Arbitrage 0,02 -0,19 *** -0,08 0,02 0,04 0,01 0,68
Mortgage-Back. 0,04 * -0,13 * -0,01 0,03 0,33 *** 0,00 0,22
Panel C (continued): The combined model
World GV Emerg Bd Default Comm. US BdPR1YR
90
Rel. Value Arb. 0,43% 0,21 *** 0,03 0,02 0,02 0,08
Short Sellers 0,75% *** -0,34 *** 0,01 -0,31 *** 0,10 0,07
US Opport. 0,46% *** 0,80 *** 0,09 ** 0,32 *** 0,04 -0,16 **
Growth 0,74% *** 0,85 *** 0,04 0,36 *** -0,12 -0,35 ***
Value 0,20% 0,77 *** 0,12 *** 0,26 *** 0,13 *** 0,02
Small Caps 1,34% *** 0,73 *** 0,08 0,46 *** 0,16 ** -0,25 ***
Long Only Lev. 0,00% 0,88 *** 0,14 * 0,47 *** 0,07 -0,14
Market Timing 0,48% ** 0,19 *** 0,02 0,09 *** 0,00 0,04
Equity non-Hed. 0,23% * 0,84 *** 0,08 ** 0,31 *** -0,02 -0,07
Foreign Exch. -0,02% 0,15 *** 0,00 0,07 *** -0,01 0,03
Sector 0,69% *** 0,63 *** 0,06 * 0,37 *** 0,00 -0,08
Funds of Funds -0,28% * 0,39 *** 0,07 * 0,14 *** 0,06 * -0,01
Non classified 4,86% *** 0,14 0,10 0,11 *** 0,14 -0,13
All funds 0,25% ** 0,44 *** 0,06 ** 0,19 *** 0,04 * -0,04
SMB HML I HML
Panel C (continued 2x): The combined model
Alpha Mkt Wd x US
91
R² adj
Rel. Value Arb. 0,02 0,03 -0,23 * 0,10 ** 0,05 0,05 * 0,36
Short Sellers -0,05 0,05 -0,14 -0,01 -0,07 -0,08 ** 0,72
US Opport. 0,00 -0,18 * 0,18 ** 0,04 * -0,29 ** 0,02 0,92
Growth -0,03 -0,21 0,15 0,10 *** -0,18 0,00 0,89
Value 0,01 -0,12 0,20 *** 0,00 -0,34 *** 0,04 ** 0,91
Small Caps -0,06 -0,27 0,14 0,05 -0,51 ** 0,06 0,65
Long Only Lev. 0,08 -0,17 0,00 0,19 *** 0,17 -0,01 0,82
Market Timing 0,06 0,02 0,21 * -0,05 -0,16 -0,12 ** 0,25
Equity non-Hed. -0,05 * -0,20 ** 0,21 *** 0,03 -0,21 *** 0,04 * 0,94
Foreign Exch. -0,03 -0,10 * -0,11 0,08 *** 0,23 *** -0,01 0,56
Sector 0,00 -0,18 0,06 0,02 0,01 0,03 0,89
Funds of Funds 0,04 -0,18 * -0,20 ** 0,08 *** -0,01 0,04 * 0,75
Non classified 0,03 0,06 0,08 -0,12 *** -0,20 -0,04 0,05
All funds 0,01 -0,16 ** -0,05 0,05 *** -0,03 0,01 0,88
Mean R²adj 0,66
US BdPR1YR
Panel C (continued 3x): The combined model
World GV Emerg Bd Default Comm.
92
No Fds
Event Driven 84 27% 69% 4%
Distressed Sec. 37 19% 78% 3%
Risk Arbitrage 38 39% 55% 5%
No sub-strategy 9 11% 89% 0%
Global 258 10% 77% 12%
International 50 10% 82% 8%
Emerging 151 8% 75% 17%
Regional Est. 57 18% 77% 5%
Global Macro 252 42% 56% 1%
Market Neutral 553 30% 65% 5%
Long/short 102 27% 71% 2%
Convertible Arb. 39 59% 41% 0%
Fixed Income 48 8% 79% 13%
Stock Arbitrage 310 29% 65% 6%
Mortgage-Back. 46 33% 63% 4%
Panel C (continued 4x): The combined model
Alpha Distr. + / 0 / -
93
No Fds
Rel. Value Arb. 8 50% 38% 13%
Short Sellers 18 44% 56% 0%
US Opport. 180 21% 76% 3%
Growth 68 28% 72% 0%
Value 100 16% 79% 5%
Small Caps 12 25% 75% 0%
Long Only Lev. 18 17% 78% 6%
Market Timing 34 12% 88% 0%
Equity non-Hed. 112 28% 71% 1%
Foreign Exch. 9 0% 78% 22%
Sector 128 30% 69% 2%
Funds of Funds 278 14% 72% 14%
Non classified 230 35% 62% 3%
All funds 2154 26% 68% 6%
Mean 25% 70% 5%
This Table presents the results of the estimation of the Single Index Model (Panel A), of Carhart’s (1997) Model (Panel B) and of our Combined Model (Panel C) for the 1/1984-6/2000 period. We report the OLS estimators for equally weighted portfolio’s per investment strategy, sub-strategy and for all funds. The last column gives the distribution of individually estimated monthly alphas for all funds with 24 monthly data or more in a specific investment style. We report the percentage of significantly positive alpha’s (+), significantly negative alpha’s (-) and alpha’s that are insignificantly different from zero (0) at the 5% level. The next to last column reports the number of individual funds used for the individual estimation of the last column. T-stat are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
Panel C (continued 5x): The combined model
Alpha Distr. + / 0 / -
94
These results are close to those found by Mitchell and Pulvino (2001) and Agarwal
(2001) for the funds following Event Driven strategies. We find that 27% of the hedge
funds show significant excess return, matching the 27% they found. This independently
confirms that our approach is able to capture important risk exposure of hedge funds.
Carhart (1997) and Gruber (1996) examine US mutual fund strategies and report
that managers prefer smaller stocks as well as growth stocks. The first evidence is
consistent with our finding, while the second one is opposite. However, this difference
does not exist for all hedge funds managers, given that the HML factor is only significant
for some strategies.
Comparing the alpha distribution of Panels B and C shows that, taking more factors
into account induces that fewer individual funds significantly out-performed the market,
and more funds have insignificant or negative excess returns.
Evidence on alphas obtained in Panel C is contrasted. The excess returns for Event
Driven, Global, Long Only Leveraged, Equity non-Hedge, and Foreign Exchange strategies
are insignificant (at the 5% level), whereas the alpha for the Fund of Funds strategy is
negative and significant. All other categories display positive and significant alphas. Our
results are in most cases confirmed by the last column. In the All Funds category, for
example, more than 25% of the individual alphas are significantly positive at the 5% level.
Considering the All Funds category, we can observe that hedge funds as a whole:
Deliver significant excess returns (one fourth of the individual funds gave significant
positive excess return) ;
Seem to prefer smaller stocks ;
Invest in Emerging Market Bonds and suffer from the US Bond market.
95
Overall it seems that the combined model does a very good job in describing hedge
funds behaviour. The average R²adj increases from 0.44 for the single factor model, to
0.60 for the 4-factor model and to 0.66 for our combined model. The combined model
gives adjusted R² higher than 0.65 for all strategies but the Market Timing (0.25), the
Non-classified funds (0.05) and Foreign Exchange funds (0.56). It seems particularly
adapted to Equity non-hedge (0.94), US Opportunistic (0.92), Sector (0.89), Global Macro
(0.85), Long only Leveraged (0.82) and Event Driven funds (0.79). The R²adj for the All
Funds category increases from 0.66 for the single factor model, to 0.84 for the 4-factor
model and to 0.88 for our combined model. The mean R²adj for the individual hedge funds
estimation is up too. Carhart’s (1997) model raises the R²adj by an average 10% over the
single index model, but our combined model increases it again by another 7%. For the All
Funds category, the increase from the CAPM to Carhart’s model is 10% and from Carhart’s
model to our combined model is another 7%.
Our R²adj are also higher than those obtained by Brown et al. (2001) and Fung and
Hsieh (1997). They report R² lower than 0.20 in all cases for groups of funds. Schneeweis
and Spurgin (1998) report R²adj between -0.09 and 0.67 with a mean of 0.31 for several
hedge funds strategies. Comparing their results with ours for strategies that exist across
the two databases, we get greater R²adj in all cases. For several HFR strategies, Liang
(1999) finds unadjusted coefficients ranging from 0.23 to 0.77, with an average of 0.49:
taking the same strategies, our R²adj range between 0.27 and 0.92 with an average of
0.63.
96
6.3 Performance over Shorter Periods
In the previous sub-sections, we discuss the performance of hedge funds using
several specifications for the 1/94-6/00 period. In order to better interpret these results,
Table 14 presents a summary of the same analysis over different sub-periods. We
subdivide the 1994-2000 period in two sub-periods of equal lengths, and then report
results of the same analysis for the Asian crisis period. The analysis of the Asian crisis
period will enable us to determine if some strategies took advantage of the crisis and
which one suffered (or not) from it. The 1984-1993 period is reported in the last column
for comparison purposes.
The last column of Table 14 confirms that the same strategies significantly out-
perform the market when the period before 1994 is considered, with only 4 exceptions.
Three strategies (Short Sellers, Market Timing, and Equity non-Hedge) do not beat the
market in the 1984-1993-period but do after 1994, while one (Foreign Exchange) does the
reverse.
When the time period is divided in two, it is interesting to note that the significance
of the abnormal performance for the 1994-2000 period is mainly due to the first sub-
period; some hedge funds strategies and sub-strategies even significantly under-perform
the market in the second sub-period (Global, Emerging, and Funds of Funds). The latter is
the only one whose significant underperformance extends to the whole 1994-2000 time
window.
97
Table 14: Performance of Hedge Funds in different Sub-
Periods
Event Driven 0,34% * 0,41% * 0,08% 0,02% -0,05% -0,21%
Distressed Sec. 0,09% 0,17% -0,11% 0,19% -0,07% 0,07%
Risk Arbitrage 0,60% *** 0,60% ** 0,31% * -0,13% 0,02% -0,29%
No sub-strategy -0,05% 0,40% -0,45% -0,17% -0,25% -0,53% *
Global -0,50% 0,23% -1,21% *** -1,02% -1,30% ** 1,01% *
International -0,21% -0,33% -0,40% -0,99% *** -1,10% *** 1,29% ***
Emerging -0,71% 0,47% -1,70% *** -1,18% -1,55% ** 0,92%
Regional Est. 0,27% 0,38% *** -0,07% -0,46% -0,54% 1,21% ***
Global Macro 0,56% *** 0,45% * 0,56% *** 0,46% -0,07% 0,85% ***
Market Neutral 0,28% *** 0,20% 0,19% ** 0,15% -0,04% 0,63% ***
Long/short 0,67% *** 0,40% * 0,72% *** 0,66% *** 0,42% ** 0,05%
Convertible Arb. 0,42% *** 0,46% *** 0,36% *** 0,40% *** 0,40% *** 0,55% ***
Fixed Income -0,26% -0,47% -0,41% -0,72% -1,23% ** 1,01% ***
Stock Arbitrage 0,22% * 0,16% 0,13% 0,08% -0,11% 0,81% ***
Mortgage-Back. 0,23% 0,58% *** -0,17% -0,13% -0,12% 0,00%
1/97-6/981/97-12/98
Asian crisis Pre-1994
1/84 - 12/931/94 - 6/00 1/94 - 12/96 1/97 - 6/00
1 sub-period 2 sub-periods
98
Rel, Value Arb. 0,43% 1,20% *** 0,26% 0,54% 1,20% *** NA
Short Sellers 0,75% *** 0,70% 0,51% 0,66% ** 0,48% 0,13%
US Opport. 0,46% *** 0,57% *** 0,41% ** 0,40% -0,05% 0,73% ***
Growth 0,74% *** 0,94% *** 0,64% ** 0,65% ** 0,19% 1,13% ***
Value 0,20% 0,26% * 0,19% 0,21% -0,18% 0,47% **
Small Caps 1,34% *** 2,56% *** 0,60% * 0,44% -0,23% 1,70%
Long Only Lev. 0,00% 0,28% -0,21% -0,20% -0,42% NA
Market Timing 0,48% ** 0,10% 0,49% 0,22% 0,23% 0,22%
Equity non-Hed. 0,23% * 0,52% ** 0,07% 0,04% -0,33% 0,06%
Foreign Exch. -0,02% 0,20% -0,25% 0,13% 0,39% *** 0,83% ***
Sector 0,69% *** 0,77% *** 0,55% * 0,42% * 0,16% 1,10% **
Funds of Funds -0,28% * -0,28% -0,43% ** -0,33% -0,48% ** 0,61% ***
Non classified 4,86% *** 4,14% *** 5,57% *** 4,38% *** 3,79% *** 3,84% ***
All funds 0,25% ** 0,29% * 0,10% 0,04% -0,24% 0,64% ***
1/97-6/981/97-12/98
Asian crisis
This table reports a summary of the results for the estimation of the combined model for different time periods. We report monthly alphas for equally weighted portfolio's per investment strategies, sub-strategies, and for all funds. NA means that we could not make the estimation for the sub-period considered because the strategy has existed for less than 24 months. T-stat (not reported) are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level, * Significant at the 10% level.
Pre-1994
1/84 - 12/931/94 - 6/00 1/94 - 12/96 1/97 - 6/00
1 sub-period 2 sub-periods
99
A closer look at the 1997-1998 suggests that most hedge funds strategies suffered
during the Asian crisis. Nineteen strategies and sub-strategies out of the 29 face negative
returns between 1997 and the middle of 1998, with five being significant (Global, Global
International, Global Emerging, Market Neutral Fixed Income and Funds of Funds). Five
strategies had significant positive returns during this period (Market Neutral Long/Short,
Convertible Arbitrage, Non Classified funds, Relative Value Arbitrage and Foreign
Exchange), but only the first three had also significant excess returns during other sub-
periods. The only sub-strategies that could have significantly benefited from the Asian
crisis are the Relative Value Arbitrage and the Foreign Exchange. But one must be
cautious because of the short estimation period.
Moreover, the division in sub-periods indicates that over-performance is rarely
sustainable over every shorter period of time: three strategies (Long/short Convertible
Arbitrage and the Non Classified funds) out-performed the market in all sub-periods we
considered; only the latter two extend their superior performance to the pre-1994 sub-
period.
6.4 Comparison with other Studies
Schneeweis and Spurgin (1998) and Liang (1999) find different results from us, but
they are mainly due to differences in the period studied and to a smaller number of funds
in their database.24 Agarwal and Naik (2004) find the same results as ours except that
Fixed Income, Risk Arbitrage and Long only Leveraged strategies significantly under-
performed the market on average, while we find only small percentages of under-
performing funds. Finally, Agarwal (2001) finds results close to ours.
24 Liang (1999) finds insignificant positive excess return for the Convertible Arbitrage, Foreign
Exchange, Funds of Funds, Market Timing, Sector and Short Selling strategies but documents that
Growth and Market Neutral strategies significantly under-perform the market.
100
VII Persistence in Performance
Our results show significant evidence of superior performance over long period of time for
most individual strategies and sub-strategies. Nevertheless, results are not stable over
shorter period of time, neither for hedge funds as a whole, nor for individual hedge funds.
Active hedge funds selection strategies could increase the expected return on a portfolio if
hedge fund performance is predictable. The hypothesis that hedge funds with a superior
average return in this period will also have a superior average return in the next period is
called the hypothesis of persistence in performance. Sirri and Tufano (1998) and Zheng
(1999) stress the importance of persistence analysis in mutual funds. The formers
document large inflows of money into last years best performers, and withdrawals from
last year’s losers. The latter finds that newly invested money in these best performing
mutual funds is a predictor of future performance.
7.1 Persistence in One-year Return-Sorted Hedge Funds Portfolios
We follow the methodology of Carhart (1997) using our combined model. All funds
are ranked based on their previous year return. Every January, we put all funds into 10
equally weighted portfolios, ordered from highest to lowest past returns. Portfolios 1
(High) and 10 (Low) are then further subdivided on the same measure. The portfolios are
held till the following January and then rebalanced again. This yields a time series of
monthly returns on each decile portfolio from 1/94 to 6/00.25 Funds that disappear during
the course of the year are included in the equally-weighted average until their death, then
portfolio weights are readjusted appropriately.
25 The corresponding table for the 1985-1993 period is available upon request.
101
Table 15: Hedge Funds Persistence based on 12 Month lagged
Returns
Std. Dev.
D 1a 1,68% 0,07 0,00 0,74 *** 0,05 0,66 *** -0,03
D 1b 1,26% 0,05 0,00 0,62 *** 0,12 0,40 *** -0,14
D 1c 1,11% 0,04 0,00 0,55 *** 0,08 0,39 *** -0,02
D 1 1,35% 0,05 0,00 0,64 *** 0,09 0,48 *** -0,07
D 2 0,89% 0,03 0,00 0,55 *** 0,10 0,33 *** 0,05
D 3 0,83% 0,03 0,00 0,50 *** 0,05 0,24 *** 0,10 **
D 4 0,82% 0,02 0,00 0,47 *** 0,06 ** 0,17 *** 0,09 ***
D 5 0,71% 0,02 0,00 0,40 *** 0,05 * 0,13 *** 0,09 ***
D 6 0,57% 0,02 0,00 0,32 *** 0,06 ** 0,13 *** 0,09 ***
D 7 0,62% 0,02 0,00 * 0,33 *** 0,03 0,12 *** 0,07 **
D 8 0,57% 0,02 0,00 0,36 *** 0,06 * 0,13 *** 0,04
D 9 0,80% 0,02 0,00 ** 0,38 *** 0,06 0,09 *** 0,00
D 10 0,89% 0,03 0,00 0,50 *** 0,07 0,04 -0,05
D 10a 0,82% 0,03 0,00 0,48 *** 0,03 0,09 ** -0,05
D 10b 0,84% 0,03 0,00 0,54 *** 0,05 0,05 0,01
D 10c 1,03% 0,04 0,00 0,51 *** 0,14 -0,03 -0,12
1-10 spread 0,45% 0,05 0,00 0,13 0,02 0,45 *** -0,01
1a-10c spread 0,65% 0,07 0,00 0,24 -0,09 0,70 *** 0,09
1-2 spread 0,46% ** 0,02 0,00 0,08 -0,01 0,15 *** -0,11 *
9-10 spread -0,10% 0,02 0,00 -0,12 * -0,01 0,05 0,06
Monthly Exc. Return Mkt Wd x US SMB HMLAlpha
102
R²adj
D 1a -0,32 0,19 -0,93 ** -0,19 0,12 0,44 0,13 0,74
D 1b -0,29 *** 0,14 * -0,38 0,02 0,05 0,09 0,11 ** 0,81
D 1c -0,18 0,10 -0,30 -0,18 0,03 0,02 0,03 0,79
D 1 -0,26 * 0,14 -0,54 * -0,12 0,07 0,18 0,09 0,79
D 2 -0,12 * 0,09 ** -0,38 ** -0,09 0,06 0,00 0,06 ** 0,85
D 3 -0,05 0,03 -0,14 0,03 0,03 -0,02 0,01 0,88
D 4 0,01 -0,01 -0,09 0,00 0,03 -0,06 0,01 0,87
D 5 -0,01 0,00 -0,22 *** -0,07 0,07 *** -0,04 0,01 0,84
D 6 0,01 -0,03 -0,11 -0,04 0,05 ** 0,07 0,00 0,82
D 7 0,00 -0,05 * -0,05 -0,01 0,05 ** 0,04 -0,01 0,80
D 8 0,06 -0,03 -0,06 -0,08 0,04 -0,02 -0,01 0,75
D 9 0,03 -0,05 -0,07 -0,07 0,03 -0,12 -0,01 0,65
D 10 0,08 -0,02 -0,05 -0,09 0,06 -0,37 * 0,00 0,44
D 10a 0,15 -0,02 -0,12 -0,11 0,09 * -0,16 0,00 0,61
D 10b 0,07 -0,01 -0,02 -0,06 0,09 * -0,34 0,01 0,44
D 10c 0,02 -0,04 -0,01 -0,11 0,01 -0,63 * -0,01 0,22
1-10 spread -0,35 ** 0,16 -0,49 -0,03 0,00 0,55 * 0,09 0,52
1a-10c spread -0,34 0,23 -0,92 * -0,07 0,11 1,06 ** 0,14 0,48
1-2 spread -0,14 0,05 -0,15 -0,03 0,01 0,18 0,03 0,43
9-10 spread -0,05 -0,03 -0,01 0,02 -0,03 0,24 * -0,01 0,04
This Table reports the result of the estimation of our combined model for the 1/94-6/00 sub-period. Each year, all funds are ranked based on their previous year's return. Portfolios are equally weighted and weights are readjusted whenever a fund disappears. Funds with the highest previous year's return go into portfolio D1 and funds with the lowest go into portfolio D10. Monthly Exc Return is the Monthly Excess Return of the portfolio, Std. Dev. is the Standard Deviation of the Monthly Excess Return. Mkt is the excess return on the Market Proxy. SMB, HML, IHML, PR1YR, W x US, US Bd, W Gvt BD, Emerg Mkt BD, Default and Comm. are factors added to adjust for size, book-to-market, one-year return momentum and for the fact that some funds invest in other than US equity market, in bonds not picked up by the risk-free rate or in commodities. All numbers in the Table are monthly percentage. *** Significant at the 1% level ** Significant at the 5% level * Significant at the 10% level.
World GV Bd Emerg Bd Default Com.I HML PR1YR US Bd
103
The monthly average return to the strategy of investing in portfolio 1 would have
been 1.35% for the 1/94-6/00 period. Conversely, the monthly (respectively maximum
and minimum) return to the strategy that invested in the lowest decile would have been
0.89% over the same period. For the 1985-1993 period, decile portfolios 1 and 10 have
earned 1.74% and 1.07% respectively.
The monthly excess returns on the decile portfolios decrease monotonically
between portfolio D1 and D6, but then increases again from portfolio D6 to portfolio D10.
Monthly excess return of portfolio D2 is the same as the one of the last portfolio. The
annualized spread is approximately 5.5% between portfolio D1 and D10. Portfolio D1a
out-performs portfolio 10c by 0.65% per month. These spreads are not significant.26
Cross-sectional variation in returns is considerably larger among previous year’s best
performing funds than previous year’s worst funds. The sub-portfolios of the bottom decile
show a modest spread of 21 basis point (0.82 to 1.03), whereas the spread in the top
decile is a substantial 57 basis point (1.68 to 1.11). The 1-2 spread is significant at the
5% level, indicating big differences between top performing funds and other portfolio
funds, but the 1-2 spread alpha is not significant, suggesting no persistence. After
controlling for the risk factors, a large part of the spread between high and low portfolios
disappears. The 1-10 spread goes from a 0.45% to – 0.09%, the 1a and 10c spread
decreases from 0.65 to –0.36%, still not significant, and the 1-2 spread reduces from a
significant 0.46% to a 0.25% non significant spread.
26 Over the whole database, the D1-D10 and D1a-D10c spreads amount to 0.58% and 0.95%
respectively, both significant.
104
Column 7 suggests that all deciles portfolios (except the last) prefer small stocks.
More important, however, is the pronounced pattern in the funds’ HML, PR1YR and
Emerging Market Bond coefficients (Emerg Bd). First, portfolio D3 to D7 prefer stocks with
high book-to-market ratios, whereas portfolios D1 and D10 prefer (but not significantly)
those with low book-to-market. Second, returns of the top decile funds are strongly,
positively correlated with the one-year momentum factor, while returns in the other
deciles are not. Third, the returns of the D5 to D7 deciles are strongly, positively related
with the Emerging Market Bond factor. This could explain why the monthly excess return
diminishes after decile D3. Thus, the different financial crises covered by our time period
may explain why funds investing in Emerging market Bond are not in the 3 best
performing decile portfolio.
Column 4 suggests that funds in top and bottom portfolios do not significantly out-
or under-perform the market, without persistence. This means that these funds are there
more by chance or misfortune, rather than by their abilities. Moreover, the standard
deviation of top and bottom deciles are the greatest of all, indicating more volatility in
returns. Things are different for the funds in the middle deciles. Managers in these
portfolios are more likely to stay in these deciles over time, and some of these managers
significantly beat the market (deciles 7 and 9).27
27 These results are reinforced when one considers the global database and when we consider
strategies individually (see section 7.4). The qualitative results for the book-to-market and momentum
strategies are unchanged, and evidence on an emerging bond market strategy for middle-decile
portfolios is stronger. Alphas are significantly positive for funds in deciles 3 to 7 and 9. However, these
values are mainly driven by the extremely good performance funds belonging to those deciles in the
1985-1993 period, which raises a legitimate suspicion over their economic significance.
105
This suggests that, even if some hedge funds managers take a lot of risk, which
lead them to have very high or low returns for short period of time, most managers follow
less risky strategies that allow them to out-perform the market for long period of time.
The stronger persistence for middle deciles with a substantially lower variance of
returns than extreme deciles is in line with the conjecture of Brown et al. (2001). Funds
that performed well – relative to the market, i.e. with a positive alpha – tend to pursue a
low variance strategy. Extreme performers tend not to remain in their situation; this can
be explained by dissolution or by the fact that they are more or less forced to take less
risk, returning to the middle of the pack. Brown et al. (2001) explain this behaviour of
funds managers by the negative penalty linked to dissolution having a relatively stronger
effect than the reward of the call-like feature of their compensation contract.
To summarize, Table 15 leads to the following conclusions:
Best performing funds follow momentum strategies whereas worst performing ones
may follow momentum contrarian strategies;28
Best performing funds do not invest significantly in Emerging Market Bond;
Average return funds prefer high book-to-market stocks, whereas best and worst
performing ones may prefer low book-to-market ones;
No persistence in performance exists for best and worst performing funds, but there is
weak evidence of persistence for middle deciles, where some funds significantly beat
28 This result may not be stable over time, since the period under review covers a bull market when
momentum strategies are likely to work. After the strong market reversal that took place after March
2000 would be very indicative of the economic significance of this result, but our database unfortunately
ends in June 2000. These issues are being investigated as a part of our ongoing research.
106
the market with persistence. Evidence is more pronounced for the 1985-1993 period,
but it is likely to be driven by the absence of dissolved funds in this period.29
7.2 Persistence over the Asian crisis
The same analysis for the Asian crisis period shows that top performing funds of
1996 had significantly lower returns in 1997.30 The alphas of decile D1 and the 1a-10c
spread are significantly negative indicating that the best performing funds (of 1996)
significantly under-performed the worst performing funds (of 1996), in 1997. These
results confirm our previous conclusion that funds in the first decile have no persistence in
returns, and that there have more volatile returns than funds in lowest decile. In the
1/97-6/98 analysis, all deciles’ alphas are negative, 5 of them being significant, but decile
1a is the only (sub)decile with positive (but not significant) alpha. This indicates that some
funds were not affected by the crisis, probably because their investment strategies were
relatively immune to it.
29 But one must be cautious with this result, given that this is not the only reason possible. The Bond
crisis in 1994, the Asian crisis in 1997-1998, etc. may also explain these differences.
30 Numerical results are available upon request.
107
7.3 Dissolution Frequencies
Figure 4 shows a histogram of hedge funds dissolution frequencies in one year as a
function of the previous year mean return decile. At the beginning of each year, all hedge
funds are put into decile rankings by their mean returns in the previous year. If a hedge
fund ceases reporting returns at any time before the end of the year, then this is counted
as dissolved.
Top 7 deciles have a more or less constant average rate of dissolution of 7%, it is
12.5% for the bottom 3 deciles. This suggests that bad performance may be a major
factor for dissolution, but that good performance is not a protection against it. This result
is consistent the finding of no persistence in the best performing funds, but that
persistence exists in the middle deciles.
7.4 One-Year Persistence for Hedge Fund Strategies
This subsection focuses on the persistence in returns for some hedge funds
strategies. We consider two strategies with more than 300 funds: Global Macro and
Market Neutral that significantly out-performed the market for the 1/94-6/00 period. In
this sub-section, we determine whether persistence in returns exists for these strategies.
We test it for the 1994-2000 period and for the Asian crisis period (1996-97 and 1997-
6/98). Results for the pre-1994 period are also indicated for comparison. We classify funds
in 10 decile portfolios, with the top and bottom decile divided in 3 for the Market Neutral
strategy. Table 16 reports a summary of our results for these strategies.
108
Figure 4: Hedge funds dissolution frequencies
0,00
0,04
0,08
0,12
0,16
1 2 3 4 5 6 7 8 9 10
Decile in Year t-1
Diss
olut
ion
Freq
uenc
y in
Y
Hedge funds dissolution frequencies by year t as a function of year t-1 decile. At the
beginning of year t, all funds are placed into decile rankings on the basis of their returns in
year t-1. If a hedge fund ceases to report returns at any time before the end of year t, it
is counted as dissolved.
Panel A reports the results of the analysis for Macro funds. They show that there is
no significant difference between good and bad performing funds. Half of the alphas
obtained are significantly positive for the whole period, but not for the extreme deciles.
These results are stronger than those obtained for the whole database. This confirms the
previous findings for these funds. The 1996-97 Asian crisis sub-periods show that some
funds (decile D3) have persistence in their return despite the Asian crisis. This could either
mean that these funds returns were not affected by the crisis, or that they benefit from it.
The second hypothesis is more plausible given that we are analyzing Macro funds that per
definition anticipate market movements.
109
Panel B shows the results for the Market Neutral funds. They are very close to
those obtained for the whole hedge funds database in Table 16 but the results are
stronger because we found significant alphas in some cases (recall that the Market Neutral
strategy represents 712 funds that is 25% of our whole hedge funds database). The only
significantly positive alphas are those from the middle deciles. Those of the top decile are
only significant for the 1985-93 sub-period. The 1-10 and 1a-10c excess returns spreads
are both significant in most of the period considered, but not the alphas, except from the
97-6/98 period. This indicates that significantly positive difference existed between best
and worst performing funds during the Asian crisis period.
As an illustration, Panel C reports Market Neutral’s spread decomposition for each
of the sub-period considered. There are some interesting differences between these
numbers and those obtained for our whole hedge funds database (see Table 16). For the
1994-2000 period, four factors have a significant effect on spreads for the Market Neutral
funds, though they were insignificant in the all funds analysis: HML, Default and
Commodity (positive) and World Government Bond (negative). In the previous period,
their effect was also significant but with the opposite sign, with HML being replaced by
IHML. This indicates that the results obtained for our whole hedge funds database may not
be valid for one specific strategy of funds, but also that there has been a sharp reversal in
strategies for this category of funds after 1994.
Table 16: Hedge Funds Strategy Persistence based on 12 Month lagged Returns
Mean excess Return
Std. Dev. Std. Dev. AlphaMean
excess Return
Std. Dev.Mean
excess Return
Std. Dev.
D 1 1,55% 6,07% 0,71% 1,92% 3,15% 0,17% 1,98% 3,92% -0,84% 1,64% 4,50% 0,91% **
D 2 1,55% 4,58% 0,63% * 2,01% 3,13% 0,12% 1,59% 2,98% 0,62% 1,49% 5,03% 1,03%
D 3 1,42% 3,97% 0,34% 1,37% 2,73% 0,46% 1,43% 3,12% 1,36% *** 1,14% 3,91% 0,57%
D 4 1,33% 3,38% 0,86% *** 1,04% 3,14% -0,31% 1,39% 3,10% 0,51% 1,44% 3,23% 0,82% **
D 5 0,99% 3,16% 0,06% 1,38% 3,07% -0,24% 1,38% 3,19% 0,05% 1,32% 5,14% 0,79%
D 6 1,36% 2,67% 0,58% *** 1,59% 2,88% -0,13% 1,66% 2,33% 0,75% * 0,39% 6,14% 0,13%
D 7 0,88% 2,49% 0,40% ** 0,76% 2,89% -0,78% 0,84% 2,69% -0,09% 0,89% 3,81% 0,93% *
D 8 1,09% 2,43% 0,50% ** 0,85% 2,66% -0,62% 0,83% 2,36% -0,49% 1,03% 3,98% 0,77% *
D 9 0,84% 2,43% 0,33% 0,93% 2,24% 0,21% 1,10% 2,02% -0,28% 1,43% 3,55% 0,57%
D 10 1,01% 3,24% 0,22% 0,90% 2,08% -0,61% 1,34% 2,06% -0,49% 1,20% 4,98% 0,37%
1-10 spread 0,54% 6,46% 0,49% 1,03% * 2,29% 0,78% 0,64% 2,95% -0,35% 0,44% 6,48% 0,54%
Pre-1994 Period
Panel A: Global Macro
Alpha
1997-6/1998 1996-1997 1987-1993
Asian crisis
1994-2000
Whole Period
Alpha AlphaMean excess Return
111
Mean excess Return Std. Dev. Mean excess
Return Std. Dev.
D 1a 1,60% 4,10% 0,59% * 1,94% 4,37% 0,16%
D 1b 0,79% 3,43% 0,24% 1,56% 3,06% 1,26% ***
D 1c 1,17% 3,10% 0,59% 0,56% 3,86% 1,19%
D 1 1,15% 3,22% 0,45% 2,30% 7,27% 0,91%
D 2 0,65% 2,36% 0,04% 1,07% 2,22% 1,43% **
D 3 0,73% 1,95% 0,20% 0,83% 2,05% 1,04% **
D 4 0,59% 1,45% 0,19% 0,70% 1,98% 0,15%
D 5 0,52% 1,04% 0,25% ** 0,86% 2,29% 0,27% *
D 6 0,54% 0,99% 0,31% *** 1,21% 2,87% 0,65% ***
D 7 0,37% 0,94% 0,18% 0,42% 3,03% 0,23%
D 8 0,34% 1,04% 0,13% 0,59% 2,06% 0,07%
D 9 0,56% 1,25% 0,22% 0,59% 1,68% 0,31%
D 10 0,60% 1,97% 0,24% 0,66% 3,45% -0,04%
D 10a 0,55% 1,78% 0,15% 1,12% 5,30% -0,98%
D 10b 0,90% 2,70% 0,42% 0,04% 2,29% 0,00%
D 10c 0,42% 3,10% 0,16% 1,11% 5,08% 0,63%
1-10 spread 0,55% 2,91% 0,21% 1,63% 7,75% 0,95%
1a-10c spread 1,18% 4,33% 0,43% 0,83% 6,49% -0,47%
Alpha Alpha
1994-2000 1987-1993
Panel B: Market Neutral
Whole Period Pre-1994 Period
112
Std. Dev.Mean
excess Return
Std. Dev.
D 1a 1,60% 3,28% 0,34% 2,16% 3,38% -0,77%
D 1b 1,45% 2,05% 0,45% 1,06% 1,90% 0,93% ***
D 1c 1,95% 1,81% 1,05% *** 1,82% 1,90% 0,20%
D 1 1,61% 1,98% 0,47% * 1,64% 1,95% 0,10%
D 2 1,15% 1,69% 0,06% 1,23% 1,60% -0,09%
D 3 0,98% 1,56% 0,02% 1,07% 1,23% 0,25%
D 4 0,65% 1,16% -0,37% ** 0,94% 0,80% 0,20%
D 5 0,67% 0,92% 0,01% 0,77% 0,71% 0,47% *
D 6 0,61% 0,99% -0,09% 0,82% 0,81% 0,18%
D 7 0,48% 0,88% -0,06% 0,65% 0,81% 0,21%
D 8 0,19% 0,64% -0,15% 0,38% 0,52% -0,06%
D 9 0,26% 0,86% -0,48% 0,52% 0,70% -0,15%
D 10 0,22% 1,25% -0,67% *** 0,43% 0,98% -0,28%
D 10a 0,26% 0,70% 0,02% 0,31% 1,15% -0,48%
D 10b 0,34% 1,70% -0,54% 0,72% 1,87% -0,67%
D 10c 0,31% 3,15% -1,26% ** 0,44% 2,30% 0,38%
1-10 spread 1,39% *** 1,56% 1,14% *** 1,21% 1,79% 0,38%
1a-10c spread 1,29% * 3,13% 1,60% * 1,72% 3,82% -1,16%
Panel B (continued): Market Neutral
Asian crisis
1996-19971997-6/1998
AlphaAlphaMean excess Return
Std. Dev.
1994-2000 1-10 spr. 0,55% * 2,91% 0,21% 0,17 * 0,09 0,16 *** 0,03 -0,3 *** 0,03
1a-10c spr. 1,18% ** 4,33% 0,43% 0,3 * 0,17 0,17 ** 0,1 -0,27 ** 0,11
1997-6/1998 1-10 spr. 1,39% *** 1,56% 1,14% *** -0,05 0,08 0,43 *** 0,02 -0,38 ** -0,28 ***
1a-10c spr. 1,29% * 3,13% 1,60% * -0,04 0,07 0,46 -0,13 -1,41 *** -0,71 ***
1996-1997 1-10 spr. 1,21% *** 1,79% 0,38% 0,33 ** 0,03 0,39 *** 0,26 0,16 -0,04
1a-10c spr. 1,72% ** 3,82% -1,16% 0,93 *** 0,06 0,52 * 0,84 ** 0,66 0,03
1985-1993 1-10 spr. 1,63% ** 7,75% 0,95% -0,1 -0,15 1,03 ** 0,85 ** -0,31 0,41
1a-10c spr. 0,83% 6,49% -0,47% 0,6 -0,04 1,09 1,31 *** -0,36 0,5
Panel C: Market Neutral spread comparison
Alpha Mkt W x US SMB HML I HML PR1YRMonthly Exc. Return
114
Std. Dev.
1994-2000 1-10 spr. 0,55% * 2,91% 0,21% -0,15 -0,24 0,01 0,54 ** 0,05
1a-10c spr. 1,18% ** 4,33% 0,43% -0,37 -0,54 ** -0,09 0,72 ** 0,16 **
1997-6/1998 1-10 spr. 1,39% *** 1,56% 1,14% *** -0,07 -0,74 *** -0,19 1,45 *** -0,23 ***
1a-10c spr. 1,29% * 3,13% 1,60% * 1,41 -1,21 *** -0,05 1,38 * -0,67 ***
1996-1997 1-10 spr. 1,21% *** 1,79% 0,38% -0,42 -0,63 ** -0,08 0,67 * -0,04
1a-10c spr. 1,72% ** 3,82% -1,16% -1,34 * -0,99 * -0,14 0,94 0,21 *
1985-1993 1-10 spr. 1,63% ** 7,75% 0,95% -0,85 ** 1,44 * -0,39 -2,36 ** -0,12
1a-10c spr. 0,83% 6,49% -0,47% -0,85 2,48 ** -0,12 -3,39 ** -0,7 **
0,34
0,26
Monthly Exc. Return Default Comm.W GV Bd Emer Bd
This Table reports the result of the estimation of our combined model. Panel A contains the results for the Global Macro funds for different time period. Panel B contains the results for the Market Neutral funds, and Panel C contains a comparison of Market Neutral spread. Each year, all funds are ranked based on their previous year's mean return. Portfolios are equally weighted and weights are readjusted whenever a fund disappears. Monthly Exc Return is the Monthly Excess Return of the portfolio, Std. Dev. is the Standard Deviation of the Monthly Excess Return. Mkt is the excess return on the Market Proxy. SMB, HML, IHML, PR1YR, W x US, US Bd, W Gvt BD, Emerg Mkt BD, Default and Comm. are factors added to adjust for size, book-to-market, one-year return momentum and for the fact that some funds invest in other than US equity market, in bonds not picked up by the risk-free rate or in commodities. All numbers in the Table are monthly percentage.
R²adj
0,43
0,35
0,62
0,47
0,68
0,4
Alpha US Bd
Panel C (continued): Market Neutral spread comparison
115
VIII Conclusion
Using one of the greatest hedge fund database ever used (2796 individual funds
including 801 dissolved), we investigated hedge funds performance using various asset-
pricing models including an extension form of Carhart’s (1997) model, combined with
Fama and French (1998), Agarwal and Naik (2004) models and an additional factor that
takes into account the fact that hedge funds may invest in Emerging Market Bonds.
Although our sample displays funds returns going back to 1984, the analysis of
the survivorship and instant history biases for the 1984-1993 period indicates that
serious concerns can be raised about the statistical reliability of the observations
reported in this time window. This corresponds to the lack of data about funds that were
dissolved prior to 1994 in the databases. Therefore, our conclusions can only be derived
for the 1994-2000 period, with a possible reinforcement with results for the 1984-1993
period whenever similar.
We demonstrate that our combined model is able to explain a significant
proportion of the variation in hedge fund returns over time. Compared to models used in
other hedge fund performance studies, our combined model does a better job describing
hedge funds behaviour. It appears particularly good for the Equity non-hedge, US
Opportunistic, Sector, Global Macro, Long only Leveraged and Event Driven funds.
116
The performance analysis shows that one fourth of individual hedge funds delivers
significant positive excess returns, that most of them seem to prefer smaller stocks, and
that many hedge funds invest in Emerging Market Bonds. Analyzing each strategy
individually lead to the additional conclusions that 10 out of 13 strategies offer
significantly positive excess return. A sub-period analysis showed that over-performance
ability is, in most cases, constant over time. But, according to our results, most funds
suffered from the Asian crisis.
The analysis of persistence in performance for our whole hedge funds database
indicates 3 main findings that complete our results of the performance analysis. Firstly,
best performing funds follow momentum strategies whereas worst performing ones tend
to be momentum contrarian. Secondly, best performing funds do not significantly invest
in Emerging Market Bond, whereas lower decile funds do. Thirdly, average return funds
prefer high book-to-market stocks, whereas best and worst performing funds may prefer
low book-to-market ones. Our main conclusion from this evidence is that there is no
persistence in performance for best and worst performing funds, but limited evidence of
persistence exists for middle decile funds. This suggests that, even if some hedge funds
managers take a lot of risk, which lead them to have very high or low returns for short
period of time, many hedge fund managers follow less risky strategies that allow them to
out-perform the market for longer period of time. The much stronger results obtained for
data before 1994 raise additional suspicion about the presence of severe bias in this part
of the database. The Asian crisis analysis suggests that top performing funds in the year
before the crisis (1996) had significantly lower returns in the first year of the crisis.
Moreover, they significantly under-performed the worst performing funds (of 1996)
during the crisis period. The analysis of dissolution frequencies indicates, on the one
117
hand, that bad performance may be a major factor for dissolution, and on the other, that
very good performance is not a protection against dissolution.
Finally, the study of two popular strategies that significantly out-perform the
market confirms that there is a persistence in positive excess returns for middle decile
funds. A further analysis of the results for the Market Neutral strategy indicates that the
differences in spread are not explained by the same factors as for the whole hedge fund
database. This stresses that funds in different strategy are not influenced by the same
factors, and that specific models could be developed for each investment style in the
future.
All these results help in understanding the performance of hedge funds and the
persistence in this performance over different time period, including a study of the Asian
crisis. The next step in the development of model that describes hedge funds behaviour,
including Trading Strategy (option writing/buying) factors, in order to account for the fact
that some hedge funds exhibit non-linear option-like exposures to standard asset-
classes, as found by Fung and Hsieh (1997, 2001).
Study 2: Hedge Fund Performance and
Persistence in Bull and Bear Markets
Daniel P.J. CAPOCCI
HEC-ULG Management School – University of Liège (Belgium)
Albert CORHAY
HEC-University of Liège, Limburg Institute of Financial Economics,
Maastricht University, and Luxembourg School of Finance, University of
Luxembourg.
Georges HÜBNER
HEC-University of Liège, Limburg Institute of Financial Economics,
Maastricht University, and Luxembourg School of Finance, University of
Luxembourg.
Capocci, Daniel, Georges Hübner and Albert Corhay, 2005, Hedge Funds Performance
and Persistence in Bull and Bear Markets, European Journal of Finance 11/5, 361-392
120
Hedge Fund Performance and Persistence in Bull and
Bear Markets
Abstract
This study tests the performance of 2894 hedge funds in a time period that
encompasses unambiguously bullish and bearish trends whose pivot is commonly set at
March 2000. Our database proves to be fairly reliable with respect to the most important
biases in hedge funds studies, despite the high attrition rate of funds observed in the
down market. We apply an original ten-factor composite performance model that
achieves very high significance levels. The analysis of performance indicates that most
hedge funds significantly out-performed the market during the whole test period, mostly
thanks to the bullish sub-period. In contrast, no significant under-performance of
individual hedge funds strategies is observed when markets headed south. The analysis
of persistence yields very similar results, with most of the predictability being found
among middle performers during the bullish period. However, the Market Neutral
strategy represents a remarkable exception, as abnormal performance is sustained
throughout and significant persistence can be found between the 20% and 69% best
performers in this category, probably due to an extreme adaptability and a very active
investment behaviour.
121
Hedge Fund Performance and Persistence in Bull and
Bear Markets
I Introduction
Since 1990, when around 2000 hedge funds were managing together assets of ca.
$ 60 billion, the subsequent growth of number and asset base of hedge funds has never
really been refuted. The industry only suffered from a relative slowdown in 1998, but has
enjoyed since then a renewed vitality with an estimated size of 8400 funds managing $900
billion assets in 2004 (Van Hedge Funds Advisors International, 2002), corresponding to
growth rates of respectively 10.8% and 21.3% respectively.
The growing trend of the sector could be remarkably sustained during the stock
market collapse that started in March 2000, when the NASDAQ Composite Index reached
an all-time high of 5132, and finished three years later with a floor level at 1253. In the
meantime, the global net asset value (NAV) of hedge funds continued to grow at a steady
10.6% (Van Hedge Funds Advisors International, 2002), contrasting with a decrease of
2.7% in worldwide mutual fund industry (Investment Company Institute, 2003).
This relatively positive attitude of investors is typically motivated by the
perceptions that hedge funds are largely market neutral, that their managers enjoy
greater flexibility in their asset allocation that enables them to achieve a better market
timing (Fung and Hsieh, 1997), or that hedge funds have a relatively low covariance with
other classes of financial assets, making them a good diversification vehicle (Schneeweis
and Spurgin, 1998; Capocci and Hübner, 2004; Kat and Amin, 2003b).
122
The vast majority of performance studies on hedge funds has not focused on their
behaviour under different market conditions. This is generally due to the particularly
bullish period corresponding to the time window under review, as most empirical evidence
reveals that data collected prior to 1994 by several data vendors displays a significant
survivorship bias, as shown by Fung and Hsieh (2000), Liang (2000) and Capocci and
Hübner (2004).
In this context, Ackermann and al. (1999) and Liang (1999) find that hedge funds
constantly obtain better performance than mutual funds, although lower and more volatile
than the reference market indices considered.
On the other hand, the issue of persistence in performance is particularly important
in the case of hedge funds because these funds experience a greater attrition rate than
mutual funds (Brown and al.,1999, 2001; Liang, 1999). Agarwal and Naik (2000) find
evidence of persistence in hedge funds performance, while Capocci and Hübner (2004)
sustain that it can be mostly found among average performers and Brown and al. (1999)
conclude that there is hardly any evidence of the existence of differential manager skills
but persistence is rather due to style effects.
Few authors have attempted to estimate the behaviour of hedge funds in bear
markets. The periods under review do not favour this exercise, as periods of downward
trends on the stock market were rare and discontinuous. For the period 1990-1998,
Edwards and Caglayan (2001) find that only three hedge fund strategies (Market Neutral,
Event Driven and Macro) provide protection to investors when stock markets head south.
More recently, Ennis and Sebastian (2003) contend that in general, hedge funds did not
provide investor protection after the market downturn of March 2000; rather, their
superior performance is mostly due to the good market timing of their managers during
the US stock market bubble that preceded it.
123
This study benefits from the fact that stock markets have experienced a long period
of depression, since stock indices have been almost continuously going down for a period
of three years. Thus, our analysis neither suffers from discontinuities between down
periods, that preclude any analysis of persistence, nor from arbitrarily chosen definitions
of a bear market, as Fabozzi and Francis (1979), Kao et al. (1998), Rao (2001), Edwards
and Caglayan (2001) and Liang (2003).
In this study, using a similar methodology as the one developed by Capocci and
Hübner (2004), we study the performance of hedge funds and its persistence during a
time window that encompasses relatively long bullish and bearish periods.
This study introduces several key modifications with respect to the previous studies
on hedge funds performance and persistence. Firstly, although Capocci and Hübner (2004)
and Liang (2001) consider a relatively short bearish sub-period with the Asian crisis, their
sample does not enable them to distinguish between unambiguously bullish and bearish
sub-periods. Our study will thus identify and separately analyse two sub-periods
corresponding to upward and downward market trends, with a pivot set at the end of
March 2000.
Secondly, we introduce a modified asset pricing model encompassing the risk
premia that proved to be relevant for assessing funds performance in previous studies,
successively proposed by Fama and French (1993), Carhart (1997), Agarwal and Naik
(2004) and Capocci and Hübner (2004). This yields a model with 10 risk premia, which
may look at first sight overspecified but one has to bear in mind that hedge funds families
are very heterogeneous and, unlike mutual funds, involve investments in many types of
assets and markets.
124
Thirdly, we specifically identify one hedge fund strategy, namely Market Neutral
that, following the results of Edwards and Caglayan (2001), supposedly hedge investors
against bearish markets. It has also been studied in an unambiguously bullish setup by
Capocci and Hübner (2004), who find that this family of funds tends to out-perform the
market during the 1994-2000 period. In this study, we perform an in-depth analysis of the
level and persistence of its performance before and after the stock markets downturn.
The study is organised as follows. Section 2 sets out the performance models we
will use. In Section 3, we provide a thorough analysis of the database. The fourth Section
studies potential biases in the database. The next Section reports the performance of
hedge funds for the whole period and the sub-periods considered. Section 6 documents
and explains the persistence in hedge fund returns over the same time windows, with a
special focus on the Market Neutral strategy. Section 7 concludes the study.
125
II Performance Measurement Models
The starting point of our study of hedge funds performance is the original Sharpe
(1964) – Lintner (1965) CAPM. As the basic multi-factor specification, we use the Carhart
(1997) model as it is that is widely used in practice and it is not dominated by any other
model in the mutual funds performance literature. Finally, we construct a multifactor
model that extends the Carhart (1997) specification by combining it with factors proposed
in Agarwal and Naik (2004) and Capocci and Hübner (2004) and by adding an additional
factor.
2.1 The Capital Asset Pricing Model
The first performance model we use is a single index model based on the classical
CAPM developed by Sharpe (1964) and Lintner (1965). Its equation to estimate is the
following:
( ) TtRRRR PtFtMtPPFtPt ,...,2,1 =+−+=− εβα (6)
where RPt = return of fund P in month t; RFt = risk-free return on month t; RMt =
return of the market portfolio on month t; εPt = error term; αP and βP are the intercept and
the slope of the regression, respectively.
126
The intercept of this equation, αp commonly called Jensen’s alpha (1968) is usually
interpreted as a measure of out- or under-performance relative to the market proxy used.
2.2 The 4-Factor Model of Carhart (1997)
The four-factor model of Carhart (1997) is an extension of the Fama and French
(1993) 3-factor model. It takes into account size and book-to-market ratio, but also an
additional factor for the momentum effect. Grinblatt, Titman and Wermers (1995) define
this effect as buying stocks that were past winners and selling past losers. This model is
estimated with the following regression:
( ) TtYRPRHMLSMBRRRR PttPtPtPFtMtPPFtPt ,...,2,1 14321 =++++−+=− εββββα (7)
where SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the
factor-mimicking portfolio for book-to-market equity (‘high minus low’)31 and PR1YRt = the
factor-mimicking portfolio for the momentum effect.32 These factors aim at isolating the
firm-specific components of returns.
31 See Fama and French (1993) for a precise description of the construction of SMBt and HMLt.
32 For a description of the construction of PR1YR see Carhart (1997).
127
2.3 The Composite Model
In order to take into account the complex characteristics of the hedge fund
industry, we implement a combination and an extension of Carhart’s (1997) 4-factor
model, the model used by Agarwal and Naik (2004) and the one used by Capocci and
Hübner (2004).
This model contains the market risk premium, Fama and French (1993) "size" and
"value" factors, Carhart’s (1997) "momentum" factor, five factors introduced by Agarwal
and Naik (2004): a factor for non-US equities investing funds (MSCI World excluding US),
two factors to account for the fact that hedge funds invest in US and foreign bond indices33
(Lehman High Yield Bond Index and Salomon World Government Bond Index) and one
factor that Capocci and Hübner (2004) proved to be highly significant, the JP Morgan
Emerging Market Bond Index, and finally a commodity factor (GSCI Commodity Index).
Furthermore, we add an additional bond index factor that is not used in previous studies,
namely the Lehman Mortgage-Backed Securities Index to take into account the fact that
various hedge funds strategies (fixed income arbitrage, mortgage-backed securities) are
exposed to this market and the Lehman High-Yield Credit Bond Index.
The market proxy used is the value-weighted portfolio of all NYSE, Amex and
NASDAQ stocks market proxy that is usually used in mutual funds performance studies.
Several additional factors, such as the MSCI Emerging Markets Index, the Lehman
BAA Corporate Bond Index and the Salomon Brothers Government and Corporate Bond
Index proposed by Agarwal and Naik (2004) and Capocci and Hübner (2004) and the Gold
33 The Lehman US Aggregate Bond Index, that was used in several previous hedge funds studies, was
found to have an extremely high correlation with the Lehman BBA Corporate Bond Index and thus was
removed from our study.
128
index used by Fung and Hsieh (1997) were not included in our extended model given their
high colinearity with our set of indices.34
( )( ) ( )( ) ( )( ) ( ) PtFttPFttP
FttPFttP
FttPFttP
tPtPtPFtMtPPFtPt
RGSCIRMORTRHYRJPMEMBI
RSWGBIRMSWXUSYRPRHMLSMBRRRR
εββββββ
ββββα
+−+−+−+−+
−+−++++−+=−
109
87
65
4321 1
(8)
where RMt = return on the Russel 3000 Index; MSWXUSt = return of the MSCI World Index
excluding US; SWGBIt = return of the Salomon World Government Bond Index; JPMEMBIt
= return of the JP Morgan Emerging Market Bond Index; HYt = return of the Lehman High
Yield Credit Bond Index et MORTt = return of the Lehman Mortgage-Backed Securities
Index, and GSCIt = return of the Goldman Sachs Commodity Index.
34 Agarwal and Naik (2003) suggest that the Goldman Sachs Commodity index is a better
approximation of the commodity market as the Gold index regarding hedge funds.
129
III Data
3.1 Database
Three main hedge fund databases are available for empirical studies: ‘Managed
Account Reports’ (MAR), ‘Hedge Fund Research, Inc.’ (HFR), and ‘TASS Management’
(TASS) (Amin and Kat, 2003a). These databases are the most used in academic and
commercial hedge fund studies.35
Data vendors do not only collect performance data. For a majority of funds, they
record other useful information such as company name, start and ending date, strategy
followed, assets under management, management and incentive fees, manager's name
etc. There is no consensus on the definition of the strategy followed but there are
similarities. MAR defines 9 strategies with a total of 16 sub-strategies. HFR defines sixteen
different strategies in two categories, 12 non-directional and 5 directional strategies, plus
the Funds of Funds and the Sector categories. Finally, TASS defines 15 strategies.
We use hedge fund data from MAR, as in Fung and Hsieh (1997), Schneeweis and
Spurgin (1998), and Amin and Kat (2003a). The database gives monthly net-of-fee
individual returns and other information on individual funds and groups them in indices.
We use 108 monthly returns on 2894 individual hedge funds plus 48 indices (16
investment styles with 3 indices for each investment style: onshore, offshore and a
combined index). These funds include 1622 funds alive at the end of the period (56%) and
1272 dissolved funds (44%).
35 The three databases have never been used together in a study, but Ackermann and Ravenscraft
(1998) and Ackermann et al. (1999) and Capocci and Hübner (2004) used a combination of HFR and
MAR while Liang (2000) uses a combination of TASS and HFR.
130
Hedge funds are classified in two categories. The Individual Funds category
features 13 strategies: Event driven – Risk Arbitrage, Event-Driven – Distressed
Securities, Global, Global Est., Global Intern., Global Emerging, US Opp.36, Macro, Mkt
Neutral, Long Only Leveraged, Sector, Short Sales and No Category, the latter one
corresponding to funds with no stated strategy and funds whose strategy does not fill in
any of the above. The Funds of Funds category features 3 strategies: Niche, Diversified
and Others.
We take the value-weighted portfolio of all NYSE, Amex and NASDAQ stocks market
proxy that is usually used in mutual funds performance studies (see e.g. Fama and
French, 1993, 1996; Carhart, 1997). Its almost perfectly correlation with the Russell 3000
index used in Agarwal and Naik (2004) suggests that both market proxies are very
similar.37 Finally, the one-month T-bill rate from Ibbotson Associates is taken as the risk-
free rate.
3.2 Basic Performance
Panel A of Table 17 contains descriptive statistics of the funds, whether living or
dead, in our database. These hedge funds data are contrasted against the descriptive
statistics of the factors introduced in equation (3) of Section 2. These statistics are
reported in panel B of Table 16.
36 This strategy has been suppressed in 1999.
37 See Capocci and Hübner (2004) for more a complete analysis of this correlation.
131
Panel A shows that the highest mean return was achieved by the Sector (1.66%),
then the Global Est. (1.29%) and Global Emerging (1.17%) follow. Average returns of
funds of funds are all around 0.70%, only followed by the Global (0.45%) strategy that
achieves the lowest mean return. This pattern is similar for the mean excess returns.
These descriptive statistics differ from the results obtained by Capocci and Hübner
(2004) for the 1994-2000 period, who find that the best performers are US Opportunistic
Small Caps, US Opportunistic Growth and Sector while the worst average performers are
Foreign Exchange, Short Sellers the and Funds of Funds, without sub-strategy. This
difference can be explained by the difference in the database used (MAR combined with
HFR for Capocci and Hübner, 2004) and the different time period studied.
The Sharpe measure (the ratio of excess return and standard deviation) offers a
much different picture: accounting for risk, Market Neutral funds appear to be the best
performers, while the funds that achieve the highest absolute returns are only among the
average risk-adjusted performers.
A look at the t-stats indicates that mean returns are significantly different from 0 at
the 5% significance level for all funds and that the mean excess returns are significantly
positive for all cases but the Global and Diversified funds of funds categories.
Panel B of Table 16 shows that the mean excess return of the Market Proxy is
0.78% per month (about 9.5% per year), only statistically different from zero at the 10%
level. This reasonable value indicates that the bullish sub-period has been almost totally
offset by the market correction. The mean excess premium of the MSCI World excluding
US is an insignificant 0.22% per month. The average SMB and HML returns are
insignificant; only the Momentum factor, with the highest mean, provides a significantly
positive value. The highest mean return for bond indices was obtained by the JP Morgan
Emerging Market Bond Index.
132
The Sharpe ratio obtained by our whole hedge fund database (0.29) is higher than
the ones for the Market Proxy (0.19), and higher than for the MSCI World Excluding US (-
0.15).
3.3 Analysis per Sub-periods
The cutting point chosen for the identification of the up and down periods has been
set at March 2000. This month corresponds to the maximum observed value of the Russell
3000 Index that reached a value of 858.48 during the session of March 24, 2000. During
the up period, the monthly index return was positive in 70% of the months (52 out of 74)
with an average yearly return of 19.4%. During the down period, the monthly index return
was positive in 39% of the months (12 out of 34) and the average yearly return was -
16.9%. Those trends are sufficiently strong to allow us the consider the whole sub-periods
as, respectively, bullish and bearish without having to use a complex rule to separate
bullish, bearish and neutral months since these rules would obviously not match the ones
used by funds managers for their market timing decisions.
The analysis of basic performance for the two sub-periods under review, presented
in Table 17, reveals some interesting differences.
133
Table 17: Descriptive Statistics of Hedge Funds Strategies and
Passive Investment Strategies
Panel A: Hedge Funds strategies Jan.1994-December 2002 (108 months)
Nb of Fds
% of the category
Living Funds
Dead Funds
Mean Return t(mean) Std. Dev. Med.
Event driven - Risk Arb 136 6,10% 85 51 0,93% 5,15 1,74% 0,92%
Event driven - Distressed Sec 106 4,70% 70 42 0,99% 5,48 2,25% 1,17%
Global* 175 7,80% 1 174 0,45% 2,47 3,80% 0,64%
Global Est. 499 22,20% 300 199 1,29% 7,15 3,25% 1,09%
Global Intern. 72 3,20% 46 26 0,88% 4,87 2,42% 0,93%
Global Emerging 157 7,00% 97 60 1,17% 6,48 5,02% 1,80%
US Opp.** 39 1,70% 0 39 0,23% 1,3 2,40% 0,21%
Macro 144 6,40% 52 92 0,82% 4,52 2,15% 0,61%
Market Neutral 635 28,30% 385 250 1,04% 5,73 0,97% 1,05%
Long Only Lev. 33 1,50% 16 17 0,92% 5,06 5,83% 1,50%
Sector 190 8,50% 111 79 1,66% 9,17 4,43% 2,07%
Short Sales 37 1,60% 24 13 0,88% 4,87 4,48% 0,67%
No category 24 1,10% 6 18 0,93% 5,12 3,45% 0,58%
Individual Funds Total 2247 100% 1186 1061 1,08% 5,98 2,28% 1,11%
FoF - Niche 114 18% 86 28 0,74% 4,1 1,33% 0,67%
FoF - Diversified 501 77% 349 152 0,71% 3,95 1,87% 0,75%
FoF - Other 32 5% 1 31 0,77% 4,27 1,69% 0,80%
Funds of Funds Total 647 100% 436 211 0,72% 3,96 1,77% 0,71%
Total 2894 100% 1622 1272 0,99% 5,49 2,14% 1,11%
134
Med. Min Max Skew. Kurt Excess return
t(mean exc.)
Sharpe ratio
Event driven - Risk Arb 0,92% -6,40% 5,50% -0,58 2,24 0,55% 3,05 0,32
Event driven - Distressed Sec 1,17% -10,80% 7,00% -1,16 6,25 0,61% 3,38 0,27
Global* 0,64% -25,80% 13,60% -2,74 21,61 0,07% 0,37 0,02
Global Est. 1,09% -9,90% 12,30% 0,11 1,59 0,91% 5,04 0,28
Global Intern. 0,93% -6,80% 8,90% 0,24 1,44 0,50% 2,77 0,21
Global Emerging 1,80% -21,70% 14,30% -0,66 3,18 0,79% 4,37 0,16
US Opp.** 0,21% -5,60% 7,40% 0,09 0,7 -0,18% -1 -0,08
Macro 0,61% -4,10% 7,00% 0,45 0,57 0,44% 2,42 0,2
Market Neutral 1,05% -2,50% 4,00% -0,22 1,05 0,66% 3,62 0,67
Long Only Lev. 1,50% -17,40% 13,30% -0,44 0,16 0,54% 2,96 0,09
Sector 2,07% -13,10% 19,90% 0,31 2,74 1,28% 7,06 0,29
Short Sales 0,67% -13,60% 13,20% 0,09 0,74 0,50% 2,76 0,11
No category 0,58% -7,80% 12,70% 1,17 3,2 0,55% 3,01 0,16
Individual Funds Total 1,11% -8,60% 8,00% -0,26 2,77 0,70% 3,87 0,31
FoF - Niche 0,67% -4,10% 5,10% 0,22 1,73 0,36% 1,99 0,27
FoF - Diversified 0,75% -7,30% 7,00% -0,12 3,54 0,26% 1,41 0,14
FoF - Other 0,80% -7,30% 5,80% -0,89 4,86 0,39% 2,16 0,23
Funds of Funds Total 0,71% -6,80% 6,60% -0,11 3,34 0,34% 1,85 0,19
Total 1,11% -8,20% 7,60% -0,2368 3,04 0,61% 3,38 0,29
The Global category has been gradually suppressed and replaced by the Global Est., Global Intern. And Global Emerging categories. Therefore, the funds disappearance is mostly due to category transfers. ** US Opportunistics ended in 1999.
Panel A (continued): Hedge Funds strategies Jan.1994-December 2002 (108 months)
135
Mean Return t(mean) Std. Dev. Median
Equity Factors
Market Proxy 0,78 1,7 4,77 1,58
MSCI World Excluding US 0,09 0,22 4,36 0,47
F&F SMB Factor 0,02 0,04 4,45 -0,36
F&F HML Factor 0,6 1,5 4,16 0,68
Momentum Factor 1,14 2,06 5,74 1,27
Bond Factors
1 month T-bill 0,37 34,69 0,11 0,4
Salomon WBGI 0,5 2,83 1,83 0,24
JPM EMBI Global 0,82 1,81 4,67 1,16
Lehman Mortgage 0,59 6,94 0,89 0,66
Lehman High Yield Credit 0,4 1,99 2,11 0,66
Commodities
Goldman Sachs Commodity 0,59 1,14 5,35 0,61
Panel B: Passive Strategies
136
Min Max Mean exc. Return t(mean exc.) Sharpe ratio
Equity Factors
Market Proxy -15,7 8,3 0,41 0,9 0,19
MSCI World Excluding US -12,9 10,3 -0,28 -0,67 -0,15
F&F SMB Factor -16,3 21,4 -0,35 -0,82 -0,18
F&F HML Factor -8,9 13,7 0,23 0,58 0,14
Momentum Factor -25,1 18,2 0,77 1,39 0,24
Bond Factors
1 month T-bill 0,1 0,6 NA NA NA
Salomon WBGI -3,4 5,9 0,13 0,72 0,39
JPM EMBI Global -24,2 10,9 0,44 0,99 0,21
Lehman Mortgage -2,6 3,2 0,22 2,66 2,99
Lehman High Yield Credit -7,37 7,49 0,03 0,17 0,08
Commodities
Goldman Sachs Commodity -12,28 15,79 0,22 1,07 0,2
Panel B (continued): Passive Strategies
This Table shows the mean returns, t-stat for mean = 0, standard deviation, medians,minimum, maximum, mean excess returns, t-stat for mean excess return = 0, and Sharperatios for the individual hedge funds in our MAR database for the whole period 01:1994-12:2002. US Opp. Funds ended in 01:1999. Sharpe ratio is the ratio of excess return andstandard deviation with a risk-free rate set at 5%. In panel A, No of Fds represent the numberof funds following a particular strategy (or sub-strategy), Living Funds and Dead Fundsrepresents the number of surviving and dead funds (in December 2002). We calculate the MeanExcess Return considering Ibbotson Associates one-month T-bills. Numbers in the table aremonthly percentage.
137
Table 19 displays summary results for the bullish and bearish sub-periods. As
expected from the nature of the time windows, excess returns obtained for the majority of
hedge funds strategies are mostly due to the bullish sub-period, with the best performers
before March 2000 also displaying the worst returns after the market reversal too place.
There are three noticeable exceptions. Firstly, the US Opportunistics strategy did poorly in
spite of favourable market conditions, which explains the disappearance of this category.
Secondly, the Global strategy seems to achieve returns that are much less dependent on
the conjuncture than the other strategies. Finally, the Short Sales strategy is the only one
that records significant excess returns during bad times but at the expense of insignificant
returns in good times.
Preliminary evidence does not seem to indicate that the behaviour of the two Event
Driven and of the Macro strategies out-perform the other ones in the bearish period, while
the returns of the Market Neutral strategy are then significant but not when excess returns
are considered. Although further evidence is obviously needed, this does not support the
findings of Edwards and Caglayan (2001) with a different definition of bearish market
conditions.
138
Table 18: Descriptive statistics of hedge funds strategies for
the bullish and bearish sub-periods
Nr of Fds Living Funds Dead Funds
Event driven - Risk Arb 113 89 24
Event driven - Dist. Sec 83 65 18
Global 175 6 169
Global Est. 400 342 58
Global Intern. 64 58 6
Global Emerging 132 108 24
US Opp. 39 0 39
Macro 121 63 58
Market Neutral 487 350 137
Long Only Lev. 31 22 9
Sector 147 126 21
Short Sales 34 25 9
No category 19 9 10
Individual Funds Total 1845 1263 582
FoF - Niche 81 57 24
FoF - Diversified 408 333 75
FoF - Other 31 18 13
Funds of Funds Total 520 408 112
Hedge funds Total 2365 1671 694
Panel A: Sub-period 01:1994-03:2000
139
Mean Return Excess return Sharpe ratio
Event driven - Risk Arb 1,23%*** 0,82%*** 0,46
Event driven - Dist. Sec 1,27%*** 0,85%*** 0,36
Global 0,57%** 0,16% 0,04
Global Est. 1,96%*** 1,54%*** 0,48
Global Intern. 1,30%*** 0,89%*** 0,35
Global Emerging 1,57%*** 1,16%*** 0,21
US Opp. 0,23% -0,18% -0,08
Macro 1,10%*** 0,68%*** 0,3
Market Neutral 1,18%*** 0,77%*** 0,75
Long Only Lev. 1,83%*** 1,42%*** 0,26
Sector 2,56%*** 2,14%*** 0,5
Short Sales 0,39%* -0,02% 0
No category 1,21%*** 0,80%*** 0,2
Individual Funds Total 1,47%*** 1,06%*** 0,45
FoF - Niche 0,92%*** 0,51%** 0,35
FoF - Diversified 0,96%*** 0,26% 0,12
FoF - Other 0,92%*** 0,50%** 0,26
Funds of Funds Total 0,95%*** 0,54%** 0,28
Hedge funds Total 1,35%*** 0,93%*** 0,42
Panel A (continued): Sub-period 01:1994-03:2000
140
Nr of Fds Living Funds Dead Funds
Event driven - Risk Arb 112 85 27
Event driven - Dist. Sec 94 70 24
Global 6 0 6
Global Est. 441 300 141
Global Intern. 66 46 20
Global Emerging 133 97 36
US Opp. NA NA NA
Macro 86 52 34
Market Neutral 498 385 113
Long Only Lev. 24 16 8
Sector 169 111 58
Short Sales 28 24 4
No category 14 6 8
Individual Funds Total 1665 1186 479
FoF - Niche 90 86 4
FoF - Diversified 416 349 77
FoF - Other 19 1 18
Funds of Funds Total 535 436 99
Hedge funds Total 2214 1622 578
Panel B: Sub-period 04:2000-12:2002
141
Mean Return Excess return Sharpe ratio
Event driven - Risk Arb 0,0025 -0,0006 -0,04
Event driven - Dist. Sec 0,0037 0,06% 0,03
Global 0,0016 -0,0014 -0,05
Global Est. -0,0021 -0,52%** -0,19
Global Intern. -0,0008 -0,0039 -0,22
Global Emerging 0,27% -0,04% -0,01
US Opp. NA NA NA
Macro 0,0019 -0,0012 -0,07
Market Neutral 0,71%*** 0,004 0,52
Long Only Lev. -1,17%*** -1,48%*** -0,23
Sector -0,0038 -0,69%**° -0,16
Short Sales 1,99%*** 1,68%*** 0,33
No category 0,0028 -0,0003 -0,01
Individual Funds Total 0,0019 -0,0012 -0,06
FoF - Niche 0,0033 0,0003 0,03
FoF - Diversified 0,0015 -0,0016 -0,13
FoF - Other 0,44%* 0,0014 0,14
Funds of Funds Total 0,0018 -0,0013 -0,11
Hedge funds Total 0,0019 -0,0012 -0,07
Panel B (continued): Sub-period 04:2000-12:2002
This Table shows the number of funds following a particular strategy (or sub-strategy), the corresponding number of living and dead funds, mean returns, mean excess returns, and Sharpe ratios for the individual hedge funds in our MAR database for the sub-periods 01:1994-03:2000 (bullish) and 04:2000-12:2002 (bearish). Sharpe ratio is the ratio of excess return and standard deviation with a risk-free rate set at 5%.*** statistically significant at the 1% level, ** statistically significant at the 5% level, * statistically significant at the 10% level.
142
For our factors, the same analysis shows that the Market and Momentum factors
gave the highest excess returns during the first sub-period, while the Book-to-Market and
Lehman Mortgage factors obtained significant positive abnormal returns during the second
one. Poorest performers were the Lehman Aggregate US Bond Index during the up market
trend period and the Market and World Excluding US factors during the down period.38
3.4 Correlations
The traditional hedge funds literature contends that, thanks to their weak correlation
between hedge funds and other securities, hedge funds are likely to improve to the risk-
return trade-off when added to a traditional portfolio (see Fung and Hsieh, 1997;
Schneeweis and Spurgin, 1998; Liang, 1999; Amin and Kat, 2003b).
This sub-section studies the ranges of correlation coefficients among and between
hedge funds and passive investment strategies. The correlations have been computed for
the whole 1994-2002 period and for two-sub-periods. In order to obtain periods with
comparable lengths, we took the bearish sub-period starting in April 2000 (33 months) and
matched it against the most bullish time window, that started in September 1998 (19
months) rather than the whole 1994-03:2000 period. Because of the extremely large
number of results to be reported, we chose to report ranges in correlations. Results are
reported in Table 19.
In each cell, correlations increase as the colour is darker. The upper part of the cell
accounts for the correlation during the whole period, while the lower part is split between
the pre- and post-March 2000 sub-periods.
38 Detailed data are available upon request.
143
Panel A reports correlations among hedge funds strategies. As typically reported (see
Liang, 2003; Capocci and Hübner, 2004) in the literature, these strategies are in general
highly correlated when indices are considered, with the exception of the Short Sellers
strategy that systematically goes conversely – as expected. However, a closer look at their
evolution over time indicates that the Global and, to a lesser extent, the Global
International strategies tend to decrease their correlation with other funds in bearish times;
on the other hand, the Global Emerging strategy follows the other strategies more closely
during periods of down markets. The no Category and Niche strategies seem to be more
correlated with the rest of hedge funds in the sub-periods than in the full period.
In Panel B, the behaviour of our explanatory variables is also of considerable
interest. Only four indices (Market, World Excluding US, SMB and Lehman High Yield) have
a high correlation with most hedge funds strategies. These results confirm that hedge funds
strategies are weakly correlated with most traditional investment tools
The first line indicates that almost all hedge funds strategies tend to follow the
market (US and international) more closely in the bearish sub-period. This strong tendency
is not invalidated for the supposedly investor-protecting strategies. In general, hedge funds
strategies sharply decrease and even reverse their loading with the momentum factor, as
they become momentum-contrarian during bad times. They also reduce their sensitivity
towards the Emerging Market Bond factor, while increasing their exposure to the Lehman
High Yield and the SMB factors. The Short Sellers strategy, for its part, noticeably switches
from a "Glamour" strategy (low loading with the HML factor) to a "Value" one in the last
sub-period. This is the only strategy that consistently invests in Value stocks in bearish
markets.
Panel C indicates that the correlation coefficients of our regressors are low enough to
raise serious multi-colinearity concerns.
144
Table 19: Correlation among hedge funds, between hedge
funds and passive investment strategies, and among
passive investment strategies
DIV
NIC
NOC
SHS
SEC
LOL
MKN
MAC
GEM
GIN.
GES.
GLO
EDS
LOL SEC SHS NOC
Panel A: Correlation among Hedge Funds strategies
GIN GEM MAC MKNERA EDS GLO GES NIC
MOM
HML
Panel B: Correlation between Hedge Funds strategies and Passive Investments strategies
ERA EDS GLO GES GIN GEM MAC MKN LOL SEC SHS NOC NIC DIV
MKT
WXU
SMB
SWG
EMB
HIY
GSC
MOR
HIY
GSC
Panel C: Correlation among Passive Investment strategies
This Table reports the ranges of correlation coefficient among hedge funds strategies (Panel A), between hedge funds strategies and passive investment strategies (Panel B) and among passive investment strategies (Panel C). For each pair of strategies (in line and in column), the upper rectangle of the cell represents the range of correlation coefficient for the whole period (01:1994-12:2002); the bottom left square represents the range of correlation coefficient for the most bullish sub-period (09:1998-03:2000); and the bottom right square represents the range of correlation coefficient for the most bearish sub-period (04:2000-12:2002). Colour codes for correlations are: >75% in black, between 50 and 75% in dark grey, between 25 and 50% in medium-dark grey, between 0 and 25% in medium grey, between -25 and 0% in light grey and <-25% in white. ERA = Event Driven – Risk Arbitrage, EDS = Event Driven – Distressed Securities, GLB = Global, GES = Global Established, GIN = Global International, GEM = Global Emerging, MAC = Macro, MKN = Market Neutral, LOL = Long only Leveraged, SEC = Sectors, SHS = Short Selling, OPP, NOC = no Category, NIC = Niche, DIV = Diversified, MKT = Market Proxy, WXU = World excluding US, MOM = Momentum, S
MOM
SWG
EMB
MOR
MKT
WXU
SMB
HML
HIYMOM SWG EMB MORMKT WXU SMB HML
147
IV Analysis of biases
4.1 Survivorship bias
In order to reduce the severity of survivorship bias, an important concern for mutual
funds (see a.o. Carhart, 1997) as well as hedge funds studies (see a.o. Ackermann et al.,
2001 and Fung and Hsieh, 2000), data vendors backfill each fund’s performance history
prior to their addition to the database. Thus, they provide data that go back before the
starting date of the database itself, usually 1993. However, before this starting date, one is
left with only surviving funds data. Brown et al. (2001), for the TASS database, and Capocci
and Hübner (2004) for the combined MAR and HFR databases have shown that data for the
pre-1994 period is indeed subject to non-negligible survivorship bias that is very likely to
hinder statistical inference (see Hendricks et al., 1997). Data starting in 1994 appears to be
more reliable according to this criterion (Capocci and Hübner, 2004).
Two definitions of this bias are commonly used in mutual and hedge fund studies:
the performance difference between surviving and dissolved funds (e.g. Ackermann et al.,
1999) and the performance difference between living and all funds (e.g. Liang, 2000).
We report the bias using both definitions for the whole period and for 2 sub-periods
1994-03:2000 and 04:2000-2002.
In Panel A of Table 20, we report the yearly returns of all funds, surviving funds and
dissolved funds. Hedge funds experience extremely high returns in 1999, when the stock
market experienced a sharp positive return, without great difference between surviving and
dissolved funds. In the subsequent years, returns gradually reduced but mostly due to the
negative returns of dissolved funds. This is a clear effect of the bearish turn of the market
after March 2000, leading to an increase in differences in hedge funds returns between the
best and the worst performing managers.
148
In Panel B, our results yield a monthly survivorship bias of 0.41% (or 4.92% per
annum) for the whole period using the first formula while in Panel C the bias of 0.13% per
month (1.51% per annum) with the second formula. This latter value is much higher than
the very low value obtained by Ackermann et al. for the period 1988-1995. It is similar to
the percentage of 1.5% from Fung and Hsieh (1998), lower than the 0.30% monthly bias
found by Fung and Hsieh (2000) and slightly higher than the percentage of 1.2% found by
Capocci and Hübner (2004) for the 1994-2000 period. It is however lower than the 3% bias
found by Liang (2001), which is also the industry consensus as stressed by Amin and Kat
(2003b).39
A look at sub-period biases indicates that the level of this bias is mostly due to the
bearish period, where its level sets at 2.61%. The bias drifts up through the very high level
of returns differential between surviving and dissolved funds, but this effect is somehow
mitigated by the decrease in the proportion of returns from dissolved funds in the database
(this proportion steadily decreases from 35.9% in 1999 to 9.1% in 2002). Thanks to this
bias-reduction effect of recent data, the global behaviour of the database in relationship to
survivorship bias is kept within reasonable bounds.
39 This consensus value quite high when compared to the 0.8-1.5 bias reported by Malkiel (1995) and
Brown and Goetzmann (1995) for US mutual funds.
Table 20: Survivorship bias in hedge funds
Year Return S.D. Obs. Return S. D. Obs. Return S. D. Obs.
1994 1,8% 1,6% 8601 3,0% 1,4% 3419 1,0% 1,8% 5182
1995 18,6% 1,0% 10641 19,9% 1,0% 4630 17,7% 1,0% 6011
1996 21,3% 1,4% 13049 23,6% 1,3% 6200 19,3% 1,6% 6849
1997 20,4% 2,0% 15860 22,4% 1,9% 8136 18,3% 2,2% 7724
1998 3,6% 3,2% 17872 4,4% 3,0% 9954 2,6% 3,4% 7918
1999 33,5% 2,5% 18798 33,8% 2,2% 12052 33,3% 2,9% 6746
2000 9,6% 2,9% 20221 14,4% 2,3% 14395 -2,3% 4,3% 5826
2001 5,7% 1,6% 20591 8,0% 1,4% 16706 -3,2% 2,6% 3885
2002 0,4% 1,3% 20771 1,2% 1,2% 18899 -4,9% 2,0% 1872
Mean 01:94-03:00 17,0% 2,0% 14137 18,0% 1,8% 7399 15,0% 2,1% 6738
Mean 04:00-12:02 5,0% 1,9% 20528 8,0% 1,7% 16667 -3,0% 3,0% 3861
Mean 94-02 13,0% 1,9% 16267 15,0% 1,8% 10488 9,0% 2,4% 5779
All Funds Surviving Funds Dissolved Funds
Panel A: Annual performance (all funds, surviving funds and dissolved funds)
150
Panel B: Living - Dead Funds Panel C: Living - All Funds
Year Return Return
1994 0,02 0,01
1995 0,02 0,01
1996 0,04 0,02
1997 0,04 0,02
1998 0,02 0,01
1999 0,01 0,00
2000 0,17 0,05
2001 0,11 0,02
2002 0,06 0,01
Bias 01:94-03:00 0,16 0,09 per Month
1,92 1,03 per Year
Bias 04:00-12:02 0,98 0,22 per Month
11,75 2,61 per Year
Bias 94-02 0,41 0,13 per Month
4,93 1,51 per Year
This Table reports the survivorship bias of calculated from our database. Our MAR database contains 2894 hedge funds, including 1622 survived funds and 1272 dissolved funds as of December 2002. In Panel B survivorship bias is calculated as the performance difference between surviving funds and dissolved funds. In Panel C survivorship bias is calculated as the performance difference between surviving funds and all funds. All returns are net of fees. Numbers in the table are yearly percentage unless otherwise indicated.
151
4.2 Instant Return History Bias
As hedge funds are not allowed to advertise, their managers consider inclusion in a
database primarily as a marketing tool. This creates a positive instant history bias or
backfilled bias (Fung and Hsieh, 2000) that occurs because a fund’s performance history is
backfilled after inclusion. The upward bias results from the likelihood that funds with a poor
track record are less likely to apply for inclusion than funds with good performance history.
We use the same two-step methodology as Park (1995), Brown et al. (1997), Fung
and Hsieh (2000) to estimate this bias for our hedge fund database. On the one hand, we
estimate the average monthly return of the “observable portfolio” which invests in all funds
from our database each month. On the other hand, we estimate the average monthly return
of the “adjusted observable portfolio” obtained from investing in all these funds after
deleting the first 12, 24 and, if possible, 36, 48 and 60 months of returns. The bias is
estimated for the whole period and for the bullish and bearish sub-periods in order to
compare our results with those obtained by Fung and Hsieh (2000) and Capocci and Hübner
(2004). Results are reported in Table 21.
For the whole period, the observable monthly return averaged 0.99%, while the
adjusted observable one was 0.88% (when deleting the 12 first months), 0.84% (24
months), 0.81% (36 and 48 months), and 0.80% (60 months). This gives an estimate of
1.32% per year, very much in line with the values of 1.4% found by Fung and Hsieh (2000)
and 1.2% found by Capocci and Hübner (2004).
152
Table 21: Estimation of instant return history bias
Mean Monthly Return
Monthly Difference
Annual Difference Av. Nb of Fds
Period 94-02
All 0,99% NA NA 1356
Without 12M 0,88% 0,11% 1,32% 1174
Without 24M 0,84% 0,15% 1,80% 999
Without 36M 0,81% 0,18% 2,16% 837
Without 48M 0,81% 0,18% 2,16% 694
Without 60M 0,80% 0,19% 2,28% 570
Sub-period 01:94-03:00
All 1,35% NA NA 1197
Without 12M 1,22% 0,13% 1,56% 945
Without 24M 1,18% 0,17% 2,04% 752
Without 36M 1,14% 0,21% 2,52% 620
Without 48M 1,14% 0,21% 2,52% 539
Without 60M 1,13% 0,23% 2.76% 498
Sub-period 04:00-12:02
All 0,19% NA NA 1715
Without 12M 0,10% 0,09% 1,08% 1489
Without 24M 0,08% 0,11% 1,32% 1256
This Table reports the instant history bias calculated from our database. Our MAR database contains 2894 hedge funds, including 1622 survived funds and 1272 dissolved funds as of December 2002. Instant history bias is calculated as the performance difference between the average monthly return using the portfolio which invests in all funds each month (the observable portfolio) and the average monthly return from investing in these funds after deleting the first 12, 24, 36 and 60 months of returns (the adjusted observable portfolio). All returns are net of fees and on a monthly basis unless otherwise indicated.
153
Contrarily to the analysis of the survivorship bias, the first sub-period is mostly
responsible for the level of the bias. Because the period was increasingly bullish, with the
highest returns being obtained around the end of the period, the bias starts at a fairly high
level and increases as more returns are removed from the estimation, consistently with the
phenomenon found by Capocci and Hübner (2004). For the “bearish” sub-period, only
partial results are available due to the small length of this period, but the bias is kept at
very reasonable levels.
One may relate the level of this bias to the one of survivorship bias in this context:
during unfavourable market conditions, there is a sharp difference in the returns between
surviving and dissolved funds that can be explained by attrition of the latter funds because
of their bad performance. As only the most successful funds tend to remain during this time
period, the corresponding instant history bias is likely to be mitigated by this self-selection
of the most successful managers towards the end of the period, while the observable
portfolio returns include returns from subsequently dissolved funds.
154
4.3 Conclusion
Overall, this examination of biases indicates that both survivorship and instant
history biases are kept to very reasonable levels for the whole period as well as for the
bullish and bearish sub-periods, but for very different reasons. Interestingly, survivorship
bias is higher for the period of down market, while there is evidence of a more important
instant history bias during the upward trending period.
One could have suspected that the high failure rate of hedge funds after March 2000
would have lead survivorship bias to suspiciously high levels, but this is avoided by the
particular behaviour of the database, and especially thanks to the increase in the number of
funds that has been observed over the same time window. Yet, the phenomenon of
elimination of the poorest performers under unfavourable market conditions is also
responsible for the remarkably low level of the instant history bias.
155
V Hedge Funds Performance
This Section aims at studying whether hedge funds, as a whole or strategy by
strategy, have significantly out-performed the market. We compute all estimations by using
Newey-West (1987) standard errors to adjust for any autocorrelation in the returns.
Table 22 reports the results for All Funds, Individual Funds and Funds of Funds, and
all funds strategies, with equally weighted portfolio excess returns for each investment
style. The model is also estimated for each fund individually.40 To analyse hedge funds
performance in more details, the last columns give the distribution of individually estimated
alphas per strategy, with the percentage of significantly positive, insignificant and negative
alphas at the 5% level.
5.1 Performance Measurement using the CAPM
Panel A of Table 22 reports performance estimates using the CAPM. The estimated
betas are rather low, except for the Long Only Leveraged, and all R-squared are below
60%, except for Long Only Leveraged and Global Est., suggesting the need to use a more
detailed model. Overall, two thirds of the individual funds strategies produce significantly
positive alphas, while the two Funds of Funds strategies out-perform the market at the 10%
level. Overall, hedge funds as a whole also significantly out-perform the market at the 1%
level. Taken individually, 32% of the alphas are significantly positive.
40 To make individual estimation, we require all funds to have consecutive monthly return history for at
least 24 months, so that relatively accurate risk measures can be estimated.
Table 22: Performance measurement using the CAPM, Carhart’s 4-factor model and the combined
model
R² adj
Event driven - Risk Arb 0,46% *** 0,26 *** 0,515 48% 51% 0%
Event driven - Dist. Sec 0,50% *** 0,3 *** 0,41 34% 64% 1%
Global -0,11% 0,47 *** 0,331 9% 78% 11%
Global Est. 0,69% *** 0,58 *** 0,719 30% 67% 2%
Global Intern. 0,37% ** 0,34 *** 0,449 22% 74% 2%
Global Emerging 0,55% 0,62 *** 0,337 20% 75% 4%
US Opp. NA NA NA NA NA NA
Macro 0,32% ** 0,3 *** 0,445 18% 72% 8%
Market Neutral 0,62% *** 0,12 *** 0,378 44% 52% 2%
Long Only Lev. 0,12% 1,05 *** 0,73 9% 80% 9%
Sector 0,99% *** 0,73 *** 0,619 31% 67% 1%
Short Sales 0,81% *** -0,74 *** 0,607 11% 88% 0%
No category 0,43% 0,31 *** 0,174 21% 78% 0%
Individual Funds Total 0,55% *** 0,39 *** 0,651 31% 65% 3%
Niche - FoF 0,31% *** 0,15 *** 0,285 43% 53% 2%
Diversified - FoF 0,24% * 0,26 *** 0,427 33% 62% 3%
Other - FoF NA NA NA NA NA NA
Funds of Funds Total 0,25% * 0,24 *** 0,419 34% 60% 4%
Hedge funds Total 0,48% *** 0,35 *** 0,614 32% 64% 3%
Alpha Distrib. + / 0 / -
Panel A: Single index model
MktAlpha
R² adj
Event driven - Risk Arb 0,41% *** 0,28 *** 0,16 *** 0,08 *** -0,01 0,67 37% 60% 1%
Event driven - Dist. Sec 0,41% *** 0,33 *** 0,23 *** 0,11 *** 0,01 0,61 26% 71% 2%
Global -0,19% 0,48 *** 0,19 *** 0,08 0,02 0,36 11% 77% 11%
Global Est. 0,58% *** 0,58 *** 0,26 *** 0,04 0,07 *** 0,87 27% 71% 1%
Global Intern. 0,24% 0,38 *** 0,15 *** 0,09 ** 0,05 * 0,54 21% 71% 7%
Global Emerging 0,43% 0,64 *** 0,31 *** 0,12 0,02 0,40 18% 78% 3%
US Opp. NA NA NA *** NA NA NA NA NA NA
Macro 0,16% 0,33 *** 0,13 *** 0,04 0,11 *** 0,63 17% 74% 8%
Market Neutral 0,55% *** 0,15 *** 0,08 *** 0,07 *** 0,01 0,55 41% 54% 3%
Long Only Lev. 0,13% 0,98 *** 0,39 *** -0,02 0,02 0,82 12% 80% 6%
Sector 0,81% *** 0,71 *** 0,43 *** 0,01 0,15 *** 0,87 26% 72% 1%
Short Sales 0,83% *** -0,66 *** -0,36 *** 0,09 -0,09 ** 0,78 20% 79% 0%
No category 0,26% 0,31 *** 0,26 *** 0,01 0,14 *** 0,36 21% 73% 4%
Individual Funds Total 0,46% *** 0,4 *** 0,2 *** 0,06 ** 0,05 *** 0,83 28% 67% 3%
Niche - FoF 0,21% ** 0,18 *** 0,11 *** 0,07 ** 0,04 ** 0,45 33% 62% 3%
Diversified - FoF 0,10% 0,29 *** 0,16 *** 0,07 ** 0,07 *** 0,64 25% 68% 5%
Other - FoF NA NA NA *** NA NA NA NA NA NA
Funds of Funds Total 0,11% 0,27 *** 0,15 *** 0,07 ** 0,07 *** 0,63 26% 66% 6%
Hedge funds Total 0,37% *** 0,37 *** 0,19 *** 0,06 ** 0,05 *** 0,80 28% 67% 4%
PR1YR Alpha Distrib. + / 0 / -
Panel B: Carhart's 4-factor model - individual funds
Alpha Mkt SMB HML
R² adj
Event driven - Risk Arb 0,39% *** 0,25 *** 0,13 *** 0,06 ** 0,01 -0,02 0,04 0,04 * 0,17 *** -0,07 0,03 0,71 37% 59% 2%
Event driven - Dist. Sec 0,40% *** 0,21 *** 0,19 *** 0,06 0,02 0,06 -0,11 0,10 *** 0,21 *** 0,18 0,03 0,69 27% 71% 1%
Global -0,10% 0,30 ** 0,12 0,01 0,04 0,18 -0,11 0,14 ** 0,16 -0,09 0,12 ** 0,42 9% 81% 9%
Global Est. 0,56% *** 0,58 *** 0,24 *** 0,03 0,08 *** 0,01 0,03 0,07 *** 0,00 -0,08 0,03 0,88 26% 71% 2%
Global Intern. 0,41% *** 0,12 ** 0,10 *** 0,05 0,06 ** 0,30 *** -0,26 *** 0,05 0,05 0,15 0,05 * 0,66 28% 67% 4%
Global Emerging 0,61% 0,31 ** 0,20 ** 0,01 0,07 0,34 ** -0,66 *** 0,22 *** 0,18 0,11 0,12 * 0,52 15% 84% 0%
US Opp. NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Macro 0,12% 0,25 *** 0,13 *** 0,01 0,11 *** 0,05 -0,14 * 0,04 0,05 0,49 *** -0,02 0,66 16% 78% 4%
Market Neutral 0,54% *** 0,12 *** 0,07 *** 0,05 *** 0,01 0,01 -0,06 0,04 *** 0,07 * 0,11 0,02 0,64 39% 57% 3%
Long Only Lev. -0,11% 1,01 *** 0,38 *** -0,08 0,00 -0,11 0,00 0,17 *** 0,06 0,71 ** 0,05 0,85 6% 83% 9%
Sector 0,73% *** 0,84 *** 0,43 *** 0,02 0,15 *** -0,12 * 0,03 0,04 -0,11 -0,18 0,06 ** 0,88 19% 78% 1%
Short Sales 0,92% *** -0,74 *** -0,39 *** 0,08 -0,07 * 0,04 -0,01 -0,07 0,25 * -0,13 0,01 0,78 23% 76% 0%
No category 0,33% 0,16 0,25 *** -0,01 0,13 ** 0,26 ** 0,01 0,18 *** -0,20 0,02 0,03 0,44 21% 78% 0%
Individual Funds Total 0,46% *** 0,34 *** 0,17 *** 0,03 0,05 *** 0,05 -0,10 * 0,07 *** 0,05 0,05 0,04 ** 0,86 26% 69% 3%
Mortg. Comm. Alpha Distrib. + / 0 / -
Panel C: The combined model - individual funds
Alpha Mkt SMB HML PR1YR W x US W Gv Bd Em. Bd High Y.
R² adj
Niche - FoF 0,24% ** 0,13 *** 0,08 *** 0,05 * 0,05 *** 0,04 -0,07 0,05 *** 0,06 -0,1 0,02 0,51 32% 64% 2%
Diversified - FoF 0,10% 0,21 *** 0,13 *** 0,03 0,08 *** 0,06 -0,17 *** 0,08 *** 0,07 0,16 0,03 0,71 24% 71% 3%
Other - FoF NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA
Funds of Funds Total 0,12% 0,2 *** 0,12 *** 0,04 0,08 *** 0,06 -0,16 ** 0,07 *** 0,07 0,14 0,03 0,70 25% 70% 3%
Hedge funds Total 0,38% *** 0,31 *** 0,16 *** 0,03 0,06 *** 0,05 -0,11 ** 0,07 *** 0,06 0,07 0,04 ** 0,84 26% 70% 3%
This Table presents the results of the estimation of the single index model (Panel A), of Carhart’s (1997) model (Panel B) and of our combined model (Panel C) for the 01:1994-12:2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, per type of funds and for all funds. The last column gives the distribution of individually estimated monthly alphas for all funds with 24 monthly data or more in a specific investment style. Results for the US Opportunistics and Other categories are not reported as they have, respectively, 0 and 1 living fund in the second sub-period. We report the percentage of significantly positive alphas (+), significantly negative alphas (-) and alphas insignificantly different from zero (0) at the 5% level. t-stats are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
Alpha Mkt SMB HML PR1YR W x US Comm. Alpha Distrib. + / 0 / -
Panel C (continued): The combined model - FoF
W Gv Bd Em. Bd High Y. Mortg.
160
5.2 Performance Measurement using Multi-Factor Models
It is presumably better to use a multi-factor model to account for all possible
investment strategies. In Panel B of Table 22, we report the results for Carhart’s 4-factor
model and in Panel C the results for our combined model applied to hedge funds.
Panels B reveals that the premium on the SMB factor is, in almost all cases,
significant, including in the Short Sellers strategy where it is negative. The coefficients of
the HML and Momentum factors are significant for four and six individual funds strategies,
respectively, and to all funds of funds strategies.
Panel C shows that the explanatory power of the HML factor seems marginal as only
three betas are significantly positive at the 5% level. The Momentum factor remains a
stronger indicator of hedge funds behaviour, with only the Short Sales strategy being
momentum contrarian over the whole period. The results with our combined model also
indicate that all additional factors add explanatory power to the regression. In particular, as
already outlined by Capocci and Hübner (2004), the Emerging Bond factor adds explanatory
power in more than 50% of the strategies with high significance levels. Event Driven
strategies are more prone to bear a high exposure to high yield bond factors, while Global
International and Emerging strategies share similar risk exposure characteristics except that
the former is more momentum-driven and the latter is naturally heavily exposed to the
Emerging Market Bond factor.
Evidence on alphas obtained in Panel C is not favourable to Funds of Funds and to
the Macro strategy. Overall, accounting for more risk premia reduces the average reported
out-performance by 0.1% per months. The individual alpha distribution shows that taking
more factors into account drives down that the proportion of individual funds and funds of
funds that significantly out-performed the market, and the distribution of performance
among strategies is also more concentrated.
161
Overall it seems that the combined model does a very good job in describing hedge
funds behaviour. The average R²adj increases from 0.61 for the single factor model, to 0.80
for the 4-factor model and to 0.84 for our combined model. This coefficient is the best one
reported in the literature so far.41
5.3 Performance over bullish and bearish sub-periods
In order to analyse the performance components in the bullish and bearish market
configurations, we only report results for our combined model. Table 23 shows the value of
the coefficients for the sub-periods 01:1994-03:2000 (Panel A) and 04:2000-12:2002
(Panel B).
41 See e.g. .Liang (1999) and Amin and Kat (2003a).
162
Table 23: Performance of hedge funds during the bullish and
bearish sub-periods
Risk Arb 0,50% *** 0,31 *** 0,19 *** 0,03 -0,07 ** -0,01 -0,01
Dist. Sec 0,50% *** 0,25 *** 0,22 *** 0,09 ** -0,07 * 0,11 ** -0,18 **
Global -0,65% ** 0,50 *** 0,02 -0,03 0,01 0,14 -0,39 **
Global Est. 0,62% *** 0,66 *** 0,31 *** -0,01 0,06 0,03 0,00
Global Intern. 0,47% ** 0,20 ** 0,13 ** 0,00 0,01 0,30 *** -0,44 ***
Global Emerging 0,27% 0,51 *** 0,13 0,09 -0,02 0,36 ** -0,98 ***
US Opp. 0,07% -0,07 0,38 ** 0,00 -0,13 0,00 -0,25
Macro 0,09% 0,32 *** 0,14 *** 0,00 0,10 ** 0,06 -0,32 ***
Market Neutral 0,53% *** 0,14 *** 0,07 *** 0,07 *** 0,02 0,00 -0,05
Long Only Lev. 0,03% 1,03 *** 0,47 *** -0,01 -0,04 -0,02 -0,08
Sector 0,95% *** 0,82 *** 0,52 *** 0,03 0,17 *** -0,05 0,00
Short Sales 0,92% *** -0,65 *** -0,45 *** 0,08 -0,05 -0,07 0,09
No category 0,25% 0,26 * 0,36 *** -0,13 0,03 0,34 *** -0,06
Ind. Funds Total 0,44% *** 0,41 *** 0,20 *** 0,03 0,04 0,06 * -0,17 ***
Niche - FoF 0,22% 0,17 *** 0,08 ** 0,10 ** 0,04 0,05 -0,12
Diversified - FoF 0,02% 0,29 *** 0,13 *** 0,06 0,08 ** 0,06 -0,28 ***
Other - FoF 0,24% 0,24 *** 0,11 ** 0,04 -0,06 -0,01 -0,19
F. of Funds Total 0,05% 0,27 *** 0,12 *** 0,07 0,07 * 0,06 -0,26 ***
Total 0,35% *** 0,38 *** 0,18 *** 0,04 0,04 0,06 -0,19 ***
PR1YR W x US W Gv BdAlpha Mkt SMB HML
Panel A: 01:1994-03:2000
163
R² adj
Risk Arb 0,04 ** 0,11 -0,02 0,00 0,74 46% 51% 2%
Dist. Sec 0,07 *** 0,51 *** -0,11 0,04 0,81 33% 66% 0%
Global 0,08 0,86 *** -1,10 ** 0,17 *** 0,67 9% 81% 9%
Global Est. 0,06 *** -0,18 -0,01 0,04 0,91 25% 72% 1%
Global Intern. 0,05 0,00 0,23 0,06 0,66 27% 70% 1%
Global Emerging 0,22 ** 0,48 -0,71 0,17 * 0,56 10% 87% 1%
US Opp. 0,00 0,34 0,50 -0,09 0,09 6% 82% 10%
Macro 0,04 -0,05 0,53 ** -0,01 0,70 15% 80% 3%
Market Neutral 0,04 *** 0,15 * -0,03 0,03 * 0,66 39% 59% 1%
Long Only Lev. 0,17 *** -0,10 0,85 * 0,01 0,80 3% 88% 7%
Sector 0,03 -0,26 0,10 0,07 ** 0,90 25% 74% 0%
Short Sales -0,06 0,33 -0,43 -0,04 0,71 17% 82% 0%
No category 0,19 *** -0,48 0,22 0,04 0,51 31% 68% 0%
Ind. Funds Total 0,06 *** 0,03 -0,05 0,05 ** 0,89 26% 70% 2%
Niche - FoF 0,05 ** 0,12 -0,30 0,01 0,51 35% 60% 3%
Diversified - FoF 0,08 *** 0,16 -0,06 0,03 0,76 21% 73% 4%
Other - FoF 0,02 0,32 * -0,06 0,03 0,49 18% 77% 4%
F. of Funds Total 0,07 *** 0,15 -0,06 0,03 0,75 23% 71% 4%
Total 0,07 *** 0,06 -0,06 0,04 ** 0,87 46% 51% 2%
Em. Bd High Y. Mortg. Comm. Alpha Distrib. + / 0 / -
Panel A (continued): 01:1994-03:2000
164
Risk Arb -0,12% 0,17 ** 0,12 *** 0,08 ** -0,02 -0,05 0,04
Dist. Sec -0,01% 0,22 * 0,18 *** 0,01 0,02 -0,16 0,10
Global -0,12% 0,36 0,29 * 0,16 -0,08 -0,08 0,71 *
Global Est. -0,19% 0,45 *** 0,15 *** 0,00 0,02 -0,08 0,08
Global Intern. -0,02% 0,06 0,12 *** 0,08 0,03 0,25 ** 0,00
Global Emerging 0,25% 0,49 ** 0,31 *** 0,06 0,04 -0,14 0,00
US Opp. NA NA NA NA NA NA NA
Macro -0,25% 0,27 ** 0,14 ** 0,03 0,05 -0,07 0,23
Market Neutral 0,37% *** 0,06 0,05 ** 0,03 0,00 0,01 -0,07
Long Only Lev. -0,50% 1,14 *** 0,18 * -0,19 -0,03 -0,44 ** 0,27
Sector -0,19% 0,97 *** 0,26 *** -0,02 0,08 ** -0,44 *** 0,34 **
Short Sales 0,40% -1,00 *** -0,21 ** 0,19 * -0,13 *** 0,38 ** -0,39 *
No category -0,05% 0,18 0,12 0,00 0,12 *** -0,05 0,13
Ind. Funds Total 0,03% 0,32 *** 0,14 *** 0,02 0,02 -0,09 * 0,06
Niche - FoF -0,05% 0,19 *** 0,08 *** 0,05 * 0,02 * -0,11 ** 0,08
Diversified - FoF -0,13% 0,19 *** 0,12 *** 0,02 0,04 *** -0,06 0,10 *
Other - FoF NA NA NA NA NA NA NA
F. of Funds Total -0,12% 0,19 *** 0,11 *** 0,03 0,04 *** -0,07 0,10 *
Total -0,01% 0,29 *** 0,13 *** 0,02 0,03 ** -0,09 * 0,07
SMB HML
Panel B: 04:2000-12:2002
PR1YR W x US W Gv BdAlpha Mkt
165
R² adj
Risk Arb -0,01 0,23 *** 0,19 0,03 0,86 7% 91% 0%
Dist. Sec 0,12 ** 0,22 *** 0,04 -0,05 * 0,74 13% 86% 0%
Global 0,27 -0,15 -0,56 0,02 0,27 0% 100% 0%
Global Est. 0,06 0,14 ** 0,38 * -0,01 0,95 5% 89% 5%
Global Intern. -0,02 0,08 0,02 -0,01 0,78 9% 87% 3%
Global Emerging -0,04 0,21 0,08 -0,04 0,71 15% 80% 4%
US Opp. NA NA NA NA NA NA NA NA
Macro 0,07 0,06 0,44 -0,05 0,65 6% 85% 7%
Market Neutral 0 0,1 *** 0,25 * -0,01 0,69 27% 68% 3%
Long Only Lev. 0,13 0,24 0,75 0,06 0,92 0% 95% 4%
Sector 0,06 -0,01 -0,01 0,05 0,92 6% 89% 3%
Short Sales -0,05 0,09 0,66 0,11 ** 0,90 0% 90% 9%
No category 0,03 0,04 0,11 -0,05 0,43 0% 100% 0%
Ind. Funds Total 0,03 0,12 *** 0,24 -0,01 0,95 13% 82% 4%
Niche - FoF -0,01 0,08 ** 0,04 0,01 0,76 14% 80% 4%
Diversified - FoF 0,01 0,1 *** 0,09 0 0,89 10% 81% 7%
Other - FoF NA NA NA NA NA NA NA NA
F. of Funds Total 0 0,09 *** 0,08 0 0,88 11% 81% 7%
Total 0,02 0,12 *** 0,2 0 0,94 13% 82% 4%
This Table presents the results of the estimation of our combined model for the 01:1994-03:2000 (Panel A) and the 04:2000-12:2002 (Panel B) sub-periods. We report the OLS estimators for equally weighted portfolios per investment strategy, per type of funds and for all funds. The last column gives the distribution of individually estimated monthly alphas for all funds with 24 monthly data or more in a specific investment style. In Panel B, results for the US Opportunistics and Other categories are not reported as they have, respectively, 0 and 1 living fund in the second sub-period. We report the percentage of significantly positive alphas (+), significantly negative alphas (-) and alphas insignificantly different from zero (0) at the 5% level. t-stats are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
Comm.
Panel B (continued): 04:2000-12:2002
Em. Bd Alpha Distrib. + / 0 / -Mortg.High Y.
166
A quick look at the alphas for the considered sub-period clearly indicates that the
major part of the performance over the total 1994-2002 period is recorded prior March
2000, with the noticeable exception of the Market Neutral strategy that sustains positive
out-performance for both sub-periods. This finding is consistent with the result obtained by
Liang (2003) who investigates the behaviour of hedge funds strategies using a piecewise
linear regression setup: Market Neutral funds obtain by far the largest standardized value
for alpha, with at the same time a very low explanatory power of the regression.
In contrast, Panel A shows that the Global strategy achieves significant negative
performance during the bullish period. It is worth reporting that, although nine individual
strategies and both funds of funds strategies recorded a negative alpha in Panel B, none of
these values are shown to be significant. A look at individual alphas reinforces this finding,
as the proportion of significantly positive alphas does not significantly differ from the total
period to the first sub-period, but Panel B shows that 27% of the Market Neutral funds
sustained positive out-performance while on average more than 80% of individual funds
managers were in line with the market.
The strategies followed by funds managers sharply differed from one sub-period to
another. All but the No-category strategies individual funds significantly followed the market
until March 2000; only the Long Only Leveraged and the Sectors funds increased their
exposure thereafter. The Global, Global International, Market Neutral and No-category
strategies were not even significantly loaded to the market risk premium. In contrast, the
Funds of Funds strategies all increased their US stock market exposure after March 2000.
Some general swings of exposures to several risk factors are observed from one
period to another Exposure to the World excluding US usually becomes negative, although
with low significance levels, in the bearish sub-period, except for Global International and
Short Sales. On the other, the broadly negative exposure to the World Government Bond
167
Index in the first sub-period fades away after March 2000 except for Global and Sectors,
although the Short Sales strategy follows a converse tendency. The loadings for the
Emerging Market Bond Index and High Yield Bond Index are generally positive in the first
and second sub-period, respectively, which possibly indicates a broad sliding of bond
strategies of hedge funds managers.
At the individual strategy level, some changes are also of particular interest after
March 2000. Event driven strategies cease to be momentum-contrarian. All Global
strategies increase their investments in small firms and reduce their exposures to bond
factors; this latter statement also holds for Macro funds. Market Neutral funds managers
relied more extensively on domestic bond indices. Strikingly, the Short Sales strategy left a
pure market-contrarian profile for a much broader mix of exposures (positive for HML,
World excluding US and Commodity Index; negative for SMB, Momentum and World
Government Bond Index).
For funds of funds strategies, the noticeable difference is the noticeable
reinforcement of the loadings to the Momentum factor and the High Yield Bond Index after
March 2000, while the exposure to the World Government Bond Index goes from very
negative to slightly positive.
168
VI Persistence in Performance
Our results show significant evidence of superior performance over the total period of
time for most individual strategies. Nevertheless, results are mostly due to the first, bullish
sub-period and the positive out-performance tends to fade away after March 2000.
Nevertheless, active hedge funds selection strategies are likely to increase the expected
return if performance is persistent, i.e. if a superior average return in a period is likely to be
followed by a superior average return in the next period for a given fund. Sirri and Tufano
(1998) document large inflows of money into last years best performers, and withdrawals
from last years' losers. Zheng (1999) finds that newly invested money in these best
performing mutual funds is a predictor of future performance. This indicates that
persistence in performance is critical for mutual funds.
This is all the more important given that we have found in the previous subsection a
substantial break in performance at the peak of the stock markets. Is persistence
sustainable over the total period, or is it likely to be observed only in a particular sub-
period?
6.1 Persistence over the total period
We follow the methodology of Carhart (1997) using our combined model. All funds
are ranked based on their previous year total return. Every January, we put all funds into 10
equally weighted portfolios, ordered from highest to lowest past returns. Portfolios 1 (High)
and 10 (Low) are then further subdivided on the same measure. The portfolios are held till
the following January and then rebalanced again. Funds that disappear during the course of
the year are included in the equally-weighted average until their death, then portfolio
169
weights are readjusted appropriately. This yields a time series of monthly returns on each
decile portfolio from 01:1995 to 12:2002.
The monthly average return to the strategy of investing in portfolios 1 and 10 would
have been, respectively, 1.07% and 0.44% for the total period. The monthly excess returns
on the decile portfolios decrease monotonically between portfolio D1 and D8, but the sub-
decile D10c obtains an excess return higher than 1%, slightly significant. The spreads
between decile excess returns are not significant. Cross-sectional variation in returns is
considerably larger for the extreme deciles than for the middle deciles, in line with the
results of Brown et al. (2001) and Capocci and Hübner (2004).
After controlling for the risk factors, the picture is dramatically altered. The D10c
portfolio, i.e. the extreme losers, enjoy a remarkable monthly out-performance of 1.77%.42
The 1a-10c spread goes from an insignificant 0.05% to a significant – 1.6%. Aside from this
extreme value, significant alphas are mostly to be found in the middle deciles, with the
most significant values (at 1% level) being observed in portfolios D4 to D8.
The pattern of loading to risk premia suggests that past winners more closely follow
the market, invest more in small firms and in emerging bond markets but less in the world
stock index than past losers. Quite naturally given the definition of the portfolios, past
winners follow momentum strategies while past losers are momentum-contrarian.
42 The poor value of the adjusted R² for this decile portfolio suggests however a very unstable behaviour
of individual funds returns inside this decile portfolio.
170
In the middle deciles, where performance seems to be persistent when accounting
for risk, we notice that these strategies are usually characterized by positive exposure to
the HML factor (value strategy), negative exposure to the world bond index but positive
exposure to the emerging bond markets, indicating arbitraging strategies on geographical
bond markets. This is a possible source for their sustained performance.
6.2 Persistence over the sub-periods
The same analysis as before is performed in Table 24 for the bullish (Panel A) and for
the bearish (Table B) sub-periods.43
Panel A of Table 24 displays, not surprisingly, very comparable results with the ones
of Table 23, but there are some important differences. Firstly, the alpha for portfolio D10c is
not significant anymore; only middle-decile portfolios have a significant alpha. This result is
consistent with Capocci and Hübner (2004) that analyse the 01:1994- 06:2000 period.
There is no significant spread between decile portfolio returns.
Loading to individual factors are to a large extent similar for stock indices, but not at
all for bond indices. During the bullish period, past winners have not invested in any bond
index, and even heavily divested from the world bond index. In contrast, they have also
significant loadings with respect to the commodity index. At the same time, past average
performers were mostly invested in the high yield bond market.
43 For the second sub-period, we used returns of the 04:1999-03:2000 period to form the first decile
portfolios.
171
Unfortunately, Panel B indicates that there is no evidence of persistence in good
performance during the bearish period. The only sustained performance is the negative one,
as past losers are found to persistently aggravate their losses in portfolios D10, D10a and
D10b. This finding is in line with our analysis of survivorship biases, reinforcing the
conjecture that there was a particularly high mortality rate after March 2000 due to poor
performance of the disappeared funds.
Top decile portfolios during that period had positive loadings in high yield bonds and
in the Momentum factor, but negative loadings in the commodity market and the HML
factor. The losing strategies, i.e. the ones persistently followed by bottom decile portfolios,
had loading of opposite signs on the same factors and, additionally, very high loadings on
the mortgage market.
We also notice that, contrarily to the "conventional wisdom" concerning the
correlation between the momentum factor and hedge funds performance during bearish
periods, past winners consistently invested in momentum strategies and past winners
consistently followed contrarian strategies after March 2000. The paradox is only illusory, as
past winners typically hold winner stocks in their portfolio and are thus naturally positively
exposed to the momentum factor with these securities. Our results simply suggest that
these funds managers did not actively manage this particular component of their portfolio.
172
Table 24: Hedge funds persistence based on 12 month lagged
returns
Portfolio St. dev
D1a 1,12% * 6,63% 0,17% 0,64 *** 0,63 *** -0,04
D1b 1,10% ** 4,75% 0,38% 0,57 *** 0,4 *** 0,03
D1c 0,97% ** 3,97% 0,47% ** 0,43 *** 0,35 *** -0,02
D1 1,07% ** 5,00% 0,34% 0,55 *** 0,46 *** -0,01
D2 0,86% *** 3,27% 0,32% * 0,48 *** 0,28 *** 0,04
D3 0,78% *** 2,42% 0,31% ** 0,37 *** 0,19 *** 0,07 **
D4 0,71% *** 2,10% 0,36% *** 0,31 *** 0,13 *** 0,07 **
D5 0,61% *** 1,69% 0,35% *** 0,26 *** 0,09 *** 0,05 *
D6 0,50% *** 1,33% 0,28% *** 0,2 *** 0,09 *** 0,07 ***
D7 0,45% *** 1,37% 0,30% *** 0,17 *** 0,08 *** 0,03
D8 0,46% *** 1,67% 0,40% *** 0,11 *** 0,09 *** -0,01
D9 0,31% 2,34% 0,34% ** 0,18 *** 0,08 *** 0,02
D10 0,44% 3,95% 0,72% ** 0,22 * 0,05 -0,04
D10a 0,54% 3,36% 0,53% ** 0,28 *** 0,09 * 0
D10b 0,03% 4,03% 0,29% 0,27 ** 0,04 -0,01
D10C 1,07% * 5,65% 1,77% *** 0,07 0,03 -0,13
1-10 spread 0,63% 5,03% -0,38% 0,33 ** 0,41 *** 0,03
1a-10c spread 0,05% 7,71% -1,60% ** 0,58 ** 0,6 *** 0,09
1-2 spread 0,21% 2,12% 0,02% 0,07 0,18 *** -0,04
9-10 spread -0,13% 2,17% -0,38% -0,04 0,03 0,06
Panel A: Decile estimation
Exc. return Alpha Mkt SMB HML
173
Portfolio R² adj
D1a 0,36 *** 0,14 -0,56 ** 0,19 ** 0,07 0,51 0,13 ** 0,77
D1b 0,29 *** 0,05 -0,19 0,11 * 0,16 -0,06 0,07 0,77
D1c 0,2 *** 0,07 -0,15 0,08 * 0,15 0,03 0,04 0,78
D1 0,28 *** 0,08 -0,29 * 0,12 ** 0,12 0,15 0,07 * 0,80
D2 0,20 *** -0,04 -0,02 0,06 0,08 -0,2 0,04 0,81
D3 0,11 *** 0,01 -0,07 0,07 ** 0,05 0,12 0,03 0,79
D4 0,08 *** 0,04 -0,13 * 0,06 ** 0,05 0,05 0,04 * 0,75
D5 0,05 *** 0,01 -0,05 0,05 ** 0,09 -0,05 0,02 0,70
D6 0,03 ** 0,02 -0,09 ** 0,05 *** 0,08 * 0,07 0,02 0,77
D7 0,01 0,04 -0,10 ** 0,04 *** 0,05 0,05 0,03 * 0,74
D8 -0,02 0,11 *** -0,18 *** 0,06 ** 0,08 0,15 0,05 ** 0,70
D9 -0,10 *** 0,19 *** -0,23 *** 0,05 0,05 0,12 0,04 0,73
D10 -0,19 *** 0,28 ** -0,29 0,04 0,12 -0,15 0,08 0,56
D10a -0,13 *** 0,22 ** -0,02 0,09 * 0,04 0,14 0,03 0,60
D10b -0,14 *** 0,29 ** -0,32 * 0,03 0,09 -0,41 0,07 0,56
D10C -0,32 *** 0,35 * -0,53 * -0,02 0,25 -0,26 0,1 0,36
1-10 spread 0,47 *** -0,2 0 0,08 0 0,3 0 0,52
1a-10c spread 0,67 *** -0,21 -0,03 0,21 -0,19 0,76 0,03 0,48
1-2 spread 0,08 *** 0,12 * -0,27 *** 0,07 * 0,04 0,35 0,03 0,54
9-10 spread 0,09 ** -0,09 0,06 0,01 -0,07 0,27 -0,04 0,18
Panel A (continued): Decile estimation
High Y. Mortg. Comm.W Gv Bd Em. Bd
This Table reports the result of the estimation of our combined model for the 01:1994-12:2002 period. Each year, all funds are ranked based on their previous year's return. Portfolios are equally weighted and weights are readjusted whenever a fund disappears. Funds with the highest previous year's return go into portfolio D1 and funds with the lowest go into portfolio D10. Monthly Exc Return is the Monthly Excess Return of the portfolio, Std. Dev. is the Standard Deviation of the Monthly Excess Return.. All numbers in the Table are monthly percentage. *** Significant at the 1% level ** Significant at the 5% level * Significant at the 10% level.
PR1YR W x US
174
6.3 Analysis of the Market Neutral strategy
This sub-section focuses on the persistence in returns for the only hedge funds
strategy that has been found to provide significant abnormal returns for both sub-periods in
the previous section, namely the Market Neutral strategy. We determine whether
persistence in returns exists for this strategy for the whole period as well as for the sub-
periods. As for the total sample, we classify funds in 10 decile portfolios, with the top and
bottom decile divided in 3. Table 26 reports our results for these strategies.
Panel A reports the results of the analysis for the global period. They show that there
is no significant difference between good and bad performing funds. All alphas but the one
of portfolio D10c are significantly positive for the whole period, although the significance
level is lower for the extreme sub-deciles. Compared to our results for the whole database,
excess returns are higher for the extreme deciles and smaller for middle deciles; however,
returns of Market Neutral funds exhibit a much lower variance, and higher alphas for the top
deciles (from D1 to D5). In a nutshell, all but the poorest past performers exhibit a
significant persistence in performance. The review of risk coefficients shows that, aside from
the fact that past best performers had a significant loading on the stock market index and
on the SMB factor while past losers had a greater focus on world stock markets, no other
clear pattern emerges.
175
Table 25: Hedge funds persistence during the bullish and
bearish sub-periods
Portfolio St. dev
D1a 2,09% ** 6,85% 0,17% 0,69 *** 0,70 *** -0,07
D1b 1,87% *** 4,46% 0,46% 0,62 *** 0,41 *** 0,19 **
D1c 1,68% *** 3,97% 0,55% ** 0,48 *** 0,41 *** -0,01
D1 1,89% *** 4,97% 0,40% 0,6 *** 0,51 *** 0,04
D2 1,44% *** 3,27% 0,41% ** 0,57 *** 0,32 *** 0,13 **
D3 1,15% *** 2,56% 0,30% ** 0,46 *** 0,21 *** 0,15 ***
D4 1,08% *** 2,35% 0,31% ** 0,39 *** 0,14 *** 0,09 **
D5 0,90% *** 1,89% 0,28% ** 0,35 *** 0,09 *** 0,09 ***
D6 0,75% *** 1,45% 0,27% *** 0,24 *** 0,10 *** 0,07 ***
D7 0,76% *** 1,45% 0,36% *** 0,21 *** 0,11 *** 0,03
D8 0,76% *** 1,67% 0,42% *** 0,13 ** 0,11 *** -0,05
D9 0,67% ** 2,08% 0,28% 0,21 *** 0,08 * -0,08
D10 0,97% ** 3,60% 0,41% 0,32 ** 0,00 -0,15
D10a 1,01% ** 3,18% 0,43% 0,35 *** 0,09 -0,12
D10b 0,77% * 3,54% 0,27% 0,25 0,04 -0,11
D10C 1,37% ** 5,35% 0,75% 0,39 -0,17 -0,24
1-10 spread 0,92% * 4,32% -0,01% 0,28 0,51 *** 0,19
1a-10c spread 0,71% 7,11% -0,59% 0,3 0,87 *** 0,17
1-2 spread 0,45% 2,19% -0,01% 0,03 0,19 *** -0,08
9-10 spread -0,30% 2,22% -0,13% -0,11 0,08 0,07
Panel A: 01:1994-03:2000
Exc. return Alpha Mkt SMB HML
176
Portfolio R² adj
D1a 0,34 *** 0,25 -0,94 *** 0,15 -0,56 1,18 0,27 *** 0,78
D1b 0,28 *** 0,18 * -0,4 ** 0,05 -0,28 -0,03 0,15 *** 0,84
D1c 0,17 ** 0,16 * -0,43 *** 0,05 -0,18 0,41 0,10 ** 0,81
D1 0,26 *** 0,19 * -0,58 *** 0,08 -0,35 0,51 0,17 *** 0,84
D2 0,13 *** 0,06 -0,21 ** 0,02 -0,05 -0,32 0,06 * 0,89
D3 0,06 * 0,06 -0,21 *** 0,05 ** 0,11 -0,16 0,04 0,89
D4 0,05 0,05 -0,22 *** 0,05 ** 0,29 ** -0,29 0,06 ** 0,88
D5 0,03 0,00 -0,07 0,05 ** 0,35 ** -0,50 ** 0,01 0,83
D6 0,02 0,02 -0,10 * 0,05 *** 0,20 ** -0,07 0,02 0,85
D7 -0,02 0,05 -0,14 ** 0,05 *** 0,16 ** 0,00 0,01 0,84
D8 -0,04 0,12 ** -0,23 *** 0,07 *** 0,06 0,27 0,06 ** 0,70
D9 -0,09 ** 0,17 *** -0,31 *** 0,06 * -0,01 0,25 0,04 0,67
D10 -0,06 0,17 -0,24 0,07 0,45 -0,78 0,07 0,46
D10a -0,14 * 0,17 0,05 0,11 * 0,23 -0,23 -0,02 0,57
D10b -0,02 0,23 -0,3 0,05 0,36 -0,63 0,06 0,40
D10C 0,02 0,09 -0,47 0,03 0,75 -1,78 0,17 0,26
1-10 spread 0,33 *** 0,03 -0,33 0,01 -0,79 ** 1,29 * 0,10 0,54
1a-10c spread 0,32 0,16 -0,47 0,12 -1,30 * 2,97 ** 0,10 0,41
1-2 spread 0,13 ** 0,14 * -0,37 *** 0,06 -0,30 0,83 ** 0,11 *** 0,55
9-10 spread -0,03 0,00 -0,07 0,00 -0,46 1,03 * -0,03 0,09
High Y. Mortg. Comm.
Panel A: 01:1994-03:2000
PR1YR W x US W Gv Bd Em. Bd
177
Portfolio St. dev
D1a -0,73% 5,83% 0,16% 0,46 * 0,33 ** -0,29 *
D1b -0,37% 5,01% 0,61% 0,28 0,14 -0,36 **
D1c -0,37% 3,67% 0,26% 0,33 * 0,18 ** -0,19 *
D1 -0,49% 4,74% 0,34% 0,36 * 0,22 ** -0,28 **
D2 -0,25% 3,03% 0,05% 0,37 *** 0,14 ** -0,15 **
D3 0,05% 1,95% 0,12% 0,3 *** 0,12 *** -0,04
D4 0,02% 1,30% -0,02% 0,27 *** 0,11 *** 0,05
D5 0,06% 1,03% 0,08% 0,2 *** 0,09 *** 0,03
D6 0,03% 0,93% 0,04% 0,15 *** 0,08 *** 0,06 **
D7 -0,12% 0,97% 0,01% 0,14 ** 0,06 ** 0,03
D8 -0,13% 1,55% 0,06% 0,14 0,12 ** 0,04
D9 -0,38% 2,68% -0,31% 0,38 *** 0,19 *** 0,23 ***
D10 -0,56% 4,42% -0,91% * 0,72 *** 0,23 ** 0,42 ***
D10a -0,34% 3,56% -0,88% * 0,69 *** 0,28 *** 0,4 ***
D10b -1,40% * 4,56% -1,36% ** 0,89 *** 0,14 0,42 ***
D10C 0,50% 6,23% -0,13% 0,5 0,33 * 0,46 **
1-10 spread 0,07% 6,20% 1,25% -0,36 -0,02 -0,7 ***
1a-10c spread -1,22% 8,71% 0,30% -0,04 0 -0,75 ***
1-2 spread -0,24% 1,93% 0,29% -0,01 0,07 -0,13 *
9-10 spread 0,18% 2,07% 0,60% * -0,33 *** -0,04 -0,19 ***
Panel B: 04:2000-12:2002
Exc. return Alpha Mkt SMB HML
178
Portfolio R² adj
D1a 0,4 *** 0,02 -0,15 0,21 0,54 ** 0,4 -0,11 0,85
D1b 0,38 *** 0,04 -0,15 0,3 ** 0,65 ** 0,19 -0,13 ** 0,82
D1c 0,21 *** -0,09 0,2 0,09 0,43 ** -0,16 -0,1 ** 0,81
D1 0,33 *** -0,01 -0,03 0,2 * 0,54 ** 0,14 -0,12 ** 0,86
D2 0,22 *** -0,19 0,17 0,12 * 0,33 ** 0,03 -0,07 ** 0,88
D3 0,11 *** -0,16 * 0,14 0,03 0,19 ** 0,14 -0,04 * 0,85
D4 0,05 *** -0,12 ** 0,11 * 0,02 0,07 0,1 -0,03 * 0,86
D5 0,02 * -0,10 ** 0,07 -0,01 0,09 ** 0 -0,01 0,85
D6 0,01 -0,04 -0,02 -0,02 0,09 ** 0,05 0 0,84
D7 -0,02 -0,03 0,01 -0,02 0,06 -0,02 0,02 0,77
D8 -0,05 ** 0,00 -0,04 -0,04 0,08 0,01 0,03 0,71
D9 -0,17 *** 0,01 0,03 -0,05 -0,08 0,3 0,05 0,84
D10 -0,43 *** -0,13 0,23 -0,07 -0,32 ** 1,09 * 0,16 *** 0,84
D10a -0,28 *** -0,12 0,16 -0,03 -0,27 * 1,25 ** 0,11 ** 0,77
D10b -0,36 *** -0,2 0,26 -0,07 -0,33 * 0,54 0,18 ** 0,78
D10C -0,71 *** -0,02 0,27 -0,12 -0,33 1,61 0,17 * 0,76
1-10 spread 0,76 *** 0,11 -0,26 0,27 0,85 ** -0,95 -0,28 *** 0,73
1a-10c spread 1,1 *** 0,04 -0,42 0,34 0,87 ** -1,22 -0,28 ** 0,75
1-2 spread 0,11 *** 0,18 -0,2 0,08 0,21 ** 0,11 -0,05 0,66
9-10 spread 0,26 *** 0,13 -0,2 0,02 0,24 ** -0,79 ** -0,11 *** 0,74
High Y. Mortg. Comm.PR1YR W x US W Gv Bd Em. Bd
This Table reports the result of the estimation of our combined model for the 01:1994-03:2000 (Panel A) and the 04:2000-12:2002 (Panel B) sub-periods. Each year, all funds are ranked based on their previous year's return. Portfolios are equally weighted and weights are readjusted whenever a fund disappears. Funds with the highest previous year's return go into portfolio D1 and funds with the lowest go into portfolio D10. Monthly Exc Return is the Monthly Excess Return of the portfolio, Std. Dev. is the Standard Deviation of the Monthly Excess Return.. All numbers in the Table are monthly percentage. *** Significant at the 1% level ** Significant at the 5% level * Significant at the 10% level.
Panel B: 04:2000-12:2002
179
Panels B and C display very different pictures. During the 1994-March 2000 period,
only the alphas of top decile funds were systematically higher than for the whole period. In
contrast, the lowest decile funds did not out-perform the market. Middle decile funds had a
clearer focus on high yield bond markets.
Panel C shows that the persistence in performance during the market collapse was
clearly sustained for portfolios D2 to D6, with high significance levels. These funds had no
particularly remarkable investment pattern, except for the median decile (D4) whose
loadings are significant for the High Yield factor (positive) and for the World Government
Bond and Momentum factors (negative), with a relatively high adjusted R² of 57.8%.
Since these decile portfolios had significant alphas for the first sub-period too, this
indicates that the superior performance of these funds was predictable irrespective of the
prevailing market conditions. We view this as a major result considering that Market Neutral
funds have traditionally been assigned the role of protecting investors against negative
market twists: this reinforces this claims on a double dimension, as our results suggest that
this performance is not only sustained during positive or negative market conditions, but
during both; however, persistence in performance is observable for the medium-to-top past
performers only, showing that only a very targeted investment behaviour in Market Neutral
Funds would provide a sustained positive abnormal return.
Finally, it is worth mentioning that the poor adjustment of the model for the best
performing decile portfolios during the down market period also signals that these funds
managers tended to pursue very active and moving investment strategies, leaving a large
importance to market timing and tactical allocation. The alternative explanation of missing
risk factors, which is also reported in Liang (2003), although theoretically possible, is not
very compelling given the proven very high accuracy of our combined model. However, this
particular aspect opens the way to additional research on hedge funds performance and
persistence during unfavourable market conditions.
180
Table 26: Hedge funds persistence for the Market Neutral
strategy
Portfolio St. dev
D1a 1,44% *** 3,75% 0,93% ** 0,28 * 0,25 *** 0,14
D1b 1,43% *** 3,50% 1,08% *** 0,4 *** 0,11 0,12
D1c 1,30% *** 2,55% 0,92% *** 0,24 *** 0,17 *** 0,03
D1 1,37% *** 2,59% 0,97% *** 0,3 *** 0,17 *** 0,09
D2 1,16% *** 1,74% 1,01% *** 0,16 ** 0,13 *** 0,14 ***
D3 0,81% *** 1,12% 0,61% *** 0,17 *** 0,06 *** 0,06 **
D4 0,66% *** 1,30% 0,54% *** 0,05 0,09 *** 0,03
D5 0,54% *** 0,99% 0,44% *** 0,04 0,06 *** 0,03
D6 0,45% *** 0,80% 0,33% *** 0,08 *** 0,04 ** 0,04 **
D7 0,31% *** 0,74% 0,25% *** 0,03 0,04 *** 0,01
D8 0,41% *** 0,86% 0,42% *** -0,01 0,02 0,00
D9 0,50% *** 1,44% 0,48% *** 0 0,01 0,00
D10 0,69% *** 2,40% 0,64% *** 0,05 0,10 ** -0,02
D10a 0,56% ** 2,51% 0,58% *** -0,15 * 0,07 -0,09
D10b 0,45% 3,00% 0,43% 0,06 0,14 ** 0,04
D10C 1,14% *** 4,18% 0,84% * 0,37 ** 0,10 0,07
1-10 spread 0,69% ** 3,18% 0,34% 0,25 * 0,07 0,10
1a-10c spread 0,30% 5,30% 0,08% -0,09 0,15 0,07
1-2 spread 0,21% 2,31% -0,04% 0,14 0,04 -0,06
9-10 spread -0,19% 1,97% -0,16% -0,06 -0,10 ** 0,02
Panel A: 01:1994-12:2002
Exc. return Alpha Mkt SMB HML
181
Portfolio R² adj
D1a 0,17 *** 0,04 -0,16 -0,04 0,16 0,36 0,01 0,28
D1b 0,10 -0,21 0,21 0,12 0,18 -0,92 * 0,06 0,13
D1c 0,19 *** 0,02 -0,08 0,02 0,05 -0,02 0,03 0,52
D1 0,16 *** -0,05 -0,01 0,03 0,13 -0,22 0,03 0,44
D2 0,03 0,07 -0,11 -0,02 -0,04 -0,05 0,03 0,33
D3 0,03 * -0,05 -0,03 0,06 *** 0,06 -0,08 0,00 0,44
D4 0,00 -0,02 -0,17 ** 0,02 0,17 ** 0,17 0,00 0,27
D5 0,00 0,02 -0,09 0,07 *** 0,06 0,11 0,00 0,33
D6 0,00 0,02 -0,07 0,05 *** 0,01 0,08 0,00 0,43
D7 -0,02 0,02 -0,11 *** 0,03 ** 0,07 * 0,16 * 0,00 0,40
D8 -0,01 0,08 *** -0,13 *** 0,03 ** 0,08 * 0,07 0,02 0,38
D9 -0,03 0,12 ** -0,10 0,05 0,10 0,22 0,05 * 0,27
D10 -0,12 *** 0,16 ** -0,12 0,06 0,15 0,64 ** 0,01 0,42
D10a -0,07 ** 0,33 *** -0,21 0,19 *** 0,21 * 0,65 ** -0,01 0,48
D10b -0,16 *** 0,18 * -0,26 0,10 0,16 0,63 -0,04 0,37
D10C -0,20 *** -0,13 0,24 -0,11 0,04 0,89 0,08 0,20
1-10 spread 0,28 *** -0,21 * 0,11 -0,03 -0,02 -0,86 * 0,02 0,23
1a-10c spread 0,36 *** 0,17 -0,4 0,08 0,12 -0,53 -0,07 0,14
1-2 spread 0,13 *** -0,12 0,1 0,05 0,17 -0,17 0,00 0,10
9-10 spread 0,09 ** -0,04 0,01 -0,01 -0,04 -0,42 0,03 0,14
Mortg. Comm.W x US W Gv Bd Em. Bd High Y.
Panel A (continued): 01:1994-12:2002
PR1YR
182
Portfolio St. dev
D1a 2,17% *** 3,58% 1,41% *** 0,22 0,32 *** 0,04
D1b 2,01% *** 3,23% 1,67% *** 0,37 ** 0,19 * 0,06
D1c 1,79% *** 2,62% 1,01% *** 0,31 *** 0,19 *** 0,02
D1 1,97% *** 2,45% 1,34% *** 0,3 *** 0,23 *** 0,04
D2 1,30% *** 2,07% 0,99% *** 0,28 *** 0,15 *** 0,22 ***
D3 0,97% *** 1,27% 0,54% *** 0,25 *** 0,07 ** 0,11 ***
D4 0,79% *** 1,50% 0,59% *** 0,07 0,08 * 0,12 **
D5 0,62% *** 1,14% 0,40% *** 0,04 0,06 * 0,04
D6 0,55% *** 0,89% 0,35% *** 0,11 *** 0,06 *** 0,06 **
D7 0,38% *** 0,72% 0,27% *** 0,01 0,04 ** 0,02
D8 0,58% *** 0,88% 0,46% *** 0 0,02 -0,03
D9 0,64% *** 1,52% 0,47% *** 0,03 -0,01 -0,04
D10 0,86% *** 2,24% 0,63% * -0,01 0,04 -0,03
D10a 0,70% ** 2,41% 0,50% * -0,14 -0,01 -0,1
D10b 0,68% ** 2,65% 0,34% -0,07 0,08 -0,07
D10C 1,31% ** 4,30% 1,10% * 0,28 0,01 0,25
1-10 spread 1,11% *** 3,04% 0,71% * 0,31 ** 0,19 ** 0,07
1a-10c spread 0,86% 5,43% 0,31% -0,07 0,31 * -0,2
1-2 spread 0,67% ** 2,24% 0,36% 0,02 0,08 -0,18 *
9-10 spread -0,22% 1,94% -0,16% 0,04 -0,05 -0,01
Panel B: 01:1994-03:2000
Exc. return Alpha Mkt SMB HML
183
Portfolio R² adj
D1a 0,27 ** 0,02 -0,18 -0,1 -0,46 1,08 0,14 * 0,39
D1b -0,11 -0,07 -0,07 0,04 -0,33 -0,06 0,11 0,11
D1c 0,23 *** 0,07 -0,25 -0,01 -0,31 0,19 0,08 0,61
D1 0,13 * 0,00 -0,17 -0,03 -0,38 0,35 0,10 ** 0,50
D2 -0,01 0,10 -0,21 -0,04 -0,07 -0,36 0,01 0,47
D3 0,04 -0,09 ** 0,02 0,07 *** 0,23 ** -0,41 ** -0,01 0,59
D4 0,04 -0,07 -0,13 0,03 0,51 ** -0,23 -0,01 0,34
D5 0,03 -0,01 -0,02 0,08 *** 0,29 ** -0,07 0,01 0,39
D6 -0,02 0,03 -0,08 0,05 *** 0,05 0,01 0,00 0,51
D7 -0,01 0,01 -0,06 0,04 *** 0,23 ** 0,12 0,01 0,52
D8 -0,01 0,06 -0,11 * 0,05 ** 0,2 ** 0 0,04 ** 0,48
D9 -0,05 0,09 -0,11 0,05 0,38 ** -0,13 0,07 ** 0,42
D10 -0,05 0,13 0,05 0,08 0,44 0,22 0,03 0,15
D10a -0,03 0,27 *** -0,11 0,22 *** 0,39 0,14 0,01 0,43
D10b 0,01 0,09 0,14 0,14 ** 0,58 * 0,47 -0,01 0,16
D10C -0,17 -0,07 0,29 -0,14 0,41 0,03 0,08 0,04
1-10 spread 0,18 * -0,13 -0,22 -0,1 -0,81 ** 0,13 0,07 0,24
1a-10c spread 0,44 ** 0,09 -0,47 0,04 -0,87 1,05 0,06 0,18
1-2 spread 0,14 * -0,09 0,04 0,01 -0,31 0,71 0,09 0,07
9-10 spread 0 -0,04 -0,16 -0,03 -0,06 -0,35 0,04 -0,11
Panel B (continued): 01:1994-03:2000
High Y. Mortg. Comm.PR1YR W x US W Gv Bd Em. Bd
184
Portfolio St. dev
D1a 0,05% 3,71% 0,05% -0,16 0,01 0
D1b 0,32% 3,78% 0,79% -0,06 0,09 -0,09
D1c 0,37% 2,15% -0,02% 0,23 0,12 0,01
D1 0,24% 2,51% 0,25% 0,01 0,07 -0,03
D2 0,91% *** 0,78% 0,72% *** 0,07 0,04 0,04
D3 0,51% *** 0,64% 0,62% *** 0 -0,01 -0,02
D4 0,42% *** 0,73% 0,49% *** -0,05 0,03 -0,03
D5 0,38% *** 0,57% 0,51% *** 0,01 0,01 0,01
D6 0,25% *** 0,55% 0,35% ** 0 0 -0,01
D7 0,17% 0,77% 0,31% * 0,02 0,03 0,00
D8 0,07% 0,73% 0,05% -0,02 0,05 0,04
D9 0,23% 1,24% -0,22% 0,11 0,1 0,15 **
D10 0,36% 2,68% -0,25% 0,49 *** 0,28 *** 0,25 ***
D10a 0,29% 2,71% -0,19% 0,17 0,28 *** 0,16
D10b 0,02% 3,58% -0,27% 0,44 ** 0,36 *** 0,38 ***
D10C 0,83% 3,98% -0,49% 1,04 *** 0,26 0,25
1-10 spread -0,12% 3,33% 0,50% -0,48 * -0,21 -0,28 *
1a-10c spread -0,78% 4,95% 0,54% -1,21 ** -0,26 -0,25
1-2 spread -0,67% * 2,23% -0,47% -0,06 0,03 -0,07
9-10 spread -0,12% 2,06% 0,03% -0,38 *** -0,18 *** -0,1
Panel C: 03:2000-12:2002
Exc. return Alpha Mkt SMB HML
185
Portfolio R² adj
D1a 0,16 * 0,55 -0,48 0,36 * 0,4 1,74 * -0,12 0,30
D1b 0,23 ** 0,03 -0,04 0,38 * 0,5 -1,08 -0,13 0,13
D1c 0,12 ** -0,14 0,18 0,11 0,19 0,56 -0,05 0,43
D1 0,17 *** 0,13 -0,10 0,27 ** 0,36 ** 0,4 -0,1 * 0,46
D2 0,00 -0,04 0,03 -0,01 0,1 0,29 0,01 0,19
D3 0,01 0,01 -0,07 0,01 0,12 ** -0,02 0 0,13
D4 -0,02 0,04 -0,10 -0,03 0,13 ** 0,17 0,02 0,59
D5 -0,01 0,04 -0,09 * -0,02 0,04 -0,01 0 0,49
D6 0,01 0,04 -0,08 0,01 0,07 0,05 -0,01 0,16
D7 -0,01 0,00 -0,12 -0,05 0,07 -0,08 -0,02 0,35
D8 -0,03 * 0,06 -0,12 -0,07 ** 0,06 0,18 -0,02 0,44
D9 -0,08 ** 0,00 0,03 -0,04 -0,03 0,7 * 0 0,16
D10 -0,18 *** -0,13 -0,06 -0,06 -0,12 1,37 ** 0,03 0,84
D10a -0,11 ** 0,15 -0,2 0,04 0,01 1,51 ** -0,01 0,60
D10b -0,26 *** 0,02 -0,39 * -0,03 -0,24 * 0,83 0,07 0,79
D10C -0,24 *** -0,71 ** 0,52 -0,15 -0,19 2,16 ** 0,05 0,51
1-10 spread 0,35 *** 0,26 -0,04 0,33 ** 0,47 ** -0,97 -0,13 * 0,53
1a-10c spread 0,39 *** 1,26 ** -1 * 0,51 * 0,58 -0,42 -0,17 0,22
1-2 spread 0,17 *** 0,17 -0,12 0,29 ** 0,26 0,11 -0,11 * 0,36
9-10 spread 0,11 *** 0,13 0,09 0,02 0,09 -0,67 ** -0,04 0,78
This Table reports the result of the estimation of our combined model for the Market Neutral strategy 01:1994-03:2002 (Panel A) period, and the 01:1994-03:2000 (Panel B) and 04:2000-12:2002 (Panel C) sub-periods. Each year, all funds are ranked based on their previous year's return. Portfolios are equally weighted and weights are readjusted whenever a fund disappears. Funds with the highest previous year's return go into portfolio D1 and funds with the lowest go into portfolio D10. Monthly Exc Return is the Monthly Excess Return of the portfolio, Std. Dev. is the Standard Deviation of the Monthly Excess Return.. All numbers in the Table are monthly percentage. *** Significant at the 1% level ** Significant at the 5% level * Significant at the 10%
W x US W Gv Bd Em. Bd High Y. Mortg. Comm.
Panel C (continued): 03:2000-12:2002
PR1YR
186
VII Conclusion
The evolution of financial markets during the 1994-2002 period has been very rich in
significant up and down market movements whose length and severity have been largely
unprecedented. In this study, we have seized this opportunity to test whether hedge funds
displayed significantly different patterns of performance levels and persistence during this
time window as well as in undoubtedly bullish and bearish market situations.
Firstly, our database constituted with 2894 funds obtained from MAR prove to be
fairly trustable with respect to the most important biases in hedge funds studies, namely
the survivorship and instant return history biases despite the high attrition rate of funds
observed after March 2000. Our original ten-factor composite performance model also raises
little suspicion concerning its ability to explain returns as we achieve very high significance
levels with very little correlation among regressors.
The analysis of performance indicates that most hedge funds significantly out-
performed the market during the whole test period, but this is mostly due to the bullish
sub-period. The pattern is somehow attenuated for funds of funds strategies. In contrast, no
significant under-performance of individual hedge funds of funds of funds strategies is
observed when markets headed south. The Market Neutral strategy provides a noticeable
exception, however, as is sustains abnormal performance over both the bullish and the
bearish sub-periods.
Persistence analysis also indicates that most of the predictability of superior
performance is to be found prior to March 2000. Our results confirm several previous
studies that found that persistence, if any, is mostly located among medium performers. In
the second sub-period, only negative persistence can be found among the past losers,
187
suggesting that bad performance has probably been the decisive factor for hedge funds
mortality.
Our analysis of the performance of the Market Neutral strategy is remarkably
encouraging and is confirmed and refined with the persistence analysis: for portfolios that
were between the 20% and 69% best performers in this category, abnormal performance
and persistence are pervasive throughout the sub-periods, probably thanks to an extreme
adaptability and a very active investment behaviour.
Obviously, these very appealing results call for a much more detailed analysis of the
Market Neutral strategy among individual hedge funds. Market timing issues do matter for
their risk exposure, and traditional asset pricing models may not fully account for their
highly unstable investment strategies. We believe that this study potentially opens the way
to a deeper examination of the properties of these particular hedge funds during negative
market conditions, but this particular field of investigation is left for future theoretical as
well as empirical research.
The Sustainability in Hedge Fund
Performance: new insights
Daniel P.J. CAPOCCI
HEC-ULG Management School – University of Liège (Belgium)
Capocci, Daniel, 2006, The Sustainability in Hedge Fund Performance: new insights,
Working Paper, HEC-ULG Management School
190
The Sustainability of Hedge Fund Performance: New
Insights
Abstract
This study analyses and decomposes hedge fund returns in order to determine a
systematic hedge fund selection criterion that enables investors to consistently and
significantly outperform equity and bond indices over a full market cycle and over bull
and bear market conditions. The methodology used is adapted from Capocci and Hübner
(2004). The measures used include the returns, volatility, Sharpe score, alpha, beta,
skewness and kurtosis. Measures incorporating the volatility display very strong ability to
assist investors in creating alpha as well as consistently and significantly outperforming
classical indices.
191
The Sustainability of Hedge Fund Performance: New
Insights
Introduction
The hedge fund industry has experienced explosive growth since the early 1990s
when approximately 2,000 hedge funds were managing assets totalling roughly $60
billion. It is estimated that today, there are roughly 10,000 hedge funds managing close
to a trillion USD in assets. The growing trend of the sector has been remarkably
sustained during the stock market collapse that started in March 2000, when the
NASDAQ Composite Index attained an all-time high of 5,132 and finished three years
later at a bottom of 1,253. In the meantime, the global net asset value (NAV) of hedge
funds continued to grow at a steady 10.6% (see Capocci et al., 2005), contrasting with a
decrease of 2.7% for the mutual fund industry worldwide (Investment Company
Institute, 2003).
This relatively positive attitude of investors is typically motivated by the
perceptions that most hedge funds tend to be largely market neutral, that their
managers enjoy greater flexibility in their asset allocation enabling them to achieve
superior market-timing skills (see Chen and Liang, 2006), or that hedge funds have a
relatively low covariance with other classes of financial assets, making them good
diversification vehicles (Amin and Kat, 2003b). Assness et al. (2001) found that this
result is at least partly spurious.
192
Hedge funds have been studied since 1997 and the early seminal studies were
Fung and Hsieh (1997) and Ackermann et al. (1999). Since then, the literature on the
subject has expanded quickly. Our analysis focuses on hedge fund performance and
persistence in hedge fund performance. Three fields exist that examine hedge fund
performance. The first includes studies that compare the performance of hedge funds
with equity and other indices (see for example, Ackermann et al., 1999; Brown et al.
1999; Liang, 1999; Amin and Kat, 2003b; Liang, 2001; Liang, 2003; Agarwal and Naik,
2004). They do not all converge in their findings. Some authors (Brown et al., 1999 and
Liang, 1999) conclude that hedge funds are able to outperform these indices, whereas
others (Ackermann et al., 1999 as well as Agarwal and Naik, 2004) are more cautious in
their conclusions.
The second field of hedge fund performance analysis compares the performance of
hedge funds with that of mutual funds. In this context, Ackermann et al. (1999) and
Liang (1999) find that hedge funds constantly obtain superior performance to mutual
funds, although lower and more volatile returns than the reference market indices
considered.
Finally, the third group of hedge fund performance analysis examines the
persistence of hedge fund returns. Persistence is particularly important in the case of
hedge funds because, as suggested by Brown et al. (1999) and Liang (2000, 2001), the
hedge fund industry has a higher attrition rate than mutual funds. Brown et al. (1999)
find that offshore hedge funds have positive risk-adjusted returns and attribute this
result to style effect and conclude that there is no evidence of particular skill of some
fund managers. Agarwal and Naik (2000) analyse the presence of persistence in hedge
fund returns using a one-year moving average period. The authors find evidence of
persistence in hedge fund performance, particularly for poor performing funds that
continue to underperform. Capocci and Hübner (2004) conclude that some low-risk
193
managers have been able to persistently create alpha between January 1994 and
December 2002.
The vast majority of performance studies on hedge funds have not focused on the
behaviour of hedge funds under different market conditions. The periods under
examination do not favour this exercise, as periods of downward trending stock markets
have been rare and discontinuous between 1994 and March 2000.44 For the period 1990-
1998, Edwards and Caglayan (2001) find that only three hedge fund strategies (market
neutral, event driven and macro) provide protection to investors when stock markets
drop.
Fund of hedge funds are particular in the hedge fund world and need particular
care. As stated by Fung and Hsieh (2006) and Liang (2003), there is a double counting
issue with funds of hedge funds that should be distinguished from individual hedge funds.
Our study makes two main contributions. First, we find a systematic way to
extract hedge funds that consistently beat traditional markets. Capocci and Hübner
(2004) indicated that some hedge funds consistently and significantly outperform the
equity and bond markets over time. They do not; however, describe a systematic way of
selecting hedge funds that outperform. We test various ways of classifying funds and
indicate how to select funds that consistently outperform the classical markets. Our
second contribution is our multi-factor model that is adapted from Capocci and Hübner’s
(2004) performance analysis model.
44 Most empirical evidence reveals that data collected prior to 1994 by several data vendors displays a
significant survivorship bias, as shown by Fung and Hsieh (2000), Liang (2000) and Capocci and
Hübner (2004).
194
Following Liang (2003), we separate individual funds from funds of funds in order
to determine if there are significant differences in exposures and in alpha creation. Our
results do not indicate that this is justified.
The study is organised as following. Section I describes the methodology. In
Section II, we report the database and analyse the descriptive statistics. The attrition
rate is calculated in Section III. In Section IV, we report the bias analysis. We report the
global results in Sections V and VI and perform further analysis in Section VII. Section
VIII concludes the study.
195
I Methodology
The starting point of our study on hedge fund performance is the original Sharpe
(1964) – Lintner (1965) CAPM. We use the Capocci and Hübner (2004) multifactor model
that extends the Carhart (1997) specification by combining it with factors specific to
hedge funds.45 Our multi-factor models contain 10 and 14 factors, respectively:
- Two equity market risk premium (US market and MSCI world excluding US)
- Fama and French (1993) size and value factors
- Carhart’s (1997) momentum factor
- Three factors to account for the fact that hedge funds invest in U.S. and
foreign bond markets (Lehman High Yield Bond Index, Salomon World
Government Bond Index and the JP Morgan Emerging Market Bond Index)
- A commodity factor (GSCI Index)
- A currency factor (the Federal Reserve Bank Trade Weighted Dollar Index)
In the second model, we add the four option factors of Agarwal and Naik (2004)
that are at-the money call option (ATMC), out-of-the-money call option (OTMC), at-the-
money put option (ATMP) and out-of-the-money put option (OTMP). As reported in Table
27, high correlations between these factors and the US market factor (ranging from -
0.87 between the market and ATMP to 0.78 between the market and ATMC) and between
these four factors (from -0.73 between ATMC and ATMP to 0.99 between ATMP and
OTMP) indicate that the use of these factors may have two issues:
45 See Capocci and Hübner (2004) for a full description of their model as well as those that contributed
to its creation.
196
1) They may be redundant with the market factor and not marginally contribute to
the return attribution decomposition;
2) They may be redundant with each other.
We do not use the Lehman Mortgage-Backed Securities Index as suggested by
Capocci et al. (2005), because this factor has low explanatory power. Several additional
factors, such as the MSCI Emerging Markets Index, the Lehman Baa Corporate Bond
Index and the Salomon Brothers Government and Corporate Bond Index proposed by
Agarwal and Naik (2004) and the Gold Index used by Fung and Hsieh (1997)46 were not
included in our extended model given their high colinearity with our set of indices.
Model 1
( )( ) ( )( ) ( )( ) ( )FttPFttP
FttPFttP
FttPFttP
tPtPtPFtMtPPFtPt
RCURRGSCIRHYRJPMEMBI
RSWGBIRMSWXUSYRPRHMLSMBRRRR
−+−+−+−+
−+−++++−+=−
109
87
65
4321 1
ββββββ
ββββα
(9)
46 Agarwal and Naik (2003) suggest that the Goldman Sachs Commodity Index is a better
approximation of the commodity market than the Gold Index regarding hedge funds.
197
Model 2
( )( ) ( )( ) ( )( ) ( )
PttPtPtPtP
FttPFttP
FttPFttP
FttPFttP
tPtPtPFtMtPPFtPt
OTMPATMPOTMCATMCRCURRGSCI
RHYRJPMEMBIRSWGBIRMSWXUS
YRPRHMLSMBRRRR
εββββββ
ββββ
ββββα
+++++−+−+
−+−+−+−+
+++−+=−
14131211
109
87
65
4321 1
(10)
where RPt is equal to the return of fund P in month t; RFt corresponds to the risk-free
return on month t; RMt equals the return of the market portfolio on month t47, SMBt is
equal to the factor-mimicking portfolio for size (small minus big), HMLt corresponds to
the factor-mimicking portfolio for book-to-market equity (high minus low) and PR1YRt
equals the factor-mimicking portfolio for the momentum effect. These factors aim at
isolating the firm-specific components of returns. MSWXUSt is equal to the return of the
MSCI World Index excluding US; SWGBIt corresponds to the return of the Salomon World
Government Bond Index; JPMEMBIt equals the return of the JP Morgan Emerging Market
47 The market proxy used is the value-weighted portfolio of all NYSE, Amex and NASDAQ stocks – a
market proxy that is usually used in mutual fund and hedge fund performance studies.
198
Table 27: Correlation between the Option Factors and the
Market Factor
Market ATM Call OTM Call ATM Put OTM Put
ATM Call 0,78 1
OTM Call 0,73 0,96 1
ATM Put -0,87 -0,73 -0,69 1
OTM Put -0,85 -0,7 -0,65 0,99 1
This table reports the correlation between the option factors and the market factor over the January 1994-December 2002 period.
Bond Index; HYt is equal to the return of the Lehman High Yield Credit Bond Index, GSCIt
corresponds to the return of the Goldman Sachs Commodity Index, CURt equals the
return of the Federal Reserve Bank Trade Weighted Dollar Index and ATMCt, OTMCt,
ATMPt and OTMPt correspond respectively to Agarwal and Naik’s (2004) at-the-money,
out-of-the money European call option factors, and at-the-money and out-of-the money
European put option factors. εPt equals the error term, while αP and βP are the intercept
and the slope of the regression, respectively.
In order to determine if some funds consistently and significantly create alpha
over time, we follow the methodology of Carhart (1997). Every year we rank all funds
based on their total return of the prior year. Every January, we place all funds into 10
equally weighted portfolios, ordered from highest to lowest past returns. Portfolios 1
(low) and 10 (high) are then further subdivided in three sub-portfolios on the same
measure. The portfolios are held until the following January and then rebalanced again.
Funds that disappear during the course of the year are included in the average until their
199
death, and then portfolio weights are readjusted appropriately. This yields a time series
of monthly returns on each decile portfolio from January 1995 to December 2002.
In each case, we also test the significance of the difference between the alpha of
the top (D1) and the bottom (D10) decile portfolios, the top (D1) and the next (D2)
decile portfolio, the next to bottom (D9) and the bottom portfolio (D10) and finally
between extremes alphas (D1a and D10c).
Since past performance is only one element in analysing past returns, we decide to
perform the decile classification methodology incorporating the Sharpe ratio48, standard
deviation, alpha, beta, skewness and kurtosis.
48 The Sharpe ratio is the ratio of excess performance over the risk-free rate to risk, as measured by
the standard deviation.
200
II Database
Four main hedge fund databases are available for empirical studies, the Managed
Account Reports, Inc./Centre for International Securities Derivatives Markets
(MAR/CISDM), Hedge Fund Research, Inc., TASS Management and the Barclay’s
database. The first three are the most used in academic studies. The data providers
collect information supplied by hedge fund managers. For a majority of funds, they
record other useful information such as company name, starting and ending date,
investment strategy, assets under management, management and incentive fees,
manager's name, manager's address, etc. Nevertheless, there is no consensus on the
definition of the strategy followed. Each provider proposes its classification, but on many
occasions there maybe some similarities.
We combine hedge fund data from MAR/CISDM with Barclay’s data. The MAR
database started with 2,246 individual funds including 1,185 funds that were still living at
the end of 2002 and 1,061 dissolved individual funds as well as 647 funds of funds
including 436 funds of funds that were still in existence at the end of 2002 and 211 funds
of funds that have been dissolved. The Barclay’s database includes 1,967 individual funds
including 1,271 funds that were still alive at the end of 2002, 696 individual dissolved
funds as well as 469 funds of funds including 384 funds of funds that were still in
existence at the end of 2002 and 85 dissolved funds of funds. In each database, we
removed funds that appear twice in the same database49 and funds with quarterly
49 This happened in three cases: when the same fund (same name, company, and returns) appeared
twice in the database; when the same fund (same name and returns) appeared twice in the database
with two different company names; and when the same fund (same company and returns) appeared
twice in the database with two different fund names.
201
returns. We further found 1,153 funds that were present in the two databases (834
existing funds and 319 dissolved funds). We obtain a total of 3,060 individual funds and
907 funds of funds including 1,910 individual funds and 588 funds of funds from the
MAR/CISDM database and 1,150 individual funds and 319 funds of funds from the
Barclay’s database. This database is one of the largest and most unique databases ever
used in hedge fund performance studies. These funds include a total of 1,873 (61,15%)
surviving individual funds, 1,190 (38,85%) dissolved individual funds, 653 (72%)
surviving funds of hedge funds and 254 (28%) dissolved funds of funds. All the returns
used are net of fees.
Most previous studies on hedge funds group individual funds and funds of funds.
We follow Liang (2003) and analyse them together and separately. We separate them for
three main reasons. First, we want to avoid double counting individual funds that are
part of funds of funds and that are in the database. This would lead to what we call the
fund of funds bias. Secondly, we separate individual funds from funds of funds because
funds of funds returns can be biased. There is a double survivorship bias in their returns.
More precisely, there are funds of funds that are dissolved and which lead to the
presence of survivorship bias in the data when we do not consider dissolved funds of
funds (this is the same notion of survivorship bias as suggested in many other academic
studies like Fung and Hsieh, 2000). On the other hand, individual funds in funds of hedge
funds portfolios can also be dissolved, which leads to the presence of a second
survivorship bias. This means that funds of funds returns should be lower than individual
fund returns by 1% to 3% annually only because of the presence of the survivorship bias
in the underlying funds.
202
Finally, the third reasons why we separate funds of funds from individual funds is
that performance and persistence models are usually less precise for funds of hedge
funds than they are for individual hedge fund strategies (see Liang, 1999). This should at
least partly be explained by the double fee structure (see Brown et al., 2002). Depending
on the performance of the individual funds compared to their hurdle rate and/or high
watermark, the funds may charge a performance fee and the mix of these fees will
impact the return distribution.
203
III Preliminary Analysis
Before analysing the presence of bias in hedge fund data, we present the
descriptive statistics, the correlation analysis and the bias analysis.
3.1 Descriptive Statistics
Panel A of Table 28 reports the descriptive statistics of the hedge fund database.
The first column indicates that the bulk of the funds reported in the database are defined
as market neutral funds or global funds that each represents around 24% of the global
individual hedge funds database. The mortality ratios50 reported are almost all between
50% and 70% indicating high mortality levels for individual hedge funds. Interestingly,
this ratio is also high for funds of funds (at 72%).
Sector funds have offered the highest mean monthly return (1.56% monthly),
whereas short sales and funds of hedge funds have offered the lowest returns (0.8%).
Funds not classified are the most volatile, whereas the least volatile funds are market
neutral funds (1.22%). The skewness column indicates that most return distributions are
negatively skewed indicating that average negative returns are higher than the average
positive returns. The excess kurtosis reported is all positive beginning with 0.87 for short
sales and topping out at 4.98 for distressed securities. This confirms the presence of fat
tails in hedge funds return distribution.
50 Ratio of dissolved funds over the period covered to the number of funds in the database for the
corresponding strategy.
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Table 28: Descriptive Statistics
N % Dead funds Mean Std dev. Median
- Distressed sec 122 4% 61% 1,03 2,65 1,09
- Risk arb 168 5% 77% 0,99 1,81 1,01
- Event driven 59 2% 17% 1,13 1,96 0,85
Event Driven Total 349 11% 61% 1,04 2,07 1,09
Global emerging 226 7% 58% 1,02 3,12 1,36
Global Macro 190 6% 69% 0,88 2,04 0,73
Global 702 23% 46% 1,13 3,08 1,12
Global Total 1118 37% 49% 0,89 2,70 1,05
Mkt ntl 731 24% 64% 1,02 1,22 1,00
Equity Hedge 332 11% 67% 1,13 2,35 1,23
Sector 277 9% 70% 1,56 3,60 1,73
Short sales 48 2% 71% 0,80 2,19 0,68
Long only leveraged 142 5% 73% 1,15 2,89 1,17
Mkt timing 43 1% 93% 1,01 1,94 0,91
Currency fund 4 0% 25% 1,20 3,53 1,14
Option strategy 3 0% 0% 1,02 2,62 1,16
No strategy 13 0% 8% 0,85 4,52 0,26
Individual funds total 3060 100% 60% 1,09 2,25 1,15
Fd of Fds 907 NA 72% 0,80 1,90 0,81
Panel A: Hedge Funds Descriptive Statistics
205
Skewness Kurtosis Min Max Sharpe score
- Distressed sec -0,95 4,98 -12,14 7,37 0,25
- Risk arb -0,51 2,72 -6,89 6,08 0,34
- Event driven 1,27 3,40 -4,16 9,66 0,39
Event Driven Total -0,63 3,85 -8,75 6,44 0,32
Global emerging -0,73 3,94 -13,66 10,97 0,21
Global Macro 0,57 1,25 -4,44 7,33 0,25
Global 0,19 2,19 -10,16 11,88 0,25
Global Total -0,48 3,82 -11,46 9,62 0,19
Mkt ntl -0,23 2,11 -4,04 4,61 0,54
Equity Hedge -0,27 2,43 -8,45 8,89 0,32
Sector 0,17 2,37 -11,44 15,33 0,33
Short sales 0,06 0,87 -5,17 7,91 0,19
Long only leveraged -0,10 1,13 -9,27 9,61 0,27
Mkt timing -0,27 1,65 -6,02 6,19 0,33
Currency fund -0,24 0,99 -10,00 10,36 0,23
Option strategy -0,91 4,29 -11,20 7,83 0,21
No strategy 1,19 3,32 -10,24 17,18 0,11
Individual funds total -0,17 2,59 -8,23 8,20 0,32
Fd of Fds -0,16 3,08 -7,32 6,93 0,22
Panel A (continued): Hedge Funds Descriptive Statistics
206
Mean Std dev. Median Skewness
Market 0,78 4,77 1,58 -0,72
MSCI w. ex US 0,09 4,36 0,47 -0,45
SMB 0,02 4,45 -0,36 0,87
HML 0,6 4,16 0,68 0,48
PR1YR 1,14 5,74 1,27 -0,73
Lehman Agg. -0,01 1,13 0,19 -0,13
Sal. WGBI 0,5 1,83 0,24 0,45
JPM EMBI 0,82 4,67 1,16 -1,64
Leh. High Yield 0,4 2,11 0,66 -0,7
GSCI 0,59 5,35 0,61 0,27
Risk-free rate 0,37 0,11 0,4 -0,99
ATM Call 0,82 84,51 -20,34 0,58
OTM Call -2,97 89,57 -30,35 0,79
ATM Put -11,88 95,02 -56,76 1,62
OTM Put -15,73 95,55 -59,39 1,81
Broad Dollar Index 0,34 1,11 0,29 0,33
Panel B: Naive Strategies Descriptive Statistics
207
Kurtosis Min Max Sharpe score
Market 0,37 -15,69 8,33 0.16
MSCI w. ex US 0,26 -12,89 10,27 0.02
SMB 5,56 -16,26 21,38 0.00
HML 1,14 -8,91 13,67 0.14
PR1YR 4,6 -25,13 18,21 0.20
Lehman Agg. 0,61 -2,73 3,87 -0.01
Sal. WGBI 0,47 -3,44 5,94 0.27
JPM EMBI 7,18 -24,2 10,87 0.18
Leh. High Yield 3,58 -7,37 7,49 0.19
GSCI 0,26 -12,28 15,79 0.11
Risk-free rate 0,15 0,11 0,56 NA
ATM Call -0,78 -99,04 216,91 NA
OTM Call -0,41 -99,1 246,85 NA
ATM Put 2,66 -95,29 386,02 NA
OTM Put 3,64 -96,21 400,33 NA
Broad Dollar Index 1,29 -2,79 3,93 NA
Panel B: Naive Strategies Descriptive Statistics
This table reports the descriptive statistics for hedge fund strategies (Panel A) and for naïve strategies (Panel B). N stands for number of funds and Std dev. is for standard deviation. Our original MAR/CISDM/Barclay’s database consists of 3,060 individual funds (including 1,160 dissolved funds) and 907 funds of funds (including 254 dissolved funds of funds) over the January 1994-December 2002 period.
208
Panel B reports the same statistics for passive investment strategies. The bond and
equity indices all have lower mean returns than the majority of the hedge fund
strategies. The equity indices returns are more volatile than most hedge fund strategies,
but the standard deviations of the bond indices are almost all lower than those of the
hedge fund strategies. The skewness and kurtosis measures indicate the same pattern as
for hedge funds, asymmetry to the left and presence of fat tails.
3.2 Correlation Analysis
Traditional hedge fund literature contends that, thanks to the weak correlation
between hedge funds and other securities, hedge funds are likely to improve the risk-
return trade-off when added to a traditional portfolio (see Fung and Hsieh, 1997; Liang,
1999 as well as Amin and Kat, 2003b). We analyse the correlation among the hedge
funds strategies, between the hedge fund strategies and the passive investment
strategies and among the passive investment strategies.51 As typically reported in the
literature (see Liang, 2003), hedge fund strategies are highly correlated, with the
exception of short sellers that systematically has the opposite result. The coefficients
reported are all higher than 0.5 (except short selling) and most of them are higher than
0.75.
To avoid any risk of multi-colinearity, we also verified the correlation between the
explanatory factors. They are all reasonably low, with the exception of the correlation
between the option factors of Agarwal and Naik (2004) and between these factors and
the market. This justifies the use of two different models.
51 We do not report the results for the sake of brevity, but complete results are available directly from
the author.
209
3.3 Survivorship Bias
The most important bias in hedge fund data is the survivorship bias (see Fung and
Hsieh, 1997; Fung and Hsieh, 2000 and Liang, 2001). When only living funds52 are
considered, there is a survivorship bias in the figures because dissolved funds tend to
have inferior performance compared to surviving funds. Survivorship bias is usually
defined as the performance difference between living funds and all funds (Fung and
Hsieh, 2000). We obtain a bias of 1.08% per year.53 This result is lower than the 0.30%
monthly bias found by Fung and Hsieh (2000), the 3% bias found by Liang (2001) and
the industry consensus bias of 3% stressed by Amin and Kat (2003a).54 On a yearly
basis, 2000 and 2001 have been years of important differences in results between living
and dissolved funds. When only individual funds are considered, figures reported are a
little higher at 1.44%. For funds of funds, we obtain 0.96%.
52 By living funds we mean funds still in operation at the moment of the analysis.
53 Complete results are available upon request.
54 We find this consensus value quite high when compared to the 0.8-1.5 bias reported by Malkiel
(1995) for US mutual funds.
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IV Global Results: Market Analysis
Our analysis has two parts. First, we focus on the performance of hedge funds by
grouping them per investment strategy. Then, we analyse the persistence in performance
and look for a systematic way of classifying funds that enables investors to consistently
and significantly outperform equity and bond indices over time.
4.1 Performance Analysis
Panel A of Table 29 reports the results obtained while using our multi-factor model
(1). The results reported are particularly strong. Every strategy but macro funds, option
strategy funds, no sub-strategy funds and funds of funds create significant alpha at the
5% significance level. On the exposure side, almost all strategies are significantly
exposed to the US equity market (inversely for short sellers) with a beta ranging from -
0.25 for short sellers to 0.66 for sector funds. Few strategies are significantly exposed to
non-US equity markets. The size factor is significantly positive for every strategy, except
for option arbitrage funds and short sellers meaning than hedge funds profit from the
small companies’ out-performance over the period under analysis by being small cap
biased. Option arbitrage strategies have been biased towards large companies. This is
perfectly in line with the strategy since option strategies tend to focus the S&P 500.
The style factor indicates a value bias for risk arbitrage and market neutral funds
and a growth bias for currency funds. Interestingly, the momentum factor is significantly
positive for most strategies indicating that many hedge funds tend to be momentum
players.
211
On the bond side, the world bond index factor is significantly negative for some
strategies but no single strategy is significantly exposed to this factor indicating an
inverse, but insignificant relation between hedge fund returns and the bond market. The
equity emerging market factor is strongly significantly positive for almost every strategy.
The exception is short sellers that are slightly negatively exposed to this factor and
currency funds, whose exposure is not significant. The r-squared are particularly high
between 0.26 and 0.89 with an average at 0.72.
We performed the same analysis adding the option factors of Agarwal and Naik
(2004) and report the results in Panel B of Table 29. A comparison of the two panels
indicates two interesting patterns.
First, for most strategies the alpha and the exposures to the factors (in terms of
significance) remain the same. Second, for global emerging markets funds, the alpha is
no longer significant, the exposure to the US equity market disappears, but the exposure
to the ATMC option factor is significant. This result interestingly indicates that the returns
offered by emerging market funds are not so highly correlated with the US equity
market, but that they offer at-the-money call option return features. Such managers
offer emerging market-like returns when the market is going up (like a call option on
developed markets since the upside potential of emerging markets is much higher than
that of developed markets in bull markets conditions). On the other side, such managers
tend to cut the exposure in bear market conditions.
Another interesting element is that the alpha of global funds is no longer
significant, but the exposure to the factor remains identical. This result indicates that
results may become unstable with the addition of auto-correlated factors. The same
result is found for the market exposure of market timers. For currency funds, there is a
significant exposure to the ATM call factor, but no significant change in the alpha or in
the other exposures.
212
Table 29: Hedge Fund Strategies Performance Analysis (1/1994-
12/2002)
- Distressed sec 0,44 *** 0,31 *** 0,06 0,22 *** 0,01 0,05 *
- Risk arb 0,43 *** 0,28 *** 0 0,14 *** 0,07 *** 0,01
- Event driven 0,58 *** 0,23 *** 0,09 * 0,12 *** 0,03 0,07 **
Event Driven Total 0,46 *** 0,28 *** 0,04 0,16 *** 0,04 0,04
Global emerging 0,47 ** 0,29 *** 0,2 *** 0,14 *** 0,01 0,08 ***
Global Macro 0,23 * 0,29 *** 0 0,12 *** 0,02 0,12 ***
Global 0,45 *** 0,47 ** 0,08 * 0,22 *** 0,03 0,08 **
Global Total 0,31 ** 0,3 *** 0,12 *** 0,14 *** 0 0,09 ***
Mkt ntl 0,49 *** 0,19 *** 0 0,09 *** 0,06 *** 0,03 *
Equity Hedge 0,51 *** 0,36 *** 0,06 * 0,17 *** 0,05 0,06 **
Sector 0,7 *** 0,66 ** -0,09 * 0,33 *** 0,01 0,12 ***
Short sales 0,56 *** -0,25 *** 0,02 -0,19 *** 0,07 -0,03 *
Long only leveraged 0,46 *** 0,47 *** 0,04 0,22 *** 0,03 0,08 ***
Mkt timing 0,41 *** 0,25 *** -0,01 0,11 *** 0,04 0,06 ***
Currency fund 0,58 ** 0,42 *** -0,05 0,17 *** -0,18 *** 0,12 ***
Option strategy 0,42 0,16 0,08 0,12 * 0,06 0,06
No strategy 0,28 0,18 0,3 * 0,32 *** -0,07 0,12 **
Individual funds total 0,47 *** 0,34 ** 0,04 0,17 *** 0,03 0,06 ***
Fd of Fds 0,2 * 0,24 *** 0,05 0,13 *** 0,04 0,08 ***
Global Index 0,4 *** 0,32 *** 0,04 0,16 *** 0,03 0,07 ***
Panel A: Model (1)
Alpha S&P MSCI w ex US SMB HML PR1YR
213
R²
- Distressed sec -0,06 0,09 *** 0,22 *** 0,04 0,07 0,82
- Risk arb 0,01 0,04 *** 0,08 0,01 -0,04 0,73
- Event driven -0,13 ** 0,07 *** -0,06 0 -0,14 ** 0,65
Event Driven Total -0,04 0,07 *** 0,11 ** 0,02 -0,01 0,82
Global emerging -0,39 *** 0,09 *** 0,16 * 0,06 * -0,28 * 0,76
Global Macro -0,08 0,05 ** 0,09 * -0,01 -0,04 0,73
Global -0,12 ** 0,07 *** 0 0,04 * -0,17 ** 0,86
Global Total -0,28 *** 0,08 *** 0,11 0,04 -0,23 ** 0,78
Mkt ntl -0,06 * 0,04 *** 0,06 0,02 * -0,08 0,77
Equity Hedge -0,07 0,05 *** 0,06 0,02 -0,13 * 0,87
Sector -0,02 0,07 *** -0,04 0,05 ** -0,02 0,88
Short sales -0,05 -0,05 * 0,05 -0,01 -0,1 0,52
Long only leveraged -0,07 0,07 *** 0,01 0 -0,17 * 0,89
Mkt timing -0,07 0,07 *** 0,15 ** 0,03 -0,03 0,63
Currency fund 0 0,12 * -0,24 -0,06 0,37 0,48
Option strategy -0,06 0,1 ** -0,01 -0,04 -0,08 0,26
No strategy -0,08 0,24 ** -0,25 0,04 -0,4 0,47
Individual funds total -0,1 *** 0,06 *** 0,05 0,03 * -0,12 * 0,88
Fd of Fds -0,15 *** 0,07 *** 0,07 0,02 -0,1 0,78
Global Index -0,11 *** 0,06 *** 0,05 0,03 * -0,11 0,86
Panel A (continued): Model (1)
WGBI EMBI HY GSCI DOLLAR
214
- Distressed sec 0,39 ** 0,28 *** 0,06 * 0,22 *** 0,02 0,05 ** -0,06 0,09 ***
- Risk arb 0,42 *** 0,22 *** 0,00 0,15 *** 0,07 *** 0,01 -0,01 0,04 **
- Event driven 0,60 *** 0,28 *** 0,09 * 0,11 *** 0,02 0,07 ** -0,12 * 0,07 ***
Event Driven Total 0,44 *** 0,25 *** 0,04 0,17 *** 0,05 0,04 * -0,06 0,06 ***
Global emerging 0,38 0,17 * 0,21 *** 0,16 *** 0,01 0,08 *** -0,37 *** 0,10 ***
Global Macro 0,27 * 0,23 *** 0,01 0,14 *** 0,03 0,12 *** -0,12 0,04
Global 0,49 *** 0,42 *** 0,09 * 0,23 *** 0,03 0,08 ** -0,15 ** 0,06 ***
Global Total 0,26 0,19 *** 0,13 *** 0,16 *** 0,00 0,09 *** -0,29 *** 0,08 ***
Mkt ntl 0,52 *** 0,13 *** 0,00 0,10 *** 0,06 *** 0,03 ** -0,07 ** 0,04 ***
Equity Hedge 0,50 *** 0,30 *** 0,07 * 0,18 *** 0,05 0,06 *** -0,08 0,05 ***
Sector 0,75 *** 0,58 *** -0,08 0,34 *** 0,02 0,12 *** -0,04 0,07 ***
Short sales 0,49 *** -0,23 *** 0,01 -0,20 *** 0,06 -0,03 0,00 -0,04
Long only leveraged 0,48 *** 0,39 *** 0,04 0,24 *** 0,03 0,08 *** -0,09 * 0,07 ***
Mkt timing 0,45 *** 0,08 0,00 0,14 *** 0,05 0,06 *** -0,11 0,07 **
Currency fund 0,67 *** 0,29 ** -0,04 0,18 *** -0,19 *** 0,12 ** 0,03 0,13 *
Option strategy 0,31 0,03 0,09 0,14 ** 0,07 0,06 -0,06 0,10 *
No strategy 0,29 0,31 0,30 0,32 *** -0,08 0,12 * -0,09 0,24 **
Individual funds total 0,48 *** 0,28 *** 0,05 0,18 *** 0,03 0,07 *** -0,12 *** 0,06 ***
Fd of Fds 0,19 0,19 *** 0,05 0,14 *** 0,04 0,08 *** -0,14 *** 0,07 ***
Global Index 0,41 *** 0,26 *** 0,05 0,17 *** 0,04 0,07 *** -0,12 *** 0,06 ***
PANEL B: Model (2)
Alpha S&P MSCI w ex US SMB HML PR1YR WGBI EMBI
215
R²
- Distressed sec 0,09 *** 0,20 *** 0,03 0,04 0,00 0,01 0,01 -0,02 * 0,83
- Risk arb 0,04 ** 0,07 0,01 -0,07 0,00 0,01 0,00 -0,01 0,74
- Event driven 0,07 *** -0,04 0,01 -0,09 0,01 0,00 -0,01 0,00 0,66
Event Driven Total 0,06 *** 0,10 * 0,02 -0,03 0,00 0,01 0,00 -0,01 0,83
Global emerging 0,10 *** 0,14 * 0,07 ** -0,33 * 0,01 *** 0,01 -0,01 * -0,02 0,77
Global Macro 0,04 0,09 0,00 -0,06 0,00 0,00 0,00 0,00 0,74
Global 0,06 *** 0,00 0,04 * -0,19 ** 0,00 0,00 0,00 0,00 0,87
Global Total 0,08 *** 0,10 0,05 * -0,28 ** 0,01 0,01 0,00 -0,01 0,79
Mkt ntl 0,04 *** 0,06 * 0,02 ** -0,10 * 0,00 -0,01 0,00 0,01 0,78
Equity Hedge 0,05 *** 0,05 0,02 -0,15 * 0,00 0,00 0,00 0,00 0,87
Sector 0,07 *** -0,05 0,05 ** -0,06 0,00 -0,01 0,00 0,01 0,89
Short sales -0,04 0,04 -0,02 -0,10 0,00 0,00 0,00 0,00 0,54
Long only leveraged 0,07 *** 0,01 0,00 -0,20 ** 0,00 0,00 0,00 0,00 0,89
Mkt timing 0,07 ** 0,14 ** 0,03 -0,12 0,00 -0,01 0,00 0,00 0,67
Currency fund 0,13 * -0,22 -0,04 0,36 0,02 ** -0,04 * -0,02 * 0,04 * 0,50
Option strategy 0,10 * -0,04 -0,04 -0,16 0,00 0,02 0,00 -0,02 0,29
No strategy 0,24 ** -0,23 0,05 -0,30 0,01 0,02 0,00 -0,01 0,48
Individual funds total 0,06 *** 0,04 0,03 * -0,15 ** 0,00 0,00 0,00 0,00 0,88
Fd of Fds 0,07 *** 0,06 0,03 -0,12 0,00 0,00 0,00 0,00 0,79
Global Index 0,06 *** 0,05 0,03 * -0,14 * 0,00 0,00 0,00 0,00 0,87
OTM CALL
OTM PUT
PANEL B (continued): Model (2)
HY GSCI DOLLAR ATM CALL
This Table presents the results of the performance estimation of the combined Model for the January 1994-December 2002 period. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index and ATMCt, OTMCt, ATMPt and OTMPt = respectively Agarwal and Naik (2004) at-the-money (ATMC), out-of-the money (OTMC) European call option factors, and at-the-money (ATMP) and out-of-the money (OTMP) European put option factors. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
EMBI ATM PUT
216
Panel B indicates that the option factors may be helpful in analysing hedge fund
returns for some specific strategies55, but that there is a serious risk of multi-colinearity.
Therefore, in the rest of the study, we report only the results of model (1).
4.2 Persistence in Performance - Returns
1. Global Database
Table 30 reports the results of the estimation for the global database (including
individual funds and funds of hedge funds) for the entire January 1995 to December
2002 period. As one would expect, the returns increase almost monotically between
deciles D1 and D10. The volatility decreases between deciles D1 and D4 and then
increases to attain its maximum at decile D10 indicating that the previous year’s best
funds are also the most volatile.
The alphas reported are significantly positive for deciles D2 to D8, but not for the
previous year’s best and worst performing funds. The factor exposures enable us to
distinguish between the deciles. Alpha creators (decile D2 to D8) have been long
equities, small cap biased and value oriented. Moreover, they have been exposed to
emerging market bonds, to high yield bonds and marginally to commodities. These alpha
creators can be distinguished from the previous year’s poorly performing funds that do
not create pure alpha and are exposed to the world excluding US equity markets while
being momentum contrarian. The previous year’s best performing funds are strongly
exposed to small companies, pure momentum players with a short exposure to the USD.
55 A closer look at the adjusted-R² indicates that it increased from 0 for most strategies to a maximum
of 0.04 for market timers confirming the fact that option factors may be redundant with the market
factor.
217
All in one, our model clearly explains most of the hedge fund’s performance and enables
us to distinguish between funds.
The spreads of the alphas reported indicate that there is no significant difference in
alpha between decile D1 and D10 or even between the extremes alphas (D1a and D10c)
but that there is a significant difference between decile D9 and D10, the bottom one
offering a significantly higher alpha (-0.48% per month) but at a cost of higher volatility.
This result indicates that there is no consistence in returns for the most volatile funds in
the database. Ideally, investors should invest in low volatility funds but if the invest in
higher volatility funds, the one offering the best past returns (decile D10) should be
favoured to the one that offer less returns even if the volatility is lower. A corollary is
that investors looking at directional hedge funds should favour the one with the highest
past performance independently of the volatility.
2. Individual Hedge Funds Versus Funds of Hedge Funds
We perform the same analysis by separating individual hedge funds from funds of
hedge funds.56 For individual funds, the mean returns and the volatility reported are
marginally higher and the alphas reported are significantly positive for all but the
previous year’s best performing funds. The volatility of these funds is so high that the
returns obtained are no longer significantly different from zero. The values obtained are
very close to the results obtained for the whole database.
56 The corresponding tables are available upon request.
218
Table 30: Hedge Fund Persistence in Performance (1/1995-
12/2002)
Mean Std dev.
D1 0,85 3,79 0,72 * 0,21 * 0,30 *** 0,07 -0,03
D2 0,73 2,28 0,36 ** 0,20 *** 0,16 *** 0,07 ** 0,01
D3 0,81 1,65 0,39 *** 0,14 *** 0,09 *** 0,09 *** 0,00
D4 0,83 1,41 0,31 *** 0,19 *** 0,04 * 0,07 *** 0,03
D5 0,93 1,46 0,35 *** 0,21 *** 0,02 0,09 *** 0,05 ***
D6 1,02 1,84 0,34 *** 0,27 *** 0,02 0,10 *** 0,05
D7 1,16 2,17 0,43 *** 0,33 *** 0,02 0,15 *** 0,06 *
D8 1,16 2,52 0,31 ** 0,40 *** -0,01 0,19 *** 0,07 *
D9 1,32 3,31 0,34 * 0,50 *** -0,05 0,29 *** 0,04
D10 1,43 4,82 0,40 0,52 *** 0,09 0,43 *** -0,02
D1a 1,26 5,14 1,36 *** 0,15 0,38 ** 0,05 -0,07
D1b 0,50 3,81 0,32 0,23 ** 0,30 ** 0,07 0,01
D1c 0,91 3,22 0,67 *** 0,21 *** 0,26 *** 0,09 * -0,06
D10a 1,30 3,72 0,44 ** 0,44 *** 0,06 0,33 *** -0,01
D10b 1,48 4,55 0,45 * 0,50 *** 0,08 0,37 *** 0,00
D10c 1,60 6,62 0,36 0,65 *** 0,12 0,56 *** -0,05
Spread 1-10 -0,58 4,72 -0,12 -0,32 0,24 -0,33 *** -0,03
Spread 1-2 0,12 2,01 -0,06 0,04 0,14 0,02 -0,06
Spread 9-10 -0,12 1,90 -0,48 *** 0,01 -0,17 ** -0,14 *** 0,06
Spread 1a-10c -0,34 7,02 0,45 -0,52 0,31 -0,46 *** -0,03
Panel A: Multi-factor estimation - Global Funds (1/1995-12/2002)
Alpha S&P MSCI w ex US SMB HML
219
R²
D1 -0,18 *** -0,30 ** 0,02 0,07 0,07 * -0,07 0,63
D2 -0,07 *** -0,19 *** 0,06 *** 0,05 0,03 -0,06 0,76
D3 -0,02 -0,12 *** 0,05 *** 0,09 * 0,03 *** 0,06 0,75
D4 0,01 -0,08 ** 0,04 *** 0,07 * 0,02 * 0,00 0,80
D5 0,04 ** -0,08 ** 0,04 *** 0,08 ** 0,01 -0,09 0,82
D6 0,07 *** -0,11 * 0,06 *** 0,07 0,01 -0,15 * 0,78
D7 0,09 *** -0,12 * 0,06 *** 0,03 0,03 -0,13 0,82
D8 0,13 *** -0,09 0,07 *** 0,05 0,01 -0,21 * 0,83
D9 0,20 *** -0,06 0,05 0,05 0,03 -0,24 * 0,85
D10 0,30 *** -0,32 *** 0,10 * 0,12 0,06 -0,25 0,83
D1a -0,27 *** -0,45 * -0,02 0,19 0,09 -0,15 0,51
D1b -0,16 *** -0,35 *** 0,02 0,04 0,07 * 0,00 0,58
D1c -0,12 *** -0,11 0,06 0,04 0,05 -0,04 0,70
D10a 0,20 *** -0,16 0,04 0,08 0,01 -0,14 0,82
D10b 0,29 *** -0,32 *** 0,09 * 0,15 0,05 -0,29 0,82
D10c 0,40 *** -0,54 *** 0,17 ** 0,14 0,12 -0,32 0,79
Spread 1-10 -0,49 *** 0,02 -0,13 -0,10 0,03 0,25 0,55
Spread 1-2 -0,12 *** -0,08 -0,05 -0,03 0,04 0,07 0,32
Spread 9-10 -0,10 *** 0,33 *** -0,05 -0,05 -0,03 0,02 0,55
Spread 1a-10c -0,69 *** 0,00 -0,26 * -0,07 -0,06 0,07 0,51
DOLLAR
Panel A (continued): Multi-factor estimation - Global Funds (1/1995-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its performance over the previous year. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index and ATMCt, OTMCt, ATMPt and OTMPt = respectively Agarwal and Naik (2004) at-the-money (ATMC), out-of-the money (OTMC) European call option factors, and at-the-money (ATMP) and out-of-the money (OTMP) European p
PR1YR WGBI EMBI HY GSCI
220
Funds of funds mean returns, alphas and standard deviations are lower than the
corresponding statistic for individual funds. Alphas are however significantly positive for
deciles D2 to D5. There are four main differences in the factor exposures. Firstly, no
single fund of fund has been momentum contrarian. Secondly, the negative exposure to
the government bond index is significantly lower. Thirdly, the emerging market bond
factor is significant for every decile when funds of funds are considered. Finally, the
currency factor is no longer significant at all. All in one, individual funds outperform fund
of funds and they can be distinguished by their respective factor exposure.
4.3 Persistence in Performance – Three Years of Data
Many investors require funds to exist for at least three years before investing in
order to be able to analyse their returns quantitatively. To take this constraint into
account, we performed the same analysis by considering three years of data to classify
funds into deciles for the next 12 months. This classification is recalculated every year on
the basis of the returns of the previous three years. Table 31 reports the results for the
global database.
The alphas reported in Table 31 are consistent with our one-year classification
period analysis. No significance for top and bottom deciles. There are however some
differences in terms of exposures. The exposure to ex-US equity markets is lower and no
more significant for top deciles. The exposure to the emerging market bond index
changes quite importantly. The bottom deciles (D9 & D10) that were not significantly
exposed to this factor are when funds are classified on three years of data. Funds cannot
be distinguished by their exposure to the world excluding US equity markets or by their
exposure to the emerging market bond index, but the R² remains high.
221
Table 31: Persistence in Performance Analysis Based on Three-
year Data (1/1997-12/2002)
Mean Std dev.
D1 0,68 3,20 0,57 * 0,17 * 0,18 0,10 * 0,00
D2 0,68 2,09 0,41 * 0,08 0,17 ** 0,06 -0,03
D3 0,81 1,38 0,43 *** 0,13 *** 0,02 0,06 *** 0,01
D4 0,79 1,43 0,35 *** 0,18 *** 0,03 0,06 *** 0,04 *
D5 0,83 1,97 0,37 *** 0,23 *** 0,05 0,09 *** 0,03
D6 0,90 1,97 0,38 *** 0,26 *** 0,02 0,09 *** 0,04
D7 0,91 2,34 0,36 *** 0,33 *** 0,01 0,14 *** 0,05 *
D8 0,99 2,91 0,29 * 0,48 *** -0,06 0,19 *** 0,07 *
D9 1,02 3,67 0,25 0,57 *** -0,07 0,26 ** 0,04
D10 1,11 5,02 0,40 0,56 *** 0,08 0,41 *** -0,03
D1a 0,59 4,38 0,39 0,41 *** 0,08 0,14 ** 0,06
D1b 0,90 3,43 1,00 *** -0,02 0,27 ** 0,02 -0,01
D1c 0,66 2,90 0,46 * 0,19 *** 0,15 * 0,12 *** -0,05
D10a 0,86 4,61 0,19 0,48 *** 0,08 0,32 *** -0,06
D10b 1,04 4,91 0,33 0,59 *** 0,06 0,41 *** 0,02
D10c 1,28 6,01 0,50 0,59 *** 0,13 0,50 *** -0,06
Spread 1-10 -0,43 3,95 -0,03 -0,39 *** 0,11 -0,30 *** 0,02
Spread 1-2 0,01 1,81 -0,20 0,09 0,03 0,08 *** 0,00
Spread 9-10 -0,10 2,05 -0,49 ** -0,02 -0,13 * -0,20 *** 0,07
Spread 1a-10c -0,69 4,28 -0,77 -0,03 -0,05 -0,18 ** 0,24 *
Panel A: Multi-factor estimation - Global Funds classified on their performance (1/1997-12/2002)
Alpha S&P MSCI w ex US SMB HML
222
R²
D1 -0,12 *** -0,31 ** 0,06 0,09 0,06 -0,35 ** 0,66
D2 0,01 -0,22 *** 0,05 * 0,11 0,01 -0,18 0,66
D3 0,00 -0,08 * 0,06 *** 0,11 *** 0,01 -0,05 0,72
D4 0,02 -0,08 ** 0,05 *** 0,08 ** 0,02 -0,03 0,80
D5 0,04 * -0,10 * 0,07 *** 0,10 * 0,01 -0,13 0,80
D6 0,06 *** -0,08 0,07 *** 0,10 ** 0,01 -0,14 0,83
D7 0,06 *** -0,10 0,08 *** 0,10 * 0,02 -0,23 * 0,87
D8 0,10 *** 0,00 0,10 *** 0,04 0,02 -0,15 0,88
D9 0,16 *** -0,06 0,08 *** 0,05 0,02 -0,17 0,89
D10 0,20 *** -0,24 ** 0,12 *** 0,03 0,06 -0,18 0,89
D1a -0,15 ** -0,20 0,05 0,09 0,05 -0,21 0,56
D1b -0,19 *** -0,49 *** 0,01 0,16 * 0,05 -0,53 ** 0,56
D1c -0,06 -0,14 0,11 *** 0,05 0,07 ** -0,19 0,71
D10a 0,21 *** -0,27 ** 0,14 *** 0,11 0,03 -0,25 0,86
D10b 0,14 *** -0,26 ** 0,19 *** -0,04 0,05 -0,36 0,88
D10c 0,27 *** -0,34 ** 0,14 *** -0,02 0,08 * -0,27 0,85
Spread 1-10 -0,31 *** -0,04 -0,03 0,07 -0,02 -0,22 0,61
Spread 1-2 -0,10 *** -0,05 0,07 * -0,08 0,01 -0,15 0,31
Spread 9-10 -0,04 0,15 -0,03 0,08 -0,04 -0,17 0,49
Spread 1a-10c -0,35 *** 0,03 0,00 0,10 -0,06 -0,34 0,43
EMBI HY GSCI DOLLAR
Panel A: Multi-factor estimation - Global Funds classified on their performance (1/1997-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its performance over the previous three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
PR1YR WGBI
223
The results obtained for individual funds and funds of hedge funds are in line with
those obtained on a global level. Individual funds outperform and create significant alpha
in almost all cases. The spreads of the alphas reported are in line with the one obtained
in the previous table. There is no significant difference in alpha between decile D1 and
D10 or between the extremes alphas (D1a and D10c) but there is a significant difference
between decile D9 and D10, the bottom one offering a significantly higher alpha (-0.49%
per month) but at a cost of higher volatility. This result confirms that if investors want to
invest in high volatility/directional hedge funds they should favour the one with the
highest past performance independently of the volatility.
224
4.4 Persistence in Performance – Other Measures
Absolute performance is the most important element of the hedge fund industry.
However, some strategies are very risky whereas others attempt to offer stable returns.
Our analysis indicates that some relatively low volatility hedge funds consistently and
significantly outperform classical equity and bond indices over time. In order to go
further in the analysis, we perform the same analysis with other ways of classifying funds
into deciles. We use the following measures as classification parameters:
1. Sharpe ratio57
2. Standard deviation58
3. Alpha
4. Beta
5. Skewness/Kurtosis
6. An adapted Sharpe ratio
57 Practically, we use the Sharpe score (ratio of mean returns over standard deviation). We would
have obtained exactly the same decile classification if we would have used the Sharpe ratio since the
same rate would have been deducted from the performance of all the funds considered.
58 We performed the same analysis using the minimum monthly return (for investors that want to limit
very bad losses in any month) and the maximum monthly return (for investors that want to achieve
punctual high returns) and the results obtained were in close to those obtained using the standard
deviation as a rule for classifying the funds. The corresponding Tables are available upon request.
225
Before using these other ways of classifying hedge funds based on past
performance, we have to check for the risk of disaggregation. Disaggregation can happen
if the deciles are not homogeneous that is when funds of the same strategies are
grouped in the same decile. We check this element and report the results for alpha and
beta in Figure 5 to Figure 8. The first two figures report the repartition of decile per
strategy. There are for example 3% of distressed funds in the global database. Figure 5
shows that there are some variations in the repartition of decile per strategy over time
but these variations are not large. We are only talking about some percentages of
differences.
The differences are reported in Figure 6. Figure 6 reports the difference between
the percentage of funds of each strategy and in each decile. Consider the following
example. There are 3% of distressed funds in the global database. Decile 1 has on
average 3.9% of distressed funds. The difference, 0.9%, is reported in Figure 6.
Figure 6 indicates that the two largest differences happen in decile D2 (-11% for
global funds and +10% for market neutral funds). Note that the percentage of global
funds decreased from around 21% to 16% and the percentage of market neutral funds
increased from 16% to 21% over time. When we look at each strategy one by one, we
see more funds of funds in decile D4 to decile D8 and less in the top deciles but marginal
differences like this can also be explained by the fact that many funds of funds have
been created recently and that the global database does not have the same unbiased
repartition every year since new funds have been added or removed every year.
226
Figure 5: Decile Repartition per Strategy (Ranking base on
Alpha)
DB D1 D2 D3 D4 D5 D6 D7 D8 D9
D10
DSRA
EDGL EMERMACRO
GLOBALMKT NTL
EQ. HEDGESECTORSHORT
LG LEVMKT TIMING
CURRENCYOPTION
NO STRATFOF
0%
5%
10%
15%
20%
25%
30%
35%
227
Figure 6: Strategy Repartition in the Alpha Ranking
D1 D2 D3 D4 D5 D6 D7 D8 D9
D10
DS
ED
MACRO
MKT NTL
SECTOR
LG LEV
CURRENCYNO STRAT
-12%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
228
Figure 7: Decile Repartition per Strategy based on Beta
DB D1 D2 D3 D4 D5 D6 D7 D8 D9 D10
DSRA
EDGL EMERMACRO
GLOBALMKT NTL
EQ. HEDGESECTORSHORT
LG LEVMKT TIMING
CURRENCYOPTION
NO STRATFOF
0%
5%
10%
15%
20%
25%
30%
35%
229
Figure 8: Strategy Repartition in the Beta Ranking
D1 D2 D3 D4 D5 D6 D7 D8 D9
D10
DSRA
EDGL EMERMACRO
GLOBALMKT NTL
EQ. HEDGESECTORSHORT
LG LEVMKT TIMINGCURRENCY
OPTIONNO STRAT
FOF
-12%
-10%
-8%
-6%
-4%
-2%
0%
2%
4%
6%
8%
10%
12%
These figures report the decile repartition between hedge fund strategies. Figure CCC report
the repatition in deciles based on alpha, Figure CCC+1 reports the difference with the global
database. Figure CCC and CCC report the same information when funds are classified in
deciles on the basis of their past beta.
230
For funds of funds for example the sum of the differences reported is 14%
meaning that there are 14% funds of funds more in the deciles reported based on alpha
than in the global database. In the present case, these 14% are ranked in middle decile.
Figure 5 and Figure 6 lead us to conclude that there is no risk of aggregation when alpha
is used as a ranking measure.
Figure 7 and Figure 8 show the same information when the ranking used to
construct the deciles is based on beta. Results are a little more mitigated even if we
remain at relatively low variations. Funds of funds tend not to be in the top decile and
global funds tend not to be in the bottom deciles. These results comfort us in the use of
beta as a ranking tool for hedge funds.
We have also considered the omega from Keating and Shadwick (2002) as well as
the Sortino ratio but we choose not to use them for the same reason. First, as a measure
based on a distribution of returns, the omega59 needs a relatively long dataset to be
estimated. Since our persistence analysis methodology is based on one year and three
years of data to rank the funds before analysing the persistence in their performance, we
cannot use the omega. We could have decided to take a longer period under review to
estimate the quality of the manager (at least five years or ten years) but then we would
have limited the period of test of the ranking methodology since the global period under
review covers 10 years of data in total.
59 The value of the Omega function at level r is the ratio of probability weighted gains relative to r, to
probability weighted losses relative to r. The Omega is like a return distribution that includes higher
moments. It gives a risk-reward measure for which returns are weighted by their probability and shows
the interest of combining different investments in a single portfolio.
231
The same issue emerges with the Sortino ratio60. By definition, hedge funds aim
at offering positive returns irrespective of the market. On a three year period, most fund
will or at least should suffer only a few months down. Because of this, our estimation of
the negative standard deviation will be unstable if we consider 1 or 3 years of data.
Another time, the data available do not allow us to cover 5 or 10 years of data to classify
funds before analysis the persistence.
Moreover, it is important to stress out that the issue is even more important is our
case because individual funds are considered mainly because most funds exist for a few
years only. On aggregate 2576 hedge funds (65% of the 3967 funds of our database)
have less than five years of data meaning that taking five years of data or more to rank
funds will lead us not to consider these funds in our analysis. In addition, 1075 funds out
of theses 2576 funds have been dissolved before the end of the period, taking longer
period of ranking to classify funds will lead to a survivorship bias in the database because
dissolved funds will not be taken into account. Three years of data seems to be the best
tradeoff between stable statistics and the length of the period under review.
60 The Sortino ratio is similar to the Sharpe Ratio, except that instead of using standard deviation as
the denominator, it uses Downside Deviation.
232
Sharpe score
Many investors investigating hedge funds focus on their risk/return
characteristics. Such investors pay a particular attention to the trade-off between the risk
and the returns offered. The Sharpe score – defined as the ratio of the average return to
the standard deviation – aims at taking risk and returns into account. It is reasonable to
use this measure while analysing the persistence in hedge fund returns. The idea behind
this analysis is the following: will investors outperform if they focus at the previous year’s
risk/return trade-offs of the hedge fund industry instead of focusing on pure performance
only. Investors want to see if hedge funds are able to produce consistent returns over
time. Various studies used the Sharpe ratio while analysing hedge fund returns (see for
example, Ackermann et al., 1999; Liang, 1999 as well as Amin and Kat, 2003a) and
most of them stressed the shortcut of this measure for alternative strategies like those
applied by hedge fund managers (see for example, Amenc et al., 2003 and Goetzmann
et. al., 2003). Nevertheless, the use of this measure remains very predominant in the
industry despite its weaknesses.
The first three columns of Table 32 report the return, the risk and the average
Sharpe score of each decile. Decile D1 contains the funds having the lowest Sharpe score
calculated using three years of data, while decile D10 includes the funds offering the
most attractive risk-return trade-off over the three years used to classify funds. Funds
included in decile D1 offer an average monthly performance of 0.7% with a monthly
standard deviation of 2.79% against a mean monthly return of 0.93% for the best
performing funds. The Sharpe score decreases slightly between decile D2 and decile D5
and increases monotically thereafter to reach 0.93 for decile D10. The sub-deciles
reported in the second part of the Table 32 indicate that the increase in the Sharpe score
is particularly for sub-decile 10a to 10c indicating that a limited number of funds strongly
distinguish themselves.
233
The alpha column indicates that there is persistence for the previous year’s top
funds. Funds classified in deciles D8 to D10 create alpha. The factor exposure indicates
that top risk-return performers have had a limited exposure to the US equity market,
they have been value-oriented and that they have been exposed to the high yield
market. On the other side, underperforming funds have not been exposed to the US
equity market but have been exposed to the world excluding US. They also have been
momentum contrarian, short world government bonds and short the USD.
The spreads of the alphas reported are not significant but for the spread between
the most attractive funds decile D9 and decile D10. Table 32 interestingly indicates that if
you invest in the top 10% of the funds that offered the highest Sharpe ratio over the last
three years, you would not only offer significant positive alpha but you would also
significantly outperform significantly the next 10%. This means that is it important to
make a good selection and also that you can make a good selection (decile D8 and D9)
or a top selection significantly better (decile D10). The results indicate that even if there
are around 30% of the funds that offer significant alpha based on the Sharpe ratio, the
top one are apart from the others.
A comparison with the results obtained when we classified hedge funds on the
basis of their performance confirm the need to take risk and return into account in order
to identify what kind of funds offer persistence in returns. Results obtained by separating
individual funds from fund of funds are in line.
234
1. Standard Deviation
Some investors focus on volatility using hedge funds as pure risk diversifiers. In
this case, investors may use hedge funds instead of bonds in their portfolio and the most
important aspect to them is to limit the volatility. We perform the same analysis by
focusing purely on volatility. Every year we classify funds on the basis of the standard
deviation of their previous three years of returns.
This analysis is interesting because it aims at determining if there is any proof of
good or bad performance in hedge fund return on the basis of the volatility of their
returns only. Stated differently, do volatile hedge funds consistently and significantly out-
or under-perform less volatile hedge funds? The answer is in Table 33.
The mean and standard deviation columns of Panel A indicate that returns
increase with volatility for low volatility funds, but that the trend is unclear for more
volatile funds (decile D5 to D10). The alpha column confirms that low volatility funds
create significant alpha and that high volatility funds do not. Interestingly, the alpha
created by decile D5 is strongly significant (as for example, decile D1), while being much
more volatile – indicating that higher volatility funds do not necessarily lack of
consistency in performance. These results enable us to divide the hedge fund industry
into three segments:
1) Low volatility funds that offer persistent over-performance;
2) Low/medium volatility funds that offer persistent over-performance;
3) High volatility funds that do not offer persistent over-performance.
235
This result leads to the conclusion that low volatility funds tend to consistently and
significantly outperform over time. Low volatile funds that cannot create consistent
performance tend to become more volatile and switch from segment one to two or three.
Higher volatility funds that offer consistent returns will have a relatively stable volatility
(since returns are relatively stable) and consequently remain in segment two, while
volatile and inconsistent managers fall in segment three.
In terms of exposures, alpha creators again exhibit slight exposures to the US
equity markets and they have been long high yield. Unlike other deciles they also have
not been momentum players. This result confirms that it is not sufficient to be a
momentum player to make money. The r-squared are very high.
The spreads of the alphas reported show the same pattern as with the Sharpe ratio.
Selecting low volatility funds enable investors to create significant and consistent alpha
over time but if you select the lowest funds that are available, you will not only offer
significant alpha but also significantly outperform the next alpha creators. The results
indicate that even if there are between 30% and 50% of the individual funds that
outperform, the top one are apart from the others.
Our results indicate that less volatile funds tend to outperform the classical
markets and to become more volatile when they cannot offer the expected performance.
As before, the results of individual funds and funds of hedge funds are in line with those
obtained for the global database with higher alpha reported for individual funds.
236
Table 32: Persistence in Performance Analysis Based on the
Sharpe score (1/1997-12/2002)
Mean Std dev. Sharpe Score
D1 0,70 2,79 0,25 0,60 * 0,03 0,23 ** 0,06 -0,01
D2 0,82 3,24 0,25 0,47 0,33 *** 0,10 0,11 ** -0,03
D3 0,72 3,62 0,20 0,15 0,51 *** 0,04 0,16 *** 0,03
D4 0,81 3,49 0,23 0,27 0,48 *** 0,04 0,21 *** 0,03
D5 0,77 3,12 0,25 0,25 0,41 *** 0,03 0,21 *** -0,01
D6 0,82 2,91 0,28 0,16 0,44 *** -0,04 0,19 *** 0,03
D7 0,87 2,58 0,34 0,23 * 0,39 ** -0,02 0,19 *** 0,06 **
D8 0,89 2,16 0,41 0,25 ** 0,30 *** -0,02 0,16 *** 0,07 ***
D9 0,89 1,58 0,56 0,37 *** 0,16 *** 0,01 0,12 *** 0,04
D10 0,93 1,00 0,93 0,49 *** 0,08 *** 0,01 0,06 *** 0,02
D1a 0,40 3,41 0,12 0,25 0,08 0,27 * 0,11 * 0,07
D1b 0,74 2,98 0,25 0,59 0,01 0,20 -0,01 -0,02
D1c 0,71 3,10 0,23 0,66 ** 0,02 0,28 *** 0,08 ** -0,05
D10a 0,94 1,31 0,71 0,45 *** 0,12 *** -0,01 0,10 *** 0,03
D10b 0,93 0,94 0,99 0,52 *** 0,06 *** 0,03 0,06 *** 0,01
D10c 0,86 0,71 1,20 0,47 *** 0,01 0,03 0,03 ** 0,02
Spread 1-10 -0,23 2,42 -0,09 -0,02 -0,05 0,21 ** -0,01 -0,03
Spread 1-2 -0,12 1,68 -0,07 -0,01 -0,30 *** 0,13 ** -0,05 *** 0,02
Spread 9-10 -0,04 0,71 -0,06 -0,46 *** 0,08 *** 0,00 0,06 *** 0,01
Spread 1a-10c -0,46 3,26 -0,14 -0,39 0,07 0,24 0,09 0,05
Panel A: Multi-factor estimation - Global Funds classified on their Sharpe Score (1/1997-12/2002)
Alpha S&P MSCI w ex US SMB HML
237
R²
D1 -0,09 ** -0,38 *** 0,06 0,15 * 0,03 -0,56 ** 0,60
D2 0,01 -0,19 0,07 0,09 0,02 -0,22 0,72
D3 0,06 * -0,15 0,14 *** 0,10 -0,01 -0,28 * 0,87
D4 0,06 ** -0,12 0,09 *** 0,07 0,03 -0,26 * 0,89
D5 0,07 *** -0,11 0,07 *** 0,04 0,02 -0,08 0,89
D6 0,12 *** -0,06 0,09 *** 0,09 0,02 -0,10 0,90
D7 0,11 *** -0,04 0,06 *** 0,04 0,03 -0,13 0,90
D8 0,11 *** -0,05 0,06 *** 0,09 * 0,02 -0,09 0,86
D9 0,07 *** -0,10 * 0,06 *** 0,10 ** 0,03 -0,01 0,81
D10 0,04 *** -0,07 0,05 *** 0,09 * 0,02 * 0,06 0,71
D1a -0,11 ** -0,26 0,02 -0,04 0,03 -0,65 ** 0,43
D1b -0,05 -0,52 *** 0,02 0,14 0,00 -0,55 ** 0,36
D1c -0,10 *** -0,36 *** 0,12 *** 0,15 * 0,06 ** -0,48 ** 0,69
D10a 0,06 *** -0,07 0,05 *** 0,10 0,04 ** 0,07 0,74
D10b 0,03 *** -0,06 0,04 *** 0,08 ** 0,02 0,05 0,75
D10c 0,03 ** -0,09 *** 0,03 *** 0,10 * 0,01 0,04 0,51
Spread 1-10 -0,13 *** -0,30 ** 0,01 0,06 0,01 -0,59 ** 0,42
Spread 1-2 -0,10 *** -0,19 ** -0,01 0,06 0,01 -0,33 * 0,51
Spread 9-10 0,03 *** -0,03 0,02 0,01 0,01 -0,11 ** 0,68
Spread 1a-10c -0,14 *** -0,13 -0,01 -0,13 0,02 -0,61 ** 0,27
Panel A (continued): Multi-factor estimation - Global Funds classified on their Sharpe Score (1/1997-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its Sharpe score over the past three years, with the Sharpe score defined as the ratio of performance to volatility. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
PR1YR WGBI EMBI HY GSCI DOLLAR
238
Table 33: Persistence in Performance Analysis Based on the
Standard Deviation (1/1997-12/2002)
Mean Std dev.
D1 0,69 0,63 0,32 *** 0,01 0,02 0,02 0,01
D2 0,76 0,96 0,34 *** 0,07 *** 0,02 0,04 *** 0,04 ***
D3 0,77 1,17 0,33 *** 0,12 *** 0,02 0,06 *** 0,03 *
D4 0,91 1,62 0,41 *** 0,20 *** 0,02 0,09 *** 0,05
D5 0,97 2,28 0,41 *** 0,28 *** 0,06 0,12 *** 0,08 *
D6 0,85 2,58 0,27 0,36 *** 0,05 0,11 *** 0,09 **
D7 0,87 2,99 0,29 * 0,45 *** 0,03 0,16 *** 0,07 *
D8 0,91 3,45 0,33 * 0,46 *** 0,02 0,22 *** 0,01
D9 0,82 4,21 0,22 0,59 *** 0,00 0,30 *** -0,01
D10 0,70 6,56 0,19 0,77 *** 0,06 0,47 *** -0,14
D1a 0,65 0,52 0,30 *** 0,00 0,02 0,01 0,01 **
D1b 0,69 0,74 0,31 *** 0,02 0,02 0,01 0,02 *
D1c 0,71 0,72 0,34 *** 0,01 0,04 *** 0,02 ** 0,01
D10a 0,68 6,21 0,17 0,67 *** 0,09 0,47 *** -0,15
D10b 0,71 6,27 0,31 0,58 *** 0,13 0,46 *** -0,16
D10c 0,67 7,94 0,11 1,04 *** 0,03 0,45 *** -0,13
Spread 1-10 -0,01 6,23 0,06 -0,76 *** -0,04 -0,45 *** 0,16
Spread 1-2 -0,07 0,44 -0,36 *** -0,07 *** 0,01 -0,03 *** -0,03 ***
Spread 9-10 0,12 2,81 -0,11 -0,18 -0,06 -0,17 *** 0,13
Spread 1a-10c -0,02 7,70 -0,04 -1,05 *** -0,01 -0,44 *** 0,14
Panel A: Multi-factor estimation - Global Funds classified on their standard deviation (1/1997-12/2002)
Alpha S&P MSCI w ex US SMB HML
239
R²
D1 0,02 -0,09 0,03 *** 0,10 *** 0,01 -0,02 0,61
D2 0,02 -0,11 0,04 *** 0,12 *** 0,02 -0,08 0,67
D3 0,04 *** -0,06 0,05 *** 0,12 *** 0,01 -0,01 0,76
D4 0,05 *** -0,07 0,07 *** 0,07 * 0,01 -0,12 0,77
D5 0,09 *** -0,11 0,07 *** 0,10 * 0,01 -0,16 0,81
D6 0,08 *** -0,09 0,07 *** 0,08 0,01 -0,24 0,82
D7 0,07 *** -0,07 0,07 *** 0,07 0,01 -0,15 0,89
D8 0,08 *** -0,14 0,12 *** 0,11 0,02 -0,30 0,89
D9 0,08 *** -0,15 0,09 *** 0,03 0,03 -0,32 0,90
D10 0,10 * -0,26 0,13 * 0,07 0,08 0,05 0,85
D1a 0,00 -0,06 0,02 0,11 *** 0,01 0,00 0,59
D1b 0,02 -0,10 0,04 *** 0,12 ** 0,02 0,01 0,53
D1c 0,02 -0,12 0,03 *** 0,10 *** 0,01 -0,06 0,63
D10a 0,12 *** -0,14 0,16 *** 0,12 0,07 0,23 0,85
D10b 0,12 -0,28 0,04 0,21 0,06 0,07 0,79
D10c 0,07 -0,51 0,20 * -0,17 0,11 -0,28 0,80
Spread 1-10 -0,09 0,17 -0,10 0,04 -0,07 -0,06 0,82
Spread 1-2 0,00 0,01 -0,01 -0,01 -0,01 0,02 0,53
Spread 9-10 -0,02 0,13 -0,04 -0,04 -0,06 -0,35 0,51
Spread 1a-10c -0,07 0,45 -0,18 * 0,28 -0,11 0,25 0,75
EMBI HY GSCI DOLLAR
Panel A (continued): Multi-factor estimation - Global Funds classified on their standard deviation (1/1997-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its standard deviation over the previous three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
PR1YR WGBI
240
2. Alpha
Hedge funds aim at offering absolute returns in any market environment.
Investors who use them as a return enhancer compare the part of their portfolio
allocated to hedge funds to the proportion of their portfolio invested in equities to
determine if they are a good return enhancer. Table 34 reports the decomposition of
hedge fund returns classified on the basis of the alpha created over a three-year period.
The current analysis is based on the following statement: do managers that create higher
alpha over a period persistently outperform the equity, bond and commodity markets
over the next period?
The mean return decreases between decile D1 and D10, the standard deviation
decreases between decile D1 and D6 before increasing again until decile D10. The trend
in alpha is not clear, but significant for the middle deciles D4 to D8. The volatility column
confirms once again that low volatility funds can create significant and consistent value
over time. No spread is significant meaning that the funds that offered the highest alpha
or lowest alpha in the past do not distinguish from each other in the future.
The exposures reported are in line with the ones previously obtained. The only
major difference is that alpha creators are momentum players according to those results.
This result confirms the instability of this factor in distinguishing pure alpha creators
since depending on the way of classifying funds, pure alpha creators will or will not be
considered momentum players.
241
3. Beta
Table 35 reports the results obtained by classifying funds on the basis of their
beta (high beta funds in decile D1). High beta funds are the most volatile and they do not
outperform classical markets over time. Almost all deciles from deciles D5 to D10
significantly and consistently create value. The factor exposures indicate that alpha
creators have not all been long US equities (decile D10 is even net short the U.S. equity
market but not significantly) but that these funds have been value oriented and exposed
to the high yield market.. The r-squared obtained are particularly high, with a maximum
of 0.94.
The spreads report very interesting results. The spread between the high beta
funds (decile D1) and the low beta funds (decile D10) is significantly positive at 0.92
meaning that high beta funds significantly underperform low beta funds by more than
ninety basis points a month when the factor exposure in taken into account. Spread 9-10
is also significant but negative. This result indicates another time that in the alpha
producers, there is a difference between the good and the top ones. The funds that offer
the highest alpha are much better than the one outperform the underperforming funds.
As one would expect, pure hedge funds should have a limited exposure to the
equity market. Our results suggest that low beta funds that also a limited volatility can
significantly and consistently create value over time.
242
4. Skewness and Kurtosis
Investors like positive skewness but do not like fat tails. Panel A of Table 36
reports the results obtained by classifying funds on the basis of their skewness (the lower
the skewness, the lower the decile). The first interest of Table 36 is that the volatilities
reported in the second column are relatively stable over the 10 deciles. This result is very
different from what we obtained previously. Second, in each case we report the skewness
and the kurtosis because our results indicate that there is a direct link between these two
measures. In Panel A, the skewness increases from decile D1 to decile D10. This means
that the distribution goes from negatively skewed to positively skewed. The kurtosis
reported in the next column goes from high values for negatively skewed returns, to low
values for unskewed return distributions. In short, skewed distributions have fat tails.
This relation is even stronger when considering negatively skewed distributions.
Panel B reports the same analysis and focuses on the kurtosis. It confirms these findings
since funds with fat tails also have the highest skewness. Funds tend to have fat tails on
the left-hand side of their mean. Volatility is on the downside. Finally, the alpha column
is not easy to interpret. In both cases, performing deciles are spread out. Since there is
no formal difference in the volatility of the deciles considered, this result again confirms
the need to take volatility into account when analysing hedge funds and when looking for
funds offering persistent performance over time. Classifying funds on the basis of their
skewness or their kurtosis is not the best way to try to understand and predict hedge
fund returns.
243
Table 34: Persistence in Performance Analysis Based on the
Alpha (1/1997-12/2002)
Mean Std dev.
D1 0,93 5,47 0,19 0,66 *** -0,03 0,22 *** -0,03
D2 0,92 3,73 0,43 0,46 *** 0,06 0,12 *** -0,03
D3 0,82 2,94 0,28 0,36 *** 0,05 0,12 *** -0,01
D4 0,87 2,17 0,50 ** 0,29 *** 0,03 0,10 *** 0,00
D5 0,79 1,89 0,44 ** 0,23 *** 0,05 0,10 *** -0,01
D6 0,84 1,76 0,51 *** 0,21 *** 0,06 0,10 *** 0,00
D7 0,78 1,78 0,36 *** 0,25 *** 0,03 0,14 *** 0,03
D8 0,77 1,88 0,26 *** 0,24 *** 0,02 0,15 *** 0,04 *
D9 0,79 2,22 0,17 0,30 *** 0,00 0,18 *** 0,09 ***
D10 0,69 3,10 -0,05 0,34 *** 0,01 0,30 *** 0,11
D1a 0,58 6,44 -0,53 0,90 *** -0,12 0,11 0,13
D1b 1,08 5,56 0,25 0,59 *** 0,02 0,26 *** -0,04
D1c 0,81 4,67 0,21 0,54 *** 0,02 0,18 *** -0,07
D10a 0,81 2,53 0,18 0,33 *** -0,05 0,22 *** 0,10 ***
D10b 0,65 3,40 -0,10 0,33 *** 0,03 0,31 *** 0,11
D10c 0,75 4,01 -0,10 0,37 ** 0,04 0,39 *** 0,12
Spread 1-10 0,24 3,98 0,11 0,33 *** -0,01 -0,08 -0,20 *
Spread 1-2 0,02 2,23 -0,17 0,15 0,01 0,08 * -0,08
Spread 9-10 0,10 1,36 -0,19 -0,02 -0,03 -0,12 *** -0,01
Spread 1a-10c -0,17 5,85 -0,15 0,51 * -0,07 -0,27 -0,04
Alpha S&P MSCI w ex US SMB HML
Panel A: Multi-factor estimation - Global Funds classified on their alpha (1/1997-12/2002)
244
R²
D1 -0,01 -0,06 0,14 *** 0,16 0,01 -0,67 0,81
D2 0,08 * -0,11 0,08 ** 0,11 0,03 -0,24 0,81
D3 0,06 * -0,11 0,10 *** 0,07 0,01 -0,23 0,81
D4 0,07 ** -0,09 0,08 *** 0,08 0,03 -0,18 0,75
D5 0,09 *** -0,15 0,07 ** 0,10 * 0,02 -0,13 0,74
D6 0,06 *** -0,13 0,07 *** 0,10 * 0,02 -0,06 0,79
D7 0,07 *** -0,10 0,05 *** 0,07 0,02 -0,03 0,85
D8 0,07 *** -0,13 0,04 *** 0,05 0,02 0,01 0,89
D9 0,04 *** -0,08 0,07 *** 0,06 0,02 -0,02 0,87
D10 0,07 *** -0,13 0,07 0,07 0,04 0,00 0,78
D1a 0,08 ** -0,33 0,21 ** 0,13 -0,07 -1,57 0,76
D1b -0,02 -0,05 0,16 ** 0,12 -0,02 -0,62 0,76
D1c 0,06 0,04 0,12 *** 0,13 0,07 * -0,10 0,76
D10a 0,06 *** -0,12 0,04 0,11 0,02 -0,25 0,79
D10b 0,04 -0,12 0,06 0,13 0,04 0,15 0,77
D10c 0,12 ** -0,13 0,10 -0,02 0,06 0,19 0,64
Spread 1-10 -0,04 0,02 0,08 0,07 -0,05 -0,62 ** 0,41
Spread 1-2 -0,04 -0,11 0,06 0,02 -0,02 -0,37 ** 0,40
Spread 9-10 -0,03 0,09 0,00 0,00 -0,04 -0,05 0,31
Spread 1a-10c -0,01 -0,27 0,09 0,13 -0,15 -1,51 ** 0,28
Panel A (continued): Multi-factor estimation - Global Funds classified on their alpha (1/1997-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. Each year, every fund is classified into a decile on the basis of its alpha (relative to the S&P 500 equity index) over the past three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
PR1YR WGBI EMBI HY GSCI DOLLAR
245
Table 35: Persistence in Performance Analysis Based on Beta
(1/1997-12/2002)
Mean Std dev.
D1 0,56 6,24 0,30 1,06 *** -0,02 0,48 *** -0,19
D2 0,76 3,80 0,09 0,71 ** 0,02 0,28 ** 0,01
D3 0,61 3,34 0,24 0,49 *** 0,07 0,24 ** 0,08 *
D4 0,99 2,61 0,18 0,42 *** 0,05 0,19 *** 0,06
D5 0,74 2,31 0,39 ** 0,32 *** 0,05 0,11 *** 0,08 *
D6 0,84 1,64 0,31 * 0,21 *** 0,06 0,10 *** 0,03
D7 0,79 1,34 0,36 *** 0,11 *** 0,05 * 0,06 *** 0,03
D8 0,81 1,12 0,36 *** 0,08 *** 0,02 0,07 *** 0,06 ***
D9 0,69 0,88 0,39 *** 0,02 0,02 0,03 *** 0,02 *
D10 0,79 0,90 0,46 *** -0,18 0,02 -0,03 0,09 ***
D1a 1,14 7,55 0,30 1,36 *** -0,10 0,45 *** -0,18
D1b 0,27 6,07 0,36 0,94 *** 0,06 0,50 *** -0,17
D1c 0,29 5,04 0,07 0,91 ** -0,04 0,41 *** -0,13
D10a 0,69 0,85 0,30 *** 0,03 0,01 0,05 *** 0,05 **
D10b 0,75 1,13 0,44 *** -0,04 0,10 -0,01 0,08 *
D10c 1,03 2,35 0,72 *** -0,60 0,00 -0,13 0,13
Spread 1-10 -0,22 6,43 -0,92 *** 1,23 *** -0,04 0,51 *** -0,29 **
Spread 1-2 -0,19 3,05 -0,31 0,35 *** -0,04 0,21 *** -0,21 ***
Spread 9-10 -0,10 1,00 -0,52 *** 0,19 *** 0,00 0,06 *** -0,07 **
Spread 1a-10c 0,12 8,82 -1,21 1,94 *** -0,10 0,59 *** -0,32
Panel A: Multi-factor estimation - Global Funds classified on their beta (1/1997-12/2002)
Alpha S&P MSCI w ex US SMB HML
246
R²
D1 0,11 ** -0,18 0,11 *** 0,04 0,02 -0,05 0,92
D2 0,07 ** -0,14 0,11 *** 0,07 0,05 * -0,28 0,94
D3 0,07 *** -0,18 0,08 ** 0,06 0,02 -0,25 0,91
D4 0,09 *** -0,14 0,09 *** 0,07 0,03 -0,19 0,87
D5 0,07 ** -0,12 0,08 *** 0,11 * 0,02 -0,18 0,78
D6 0,07 *** -0,12 0,09 *** 0,14 *** 0,03 -0,08 0,80
D7 0,05 *** -0,13 0,04 ** 0,10 *** 0,02 -0,13 0,74
D8 0,03 *** -0,08 0,06 *** 0,08 *** 0,01 -0,04 0,72
D9 0,02 ** -0,07 0,05 *** 0,11 *** 0,00 0,02 0,59
D10 0,01 -0,05 0,04 ** 0,09 * 0,01 -0,12 0,68
D1a 0,30 *** -0,36 0,13 0,04 -0,04 -0,28 0,84
D1b 0,11 *** -0,29 0,10 ** 0,05 0,04 -0,24 0,92
D1c 0,09 *** -0,05 0,11 *** 0,08 0,02 0,05 0,95
D10a 0,03 ** -0,08 0,02 * 0,06 0,01 -0,06 0,36
D10b 0,04 * -0,12 0,04 ** 0,09 0,00 -0,26 0,25
D10c -0,05 -0,02 0,03 0,13 * 0,00 -0,03 0,82
Spread 1-10 0,11 ** -0,12 0,08 * -0,04 0,01 0,01 0,92
Spread 1-2 0,05 -0,02 0,01 -0,02 -0,03 0,21 0,75
Spread 9-10 0,02 -0,03 0,01 0,02 -0,01 0,07 0,78
Spread 1a-10c 0,35 *** -0,32 0,11 -0,08 -0,04 -0,28 0,87
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. Each year, every fund is classified into a decile on the basis of its beta (relative to the S&P 500 equity index) over the past three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
Panel A (continued): Multi-factor estimation - Global Funds classified on their beta (1/1997-12/2002)
PR1YR WGBI EMBI HY GSCI DOLLAR
247
Table 36: Persistence in Performance Analysis Based on the
Skewness and Kurtosis (1/1997-12/2002)
Mean Std dev. Skewness Kurtosis
D1 0,79 1,98 -2,32 12,24 0,39 ** 0,16 *** 0,06 * 0,05 **
D2 0,75 2,26 -1,32 5,71 0,27 ** 0,31 *** 0,03 0,04 *
D3 0,96 2,65 -0,26 1,34 0,5 *** 0,37 *** -0,01 0,14 ***
D4 0,82 2,66 -0,54 2,51 0,28 0,41 *** -0,02 0,13 ***
D5 0,83 2,85 -0,03 2,36 0,38 ** 0,32 *** 0,09 0,15 ***
D6 0,94 2,9 0,24 1,59 0,39 * 0,38 *** 0,02 0,18 ***
D7 0,76 2,88 0,29 2,1 0,19 0,37 *** 0,03 0,22 ***
D8 0,76 2,65 0,35 1,02 0,25 0,32 *** 0,03 0,18 ***
D9 0,83 2,28 0,42 3,32 0,26 * 0,25 *** 0,03 0,19 ***
D10 0,92 2,47 0,89 3,31 0,33 ** 0,28 *** 0,04 0,21 ***
Panel A: Multi-factor estimation - Global Funds classified on their skewness (1/1997-12/2002)
Alpha S&P MSCI w ex US SMB
248
R²
D1 0,05 0,01 -0,22 ** 0,07 *** 0,16 ** 0,06 ** -0,36 ** 0,68
D2 0,06 *** 0,04 -0,09 0,08 *** 0,15 *** 0,01 -0,23 *** 0,83
D3 0,01 0,02 -0,04 0,06 *** 0,11 * 0,01 -0,12 0,85
D4 0,03 0,05 ** -0,05 0,08 *** 0,09 0,01 -0,2 * 0,86
D5 0 0,06 * -0,16 *** 0,08 *** 0,11 * 0,03 -0,2 0,86
D6 0 0,09 *** -0,11 0,08 *** 0,06 0 -0,17 0,85
D7 0,03 0,09 *** -0,09 0,07 *** 0,02 0,03 -0,09 0,87
D8 -0,01 0,07 *** -0,05 0,1 *** 0,07 0,03 0,04 0,83
D9 0,05 0,09 *** -0,17 ** 0,05 *** 0,08 0,01 -0,1 0,85
D10 0,02 0,12 *** -0,16 ** 0,08 *** 0 0,02 0,04 0,87
Panel A (continued): Multi-factor estimation - Global Funds classified on their skewness (1/1997-12/2002)
HML PR1YR WGBI EMBI HY GSCI DOLLAR
249
Mean Std dev. Skewness Kurtosis
D1 0,96 2,78 0,16 1,41 0,44 *** 0,36 *** 0,03 0,2 ***
D2 0,77 2,76 0,25 1,84 0,24 0,37 *** 0,01 0,15 ***
D3 0,92 2,73 0,3 2,55 0,43 ** 0,33 *** 0,08 0,14 ***
D4 0,85 2,68 0,06 0,36 0,37 ** 0,36 *** 0,04 0,18 ***
D5 0,82 2,8 -0,2 1,86 0,3 * 0,32 *** 0,05 0,22 **
D6 0,75 2,62 -0,72 3,42 0,18 0,39 *** -0,05 0,16 ***
D7 0,87 2,47 0,39 2,1 0,37 ** 0,26 *** 0,06 0,15 ***
D8 0,77 2,26 -0,86 3,9 0,21 0,34 *** -0,01 0,11 ***
D9 0,88 2,14 -0,82 4,03 0,37 *** 0,27 *** 0,04 0,11 ***
D10 0,75 1,93 -0,89 4,21 0,27 * 0,19 *** 0,04 0,1 ***
MSCI w ex SMB
Panel B: Multi-factor estimation - Global Funds classified on their kurtosis (1/1997-12/2002)
Alpha S&P
250
R²
D1 0 0,07 *** -0,04 0,06 *** 0,04 0,03 -0,02 0,86
D2 0 0,07 ** -0,09 0,09 *** 0,07 0,01 -0,19 0,84
D3 0,01 0,07 ** -0,12 * 0,08 *** 0,06 0,02 -0,09 0,84
D4 0,04 0,03 -0,06 0,06 *** 0,07 0,01 -0,02 0,88
D5 0,02 0,07 *** -0,13 0,07 *** 0,07 0,02 -0,18 0,88
D6 0,03 0,07 *** -0,08 0,09 *** 0,1 0,02 -0,24 * 0,86
D7 0 0,09 *** -0,18 *** 0,07 *** 0,08 0,02 -0,14 0,86
D8 0,05 ** 0,07 *** -0,07 0,09 *** 0,11 ** 0,02 -0,18 0,86
D9 0,06 *** 0,06 *** -0,13 * 0,06 *** 0,1 * 0,04 * -0,11 0,83
D10 0,03 * 0,06 *** -0,2 *** 0,09 *** 0,13 *** 0,03 -0,22 * 0,8
HY GSCI DOLLARHML PR1YR WGBI EMBI
Panel B (continued): Multi-factor estimation - Global Funds classified on their kurtosis (1/1997-12/2002)
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its skewness (Panel A) and kurtosis (Panel B) over the previous three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
251
5. An Adapted Sharpe Ratio
As a final and combined risk measure, we use the new risk measure developed
by Capocci et al. (2007)61. This measure xR is defined as:
xxxx KCCSVR 2
241
61
21
+−= (11)
Where 0WIcC ≡
is the product of the (intrinsic) risk perception coefficient, c,
and the (wealth-related) proportion of risky investment to initial wealth 0/WI .
The risk measure reported in (3) is a measure that integrates not only the
variance as a measure of risk but also skewness and kurtosis. As stated previously
investors do not like volatility, negative skewness and positive kurtosis. In other
words, this risk measure accounts for volatility, asymmetry and the fat tails. The level
of C depends on the appetite for risk of the investor62. Capocci et al. (2007) consider
three representative levels. We focus on average investors but results are in line for
dynamic and protective investors.
61 For more details, please see Part 3 of the Thesis.
62 Capocci et al. (2006) estimate C as 10 for a dynamic investor that does not put much weight on
the extreme risks, 35 for an average investor and 60 for a very protective investor who mostly fears
the tail event of a distribution.
252
This risk measure can also be used as an adapted Sharpe ratio that takes into
account the other aspects of risk that are not taken into account by the standard
deviation. Such an adapted Sharpe score would be defined as mean return divided by
the new risk measure: xR as defined in (11)63.
Results are reported in Table 37 (the adapted Sharpe Score are multiplied by
100 to be comparable). The five first columns report the mean return, standard
deviation, skewness, kurtosis and adapted Sharpe for each decile and each spread.
Fund with the highest Sharpe score have been classified in the bottom deciles while
those with the lowest one in the top deciles. There is no clear trend in the adapted
Sharpe reported. More interestingly, the alpha of the deciles that include the funds
with the lower adapted Sharpe over the ranking period tend to significantly and
consistently outperform over time. The first columns indicates that these deciles have
had a limited volatility, depending on the decile considered negative (decile D1) or
positive skewness (decile D2 and D3) and positive kurtosis. The factor exposure of
these deciles indicate that the funds included in deciles D1 to D3 distinguish
themselves from the other funds (at least for decile D2 and D3) by having been
relatively lowly exposed to the equity market, with no momentum or contrarian bets,
that they have not been exposed to emerging market bond and that more globally, the
R² reported for them are lower than for the other deciles. The spreads help us to
understand why decile D1 is so different from decile D2 and D3.
These results indicate that when higher moments are considered results are
mitigated. There are still around one third of the funds in our database that
consistently outperform over time but it is not easy to extract them.
63 An adapted version of the Sharpe ratio would be defined as the excess mean return divided by
the adapted risk measure.
253
Spread 1-2 and spread 9-10 are significantly negative. A negative spread 1-2
indicates that there is a significant difference between the least attractive funds in
terms of adapted Sharpe ratio. The worst ones (decile D1) are much less attractive
than the next to worst one (decile D2). On the other side, the next to top one (decile
D9) also significantly underperform the top one (decile D10). Such a result is
astonishing because the extremes (decile D1 and D10) outperform the neighbour at
the two end of Table 37.
6. Other Measures – Conclusion
Table 38 summarises the persistence analysis. Panel A reports the alpha
column and Panel B the U.S. equity exposure. Panel A interestingly indicates that
classifying hedge funds on the basis of their past returns and investing in the previous
year’s best performing funds does not allow the investor to significantly and
consistently outperform classical bond and equity indices. However, a deeper analysis
indicates that lower volatility funds (classified in the middle deciles) do significantly
and consistently outperform the indices considered. This result is directly confirmed by
the Sharpe score, the pure volatility analysis, the alpha and the beta classifications.
Moreover, the skewness and kurtosis analysis showed that when funds cannot be
differentiated by their volatility, pure alpha creators cannot be identified. These results
provide a simple way to create pure alpha using hedge funds. Volatility and returns
should be considered together to easily identify funds that should outperform classical
markets in the future. One can significantly and consistently outperform stock and
bond markets by buying hedge funds that offer the most appealing risk-return
characteristics over a three-year period and by rebalancing the portfolio every year.
254
Table 37: Persistence in Performance Analysis Based an
adapted Sharpe score (1/1997-12/2002)
Mean Std dev. Skew. Kurtosis Adapted Sharpe
D1 1,08 2,40 -0,40 3,80 0,50
D2 1,04 2,40 0,40 1,20 1,70
D3 0,81 1,80 0,10 2,10 0,80
D4 0,65 1,70 -0,60 2,30 0,50
D5 0,59 2,00 -0,70 2,50 0,40
D6 0,73 2,50 -0,20 1,10 1,20
D7 0,85 3,00 -0,10 2,10 0,80
D8 0,85 3,20 -0,10 2,40 0,70
D9 0,71 3,30 -0,10 2,30 0,60
D10 1,04 3,10 0,40 2,00 1,00
D1a 1,05 2,60 0,50 1,60 1,30
D1b 1,14 2,70 -1,40 9,50 0,20
D1c 1,10 2,10 -0,20 1,90 1,10
D10a 1,12 3,10 0,50 1,40 1,50
D10b 0,97 3,50 0,00 1,80 0,01
D10c 1,02 2,90 0,90 3,80 0,01
Spread 1-10 0,05 1,10 -0,50 2,00 0,00
Spread 1-2 0,05 1,60 0,90 4,10 0,00
Spread 9-10 -0,32 0,70 -0,50 0,10 -3,80
Spread 1a-10c 0,03 1,10 0,10 1,70 0,00
255
R²
D1 -0,06 0,06 *** 0,10 * 0,02 -0,18 0,76
D2 -0,15 0,06 0,08 0,01 -0,09 0,52
D3 -0,23 *** 0,04 0,10 *** 0,02 -0,26 ** 0,65
D4 -0,18 *** 0,09 *** 0,13 *** 0,02 -0,16 0,76
D5 -0,07 0,07 *** 0,09 0,02 -0,13 0,82
D6 -0,08 0,10 *** 0,08 0,04 -0,04 0,82
D7 -0,10 0,08 *** 0,09 0,02 -0,04 0,91
D8 -0,11 0,08 *** 0,09 0,03 -0,09 0,88
D9 -0,09 0,08 *** 0,05 0,02 -0,22 0,87
D10 -0,03 0,08 *** 0,04 0,03 -0,13 0,86
D1a 0,00 0,06 ** 0,09 0,01 -0,07 0,78
D1b -0,12 0,08 *** 0,09 0,03 -0,35 * 0,63
D1c -0,06 0,04 ** 0,14 *** 0,02 -0,14 0,76
D10a -0,08 0,07 * 0,04 0,01 -0,17 0,84
D10b -0,02 0,10 *** 0,08 0,03 -0,17 0,85
D10c -0,01 0,07 ** 0,00 0,03 -0,06 0,80
Spread 1-10 -0,03 -0,01 0,06 -0,01 -0,09 0,61
Spread 1-2 0,08 0,01 0,02 0,01 -0,13 0,34
Spread 9-10 -0,06 0,01 0,02 -0,01 -0,12 0,07
Spread 1a-10c 0,02 -0,01 0,09 -0,03 -0,05 0,29
DOLLAR
This Table presents the results of the persistence in performance estimation of the combined Model for the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its adapted Sharpe score (Panel A) over the previous three years. S&P stands for the market factor, MSWXUSt = return of the MSCI World Index excluding US, SMBt = the factor-mimicking portfolio for size (‘small minus big’), HMLt = the factor-mimicking portfolio for book-to-market equity (‘high minus low’), PR1YRt = the factor-mimicking portfolio for the momentum effect, EMBIt = return of the JP Morgan Emerging Market Bond Index; SWGBIt = return of the Salomon World Government Bond Index; HYt = return of the Lehman High Yield Credit Bond Index, GSCIt = return of the Goldman Sachs Commodity Index, DOLLAR = return of the Federal Reserve Bank Trade Weighted Dollar Index. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
Panel B (continued): Multi-factor estimation - Global Funds classified on their beta (1/1997-12/2002)
WGBI EMBI HY GSCI
256
Table 38: Summary of Alpha Creation and Equity Exposure
D1 0,57 * 0,6 * 0,32 *** 0,19
D2 0,41 * 0,47 0,34 *** 0,43
D3 0,43 *** 0,15 0,33 *** 0,28
D4 0,35 *** 0,27 0,41 *** 0,5 **
D5 0,37 *** 0,25 0,41 *** 0,44 **
D6 0,38 *** 0,16 0,27 0,51 ***
D7 0,36 *** 0,23 * 0,29 * 0,36 ***
D8 0,29 * 0,25 ** 0,33 * 0,26 ***
D9 0,25 0,37 *** 0,22 0,17
D10 0,4 0,49 *** 0,19 -0,05
Kendall Tau -0,56 -0,07 -0,43 -0,35
Panel A: Alpha creation
Returns Sharpe Score Std dev. Alpha
257
D1 0,3 0,39 ** 0,44 *** 0,45 ***
D2 0,09 0,27 ** 0,24 0,7 **
D3 0,24 0,5 *** 0,43 ** 0,53 ***
D4 0,18 0,28 0,37 ** 0,16
D5 0,39 ** 0,38 ** 0,3 * 0,01
D6 0,31 * 0,39 * 0,18 0,08
D7 0,36 *** 0,19 0,37 ** 0,09
D8 0,36 *** 0,25 0,21 0,13
D9 0,39 *** 0,26 * 0,37 *** -0,03
D10 0,46 *** 0,33 ** 0,27 * 0,25
Kendall Tau 0,54 -0,31 -0,31 -0,47
Adapted Sharpe
Panel A (continued): Alpha creation
KurtosisSkewnessBeta
258
D1 0,17 * 0,03 0,01 0,66 ***
D2 0,08 0,33 *** 0,07 *** 0,46 ***
D3 0,13 *** 0,51 *** 0,12 *** 0,36 ***
D4 0,18 *** 0,48 *** 0,2 *** 0,29 ***
D5 0,23 *** 0,41 *** 0,28 *** 0,23 ***
D6 0,26 *** 0,44 *** 0,36 *** 0,21 ***
D7 0,33 *** 0,39 ** 0,45 *** 0,25 ***
D8 0,48 *** 0,3 *** 0,46 *** 0,24 ***
D9 0,57 *** 0,16 *** 0,59 *** 0,3 ***
D10 0,56 *** 0,08 *** 0,77 *** 0,34 ***
Kendall Tau 0,78 -0,39 0,82 -0,39
Panel B: US equity exposure
Returns Sharpe Score Std dev. Alpha
259
Beta Skewness Kurtosis Adapted Sharpe
D1 1,06 *** 0,16 *** 0,36 *** 0,33 ***
D2 0,71 ** 0,31 *** 0,37 *** 0,19 ***
D3 0,49 *** 0,37 *** 0,33 *** 0,11 ***
D4 0,42 *** 0,41 *** 0,36 *** 0,17 ***
D5 0,32 *** 0,32 *** 0,32 *** 0,27 ***
D6 0,21 *** 0,38 *** 0,39 *** 0,31 ***
D7 0,11 *** 0,37 *** 0,26 *** 0,39 ***
D8 0,08 *** 0,32 *** 0,34 *** 0,4 ***
D9 0,02 0,25 *** 0,27 *** 0,46 ***
D10 -0,18 0,28 *** 0,19 *** 0,43 ***
Kendall Tau -1 -0,11 -0,52 0,66
Panel B (continued): US equity exposure
This Table summarises the persistence in performance analysis. Panel A reports the alpha, Panel B reports the equity exposure. These results are based on the January 1994-December 2002 period. We report the OLS estimators for equally weighted portfolios per investment strategy, sub-strategy and for all funds. Each year, every fund is classified into a decile on the basis of its data over the past three years. T-statistics are heteroskedasticity consistent. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
260
In order to quantitatively determine if there is a correlation between the alphas
produced and/or the market exposures, that is to determine if some measures are
redundant, we report the Kendall Tau correlation coefficients in Table 39. Kendall’s
coefficient evaluates the degree of similarity between two sets of ranks given to a same
set of objects. Kendall Tau is used to measure the degree of correspondence between
two rankings and assessing the significance of this correspondence. In other words, it
measures the strength of association of the cross tabulations. This coefficient depends
upon the number of inversions of pairs of objects which would be needed to transform
one rank order into the other64. We use this tool to determine if there is redundancy in
the alpha and in the equity exposure produced by different ways of ranking funds in the
persistence analysis.
Table 39 reports the results. Panel A contains the Kendall coefficients for the
alphas Panel B contains the same factors obtained for the equity market exposure. Panel
A indicates that the only significant correlations exists between the alphas produced by
the standard deviation and alpha series (the coefficient is at 0.52 significantly positive)
and between returns and the adapted Sharpe (0.51 significantly positive). These results
indicate that the corresponding series evolves linearly even if a closer look at the
significance level indicates that the corresponding significant alphas do not correspond to
the same deciles. It seemed to us at first sight that the ranking based on standard
deviation and the beta were simply opposite but the Kendall Tau coefficients do not
confirm our believes. More globally, it is interesting to note that the Sharpe score, the
beta, skewness and kurtosis have not been correlated confirming that these ways of
ranking are completely independent from any other.
64 For more information please see Kendall (1938, 1948) or Abdi (2007).
261
Table 39: Kendall Tau Estimation
[1] Returns 1 *** 0,04 -0,02 -0,02 -0,25 0,49 * 0,14 0,51 **
[2] Sharpe Score 1 *** -0,09 -0,36 0,14 -0,02 0,12 0,22
[3] Std dev. 1 *** 0,52 ** -0,49 * 0,09 0,09 0,25
[4] Alpha 1 *** -0,39 0,13 -0,23 -0,07
[5] Beta 1 *** -0,14 -0,09 -0,52
[6] Skewness 1 *** 0,16 0,27
[7] Kurtosis 1 *** 0,14
[8] Adapted Sharpe 1 ***
[1] Returns 1 *** -0,38 0,87 *** -0,29 -0,87 *** -0,20 -0,45 * 0,78 ***
[2] Sharpe Score 1 *** -0,33 -0,33 0,33 0,75 *** 0,22 -0,60 **
[3] Std dev. 1 *** -0,33 -1,00 *** -0,07 -0,49 * 0,64 ***
[4] Alpha 1 *** 0,33 -0,39 0,00 -0,07
[5] Beta 1 *** 0,07 0,49 * -0,64 ***
[6] Skewness 1 *** 0,18 -0,43
[7] Kurtosis 1 *** -0,36
[8] Adapted Sharpe 1 ***
[1] [2]
[6] [7] [8]
[3] [4] [5] [6]
This Table reports that Kendall Tau between the alphas obtained usingthe various ways o ranking funds into deciles (returns, Sharpe score, standard devition, alpa, beta, skewness, kurtosis and adapted Sharpe). *** Significant at the 1% level, ** Significa
Panel A: Kendall Tau between the Alphas
Panel B: Kendall Tau between the US equity market betas
[7] [8]
[1] [2] [3] [4] [5]
262
As expected, panel B shows a different pattern. Independently of the basis of the
ranking most beta exposures are significantly correlated between each other (returns and
standard deviation, returns and beta, return and adapted Sharpe, Sharpe score and
skewness, Sharpe score and adapted Sharpe, standard deviation and beta, standard
deviation and adapted Sharpe and beta and adapted Sharpe).
This result can be explained by the fact that the beta exposures evolve linearly
(up-down, down-up, up-down-up or down-up-down) in several cases (Sharpe score,
alpha and skewness). In two cases they even evolve perfectly linearly (standard
deviation and beta with a Kendall Tau of 1).
It is interesting to note that the adapted Sharpe score is highly correlated with its
adapted version. This result suggest even if the Sharpe ratio does not count for skewness
and kurtosis, most hedge fund managers (at least when aggregated in deciles) offer the
same skewness and kurtosis characteristics. In this case, the Sharpe ratio is a good
approximation for one of its extended version.
The alpha and the kurtosis are the only series that are correlated with no other,
being the only to differentiate completely from all the others in terms of evolution of the
market exposure.
263
V Further Analysis
Our results may be due to specific aspects of our methodology, to the time period
covered or to the market conditions. To handle these issues, we perform several further
analyses that should confirm the stability of our findings. We perform two additional
checks. Firstly, we perform the same analysis but and divide the analysis period into sub-
periods in order to determine if the period covered or the market conditions can explain
at least partly our results. Secondly, we rank the funds based on past statistics each July
instead of each January.
5.1 Sub-Period Analysis
To determine if the results obtained are due to the analysis period, we divide this
period in two ways. Firstly, we will take March 2000 as the turning point between bull
and bear market conditions.65 Secondly, we will define bull market as positive months for
the S&P 500 and bear market as negative months for the S&P 500.66
65 We perform the same analysis using September 2000 (the top of the S&P 500) instead of April 1st
as the turning point and the results obtained are very similar.
66 We do not report the results for the sake of brevity, but all the tables are available upon request.
264
1. March 2000 as a Turning Point
March 2000 coincides with the top of the NASDAQ composite index. We perform
the same analysis as previously twice using on one side data before this date, on the
other side, data after this date. There are 39 months before the end of March 2000
(starting from January 1997) and 31 months after this date (starting from April 2000).
The results are clear: before 2000 almost half of the hedge funds significantly outperform
and create pure alpha. These funds have had a limited exposure to the equity markets
and a low volatility. After 2000, only 20% to 30% of the funds – with the same
characteristics – do outperform. These results confirm the results obtained by Capocci et
al. (2005) who found that hedge funds considered as an industry have not been able to
outperform traditional markets during the market turmoil between 2000 and 2002 even if
20% to 30% of the funds do.
265
2. Up and Down Months of the S&P 500
Another way of separating bull and bear markets is to take the positive months of
the S&P 500 as bull market conditions and negative months bear market conditions. Over
the period covered, 39 months have been positive for the S&P500 while 33 months have
headed south. Our results indicate that no single decile significantly and consistently
outperforms the classical markets during bull market conditions. Top performers even
underperform (but not significantly) during market rally. These results confirm that
hedge funds face difficulties beating classical indices during bull markets. An investor
investing in the previous year’s best or worst performing funds, in funds offering the best
risk-return trade-off, in funds offering the best alpha, the one that looks for positive
skewness or investors who avoid fat tails would not have been able to create significant
alpha in bull market conditions. During bear market conditions there is consistent alpha
creation for around one third of the deciles. These are another time the low volatile decile
confirming our previous results.
Interestingly, the standard deviation and the beta results suggest however, that
there are still possibilities to create pure alpha. Low volatility funds unexposed to the
equity markets have been able to create significant and consistent alpha over bull market
periods. These results confirm that integrating volatility in the way of classifying funds
helps investors in creating consistent and significant value over time.
266
5.2 Date Impact
To remove any effect that could arise from the January Effect (stock prices tend to
go up between December and January; see for example, Bhardwaj and Brooks, 1992 and
Kramer, 1994), we perform the same analysis by classifying the funds in July instead of
January.67 The first important point to stress is that the same low volatility middle deciles
create alpha. The differences with previous results are that deciles D8 and D9 offer
significantly positive alpha using the January classification date, whereas these alphas
are only marginally significant using the June date. Inversely, decile D10 alpha is
significantly positive using the June classification, but only marginally so using the
January classification. These results should be due to the slight difference in the analysis
period since January to June 1994 is omitted when classifying funds in June.
Factor exposure analysis indicates that classifying funds in January or in June
leads to very close results. Alpha creators are still mildly volatile, with a limited exposure
to the market, a small cap bias and value oriented. Moreover, there is a long exposure to
emerging market bonds and to the high yield market. The best measure remains the
Sharpe score, the standard deviation and the beta. The exposures to the majority of
factors do remain the same using these three best performing measures. There are some
marginal differences in exposures (from slightly exposed to significantly exposed and
inversely) but nothing major. The r-squared are high, ranging from 0.6 to 0.9.
Altogether, this section confirms that classifying funds in July rather than in January does
not change our results significantly.
67 The corresponding tables are available on request.
267
VI Frictions in the Real World
Hedge funds can offer persistence over time. This is a very attractive conclusion to
investors but, and there is naturally a but, it is not easy for investors to profit from this
opportunity even in applying the simple strategy of buying the funds that offered the
greatest risk-return trade-off or the funds with low betas. We call this issue “frictions the
real world”.
Why can investors not easily profit from our results? The first element to this
conclusion is liquidity. Hedge funds are not liquid investments even if they tend to
become more liquid (at least for equity listed related strategies). In the best case, hedge
funds offer monthly liquidity with a 30-day notice period meaning that it takes minimum
one month to get out of a fund. In this best case, if investors decide to close a position
based on ranking early in the year, it will take them at least one month before being able
to sell and maybe 2 or 3 weeks to get the cash, meaning that they cannot be invested
before the end of March. In this particular case, they get an estimation of performance at
the end of the by the middle of January, sell the position before the month end for the
end of February and get the case in March to be able to invest for April 1st. In the worst
case, funds offer yearly liquidity with six months of notice. Another concern regarding the
liquidity of hedge funds is that, most hedge funds have lockup period in place meaning
that you cannot sell the position before the lockup period ends. This period lengths
usually minimum one year and goes up to three years. Finally, many funds have gate in
place. A gate is the maximum percentage of assets that can be sold by investors at any
single liquidity date. It ranges from 10% to 30% meaning that redemptions will be
blocked in case of large sell-off.
268
Funds that report to the database have not to be open to investment or to have
minimum assets. In fact, most funds that are closed to new investors continue to report
to databases in order to promote the name of the company (particularly in case of launch
of a new fund). This means that at least some funds that are considered in studies like
ours cannot be considered for investments. Usually, the funds that are closed to
investments reach their target size because of their good past performance.
Finally, there is always a data problem with hedge fund databases. When a fund
frauds, it stops reporting to databases but its past performance remains in the database
with false figures. This may lead to a wrong choice. Moreover, as it has been mentioned
in many papers in the past. Hedge fund managers report their performance on a
voluntary basis meaning that fraud is even facilitated compared to mutual fund
databases. Moreover, even if most funds report real returns net of all fees, some of them
use pro-forma estimation or manage account performances that cannot be replicated
easily.
All these issues confirm the need to take all our results with care. These are
always based on underlying hypothesis regarding liquidity, the quality of data, aso.
269
VII Conclusion
This study brings new insights in the research analyzing the persistence in hedge
fund returns. Previous studies have all been focused on past performance as the unique
tool to analyse alpha creation. We go one step further in decomposing hedge funds
returns and analysing the persistence in hedge fund returns. Our study uses other
measures such as the Sharpe score, standard deviation, alpha, beta, skewness and
kurtosis.
We find a consistent, systematic way of creating pure alpha using a simple
classification methodology based on basic statistics: risk-return trade-off measure (the
Sharpe score), volatility and to a lesser extent, the beta exposure appear to be the best
and most stable way of classifying hedge funds in order to detect persistency in the
returns. Funds offering the highest Sharpe score, funds with a limited volatility and/or
funds with a limited exposure to the equity market consistently and significantly
outperform equity and bond markets. These results hold not only for a full market cycle,
but also when separating bull and bear market conditions.
This analysis is of particular interest because it clearly proves that some funds
consistently and significantly outperform classical markets. The important element used
to detect these funds is the methodology by which they are classified.
The next steps would be to focus on specific strategies and determine what way of
classification is most suitable for each hedge fund strategy. Another idea would be to
develop and use a measure combining the returns, volatility, skewness and kurtosis to
classify funds. Such a measure for classifying hedge funds may be the final step in the
decomposition of hedge fund returns.
Part two: Analysis of Hedge Fund’s Market Exposure
272
The Neutrality of Market Neutral Funds
Daniel P.J. CAPOCCI
HEC-ULG Management School – University of Liège (Belgium)
This paper has been awarded Best Doctoral Paper at the Global Finance Conference in
Dublin (2005)
Capocci, Daniel, 2006, The Neutrality of Market Neutral Funds, forthcoming Global
Finance Journal
273
The Neutrality of Market Neutral Funds
Abstract
Using an original database of 634 market neutral hedge funds, this study formally
analyses the market neutrality of market neutral funds which are particular in the hedge
fund universe since the only objective of these funds is to provide positive returns
completely independent of the market conditions. We start by analysing this neutrality
using various market neutral indices before focusing on individual fund returns. Finally,
an analysis based on ex-post beta helps us explaining and confirming our previous
results. We perform this analysis over the global January 1993- December 2002 period
as well as on bull and bear market periods.
274
The Neutrality of market neutral funds
Introduction
Hedge funds considered as a whole have been studied since 1997. The precursors
of the academic world were Fung and Hsieh (1997) in their Review of Financial Studies
paper and Ackermann, McEnally and Ravenscraft (1999) in their Journal of Finance
article. Since then, the literature on the subject has expanded strongly and more and
more researchers are focusing on these investment products.
Hedge fund studies can be classified in four global categories. In the first one, we
report studies that are focused on hedge fund performance. This includes mainly studies
that compare the performance of hedge funds with equity and other indices (see for
example Ackermann, McEnally and Ravenscraft, 1999; Brown, Goetzmann and Ibbotson,
1999; Liang, 1999; Amin and Kat, 2001; Liang, 2001; Barès, Gibson and Gyger, 2002;
Liang, 2003; Agarwal and Naik, 2004; Capocci and Hübner, 2004). Results of such
studies are mitigated. The second field of hedge fund performance analysis compares the
performance of hedge funds with the one of mutual funds. In this context, Ackermann,
McEnally and Ravenscraft (1999) and Liang (1999) find that hedge funds constantly
obtain better performance than mutual funds, although lower and more volatile than the
reference market indices considered. Finally, performance analysis includes the study of
the persistence of hedge fund returns. Persistence is particularly important in the case of
hedge funds because, as suggested by Brown, Goetzmann and Ibbotson (1999) and
Liang (2000, 2001), the hedge fund industry has an attrition rate higher than mutual
funds. Brown, Goetzmann and Ibbotson (1999) are in this category. They prove that
offshore hedge funds have positive risk adjusted returns, but they input this result to
style effect and conclude that there is no proof of particular capacity of some fund
275
managers. Agarwal and Naik (2000) analyse the presence of persistence in hedge fund
returns using a one-year moving average period. They prove that there is proof of
persistence in hedge fund's performance, particularly for bad performing funds that
continue to underperform. Capocci and Hübner (2004) and Capocci, Corhay and Hübner
(2004) use the decile analysis developed in Carhart (1997) in order to determine if
persistence is present in hedge fund returns. The first concluded that some low-risk
managers have been able to consistently create alpha over the period studied (1/94-
6/00). The second focused on the period starting 1/94 but ending 12/02 and concluded
that over this global period that included a bear market, excess return creation was
present in most of the cases and there was a clear proof of persistency in hedge fund
returns.
It is important to stress that few authors have attempted to estimate the
behaviour of hedge funds in bear markets. The periods under review do not favour this
exercise, as periods of downward trends on the stock market were rare and
discontinuous before March 2000. For the period 1990-1998, Edwards and Caglayan
(2001) found that only three hedge fund strategies (Market Neutral, Event Driven and
Macro) provide protection to investors when stock markets head south. More recently,
Ennis and Sebastian (2003) contend that in general, hedge funds did not provide investor
protection after the market downturn of March 2000; rather, their superior performance
is mostly due to the good market timing of their managers.
On the other hand, the second global category includes authors that both try to
analyse and describe hedge funds investment style and to explain these features with
style models (see for example Fung and Hsieh, 1997; Brown, Goetzmann and Park,
1998; Brealy and Kaplanis, 2001, Brown and Goetzmann, 2001, Liang 2001; Liang
2003). In this context, Fung and Hsieh (1997) applied Sharpe's style analysis (see
Sharpe, 1992) to a large sample of hedge funds and CTA. They assumed that fund
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returns are linearly related to the returns on a number of factors and measured the
factor by 8 mimicking portfolios, found that the regressions have little explanatory power
and suggested that the low R²adj is due to the fund's trading strategy. A particular aspect
that has been taken into account more recenthly is the style drift in hedge fund returns.
This effect comes from the fact that hedge fund managers are opportunity driven and
therefore change style over time. Brown, Goetzmann and Park (1998) analyse hedge
fund returns during the 1997-98 Asian crisis. They use rolling regression to take the style
drift into account. The methodology consists in realiazing a set of linear regressions and
moving the estimation perdio of each of them by one observation. This simple technique
enables to observe style variation of a manager over time. This methodology has one
major drawback: the choice of a number of observations used for the estimation.
McGuire, Remolona and Tsatsaronis (2005) apply the same methodology. To handle with
this issuer, Posthuma and Van der Sluis (2005) propose to use a dynamic style model in
which beta can vary over time developed by Swinkels et Van der Sluis (2001). This
technique is adaptive in the sense that changes in th style exposures are piced up
automatically from the data. Unlike the ad hoc rolling regression approach, the time
variation in the exposures is explicitly modelled. No restrictions are imposed on the
betas. As stressed by Posthuma and Van der Sluis, this model is a state-space model and
can be estimated by using standard Kalman filter techniques68. No window size and ad
hoc chosen length need to be used. The Kalman filter procedure chooses the optimal
weigthing scheme directly from the data. The filter is an adaptive system based on the
measurement and updateing equations.
68 See Pollock (1999) for a detailed presentation of the Kalman filtering and space-state models.
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A third part of the literature finally focuses on the correlation of hedge funds with
other investment products and analyses the power of diversification of hedge funds. Fung
and Hsieh (1997) and Schneeweis and Spurgin (1998) proved that the insertion of hedge
funds in a portfolio could significantly improve its risk-return profile thanks to their weak
correlation with other financial securities. This low correlation is also emphasised by
Liang (1999), Agarwal and Naik (1999) and Capocci and Hübner (2004). Amin and Kat
(2001) found that stand-alone investment hedge funds do not offer a superior risk-return
profile, but that a great majority of funds classified as inefficient on a stand-alone basis
are able to produce an efficient payoff profile when mixed with the S&P 500. They obtain
the best results when 10-20% of the portfolio value is invested in hedge funds. Taking all
these results into account, hedge funds seem to be a good investment tool. Amenc and
Martellini (2002) proved on the basis of ex-post estimations that the inclusion of hedge
funds in a portfolio can lead to a significant decrease in the volatility of a portfolio
without leading to a significant change in the returns. This means that a stronger risk
control does not correspond with a decrease in return.
Finally other authors have analysed various other aspect of the hedge fund
industry. This category includes the ”other studies”. Schneeweis and Spurgin (1999),
Amenc, Curtis and Martellini (2002), Amenc, Martellini and Vaissié (2002) and Berényi
(2002) have studied the risks involved in hedge fund investing. Schneeweis and Spurgin
and Amenc, Martellini and Vaissié (2002) proved that hedge fund returns are not only
exposed to the market risk, but that other risks like volatility risk, default risk or liquidity
risk have to be considered. Liang (2000) analysed the presence of survivorship bias in
hedge fund data and Fung and Hsieh (2000) included other biases in their analysis.
Ackermann and Ravenscraft (1998) emphasised that the stronger legal limitations for
mutual funds than for hedge funds hinder their performance. Various authors study
hedge fund indices. There are many different hedge funds’ indices providers like EACM,
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HFR, CSFB/Tremont, Zurich Capital, Van Hedge, Hennessee Group, Hedgefund.net, LJH
Global Investment, Mar, Altvest and Magnum.69 Brooks and Kat (2001) Amenc and
Martellini (2002) studied this aspect in detail.
CTAs are a particular category in the hedge fund world. Some authors consider
them as part of the hedge fund world (Fung and Hsieh, 1997; Schneeweis and Spurgin,
2000), whereas others study them by separating them from hedge funds (Liang, 2003)
or study them on a stand-alone basis (Fung and Hsieh, 2000a; Gregoriou and Rouah,
2003; Capocci, 2004b). In this study, we only study market neutral funds and do not
include CTAs.
69 See Amenc and Martellini (2002) for a complete description of these hedge fund indices providers.
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I Interest of the study
This study aims at analysing the exposure to the equity market for market neutral
funds. At first sight, it can seem quite reductive to focus on a particular strategy since
the bulk of the literature considers hedge funds as a whole. Three independent reasons
justify this choice. Firstly, market neutral funds are particular since their objective is to
create alpha while completely hedging the exposure to the market. Other hedge fund
strategies are generally at least partially exposed to the market and results particular to
market neutral funds may not be true for other hedge fund strategies. Recently, in their
study based on a very large database of a total of 2894 individual funds, Capocci, Corhay
and Hübner (2004) concluded that equity market neutral funds present interesting
characteristics that need further investigation. This is exactly the objective of the present
study. Secondly, as suggested in several studies, market neutral funds represent a high
percentage of the hedge fund industry. According to our database described hereafter, as
much as 28.3% of the global MAR/CISDM individual funds in the database are market
neutral funds. Other authors also report high numbers of market neutral funds in their
database (see for example Capocci and Hübner, 2004 and Capocci, Corhay and Hübner,
2004). A high number of market neutral funds allow to analyse them in more detail and
to obtain global results. Thirdly, more and more authors however consider individual
strategies to better understand their particularities. Mitchell and Pulvino (2002) only
focused on risk arbitrage, Fung and Hsieh (2002a) on fixed income arbitrage funds;
Capocci (2004a) has analysed the inclusion of convertible arbitrage funds in a classical
portfolio. Gatev, Goetzmann and Rouwenhorst (1999) study relative value funds on a
stand-alone basis. Market neutral funds should also be studied on a stand-alone basis to
understand their particularities. Navone’s (2001) look at the diversification benefits from
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adding market neutral funds to a portfolio of mutual funds could significantly help the
risk return trade-off but he did not look at their neutrality.
Market neutral funds are defined as funds that take long and short positions in
various securities while trying to avoid exposure to the equity market. Sub-strategies are
arbitrage market neutral funds, which are managers that apply market neutral arbitrage
strategies. This category includes, among other things, convertible arbitrage funds that
buy undervalued convertibles, while hedging all intrinsic value and fixed income arbitrage
funds that exploit pricing anomalies in the global fixed income. Another sub-strategy is
long/short market neutral funds also named equity market neutral funds. These funds
simultaneously take long and short positions of the same size within the same market.
Managers take advantage of relative price discrepancies. Typically the strategy is based
on quantitative models for selecting specific stocks with equal dollar amounts comprising
the long and short sides of the portfolio. In theory, market risk is greatly reduced but it is
very difficult to make a profit on a large diversified portfolio, so stock picking is critical.
The final sub-strategy is mortgage-backed funds that invest in mortgage-backed
securities but also in futures and options. Usually they focus on AAA-rated mortgage
bonds.
Market neutrality implies dollar neutral, beta neutral or both. Dollar neutral
strategies have zero net investment, i.e. equal dollar amount in long and short positions.
Beta neutral strategies target a zero total portfolio beta (i.e. beta of the long positions
equals the beta on the short side. While dollar neutrality has the virtue of neutrality, beta
neutrality better defines a strategy uncorrelated with the market return. Many managers
of such strategies balance their long and shorts in the same sector or industry. By being
sector neutral, they avoid the risk of market movements affecting some sectors or
industries differently than others.
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The study is organised as followed. Section III describes that database. In section
IV we report the descriptive statistics and analyse the attrition rate present in our
database. In section V we present our methodology. We report the global results in
section VI and the results obtained for individual funds in section VII. We perform a sub-
period analysis in section VIII. Section IX concludes the study.
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II Database
Four main hedge fund databases are available for empirical studies, the Managed
Account Reports, Inc/Centre for International Securities Derivatives Markets, Hedge Fund
Research, Inc, TASS Management and the Barclays database. The first three ones are the
most used in academic studies. The Barclay database is currently under investigation by
various authors but it has not yet been used in published studies. The data provider
collects various information on the funds included. For a majority of funds, they record
other useful information such as company name, start and ending date, strategy
followed, assets under management, management and incentive fees, manager's name,
manager's address, etc. There is no consensus on the definition of the strategy followed
but there are similarities. MAR/CISDM defines 9 strategies with a total of 16 sub-
strategies. HFR defines 16 different strategies in 2 categories, 11 non-directional and 5
directional strategies, plus the Funds of Funds and the Sector categories. TASS defines
15 strategies. Finally, Barclays defines 20 individual strategies.
We use hedge fund data from MAR/CISDM, as in Fung and Hsieh (1997),
Schneeweis and Spurgin (1998), Amin and Kat (2001), and Capocci, Corhay and Hübner
(2004). The database gives monthly net-of-fee individual returns and other information
on individual funds and groups them in indices. The whole database consists of 634
individuals market neutral funds including 398 surviving funds (62.8%) and 236 (37.2%)
dissolved funds. We use 120 monthly returns between January 1993 and December
2002.
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III Descriptive statistics and attrition rates
Before analyzing the presence of bias in hedge fund data, we present the
descriptive statistics, the correlation analysis and the attrition rates in this section.
3.1 Descriptive statistics
In Panel A of Table 41 contains descriptive statistics of the funds, whether alive or
dead, in our database. We report the statistics for the whole market neutral database
and we divide this database in arbitrage funds, long/short funds, mortgage backed
securities funds and non-classified funds.70 These hedge fund data are contrasted with
the descriptive statistics of the S&P 500 that represent the equity market. Panel B of
Table 41 reports the same descriptive statistics when funds were classified in decile
based on the average performance of the funds over the whole period.
Panel A of Table 40 indicates that market neutral funds offered an average
monthly return of 1.08% over the period studied with a monthly standard deviation of
O.94%. Arbitrage funds offered almost the same return with the same volatility whereas
long/short funds offered 1.16% with a monthly volatility of 1.16%. Mortgage fund
returns are more volatile than the other market neutral funds. All average returns are
significantly positive. Median returns indicate the same pattern except that mortgage-
backed funds have an impressively high median return compared with the other funds
studied. This result can be explained but the low skewness and extremely large kurtosis
of mortgage-backed securities funds. Minimum monthly returns are relatively high with a
total of –2.54% for market neutral funds except for mortgage backed funds (-8.74%).
On the other side, the maximum is also relatively low for all strategies, particularly for
70 There are 3 funds with no sub-strategy. The data regarding these funds ended in January 2001.
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arbitrage funds (2.93%) and mortgage backed funds (2.84%). Mortgage backed
securities have largely negatively skewed returns’ distribution (skewness of –4.11) with
fat tails (kurtosis of 26.45). All other sub-strategies except long/short funds and the
strategy considered as a whole all have significantly negative skewness, which leads to
negatively skewed return distribution. All classifications also have significantly positive
kurtosis which leads to the presence of fat tails (a least to some extent). Long/short
funds have positively skewed return distribution.
The Sharpe score (it is defined as the ratio of average return over the standard
deviation) indicates that arbitrage funds offer a better trade-off than long/short funds,
which, in turn offer a better trade-off as mortgage-backed securities funds.
By comparison, the equity index has a low average monthly return of 0.69%,
which is in line with the long-term return of the equity market of around 8%. This return
is weakly and significantly positive with a relatively high volatility of 4.47%. The median
return is however as high as the median return of market neutral funds considered as a
whole and higher than all the sub-strategies except the mortgage-backed index. The
minimum and maximum for the index are more extreme than those obtained for the
hedge funds and the return distribution of the index is neither skewed, nor has fat tails.
This is in line with previous results indicating normality of returns for the stocks indices
(see for example Fung and Hsieh, 1999).
Panel B reports the same descriptive statistics when we classify all these funds in
decile on the basis of their average performance over the whole period studied. Decile 1
contains the worst performing funds over the period and decile 10 the best performing
ones. The dead fund column indicates that bad performing funds have more chance to be
dissolved. On the average, 52% of the funds in the worst 3 deciles are dissolved against
31% on the average for the top 3 deciles. Moreover 62% of the funds in decile 1 are
dissolved. Interestingly, fewer funds from deciles 5 to 9 have been dissolved compared
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to decile 10 and middle decile fund returns are more stable than worst and top
performing decile (see standard deviation). These results are in line with the one
obtained by Capocci and Hübner (2004) in their dissolution frequencies analysis but their
deciles were constructed on the basis of previous year’s performance. The minimum and
maximum columns indicate that very low minimum will lead to lower decile (decile 1
minimum is extremely low compared to other minimums), but that high maximum does
not necessarily lead to higher decile (decile 1 maximum is the second highest maximum
over the 10 deciles). Skewness and kurtosis results do no lead to particular remarks. We
can however note that some skewness are significantly positive (deciles 2, 7 and 9)
whereas others are significantly negative (deciles 1, 4, 5 and 6) and that all kurtosis that
are significant are positive. There is only one insignificant negative kurtosis.
3.2 Correlation analysis
As suggested in the introduction, the traditional hedge funds literature contends
that, thanks to the weak correlation between hedge funds and other securities, hedge
funds are likely to improve the risk-return trade-off when added to a traditional portfolio
(see Fung and Hsieh, 1997; Schneeweis and Spurgin, 1997; Liang, 1999; Amin and Kat,
2001). The first step of the analysis of the neutrality of equity market neutral funds is to
check the correlation of these funds with the equity index as approximate by the S&P 500
index. The correlation coefficients are reported in the Table 41.
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Table 40: Descriptive statistics and decile descriptive statistics
No of Fds % of the strategy
Living Funds Dead Funds S. D.
Market neutral funds 634 100% 398 236 1,08% *** 0,94%
- Arbitrage funds 281 44,30% 175 106 1,03% *** 0,92%
- Long/short funds 306 48,30% 197 109 1,16% *** 1,16%
- Mortgage backed funds 44 6,90% 26 18 1,06% *** 1,32%
- No sub-strategy 3 0,50% 0 3 0,73% *** 1,11%
Index NA NA NA NA 0,69% * 4,47%
Panel A: Strategy, sub-strategies and index descriptive statistics
Mean Return
287
No of Fds % of the strategy
Living Funds Dead Funds S. D.
Market neutral funds 634 100% 398 236 1,08% *** 0,94%
- Arbitrage funds 281 44,30% 175 106 1,03% *** 0,92%
- Long/short funds 306 48,30% 197 109 1,16% *** 1,16%
- Mortgage backed funds 44 6,90% 26 18 1,06% *** 1,32%
- No sub-strategy 3 0,50% 0 3 0,73% *** 1,11%
Index NA NA NA NA 0,69% * 4,47%
Panel A (continued): Strategy, sub-strategies and index descriptive statistics
Mean Return
288
No of Fds Living Funds Dead Funds S. D.
Decile 1 63 38% 62% -0,34% 3,53%
Decile 2 63 43% 57% 0,28% *** 1,21%
Decile 3 63 62% 38% 0,55% *** 0,59%
Decile 4 63 56% 44% 0,72% *** 0,95%
Decile 5 64 80% 20% 0,89% *** 0,84%
Decile 6 64 72% 28% 1,10% *** 1,04%
Decile 7 63 71% 29% 1,21% *** 1,28%
Decile 8 63 71% 29% 1,40% *** 1,10%
Decile 9 63 81% 19% 1,75% *** 1,43%
Decile 10 63 56% 44% 2,70% *** 2,41%
Panel B: Decile descriptive statistics (120 months)
Mean Return
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Median Min Max Sharpe score
Decile 1 -0,20% -17,50% 8,50% -1,28 *** 5,02 *** -0,1
Decile 2 0,30% -2,30% 4,40% 0,51 *** 0,78 *** 0,23
Decile 3 0,60% -1,00% 2,10% 0,01 -0,02 0,93
Decile 4 0,80% -2,40% 2,40% -1,11 *** 1,94 *** 0,76
Decile 5 1,00% -4,20% 2,70% -1,9 *** 10,31 *** 1,05
Decile 6 1,20% -2,70% 4,20% -0,27 *** 1,24 *** 1,07
Decile 7 1,20% -2,70% 5,90% 0,36 *** 2,05 *** 0,95
Decile 8 1,40% -2,50% 4,40% 0,01 1,02 *** 1,27
Decile 9 1,70% -2,40% 6,30% 0,3 ** 0,72 *** 1,23
Decile 10 2,50% -4,10% 9,20% 0,11 0,31 1,12
Panel B (continued): Decile descriptive statistics (120 months)
This Table shows the number of funds (No of Fds), percentage of the strategy (% of the strategy), the number of living funds, the number of dead funds, the mean return, the standard deviation (S.D.), the median, the minimum (min), the maximum (max), the skewness, the kurtosis and the Sharpe score for the individual hedge funds in our MAR/CISDM database for the whole period 01:1993-12:2002. No sub-strategy ended in 01:12001. Sharpe score is the ratio of return and standard deviation. Panel A focus on strategy, sub-strategy and index descriptive statistics, Panel B on decile descriptive statistics. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.
KurtosisSkewness
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Table 41: Correlation between market neutral strategies and
equity index
Market neutral funds
Arbitrage funds
Long/short funds
Mortgage backed funds
No sub-strategy Index
Market neutral funds 1
- Arbitrage funds 0,91 1
- Long/short funds 0,92 0,7 1
- Mortgage backed funds 0,49 0,45 0,3 1
- No sub-strategy 0,62 0,58 0,53 0,37 1
Index 0,54 0,46 0,54 0,19 0,3 1
This Table reports the correlation coefficients among market neutral sub-strategies and between market neutral funds strategies and the index. The database consists of 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. The period covered is 01:1993-12/2002 period.
Table 41 indicates that the correlation between the market neutral index and its main
components, arbitrage and long/short funds is higher than 90%. This result is logical since
these 2 sub-strategies represent a total of more than 90% of the funds in the database. The
correlation between the market neutral index and the mortgage funds is significantly lower
at 0.49. The correlation between the market neutral sub-strategies ranges from 0.37
(between mortgage-backed funds and no sub-strategy funds) to 0.7 (between arbitrage
funds and long/short funds). These figures are reasonably high and suggest that the sub-
classification has a sense since no sub-strategies are completely correlated. The correlation
between market neutral funds (considered as a whole or per sub-strategies) ranges from
0.19 (between no sub-strategy funds and the index) to 0.54 (between market neutral funds
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and the index). These figures are reasonable but relatively high for the index. These results
are in line with previous results obtained by Schneeweis and Spurgin, 1998; Liang, 1999;
Amin and Kat, 2001 and Capocci and Hübner, 2004).
Figure 9 reports the average, median, minimum and maximum individual correlation
between market neutral fund index and its sub-strategies and the equity index.71 We
describe Figure 9 using market neutral funds as an example. The bottom line of the block
represents the minimum individual correlation between market neutral funds and the equity
index, -0.29 in the first case. The upper part of the grey block ended at the average
correlation between market neutral funds and the index, 0.15 for market neutral funds. The
median is reported below the white part of the block at 0.3 for market neutral funds. Finally,
the top of the box is the maximum individual correlation between a single market neutral
fund and the equity index.
Figure 9 indicates that the individual correlation between individual hedge funds and
the equity index vary strongly for the strategy and the sub-strategies considered and that
the individual correlation between hedge funds and the index are much lower than the
correlation between hedge funds indices and the equity index. This result indicates that even
if individual market funds are not correlated with the equity index, it is important to consider
individual funds because index aggregation can increase the correlation and the exposure to
the equity market. This point is particularly important for the beta analysis. The sub-strategy
correlation analysis also reported in Figure 9 confirms this topic since the correlation
between the sub-indices and the equity market is lower than the correlation of the global
market neutral index that contains all these sub-strategies.
71 We removed 3 funds with few data to perform the correlation analysis at the individual fund level. We do
not report the result of the no sub-strategy index because it includes only 3 individual funds.
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Figure 9: Minimum, maximum, median and mean individual
correlations between market neutral funds and the equity
index
-60%
-40%
-20%
0%
20%
40%
60%
80%
Market NeutralFunds
Arbitrage Funds Long/short Funds Mortgage backedFunds
This figure reports the minimum, maximum, median and mean individual correlations
between market neutral funds and the equity index between January 1993 and December
2002.
3.3 Birth and attrition rates
Attrition rates of hedge funds are largely publicized in academic studies (see for
example Fung and Hsieh, 1997; Liang, 2000; Liang 2003). This rate can be defined as the
percentage of funds in the database that are dissolved each year. Table 42 reports the birth
rate and the attrition rate of the fund in our database for each year under review.
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Table 42: Birth and attrition rates
Year start New Dissolved Year end Birth rate Attrition rate
1993 63 27 1 89 42,90% 1,60%
1994 89 50 2 137 56,20% 2,20%
1995 137 44 18 163 32,10% 13,10%
1996 163 74 13 224 45,40% 8,00%
1997 224 80 19 285 35,70% 8,50%
1998 285 78 39 324 27,40% 13,70%
1999 324 58 36 346 17,90% 11,10%
2000 346 47 32 361 13,60% 9,20%
2001 361 69 34 396 19,10% 9,40%
2002 396 44 42 398 11,10% 10,60%
Total 571 236 Average 30,10% 8,70%
This Table reports the number of funds at year start, the number of new funds, the number dissolved funds, the birth rate and the attrition rate for the market neutral funds in our database. Birth rate is defined as the ratio between the number of new funds and the number of funds at year start. The attrition rate is defined as the ratio of dissolved funds to number of funds at year start. The database consists of 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. The period covered is 01:1993-12/2002.
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Table 42 indicates that birth rates are much higher than attrition rate but that this
rate diminished over time from more than 50% in 1994 to 11% in 2002. On the other side,
the attrition rate is very low for the first 2 years under investigation and is almost stable
between 1995 and 2002 ranging from 8% to 13.7%. The high level of dissolution in 1998
should probably be due to the Russian, the Asian crisis and the bailout of Long Term Capital
Management, LTCM. The average birth rate in around 30% and the average attrition rate is
8.7% indicating that each year, on average around 8.7% of the fund in the industry are
dissolved. Table 42 also indicates that the total number of funds has increased linearly over
the period. These results are in line with the results obtained by Liang (2000) for the TASS
database but lower than the 14% obtained by Brown, Goetzmann and Ibbotson (1999).
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IV Survivorship bias analysis
Survivorship bias is particularly important in the case of hedge funds (see Fung and
Hsieh, 1997; Fung and Hsieh, 2000; Ackermann, McEnally and Ravenscraft, 1999; Capocci
and Hübner, 2004). Usually this bias is studied on a global basis for full databases including
a variety of different strategies. In this study, since we focus on market neutral funds, we
will analyse the presence of survivorship bias for the funds in our database.
Survivorship bias can be defined in 2 ways: the performance difference between
surviving and dissolved funds (e.g. Ackermann et al., 1999) and the performance difference
between living and all funds (e.g. Fung and Hsieh, 2000). We report the bias using both
definitions.
Panel A of Table 43 indicates that the returns have been less interesting in recent
years compared to the past. The most difficult years for market neutral funds have been
1994 (bond market crisis), 1998 (Russian, Asian crisis and the LTCM bailout) and 2002 (3rd
year of bearish market). The average return for the funds that survived over the whole
period is 1.22%, higher than the whole funds in the database average return of 1.08% and
higher than the returns of funds that have been dissolved during the period studied with a
performance of 0.77%. Standard deviation is interesting because it indicates that in recent
years the volatility of the dissolved funds has increased dramatically compared to surviving
funds. This indicates that volatile funds have been more exposed to dissolution in 2001 and
2002.
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Panel B reports the difference of performance between living and dead funds (left
side) and living and all funds (right side). Table 43 indicates that the difference in
performance between living funds and dead funds has increased dramatically compared to
the difference between living funds and all funds in recent years to almost 1% in 2000 and
2002. The total bias is 5.4% using the first formula and 1.68% using the general one. The
latest figure is the generally used one in hedge fund studies and can be compared to past
results.
This latter value is much higher than the very low value obtained by Ackermann et al.
for the period 1988-1995. It is similar to the percentage of 1.5% from Fung and Hsieh
(1998), lower than the 0.30% monthly bias found by Fung and Hsieh (2000) and slightly
higher than the percentage of 1.2% found by Capocci and Hübner (2004) for the 1994-2000
period. It is however lower than the 3% bias found by Liang (2001), which is also the
industry consensus as stressed by Amin and Kat (2001).72
72 This consensus value is quite high when compared to the 0.8-1.5 bias reported by Malkiel (1995) and
Brown and Goetzmann (1995) for US mutual funds.
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Table 43: Survivorship bias
Year Return S.D. Return S. D. Return S. D.
1993 1,41% 0,43% 1,47% 0,47% 1,37% 0,47%
1994 0,25% 0,62% 0,45% 0,65% 0,10% 0,68%
1995 1,54% 0,55% 1,69% 0,58% 1,37% 0,75%
1996 1,56% 0,46% 1,88% 0,42% 1,16% 0,63%
1997 1,41% 0,92% 1,58% 0,94% 1,20% 1,02%
1998 0,58% 1,42% 0,64% 1,33% 0,48% 1,61%
1999 1,44% 0,80% 1,54% 0,78% 1,26% 0,91%
2000 1,41% 1,14% 1,64% 1,13% 0,70% 1,44%
2001 0,80% 0,74% 0,85% 0,65% 0,56% 1,39%
2002 0,36% 0,63% 0,43% 0,59% -0,55% 2,96%
Average 1,08% 0,77% 1,22% 0,76% 0,77% 1,19%
All Funds Surviving Funds Dissolved Funds
Panel A: Annual performance (all funds, surviving funds and dissolved funds)
298
Living - Dead Funds Living - All Funds
Year Return Return
1993 0,10% 0,06%
1994 0,35% 0,20%
1995 0,32% 0,15%
1996 0,73% 0,32%
1997 0,38% 0,17%
1998 0,16% 0,07%
1999 0,28% 0,09%
2000 0,94% 0,23%
2001 0,29% 0,05%
2002 0,97% 0,06%
Bias 93-02 0,45% 0,14% per Month
5,40% 1,68% per Year
Panel B: Survivorship bias
This Table reports the survivorship bias of our database. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. In Panel B survivorship bias is calculated as the performance difference between surviving funds and dissolved funds (left-hand side) and as the performance difference between surviving funds and all funds (right-hand side). All returns are net of fees. Numbers in the table are yearly percentage unless otherwise indicated.
299
V Methodology
The objective of this study is to determine if market neutral funds are exposed to the
equity market or if they are really market neutral. The methodology used in this study is
two-fold. The first part of this analysis has the objective to analyse the exposure of market
neutral funds to the equity market. We perform this analysis in three steps. First, we
analyse market neutral funds grouped per sub-strategy. Secondly, we classify them in decile
on the basis on the global performance over the period studied in order to determine which
funds were the most exposed to the market. Thirdly, we classify them using Carhart’s
(1997) methodology in order to determine if there is a pattern to detect portfolio’s
constructed on the basis of previous year’s performance. Each year, we classify funds on the
basis of their previous year performance and we create return series. Then, we estimate the
exposure to the market for all these deciles in order to determine if best or worst performing
funds are more or less exposed to the market.
In the second part of the analysis we perform the same analysis for individual funds
and by extracting a bull and a bear market period. For individual funds, we also perform an
ex-post beta analysis. This methodology uses the same results as previously but differently.
We classify the funds in decile on the basis of their ex-post betas and analyse their
descriptive statistics. This part of the analysis has the objective to determine if it is the same
funds that performed well in bear/bull market and in the whole period. Does the beta
exposure explain better or worst returns?
300
The model used is a single index model based on the classical CAPM developed by
Sharpe (1964) and Lintner (1965). Its equation to estimate is the following:
TtRR PtMtPPFtPt ,...,2,1 * =++= εβα (12)
Where RPt = return of fund P in month t; RMt = return of the equity market portfolio, in our
case the S&P 500 on month t; εPt = error term; αP and βP are the intercept and the slope of
the regression, respectively. The intercept of this equation, αp commonly called Jensen’s
alpha (1968) is usually interpreted as a measure of out- or under-performance relative to
the market proxy used. The beta is interpreted as a measure of the dependence of a fund’s
return to the index. It is a relative measure. We compute all estimations by using Newey-
West (1987) standard errors to adjust for any autocorrelation in the returns
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Table 44: Market exposure analysis
S. D. R²adj
Market neutral funds 1,08% *** 0,94% 1,00% *** 0,11 *** 0,29
- Arbitrage funds 1,03% *** 0,92% 0,97% *** 0,1 *** 0,21
- Long/short funds 1,16% *** 1,16% 1,05% *** 0,14 *** 0,29
- Mortgage backed funds 1,06% *** 1,32% 1,02% *** 0,06 * 0,03
- No sub-strategy 0,73% *** 1,11% 0,62% *** 0,08 *** 0,08
Panel A: Market exposure for market neutral funds
Average return Alpha Market
302
S. D. R²adj
Decile 1 -0,34% 3,53% -0,48% 0,21 *** 0,06
Decile 2 0,28% 1,21% 0,22% * 0,1 *** 0,12
Decile 3 0,55% *** 0,59% 0,51% *** 0,05 *** 0,12
Decile 4 0,72% *** 0,95% 0,64% *** 0,11 *** 0,29
Decile 5 0,89% *** 0,84% 0,85% *** 0,06 *** 0,08
Decile 6 1,10% *** 1,04% 1,01% *** 0,13 *** 0,31
Decile 7 1,21% *** 1,28% 1,15% *** 0,09 *** 0,08
Decile 8 1,40% *** 1,10% 1,32% *** 0,11 *** 0,19
Decile 9 1,75% *** 1,43% 1,66% *** 0,14 *** 0,19
Decile 10 2,70% *** 2,41% 2,56% *** 0,2 *** 0,13
The table reports the market exposure analysis. Panel A presents the average return, the standard deviation (S.D), the alpha, the market exposure (the beta) and the R²adj. Panel B presents the same information when funds are classified in deciles on the basis of their performance over the period studied. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level.. t-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
Alpha MarketAverage return
303
VI Strategy and decile analysis
This section reports the results of the exposure analysis obtained using strategy and
sub-strategy indices and on the basis of the decile classification. Panel A of Table 44 reports
the results for the market neutral strategy and various market neutral sub-strategies.
Panel A reports the average return and standard deviation of returns over the period
studied as well as the results of the regression analysis. A comparison between the average
return and the alpha indicates that they are relatively close to each other, which indicates
that only a small part of market neutral returns can be explained by the market. The R²adj
are relatively low, most market neutral indices indicating that the market cannot explain a
big proportion of the average return of the indices even if the 29% R²adj obtained for market
neutral funds is relatively high for this kind of model. The betas indicate however that all
indices except mortgage-backed securities funds are significantly exposed to the equity
market at the 1% significance level. On an absolute term however, the beta obtained is low
between 0.06 for mortgage backed securities and 0.14 for long/short funds.
Panel B reports the results obtained using the decile classification. These results are
based on decile constructed on the basis of the performance over the period studied. As
previously, top performing funds are reported in Decile 10 and worst performing funds are
reported in Decile 1. Panel B indicates the same pattern as Panel A, the difference between
the alpha and the average return is relatively low, the R²adj are relatively low, but all
market betas are significantly positive even if they are all low in absolute term. Top and
worst performing funds have however the highest market exposure.
304
Figure 10: Lagged 12-month decile description
0
50
100
150
200
250
300
350
400
450
1993
1994
1995
1996
1997
1998
1999
2000
2001
Avera
ge05101520253035404550
Funds per year Funds per decile
This figure reports the yearly lagged 12-month decile description. The left-hand axis reports
the number of funds per year. The right-hand axis reports the number of funds per decile.
The average is for the January 1994 to December 2002 period.
In a second step, we perform the same analysis on the basis of Carhart (1997)
methodology. The objective of this analysis is to determine if last year best or bad
performers are more exposed to the market. Each year, we classify the funds on the basis of
their previous year performance and we create return series. Then, we estimate the
exposure to the market for all these deciles in order to determine if best or worst performing
funds are more or less exposed to the market.
305
Before analysing the results of this analysis, we report the number of funds in each
decile in Figure 10. It reports the number of funds in the analysis each year (left axis) and
the number of funds per decile each year (right axis) as well as the average number of funds
per year over the whole period and the average number of funds per decile. Figure 10
indicates that the average number of funds per year is 264 with decile of 28 funds on
average. Over the whole period, decile 1 (worst performing funds) would have offered
0.72% per month against 1.26% for decile 10 (best performing funds) and 0.69% for the
index.
A comparison between the average return and the alpha obtained in Table 45
indicates that the market exposure cannot explain the performance of market neutral funds
since the alphas obtained before and after the regression are very close. Moreover, the R²adj
obtained is very low, which confirms the results. On the other hand however, the market
column indicates that 6 out of 10 deciles are significantly exposed to the market. These
deciles are spread but the 3 top performing deciles are all significantly exposed to the
market. The spreads reported on the bottom of Table 45 indicate that the spread between
decile 1 and decile 10 is significantly positive but that the spreads between decile 1 and
decile 2 and between decile 9 and decile 10 are not significantly different from zero.
These results suggest that the exposure of market neutral funds to the equity market
is not clear. Even if the 6 out of 10deciles's exposure are significantly positive, in absolute
term, the market factor does not explain a large part of the alpha created by market neutral
funds and the low R²ADJ obtained suggest that the exposure does not describe market
neutral fund returns well. In absolute term, the market factors are another time very low.
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Table 45: Lagged 12-month decile exposure
Portfolio S. D. R² adj
D1 0,72% *** 2,14% 0,70% *** 0,11 *** 0,06
D2 0,62% *** 1,32% 0,63% *** 0,07 * 0,05
D3 0,60% *** 0,83% 0,65% *** 0,04 ** 0,03
D4 0,48% *** 0,75% 0,49% *** 0,03 * 0,03
D5 0,61% *** 0,82% 0,61% *** 0,06 *** 0,11
D6 0,67% *** 0,95% 0,67% *** 0,03 0,01
D7 0,79% *** 1,22% 0,80% *** 0,06 * 0,03
D8 0,89% *** 1,09% 0,88% *** 0,08 *** 0,1
D9 1,11% *** 1,66% 1,04% *** 0,11 ** 0,08
D10 1,26% *** 2,38% 1,33% *** 0,11 ** 0,04
1-10 spread 0,54% ** 2,71% 0,63% *** 0 -0,01
1-2 spread -0,10% 1,69% -0,07% -0,04 0,01
9-10 spread 0,15% 2,03% 0,29% -0,01 -0,01
The table reports the market exposure using deciles constructed on the lagged-12 month performance (see Carhart 1997). It reports the average return, the standard deviation (S.D), the alpha, the market exposure (the beta) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level. t-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
Average return Alpha Market
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VII Individual fund analysis
In this section, we base our analysis on the individual fund return series in order to
determine if the results previously obtained using strategy and sub-strategy indices are still
valid. In the first sub-section, we analyse the market exposure. In the second one, we look
at the ex-post beta exposure.
7.1 Market exposure
As we suggested in the correlation analysis, it is important to check if the results
obtained on a strategy or sub-strategy basis are still valid on an individual fund basis. To
check this, we perform the same analysis using the returns of individual funds.73 Results are
reported in Table 46. Table 46 reports the average return, the return distribution which is
the percentage of average monthly returns that are significantly positive (+), significantly
negative (-) and not significant (0) on the one side, and the results of the regression of the
other. Like average return, individual alpha and beta are classified as significantly positive at
the 5% significance level, significantly negative or not significant.
73 We require all funds to have at least 24 months of data to perform this analysis. This lead us to remove
172 funds (74 arbitrage funds, 92 long/short funds, 5 mortgage backed funds and 1 no sub-strategy fund)
from the database and leave us with a total of 462 funds (207 arbitrage funds, 214 long/short funds, 39
mortgage backed securities funds and 2 no sub-strategy funds).
308
The left-hand side of Table 46 indicates that the vast majority of individual average
returns are significantly positive and that around 20% of them are not significantly different
from 0. Very few average returns are significantly negative over the period studied. The
average returns and alphas obtained for individual funds are higher compared to the ones
obtained while studying funds agglomerated in indices. Alphas are always lower than the
corresponding average return but the differences are relatively small. Nevertheless, much
more alphas are concentrated around 0, being not significantly different from it. The
percentage of market neutral funds average return not significantly different increases from
21% to 38% when the market impact is taken into account. Results are similar for the main
sub-strategies, but they explain more precisely the ones previously obtained. The inclusion
of the market index puts many significantly positive average return back to no significance
even if the quantitative impact on alpha is small.
On an absolute term, the market exposure remains obviously the same here as it was
in previous analysis. It is however particularly interesting to underline that the beta
distribution for individual funds indicates that the majority of betas are not significantly
different from zero. This result is not inline with the previous one and it indicates that almost
two-third of the individual beta exposure for market neutral funds are not significantly
different from zero and not exposed to the market. This result could be explained by 2
reasons. First, the aggregation of funds in indices leads to an increase in the exposure to the
equity market. This first reason is in line with the results obtained in the correlation analysis
and stresses the importance that it is of major importance to consider individual funds in
empirical analysis because results based on indices could be biased. Secondly, since the bulk
of the funds are not significantly exposed to the market but one third of the funds are and
only five percent of the funds are negatively significantly exposed to the market, the funds
significantly exposed could bias the results. These two remarks are of particular interest.
Table 46: Individual fund market exposure
+ 0 - + 0 - + 0 -
Market neutral funds 1,02% 78% 21% 1% 3,30% 0,95% 62% 38% 0% 0,13 32% 63% 5% 0,08
- Arbitrage funds 1,03% 84% 16% 0% 2,50% 0,94% 71% 29% 0% 0,09 33% 63% 3% 0,05
- Long/short funds 1,03% 71% 27% 2% 4,30% 1,00% 52% 47% 0% 0,16 36% 57% 7% 0,1
- Mortgage backed funds 0,89% 85% 13% 3% 3,00% 0,75% 67% 33% 0% 0,11 8% 92% 0% 0,03
- No sub-strategy 0,45% 50% 50% 0% 1,30% 0,36% 50% 50% 0% 0,18 50% 50% 0% 0,12
The table reports the individual fund market exposure. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure (the beta), the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. T-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
Return distribution (5%)
Alpha distribution (5%) Beta distribution (5%)Average
return S.D. Alpha Market R²adj
Table 47 : Individual Fund Market Exposure – Multi factor model
Alpha <0 0 >0 Mkt <0 0 >0 Mkt² <0 0 >0 Mkt³ <0 0 >0 R² adj
Market neutral funds 1,21% 0% 35% 65% 0,13 5% 73% 22% -1,13 14% 82% 3% 2,51 9% 82% 9% 0,10
- Arbitrage funds 1,10% 0% 25% 75% 0,09 4% 77% 19% -0,69 12% 83% 5% -1,35 7% 82% 11% 0,09
- Long/short funds 1,27% 0% 50% 50% 0,17 7% 69% 24% -1,30 15% 83% 1% 6,16 11% 82% 7% 0,12
- Mortgage backed funds 1,47% 0% 8% 92% 0,08 5% 79% 15% -2,34 15% 85% 0% -4,47 10% 87% 3% 0,09
- No sub-strategy 0,77% 0% 50% 50% -0,01 0% 100% 0% -4,59 50% 50% 0% 148,98 0% 100% 0% 0,21
The table reports the individual fund market exposure. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure (the beta), the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. T-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
Table 48: Bull and Bear Beta Estimation
Alpha <0 0 >0 Bear Beta <0 0 >0 Bull
Beta <0 0 >0 R² adj
Market neutral funds 1,22% 1% 47% 47% 0,17 5% 62% 32% 0,05 8% 79% 13% 0,31
- Arbitrage funds 1,15% 1% 38% 38% 0,14 6% 60% 33% 0,04 7% 81% 12% 0,22
- Long/short funds 1,24% 1% 60% 60% 0,19 5% 64% 31% 0,09 8% 76% 14% 0,30
- Mortgage backed funds 1,58% 2% 23% 23% 0,20 2% 70% 27% -0,10 7% 86% 7% 0,11
- No sub-strategy 0,90% 0% 33% 33% 0,18 0% 33% 67% 0,01 0% 100% 0% 0,10
The table reports the individual fund market exposure. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure in bull markets (bull beta estimated when the S&P500 is up over the month under review) and in bear markets((bear beta estimated when the S&P500 is down over the month under review ) as well as the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. T-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
312
7.2 Non linearities in market exposure
In order to complete our analysis we perform two additional analysis. We first
check the co-skewness and the co-kurtosis of market neutral funds with the equity
market using a multi-factor CAPM based on the underlying idea developed by Kraus and
Litzenberger (1976), Fang and Lai (1997), Harvey and Siddique (2000) and Dittmar
(2002). Our four-moment CAPM use not only the beta of the market as a regression
factor but also the beta of the market factor squared as well as the beta of the market
cubed. The objective of this calculation is to have an estimation of the co-skewness
(market squared) and the co-kurtosis (market beta cubed) between the fund or the
strategy considered and the market. A negative beta to the market squared indicates
that the fund or strategy considered tend to move the distribution of the return of the
index to the left (negative asymmetry) while a positive co-skewness indicates a positive
impact of the asymmetry of the return distribution. The beta cubed reports the same
information for the co-kurtosis. The inclusion of the fund or the strategy may lead to
bigger tails (positive beta) or to lower tails (negative beta). Results are reported in Table
47. Table 47 firstly confirms that the market exposure tend to be low for the bulk of the
managers even if up to one fourth of the fund may be significantly exposed to the
market. Secondly, all the strategies considered have a negative impact on skewness
indicating that considered globally, market neutral strategies tend to lead to negatively
skewed distribution. Interestingly, the repartition of the beta squared shows that more
than 80% of the individual estimations have no significant impact on skewness. However,
the impact is negative for around 15% of the funds considered. The results are almost
the same when co-kurtosis is considered in the sense that the bulk of the individual funds
do not have any impact on the kurtosis of the market return distribution but that around
10% will turn the kurtosis to positive or negative levels. All in one, these results show
313
some impact on the distribution of the returns for some funds but that the impact is
marginal for most individual funds considered.
For our second additional estimation we apply two types of piecewise regressions
following the underlying idea of Faff (2001) and Galagedera and Faff (2004). We
separated the bull and the bear market beta to determine if the beta of the fund or the
strategy considered remains constant over bull or bear market conditions. Results are
reported in Table 48. Table 48 reports the bull and bear alphas and betas. The first
element to stress out is that the alphas reported are relatively high and that a little more
than half of the funds in the dataset offers significantly positive alpha (mainly arbitrage
and mortgage funds). On the beta side, the bear betas are much higher than the bull
betas confirming that hedge funds tends to have a higher exposure to markets in
turbulent market conditions. The individual beta repartitions reported also indicate a
higher beta exposure in bear market conditions where around one third of the exposures
are positive while it is around 10% in bull market conditions. These results indicate some
presence of non-linearities even if there are not as high as one could expect.
7.2 Ex-post beta analysis
In the second step of the analysis we use the results obtained in the first part of
this section to study the link between the beta and the performance of the funds. We use
the individual results obtained in the previous section but we classify funds in Table 49
on the basis of the betas from the lowest to the highest one.
Table 49 indicates that there is no clear pattern in the average return column. The
figure indicates that the highest average returns are spread between decile 8, decile 1,
decile 10 and decile 6. The return distribution however indicates that more insignificant
returns are offered by low beta funds (see decile 1) and by high beta funds (decile 9 and
314
10). This means that the best performing market neutral funds are those that are not
exposed to the market. The standard deviation column indicates that the same decile 1,
decile 9 and decile 10. These results also indicate an interesting pattern. Negatively
exposed and strongly positive exposed funds are more volatile than market neutral
funds. This result is in line with the objective of market neutral funds which is to offer low
volatility positive returns over time.
A closer look at the regression results indicates that the highest alphas are offered
by the same deciles that offered high average returns but with lower absolute values.
Please note that the alpha for middle decile funds is weakly exposed to the market and
very close to the values obtained for the average returns confirming the fact that these
funds are unexposed to the market. The distribution of the alpha indicates the same
pattern as the return distribution with higher figures for alpha’s not significantly different
from zero. This remark is particularly true, strongly exposed or negatively and
significantly exposed deciles (decile 1, decile 9 and decile 10) indicating that these funds
were not able to offer significantly positive returns when the market impact was taken
into account or, in other words that the market can explain a major part of their returns.
This could be explained by the fact that funds reported in decile 1 benefited mainly from
bear market and funds in deciles 9 and 10 did so from bull market conditions. This result
is also true for other deciles but less precise.
315
As we could expect, and by construction, the beta analysis indicates that the betas
are increasing over the decile. More interestingly, the beta distribution columns indicate a
clear pattern. No betas are significantly positive for the more weakly exposed deciles
(deciles 1 to decile 3). This logical result confirms our previous suggestion that low decile
funds profit from the bear market. Then, the number of significantly positive returns
increase monotonically and the percentage of significantly negatively exposed to the
market funds go to zero after decile 4, indicating that there has been more positively
market exposed funds than negatively exposed funds over the period studied. As before
the R²adj are low except for decile 10. This result can be explained by the fact that funds
reported in decile 10 are more exposed to the market. All over, this analysis suggests
that most market neutral funds are not significantly exposed to the market.
Table 49: Ex-post beta analysis
+ 0 - + 0 - + 0 -
Decile 1 1,14% 59% 39% 2% 4,90% 1,07% 39% 61% 0% -0,27 0% 54% 46% 0,1
Decile 2 0,89% 85% 15% 0% 2,60% 0,90% 70% 30% 0% -0,06 0% 96% 4% 0,01
Decile 3 0,96% 98% 2% 0% 1,60% 0,96% 83% 17% 0% -0,01 0% 100% 0% -0,01
Decile 4 0,81% 91% 9% 0% 1,20% 0,80% 83% 17% 0% 0,02 4% 96% 0% 0
Decile 5 1,00% 89% 9% 2% 1,90% 1,00% 81% 17% 2% 0,04 13% 87% 0% 0
Decile 6 1,07% 89% 9% 2% 2,00% 1,05% 83% 17% 0% 0,07 30% 70% 0% 0,03
Decile 7 0,96% 78% 20% 2% 2,80% 0,90% 59% 41% 0% 0,12 48% 52% 0% 0,07
Decile 8 1,24% 85% 13% 2% 3,90% 1,17% 67% 33% 0% 0,21 63% 37% 0% 0,1
Decile 9 1,00% 61% 39% 0% 4,70% 0,80% 26% 74% 0% 0,37 83% 17% 0% 0,16
Decile 10 1,11% 41% 57% 2% 8,00% 0,85% 26% 74% 0% 0,8 83% 17% 0% 0,31
The table reports the ex-post beta. Deciles are constructed on the basis of the market exposure of the individual funds. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure (the beta), the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. t-stats are heteroskedasticity consistent. The period covered is 01:1993-12:2002.
Average return
Return distribution (5%) S.D. Alpha
Alpha distribution (5%) Market
Beta distribution (5%)R²adj
317
VIII Sub-period analysis
Since our analysis period covers a bull and a bear period, we will perform the same
analysis as in section VI in dividing the analysis period in 2 sub-periods. We chose the bull
and a bear market as defined by Capocci, Corhay and Hübner (2004). The cutting point
chosen for the identification of the up and down periods has been set at March 2000. This
month corresponds to the maximum observed value of the Russel 3000 (that contains 95%
of the capitalisation of the American equity market) 500 Index that attained a value of
858.48 during the session of March 24, 2000. During the up period, the monthly index
return was positive in 70% of the months (52 out of 74) with an average yearly return of
19.4%. During the down period, the monthly index return was positive in 39% of the
months (12 out of 34) and the average yearly return was -16.9%. Those trends are
sufficiently strong to allow us to consider the whole sub-periods as, respectively, bullish and
bearish without having to use a complex rule to separate bullish, bearish and neutral months
since these rules would obviously not match the ones used by fund managers for their
market timing decisions.
8.1 Market exposure
Panel A of Table 50 reports the result of the beta analysis for funds considered in
indices and for funds classified on the basis of their performance over the period studied in
order to determine if best or worst performing funds have been more or less exposed to the
equity market over the bullish and bearish period studied.
318
The results obtained for the bullish period (see Panel A of Table 50) indicates that the
alphas reported are higher than those obtained over the whole period. This result is quite
astonishing because it seems to indicate that market neutral funds have been able to
outperform the market index over the period studied. The market and R²adj columns
however indicate that this significant alpha was created totally independently of the market
direction because all market factors are not significantly different from zero. Moreover, the
R²adj are very low indicating that the market factor cannot explain the returns. More
precisely, this result confirms the non-exposure to the market for market neutral funds but
the ability to create absolute performance over the bullish period studied. Mortgage backed
funds’ results even indicate that the funds were negatively (but not significantly) exposed to
the market and that they create absolute alpha.
The second part of Panel A of Table 50 reports the deciles’ regression analysis for the
bull period. It indicates the same pattern as over the whole period with higher absolute
numbers with the same level of significance indicating that all but the worst performing
funds were able to create significantly positive alpha over the period studied with no
exposure to the market as indicated by the market and the R²adj columns. This means that
these funds do not offer absolute74 significantly positive returns over this period. On the
other side, the funds reported in the other deciles offered significantly positive absolute
returns over the period studied.
74 We use the term absolute to underlie the fact that these funds were not significantly exposed to the
market, which means that these figures have to be considered on an absolute basis rather than in
comparison with the index considered.
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Panel B of Table 50 shows that the average return for every strategy (the exception
being the no sub-strategy category) was higher over the whole period than over the bear
market period studied. This result is inverse from the one obtained for the bull market
period and is logical since managers face more difficulties in finding investment opportunities
when stocks’ prices (good and bad one) were decreasing. Standard deviations are also in
almost all cases higher. Alphas indicate the same pattern. Interestingly, the beta reported
are significantly positive in all cases over this time period indicating that the funds were
significantly exposed to the market over this period. The market exposure can explain a
bigger part of the alphas generated since the R²adj are much higher than the one obtained
over the bull market. On an absolute term however, the alphas generated by the market
neutral funds are significantly positive. The reasons explaining this result are however
completely different from the one explaining the alpha in the bull market. In the bull market
period the market exposure could not explain the alpha created by the funds leading to
significantly positive alphas with extremely low R²adj. On the other side, in the second case,
the bullish period, the funds significantly outperformed the market with a significant
exposure to it and comparatively high R²adj. This result is particularly important.
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Table 50: Indices and deciles sub-period analysis
S.D. R²adj
Market neutral funds 1,49% *** 1,11% 1,52% *** -0,01 -0,06
- Arbitrage funds 1,40% *** 1,08% 1,48% *** -0,03 -0,04
- Long/short funds 1,72% *** 1,34% 1,65% *** 0,03 -0,05
- Mortgage backed funds 0,73% 2,52% 1,04% *** -0,12 -0,01
- No sub-strategy 0,64% *** 1,16% 0,74% *** -0,04 -0,03
Decile 1 -0,36% 0,03 -0,07% -0,12 -0,03
Decile 2 0,42% 1,87% 0,41% 0 -0,06
Decile 3 0,54% *** 0,60% 0,60% *** -0,03 -0,02
Decile 4 0,85% *** 1,01% 0,94% *** -0,03 -0,03
Decile 5 1,01% *** 1,41% 1,23% *** -0,09 0,03
Decile 6 1,24% *** 0,96% 1,18% *** 0,02 -0,04
Decile 7 1,46% *** 1,39% 1,52% *** -0,03 -0,05
Decile 8 1,62% *** 1,41% 1,58% *** 0,02 -0,06
Decile 9 2,60% *** 1,39% 2,53% *** 0,03 -0,05
Decile 10 4,27% *** 2,33% 4,04% *** 0,09 -0,03
Panel A: 9/98-03/00
Average return Alpha Market
321
Average return S.D. Alpha Market R²adj
Market neutral funds 0,71% *** 0,77% 0,84% *** 0,09 *** 0,35
- Arbitrage funds 0,75% *** 0,70% 0,85% *** 0,07 *** 0,22
- Long/short funds 0,65% *** 1,08% 0,82% *** 0,11 *** 0,29
- Mortgage backed funds 0,87% *** 0,88% 0,95% *** 0,06 *** 0,1
- No sub-strategy 0,69% *** 1,31% 0,81% * 0,14 0,11
Decile 1 -0,59% 3,37% 0,03% 0,43 *** 0,43
Decile 2 -0,15% 0,99% -0,03% 0,08 *** 0,15
Decile 3 0,48% *** 0,67% 0,58% *** 0,07 *** 0,27
Decile 4 0,40% ** 1,06% 0,65% *** 0,17 *** 0,67
Decile 5 0,54% *** 0,52% 0,61% *** 0,05 *** 0,21
Decile 6 0,61% *** 0,92% 0,78% *** 0,11 *** 0,42
Decile 7 0,83% *** 0,67% 0,83% *** 0 -0,03
Decile 8 0,97% *** 0,80% 1,06% *** 0,06 ** 0,13
Decile 9 1,17% *** 1,06% 1,26% *** 0,07 * 0,08
Decile 10 1,97% *** 1,42% 2,06% *** 0,06 0,02
This table reports the market exposure analysis over sub-periods. Each Panel presents the average return, the standard deviation (S.D), the alpha, the market exposure (the beta) and the R²adj. Panel B presents the same information when funds are classified in deciles on the basis of their performance over the period studied. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level. t-stats are heteroskedasticity consistent. Panel A presents the bullish period (09:1998-03:2000), Panel B presents the bearish period (04:2000-12:2002).
Panel B: 4/0-12/02
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The second part of Panel B indicates exactly the same pattern, lower alpha for most
decile in absolute term significant (in statistical term but low in absolute term) exposure to
the equity market for the same deciles and relatively high R²adj. An interesting point to
stress here is that these results are not exact to performing funds that could create alpha
with no exposure to the market. These funds create positive absolute returns (while
remaining market neutral funds) whereas worst performing market neutral funds create
alpha compared to the equity market (which was strongly negative over this period). This
result interestingly stresses that most bad performing market neutral funds out-perform the
equity market without offering significantly positive performance but that the best
performing funds significantly out-performed the equity market and offered significantly
positive returns over the bearish market after March 2000.
Table 51 reports the same results based on the decile classification from Carhart’s
(1997). The average return and standard deviation column indicates that the top and bottom
decile funds, the most volatile one has not offered significantly positive return over the
period covered. This result is confirmed by the regression results. No alpha is significantly
positive when the market impact is taken into account. Interestingly, no deciles but decile 9
are exposed to the market. Most deciles are even negatively (but not significantly) exposed
to the equity market. The R²adj are low. All these results suggest that low volatility market
neutral funds create value on an absolute basis (without exposure to the equity market) but
that almost none of them benefit from the market sharp increase. Moreover, this strong bull
market has a negative (but not significant) impact on the performance.
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Panel B of Table 51 indicates that even if the average return of the previous year top
and worst performing funds are not significantly different from zero, the other deciles offer a
significantly positive alpha. These results are stronger than before, confirming that volatile
funds cannot create persistent value over time. In absolute term, top funds however offered
better (but not significantly positive) alphas than bad ones. Bottom and particularly top
deciles had the highest volatility confirming our previous results. Over the bearish period, no
decile but the one containing last year worst performing funds have been significantly
exposed to the market. Interestingly, the alpha of this decile is significantly positive whereas
its average return was not. This result can be explained by the fact that funds in this decile
were significantly exposed to the market. In fact, the average return is lower than the alpha.
Since the market went down over the period studied, the exposure of the fund to the market
has unable the manager to offer significantly positive alpha compared to the index whereas
its average return was not different from zero. The spread between decile 1 and decile 2 is
significantly negative confirming this remark.
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Table 51: Lagged 12-month decile sub-period analysis
S.D. R²adj
Decile 1 0,40% 1,09% 0,17% 0,02 -0,05
Decile 2 0,56% * 1,28% 0,15% -0,01 -0,05
Decile 3 0,46% ** 0,88% 0,15% -0,03 -0,03
Decile 4 0,28% ** 0,57% 0,12% -0,03 -0,02
Decile 5 0,43% *** 0,70% 0,18% 0,04 0
Decile 6 0,35% ** 0,74% 0,15% -0,05 -0,01
Decile 7 0,44% * 1,12% 0,11% -0,05 -0,05
Decile 8 0,59% ** 1,14% 0,26% -0,01 -0,06
Decile 9 1,02% ** 1,86% 0,50% 0,11 ** 0,11
Decile 10 1,40% * 3,14% 0,57% 0 -0,06
1-10 spread 1,00% 2,93% 0,41% -0,02 -0,06
1-2 spread 0,16% 1,02% -0,02% -0,03 -0,01
9-10 spread 0,38% 2,00% 0,07% -0,11 0,1
Panel A: 9/98-03/00
Average return Alpha Market
325
S.D. R²adj
Decile 1 0,65% 2,71% 0,83% *** 0,09 ** 0,11
Decile 2 0,53% ** 1,32% 0,92% *** 0 -0,03
Decile 3 0,37% *** 0,81% 0,76% *** 0,02 -0,02
Decile 4 0,45% *** 0,79% 0,53% *** 0,01 -0,03
Decile 5 0,56% *** 0,60% 0,67% *** 0,01 -0,03
Decile 6 0,67% *** 0,62% 0,73% *** 0,01 -0,02
Decile 7 0,72% *** 0,78% 0,93% *** 0,04 0,00
Decile 8 0,82% *** 0,64% 0,96% *** 0,03 -0,01
Decile 9 1,20% *** 0,83% 1,33% *** 0,01 -0,03
Decile 10 0,53% 2,50% 1,77% *** 0,13 0,01
1-10 spread -0,13% 3,31% 0,94% * 0,03 -0,03
1-2 spread -0,12% 2,05% 0,09% -0,09 ** 0,12
9-10 spread -0,67% 2,23% 0,44% 0,11 0,03
The table reports the market exposure using deciles constructed on the lagged-12 month performance (see Carhart 1997). It reports the average return, the standard deviation (S.D), the alpha, the market exposure (the beta) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. *** Significant at the 1% level, ** Significant at the 5% level and * Significant at the 10% level. t-stats are heteroskedasticity consistent. Panel A presents the bullish period (09:1998-03:2000), Panel B presents the bearish period (04:2000-12:2002).
Panel B: 04/00-12/02
Average return Alpha Market
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8.2 Individual funds
Table 52 reports the sub-period analysis obtained for individual funds.75 As one could
expect, the average return obtained for the bull market are higher than those obtained over
the whole period (except for mortgage backed funds) and a higher proportion of theses
returns are significantly positive. The alpha column and distribution reports the same
pattern. The market exposure however indicates differences. Whereas it was on the average
positive over the whole period with one third of the beta being significantly positive, almost
all betas are not significantly different from zero over the bull market. This result indicates
that individual market neutral funds are not exposed to the market in bull markets. The
R²adj obtained confirms this result.
Panel B’s average returns are much lower but the average returns are spread in the
same way as before for market neutral funds arbitrage funds and long/short funds. For
mortgage backed funds, more average returns are significantly positive over the bear
period. The alpha’s obtained are also lower and there are some differences in the proportion
of significantly positive alphas and alphas not significantly different from zero for arbitrage
funds (more alphas are not significantly different from zero over the bear period) and
long/short funds (more alphas are significantly different from zero over the bear period).
The market exposure over the bull market are more spread with up to 31% significantly
positive alphas (arbitrage funds) and there are up to 18% of significantly negative alpha’s
75 We require all funds to have returns for the whole period between September 1998 and March 2000.
This lead us to remove 200 funds (90 arbitrage funds, 96 long/short funds, 13 mortgage backed funds and
1 no sub-strategy fund) from the database and leave us with a total of 262 funds (146 arbitrage funds, 138
long/short funds, 29 mortgage backed securities funds and 2 no sub-strategy funds) for the 9/98-3/00
period analysis. This lead remove 125 funds (60 arbitrage funds, 52 long/short funds, 11 mortgage backed
funds and 2 no sub-strategy fund) from the database and leave us with a total of 337 funds (147 arbitrage
funds, 162 long/short funds and 14 mortgage backed securities funds) for the 4/00-12/02 period analysis.
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for some strategy (mortgage backed funds for example) indicating that these funds did not
short the market. These results indicate that Arbitrage funds and mortgaged backed funds
seemed to perform better in bull market (with more significantly positive alpha) without
being exposed to the market. On the other side when the market was down they were able
to create positive alpha but are more exposed to the market. On the other side, regarding
market exposure, in bear market, market neutral managers considered as a whole seemed
more to be exposed to the market, on the long on or the short side. Interestingly, market
neutral funds were significantly and negatively exposed to the market only during bear
market.
Table 52: Sub-period individual funds results
+ 0 - + 0 - + 0 -
Market neutral funds 1,57% 58% 42% 0% 3,76% 1,65% 61% 38% 0% -0,03 6% 92% 2% 0,01
- Arbitrage funds 1,52% 77% 23% 0% 2,38% 1,55% 84% 16% 0% -0,01 3% 94% 3% 0
- Long/short funds 1,81% 23% 77% 0% 4,55% 1,87% 21% 79% 0% -0,02 6% 94% 0% 0,02
- Mortgage backed funds 0,83% 38% 62% 0% 4,12% 1,10% 65% 35% 0% -0,11 0% 100% 0% 0,02
- No sub-strategy 0,64% 100% 0% 0% 1,16% 0,74% 100% 0% 0% -0,04 0% 100% 0% -0,03
R²adjAverage return
Return distribution (5%) S.D. Alpha
Alpha distribution (5%) Market
Beta distribution (5%)Panel A: 9/98-03/00
+ 0 - + 0 - + 0 -
Market neutral funds 1,57% 58% 42% 0% 3,76% 1,65% 61% 38% 0% -0,03 6% 92% 2% 0,01
- Arbitrage funds 1,52% 77% 23% 0% 2,38% 1,55% 84% 16% 0% -0,01 3% 94% 3% 0
- Long/short funds 1,81% 23% 77% 0% 4,55% 1,87% 21% 79% 0% -0,02 6% 94% 0% 0,02
- Mortgage backed funds 0,83% 38% 62% 0% 4,12% 1,10% 65% 35% 0% -0,11 0% 100% 0% 0,02
- No sub-strategy 0,64% 100% 0% 0% 1,16% 0,74% 100% 0% 0% -0,04 0% 100% 0% -0,03
Beta distribution (5%)R²adj
The table reports the individual fund market exposure. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure (the beta), the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. t-stats are heteroskedasticity consistent. Panel A presents the bullish period (09:1998-03:2000), Panel B presents the bearish period (04:2000-12:2002).
Panel B: 4/00-12/02 Average return
Return distribution (5%) S.D. Alpha
Alpha distribution (5%) Market
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8.3 Ex-post beta sub-period analysis
Table 53 reports the beta ex-post analysis over the 2 sub-periods considered.
Panel A reports higher average returns for the bull market period compared to the whole
period but fewer of these returns are significantly positive. The standard deviations of the
returns are lower for the bull market compared to the global period. The regression
results report higher alphas than previously for all deciles but fewer of them are
significantly positive. As before and by construction the exposure to the market increases
but the absolute level over the bull market are lower than before indicating that market
neutral funds are less exposed to the market during bull market than during a whole
investment cycle. Fewer individual betas are significantly positive over the bull market
conditions compared to the whole period studied. The R²adj are close to zero for all
deciles except the high beta decile. All in one these results indicate that market neutral
funds could offer absolute alpha during the bull market without being exposed to the
market.
Panel B of Table 53 indicates that over the bear market period covered, market
neutral funds offered higher average returns compared to the whole period and to the
bull market period but fewer returns are significantly positive compared to the whole
period and less strict compared to the bull market. The standard deviation is close to
those obtained over the whole period and higher than those obtained over the bull
market period. Alphas are lower than over the whole period and fewer of them are
significantly positive. The market exposure increases logically by construction with
extreme’s beta value higher (respectively lower) for high (respectively low) beta funds.
This confirms our previous results that in the bear market period, market neutral fund’s
beta are higher in absolute term. The beta distribution confirms this result. The R²adj
obtained are also relatively high for top and bottom deciles indicating that fund’s market
exposure help explaining returns for the highest negatively and positively exposed funds.
Table 53: Ex-post beta sub-period analysis
+ 0 - + 0 - + 0 -
Decile 1 1,69% 15% 85% 0% 9,10% 3,03% 19% 81% 0% -0,54 0% 96% 4% 0,04
Decile 2 1,66% 27% 73% 0% 5,20% 2,24% 50% 50% 0% -0,23 0% 100% 0% 0,02
Decile 3 1,66% 50% 50% 0% 3,50% 1,99% 81% 19% 0% -0,13 0% 92% 8% 0,02
Decile 4 1,16% 62% 38% 0% 2,60% 1,36% 69% 31% 0% -0,08 0% 96% 4% 0
Decile 5 1,32% 96% 4% 0% 1,40% 1,42% 100% 0% 0% -0,04 0% 100% 0% -0,02
Decile 6 1,37% 85% 15% 0% 1,60% 1,40% 81% 19% 0% -0,01 0% 100% 0% -0,05
Decile 7 1,01% 69% 31% 0% 2,30% 0,96% 69% 31% 0% 0,02 0% 100% 0% -0,05
Decile 8 1,34% 69% 27% 4% 2,30% 1,20% 69% 27% 4% 0,06 4% 96% 0% -0,01
Decile 9 1,89% 50% 50% 0% 3,90% 1,47% 50% 50% 0% 0,17 12% 88% 0% 0,01
Decile 10 2,68% 50% 50% 0% 5,80% 1,44% 23% 77% 0% 0,5 46% 54% 0% 0,16
Panel A: 9/98-03/00 Average return
Return distribution (5%) S.D. R²adjAlpha
Alpha distribution (5%) Market
Beta distribution (5%)
+ 0 - + 0 - + 0 -
Decile 1 1,50% 36% 64% 0% 5,10% 0,95% 27% 73% 0% -0,37 0% 39% 61% 0,17
Decile 2 0,78% 61% 39% 0% 2,20% 0,63% 33% 67% 0% -0,11 0% 76% 24% 0,06
Decile 3 1,04% 91% 9% 0% 1,40% 0,98% 85% 15% 0% -0,04 0% 82% 18% 0,02
Decile 4 0,88% 91% 9% 0% 1,10% 0,87% 85% 15% 0% 0 0% 100% 0% -0,03
Decile 5 0,70% 91% 9% 0% 1,00% 0,73% 91% 9% 0% 0,01 0% 100% 0% -0,02
Decile 6 0,79% 76% 24% 0% 1,50% 0,84% 76% 24% 0% 0,03 9% 91% 0% 0
Decile 7 0,86% 76% 24% 0% 1,80% 0,96% 74% 26% 0% 0,07 50% 50% 0% 0,06
Decile 8 0,73% 53% 47% 0% 2,00% 0,93% 56% 44% 0% 0,14 71% 29% 0% 0,13
Decile 9 0,33% 3% 94% 3% 4,40% 0,75% 29% 68% 3% 0,28 47% 53% 0% 0,13
Decile 10 -0,55% 0% 94% 6% 8,10% 0,76% 24% 70% 6% 0,88 88% 12% 0% 0,36
The table reports the individual fund market exposure. It reports the average return, the return distribution at the 5% level. (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the standard deviation (S.D), the alpha, alpha distribution at the 5% level (+ are significantly positive, 0 not significantly different from 0 and – significantly negative), the market exposure (the beta), the beta distribution (+ are significantly positive, 0 not significantly different from 0 and – significantly negative) and the R²adj. Our MAR/CISDM database contains 634 individual market neutral funds, including 398 survived funds and 236 dissolved funds as of December 2002. t-stats are heteroskedasticity consistent. Panel A presents the bullish period (09:1998-03:2000), Panel B presents the bearish period (04:2000-12:2002).
Panel B: 04/00-12/02 Average return
Return distribution (5%) S.D. Alpha
Alpha distribution (5%) Market
Beta distribution (5%)R²adj
333
IX Conclusion
This study focuses on the neutrality of market neutral funds. It has the objective
to determine if so-called market neutral funds are really not exposed to the equity
market. We will analyse this topic over a complete market cycle going from January 1993
to December 2002 and over bull and bear market conditions covering respectively the
September 1998 to March 2002 and the April 2000 to December 2002 periods.
In the first descriptive part of the analysis, we will focus on the literature, the
interest of the study, on the descriptive statistics, attrition and birth rates and on the
presence of survivorship bias in the data. The core of the study is based on a
methodology that use classical exposure measures like the beta in an original way. We
will perform the analysis using strategy and sub-strategy indices and using individual
funds data in order to determine if we obtained the same results.
The results obtained using sub-strategy indices indicate the beta obtained are low
on an absolute term but significantly positive. Decile analysis indicates that top and worst
performing funds (over the whole period) have the highest market exposure. The
analysis of the decile constructed in the previous year’s performance as a tool of
classification suggests that the exposure of market neutral funds to the equity market is
not clear. In all cases, market factors are significantly positive but they do not explain a
major part of the alphas that are relatively the same as the average return and the
calculations usually give low R²adj.
The individual fund analysis results indicate that on the average, one third of the
individual funds were significantly positively exposed to the market while two third of the
alphas are significantly positive (especially for worst and best performing funds that also
offer the more volatile returns). Then, the ex-post beta analysis indicates that negatively
exposed and strongly positive exposed funds are more volatile than market neutral
334
funds. Middle decile funds returns are the only real market neutral funds. Some funds are
strongly positively or negatively exposed to the market over the period studied, but most
market neutral funds are not significantly exposed to the market.
We had to perform an analysis at the individual fund level to find out this result
because market neutral index analysis lead to more controversial results. This study
stresses the importance of considering individual funds when performing market neutral
empirical analysis. This result could be explained by 2 reasons. First, the aggregation of
funds in indices leads to an increase in the exposure to the equity market. This first
reason is in line with the results obtained in the correlation analysis and stresses the
point that it is of major importance to consider individual funds in empirical analysis
because results based on indices could be biased. Secondly, since the bulk of the funds
are not significantly exposed to the market but one third of the funds are and only five
percent of the funds are negatively significantly exposed to the market, the funds
significantly exposed could bias the results.
The sub-period analysis also reports very interesting results. First, most bad
performing market neutral funds out-perform the equity market without being
significantly exposed to the market but best performing funds significantly out-performed
the equity market and offered significantly positive returns over the bearish market after
March 2000. Secondly, on a strategy and sub-strategy basis, over the bullish period no
index or decile has been significantly exposed to the market. Over the bearish period, all
but the best performing deciles have been significantly exposed to the market but they
all, except the best performing funds create significant alpha. The decile classification
based on previous year’s performance interestingly add to these results that they were
very few funds significantly positively exposed to the market during the bullish period
and that there was no clear pattern in the bear period results for these calculations.
Thirdly, arbitrage funds and mortgaged-backed funds perform better in bull market
335
without being exposed to the market. On the other side when the market is down they
are able to create positive alpha but are exposed to the market. On the other side,
regarding market exposure, in bear market, market neutral managers considered as a
whole tend more to be exposed to the market, on the long or the short side.
Interestingly, some market neutral funds are significantly negatively exposed to the
market only during bear market.
Our analysis leads to the conclusion that most market neutral funds are not
significantly exposed to the equity market, but that they tend to be more exposed during
bear market than during bull market without being negatively impacted.
Part 3: Hedge Funds as Diversification Tools
Diversifying using Hedge Funds: A Utility-
Based Approach
Daniel P.J. CAPOCCI
HEC-ULG Management School – University of Liège (Belgium)
Frédéric Duquenne
HEC-ULG Management School – University of Liège (Belgium)
Georges Hübner
HEC-University of Liège, Limburg Institute of Financial Economics,
Maastricht University, and Luxembourg School of Finance, University of
Luxembourg.
Capocci, Daniel, Frédéric Duquenne and Georges Hübner, 2006, Diversifying using Hedge
Funds: A Utility-Based Approach, Working paper, HEC-ULG Management School
339
Diversifying using Hedge Funds: A Utility-Based
Approach
Abstract
This paper develops an adapted efficient frontier that integrates higher moments
in the measurement of risk. This new efficient frontier is based on the Taylor’s
decomposition of Bell’s (1988, 1995) utility function. We apply this new methodology to
determine if the inclusion of hedge funds in a classical portfolio of equity and bond
mutual funds allows investors to reach a significantly higher level of satisfaction when not
only volatility but also skewness and kurtosis are included in the portfolio. Estimations
are performed for various levels of risk aversion, various levels of allocation to the risky
asset and by separating different kind of hedge fund investments.
340
Diversifying using Hedge Funds: A Utility-Based
Approach
Introduction
Hedge funds have been widely studied since 1997. Almost all areas of the
industry are under research. From performance to risk analysis, from style analysis to
their use as a diversification tool, the interest in hedge fund analysis is growing and the
literature more and more explain the specificities of these “dark angels”.76
Hedge fund studies can be classified in four global categories. The first one, which
is by large the richest in quantity, encompasses papers that focus on hedge fund
performance (see for example Ackermann et al., 1999; Agarwal and Naik, 2000; Amin
and Kat, 2003; Liang, 2001; Edwards and Caglayan, 2001; Capocci and Hübner, 2004;
Agarwal and Naik, 2004; Malkiel and Saha, 2005). The second global category includes
articles that analyse and describe hedge funds investment style and explain these
features with style models (see for example Fung and Hsieh, 1997; Brown et al., 2001;
Brealy and Kaplanis, 2001, Brown and Goetzmann, 2001, Liang 2001; Liang 2003). A
third stream of the literature focuses on the correlation of hedge funds with other
investment products and analyse the power of diversification of hedge funds (see for
76 “Angels” because hedge funds have been seen as the new perfect tool create returns when the
traditional markets can no more offer attractive returns. “Dark” because many investors have invested
in these products without being aware of the underlying strategy or the real risk involved with the
strategy applied.
341
example Fung and Hsieh, 1997; Schneeweis and Spurgin, 1998; Liang, 1999; Agarwal
and Naik; 2000). Finally, other studies analyse miscellaneous aspects of the hedge fund
industry. This category includes the “other studies” focusing on the risks involved in
hedge fund investing (see Jorion, 2000 or Lo, 2001); the presence of bias in the data
(see for example Liang, 2000; Fung and Hsieh, 2000 and Malkiel and Saha, 2005); or
the difference between the indices available (see for example Amenc and Martellini,
2002 and Fung and Hsieh, 2002a).
The current study belongs to the third stream. It aims at determining if an
investor that combines hedge funds with traditional investments really improves its
satisfaction by combining the two families of investments. The underlying idea of our
analysis is the same as the spanning tests developed by Huberman and Kandel (1987).
The main differences introduced by our methodology are twofold. First, the original
spanning is based on the mean and the variance and on the hypothesis of quadratic
preferences whereas ours is based on Bell’s (1988, 1995) utility function, that combines
a linear and an exponential form. Second, we not only look at the impact of inserting a
particular security in a portfolio’s efficient frontier but we include a single risk
specification including skewness and kurtosis in the analysis, but study a wide range of
risk measures corresponding to different investor profiles. Our final objective is to
determine if the integration of hedge funds in a diversified portfolio of stocks and bonds
helps the investor to increase significantly his utility for a reasonable specification.
The paper is organised as following. In section I we summarize the use of utility
functions and introduce the characteristics of the Bell (1985) utility function. The
methodology used as well as the database are described in Section II. Section III
reports the results and Section IV concludes the paper.
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I Utility functions and Spanning
1.1 Utility functions and the Bell function
Several strudies have stressed the limitations of traditional performance
measures focusing on risk (as measured by the standard deviation and the return).
Jagannathan and Korajczyk (1986) demonstrate that it is possible for fund managers to
construct portfolios that show artificial timing ability when no true timing ability exists
while investing in options or levered securities. More recently Goetzmann et al. (2006)
show that statistics can yield attractive statistics in terms of classical measures like the
Jensen’s alpha using a simple rebalancing strategy. These authors conclude that
manipulation-proof performance measures can be completely characterized as the
weighted average of a utility-like function, which is exactly the focus of our study.
The utility function concept is widely used to model the process of decision
making. It offers a lot of applications in various disciplines including finance,
microeconomics and operational research, etc. In finance, portfolio selection theory
examines how a rational investor behaves when choosing his investments in a
framework of uncertainty about his futures outcomes. Many authors have devoted their
time searching for alternative ways of modelling an investor’s preference and deriving
the composition of his ideal portfolio. Based on its mean-variance approach, the CAPM is
still used as a benchmark “…but mean-variance analysis is only appropriate when
returns are normally distributed or investors’ preferences are quadratic (Fund and Hsieh,
1997). In actual applications, and particularly in the case of hedge funds, returns are
typically not normally distributed and utility functions have a higher order than
quadratic. Levy and Markowitz (1979) justify the practice of using mean-variance
343
analysis by showing that mean-variance analysis can be regarded as a second-order
Taylor series approximation of standard utility functions.
The utility function concept used in the framework among uncertain investment
outcomes is sustained by a strong theoretical justification. Von Neuman and
Morgenstern (1947) proved that, when we accept some hypothesis about the concept of
rational choice, a decision maker can be thought of as comparing alternatives based on
his expected utility. The standard mean variance utility function of Markowitz (1959) and
Sharpe (1970) can be viewed as an approximation to the more basic von Neuman and
Morgenstern utility function and more particularly to the isoelastic family of utility
functions.
There are various classes of utility functions. The most common are the
exponential, logarithmic, power and quadratic specifications. Each has specific
properties, drawbacks and advantages (see Spanier and Oldman, 1987 for a detailed
presentation of more than 400 utility functions). A usable utility function has must
satisfy at least some basic desirable properties:
(a) Non-satiety with respect to wealth: an increase in wealth always
increases the utility. The first derivative of the utility function of wealth
should positive
(b) Risk aversion: the speculator is not a gambler. He invests despite the
underlying risks and always requires a compensation. He will always
give more utility to a certain gain than to a random result with the
same expected return. This property involves that the second-order
derivative to be negative.
(c) Risk assets are not inferior goods.
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Classical utility functions like the exponential, logarithmic, power and quadratic
do not offer all these desirable properties. The main issue with the exponential utility
function is that the ARA77 is constant (and that its range of variation is the largest
possible, i.e. [0, +∞[) implying that investors invest constant amounts in risky assets as
their wealth increases, but in decreasing proportional amounts. The logarithmic utility
function and the power utility function have a constant RRA and are isoelastic, thus an
investor with a non-constant RRA cannot be characterized. Cohn et al. (1975), Friend
and Blume (1975) and Morin and Suarez (1983) find empirical support for decreasing
RRA. Finally, the quadratic utility function involves satiety and growing risk aversion.
Considering these elements, it seems that none of the popular utility functions
listed above has all the desirable properties. This is not the case with Bell’s function. Bell
(1988, 1995) introduces a new kind of utility function that displays appealing
characteristics and permits easy interpretation of alternatives in terms of risk and
return. In other words, Bell’s utility function is such that its expected value can be
expressed as a function of the wealth increase r, and the risk R, of an alternative x.
⎣ ⎦ [ ]00 ),~(),~()~,( WxRxrfxWUE = (13)
77 ARA stands for Absolute Risk Aversion, RRA for Relative Risk Aversion. ARA is the ratio of the
second-order derivative to the first order one. See Arrow (1971) for more details.
345
Bell’s function is a combination of a linear and an exponential utility function and
more commonly known as “linear plus exponential”, aka linex functions:
cWbeWWU −−=)( (14)
0,with ≥cb
The expected utility in the case of an additive random wealth x~ is then equal to
⎣ ⎦ [ ] ( )[ ] )~()~(~)~,( )~()~(
0~
000 xRbeebexrWeexWExWUE xrWcxcrcWxaaW +−−−−− −−+=−+=
(15)
where the measure of wealth increase )~(xr is the expected return of the
alternative )~(xE .
346
The measure of risk can be isolated from this expression:
[ ])(ln1)~( )~( xxceEc
xR −−= (16)
The measure of risk incorporates one parameter c, which is specific to the
investor. Parameter c depends on the distribution of return only, and particularly on the
tail of the distribution: investors with a high c place more emphasis on the possibility of
bad outcomes. On the other side, parameter b does control the degree of aversion to
risk, as a weight assigned to risk by the investor in his utility function. Thus, parameter
c constitutes relative riskiness and b aversiveness to that riskiness. Bell (1988, 1995)
shows that the linear plus exponential utility function has the feature that expected
utility can be written as a function of mean final wealth and risk of the final wealth
distribution.
347
(1) It is an increasing and concave function of wealth.
(2) The two parameters b and c leaves flexibility to match personal attitudes.
(1) Alternatives can be compared using a function of risk and return.
(2) It has a decreasing ARA (absolute risk aversion) and its range of variation is the largest possible.
(1) The RRA (relative risk aversion) is decreasing then increasing with respect to W.
(2) With this function, if two alternatives are judged to be equivalent at two different levels of wealth, they will be judged equivalent at all levels of wealth.
(1) It is a non-polynomial function as it includes an exponential.
(2) It is a proper utility function as the successive derivatives alternative in sign .
The function provides a new form of second order approximation that has very satisfying properties.
348
1.2 Spanning
Altough our methodology is not based on spanning, the underlying hypothesis is
similar, we want to determine whether or not the addition of a security (in our case
hedge funds) enables investors to access a significantly superior efficient frontier.
When investors condition their investment choices on the first two moments of
the distribution of returns, they want to know whether adding risky assets will improve
the minimum-variance frontier. This issue is addressed by the notion of spanning
introduced by Huberman and Kandel (1987). Under their approach, an investor with a
quadratic utility function is indifferent to adding securities in his portfolio if the
minimum-variance frontier of his initial portfolio coincides with the minimum variance
portfolio that includes the new securities. Mean-variance spanning is attained if the new
frontier does not significantly differ from the old one.
There are two approaches to test for spanning: the regression approach and the
stochastic discount factor approach. Huberman and Kandel (1987) propose a
multivariate regression-based approach to test of this hypothesis. The real question to
be asked is the following: “Can investors maximise utility by holding just a smaller set of
K assets conditional on the existence of N+K assets?” or said differently, “Can investors
benefit from investing a new set of N assets conditional on K assets?”
The spanning properties of different classes of financial assets have been studied
by several authors. Ferson et al. (1993) generalise the test and integrate the issue of
heteroskedasticity in the testing while De Roon et al. (2001) test for spanning with
futures contracts and non-traded assets and Kan and Zhou (2001) study tests of mean-
variance spanning in detail.
One should estimate the linear relation that exists between the returns of the
existing portfolio and of the additional securities considered. The null hypothesis of
absence of additional diversification with the additional portfolio (spanning) involves that
349
the intercept of the regression and the slope coefficient are not significantly different
from 0 and 1 repsectively. These conditions imply that the regression line passes
through the origin and that the sum of the coefficients of the independent variables
equal 1 for each estimation. If the conditions are both satisfied, the minimum-variance
frontier that includes the added securities does not statistically differ, from a mean-
variance perspective, from the original portfolio the investors including new securities
cannot increase their utility by adding the new securities considered.
The null hypothesis can be tested in three ways. Huberman and Kandel (1987)
provide a likelihood ratio test of spanning and derive its finite sample distribution under
normality assumptions. The Wald test and the Lagrange multiplier test are two
alternative asymptotic tests described in detail by Kan and Zhou (2001). Note all three
tests are increasing transformation of each other. When the residuals exhibit conditional
heteroskedasticity, the three classical three tests will no longer be asymptotically Chi²
distributed under the null hypothesis. In this case, Hansen’s (1982) GMM is the common
viable alternative that relies on the moment conditions of the model. These results have
been stressed by Ferson et al. (1993) and Kan and Zhou (2001). Newey and West
(1987) show that the GMM version of the likelihood ratio test and the Lagrange
multiplier test have exactly the same form as the Wald test.
Generalised methods of moments versions of the tests have been developed by
Ferson et al., 1993 by considering non-normality and heteroskedasticity. They consider
non-normality and heteroskedasticity. Bond and Windmeijer (2005) compare the finite
sample performance of a range of tests of linear restrictions for linear panel data models
estimated using the generalised method of moments (including standard asymptotic
Wald tests based on one-step and two-step GMM estimators; two bootstrapped versions
of these Wald tests; a version of the two-step Wald test that uses a finite sample
corrected estimate of the variance of the two-step GMM estimator; the LM test; and
350
three criterion-based tests that have recently been proposed (see Kan and Zho, 2001).
The corrected two-step Wald test performs similarly to the standard one-step Wald test,
while the bootstrapped one-step Wald test, the LM test, and a simple criterion-difference
test can provide more reliable finite sample inference in some cases. Following these
results and Kan and Zho (2001) we will focus on the GMM Wald test.
Kan and Zhou (2001) propose a step-down procedure to separate the two
approaches to test for spanning (regression approach and stochastic discount factor
approach). The advantages are 1) cause of the rejection is known and 2) the approach
gives the flexibility to assign different significant levels to each test. Under this
methodology, first one has to test whether the intercept is equal to zero before testing if
the sum regression coefficients is equal to one conditional on the intercept being equal
to zero. If the rejection is due to the first test, then the two tangency portfolios are very
different. If the rejection is due to the second test, one can consider the two global
minimum variance portfolios are very different.
The second approach, the stochastic discount factor approach has been
developed by DeSantis (1993) and Bekaert and Urias (1996). Bekaert and Urias (1996)
exploit the duality of Hasen-Jagannathan (1991) bound and the mean-variance frontier.
They suggest that the stochastic discount factor based spanning tests using GMM have
equivalent hypotheses as Huberman and Kandel (1987) and they project a stochastic
discount factor and test whether the N-test assets can explain the variance of the
stochastic discount factor. The null hypothesis of Huberman and Kandel (1987) can be
proved (see Kan and Zhou, 2001) and is equivalent to the null of Bekaert and Urias
(1996). DeSantis (1993) also projects the stochastic discount factor on the gross return
and the expected return does not appear as a parameter in the DeSantis (1993)
specification, but the null hypothesis remains equivalent.
351
Kooli (2007) applies spanning to the diversification benefits of hedge funds and
funds of hedge funds and finds that hedge funds as an asset class improve the mean-
variance frontier of sets of benchmarks portfolios but that investors who already hold a
diversified portfolio do not improve their statistics using hedge funds. The author further
observes that funds of hedge funds offer diversification for mean-variance investors.
352
II Methodology and data
Portfolio selection within a mean-variance-skewness framework has been
considered by Lai (1991), Chunhachinda et al. (1997), Sun and Yan (2003), Chan et al.
(2003), Harvey et al. (2004). Only recently, however, have studies focused on a four-
moment framework (see, Guidolin and Timmermann, 2002; Harvey et al., 2004).
Guidolin and Timmermann (2002) use a Taylor series expansion of the investors’
objective function to determine the optimal portfolios. They consider an m-th order
Taylor series expansion of a generic utility function );( θTtWU + .
Davies et al. (2004) analyse the impact of inserting/deleting hedge funds in a
hedge fund portfolio focusing on co-moments while Davies et al. (2005) incorporate
investor preferences for higher moments of a return distribution into a polynomial goal
programming optimization model. Jurczenko and Maillet (2006) build a four-moment
efficient frontier for portfolio including hedge funds using a non-parametric
methodology. These studies all focus on portfolio selection but do not specifically study
the spanning properties of a particular portfolio or a class of assets. These approaches to
multi-moment analysis are highlighted below before we present our utility-based
methodology using a Taylor expansion.
353
2.1 Classical portfolio selection approaches
We consider the problem of an investor who selects a portfolio from risky assets
in the mean-variance-skewness-kurtosis framework. In our model, we combine and
adapt the tools presented in the previous section. First, we do not make the assumption
of quadratic or power utility function but consider the Bell (1988, 1995) utility function.
Second, our tests are based on the same underlying idea as the spanning test but the
risk measure is extended to include the third and fourth central moment of the portfolio
returns distribution. Moreover, we do not only look at the slope of the capital market line
but we also compare the level of returns achieved for a certain level of risk.
Considering the set of Von Neumann-Morgenstern’s axioms about rationale
choice, we set that investors maximise their expected utility function at each period to
derive their optimal investment choice. This is the most general and commonly accepted
framework of portfolio selection theory referred as the )(UE approach. The problem with
this approach is that it is difficult to implement in practice because the information
requirements are strict. Investors must be able to provide a detailed specification of
their tastes, represented by a specific utility function as well as complete pattern of their
beliefs, described by a joint subjective probability distribution. As the returns may be
infinite, it is impossible to reliably define such a probability distribution and to calculate
the exact value of the expected utility. Moreover, maximizing expected utility among all
feasible portfolios is often a complex mathematical problem that requires a considerably
greater number of calculations.
354
This is why portfolio selection methods aim at being as close as possible to the
model that maximises the expected utility of investors without encountering
informational and computational problems. The general approximating approach to
expected utility consists in estimating the subjective distributions of the investment
outcomes by k parameters so that the preference ordering kV is defined over a set of k-
values vectors. These parameters correspond in most cases to the first k moments of
the distribution: kmmm ,...,, ,21 provided that they exist.
),...,,( ,21 kk mmmV (17)
A sufficient condition for kV to be a preference ordering consistent with )(UE is
that the utility function of the individual is a polynomial of degree n. In this case there is
no approximation to be made. Amongst usual utility functions, the quadratic is the only
one satisfying this condition. The other more appropriate functions (exponential,
logarithmic, power and Bell’s) are non-polynomials so that defining a preference
ordering among the first n moments of the distributions of uncertain outcomes will
generally only result from an approximation to the actual expected utility of the investor.
To isolate the impact of each moment, these non-polynomials are typically
expanded using a Taylor series approximation of the utility functionU . This technique
consists in fitting a polynomial of degree k to )(WU at one value (either 0 or W ).
355
A first attempt to approximate )(UE is to estimate the probability distribution by
its first two moments, leading to the mean-variance approximation (see for example
Tobin, 1969; Huberman and Kandel, 1987). However, this methodology cannot be used
when the returns are not normally distributed as it is the case for hedge funds (see for
example Ackermann et al., 1999; Fung and Hsieh, 2001; Agarwal and Naik, 2004;
Malkiel and Saha, 2005 and Kat and Miffre, 2005). Not only are hedge fund return
distributions asymmetric and leptokurtic, they also tend to display co-skewness and co-
kurtosis with the return of other assets classes, due to option-like features of alternative
investments (see Weisman, 2002, Goetzmann et al. 2003, Agarwal and Naik, 2004; and
Davies et al., 2004a).
The inclusion of higher moments in the efficient frontier analysis has been studied
for years. Several alternative approaches have been developed, yet no single conclusive
approach has emerged. As stated in Jurczenko and Maillet (2006): “we can distinguish
between primal and dual approaches for determining the mean-variance-skewness-
kurtosis efficient frontier.”
Primal approaches include the polynomial goal programming (PGP) approach to
determine the set of the mean-variance-skewness-kurtosis (see Davies et al., 2004).
There are two main shortcomings of this approach. The first one is that the allocation
problem solved cannot be precisely related to the expected utility function, since the
choice of the parameter used to weight the moment deviations is not related to the
parameters of the utility function. The second shortcoming is that the estimation does
not comply with the Pareto-optimal definition of an efficient portfolio frontier. Minimizing
deviations from the first four moments simultaneously only guarantees a solution that is
close to the mean-variance-skewness-kurtosis efficient frontier. Other authors tend to
analytically solve the mean-variance-skewness-kurtosis portfolio optimization problem
(see Athayde and Flôres, 2002 and Adcock, 2005). These approaches are partial since
356
they are mainly focused on one objective of the optimization program at the cost of the
others.
Dual approaches use Taylor series expansion of the investors’ objective functions
to determine the optimal portfolios (see Jondeau and Rockinger, 2005 and Jurczenko
and Maillet, 2006). The main drawback of this approach is that the Taylor series
expansion may converge to the expected utility only under restrictive conditions (such
as for the exponential). Moreover there is no rule in general for selecting the order of
truncation. Hlawitschka (1994) finds that adding terms to a Taylor-series expansion
does not necessarily improve the approximation, even when the series converges,
however, Ederington (1986) finds that extending the expansion to a fourth term
generally improves the approximation, and never worsens it.
We base our analysis on a dual approach since our utility function includes an
exponential, the first and main drawback of the approach does not apply and secondly,
we decide to select the mean-variance-skewness-kurtosis order of truncation as it seem
to be the most comprehensive.
2.2 Taylor approximation and risk measure
Following Loistl (1979) and Hlawitschka (1994) we approximate the distribution
on the basis of the first four moments. Bell’s function is approximated using a Taylor
series expansion on the choice of a four-order approximation is justified as we analyse
hedge fund return and, as the descriptive statistics indicate, hedge fund returns may be
skewed and have fat tails. The integration of skewness and kurtosis will enable us to
take these statistics into account.
357
The Taylor approximation expresses any function f which is n+1 times
differentiable over an open interval I that contains x and hx + . If the function f is a
polynomial of degree n, then the Taylor series expansion is a finite series with n terms.
On the other hand, if f is non-polynomial, then the Taylor series expansion is an
infinite series (see Loistl, 1976):
!)()(
0
)(
jhxfhxf
j
j
j∑∞
=
=+ (18)
When x is viewed as a random variable, the most common use of this formula is
the expansion of f around its mean argument x .
Now consider a utility function of the random variable )(WU . The Taylor’s series
expansion of this function around the mean end-of-period wealth )1(0 RWW += – where
R is the mean rate of return of the investment – equals:
...)(!
)(...)(2
)()()()()( ''2
' +−
++−
+−+= WUnWWWUWWWUWWWUWU n
n
(19)
358
An intuitive idea is that the more terms are kept in the expansion, the closer the
approximation will be to the expected utility value. If we truncate the series to keep the
first four terms, we have78:
[ ] )()(241)()(
61)()(
21)()( '''''''''2 WUWKWUWSWUWWUWUE +++≅ σ
(20)
with )(WS 3)( WWE −= and )(WK 4)( WWE −=
Applied to Bell’s function, the decomposed function including four moments is:
)(24
)(6
)(2
)()( 44
33
22
WWcbeWWcbeWWcbeWWcbeWWU WcWcWcWc −−−+−−−+= −−−−
(21)
with b, c >0
78 As stated by Guidolin and Timmermann (2002), it is often sufficient to only consider the first four
moments of the wealth distribution since the associated derivatives of the utility function and
moments of the wealth distribution are more intuitive to interpret.
359
Our objective is to determine if including hedge funds in a portfolio consisting of
equity and bond mutual funds significantly improves the risk-return trade-off for the
investor. We perform two sets of tests, 1) we test whether the returns on the capital
market line (CML) achieved for a certain risk level are significantly higher when new
securities are included in the set of risky assets, 2) we test whether the slope of the
capital market line for a defined level of risk changes when new securities are included
in the set of risky assets.
2.3 Risk Measure
Our objective is to determine if including hedge funds in a portfolio consisting of
equity and bond mutual funds significantly improves the risk-return trade-off for the
investor. Practically, we test whether the returns achieved on one side and the slope of
the capital market line (CML) on another significantly change for a defined level of risk
changes when new securities are included in the set of risky assets.
The difference between the capital market line determined in our case and the
classical one is the nature of the risk measure used. We can extract the risk measure
from equation (9).
Define 0W as the initial value of the investors’ wealth and I as the global amount
invested in the risky asset. The total amount invested in the risk-free asset is IW −0 . If
the risk-free rate gives a return equal to r
and the risky asset a return equal to m , as
we consider that everything that is not invested in the risky asset is invested in the risk-
free asset. If we define the risk premium as rx −Θ= , the utility function becomes:
360
)()1())(( )1(0
0 cIxrcW eEbeIxrWxWU −+−−++= (22)
and the expected utility is:
)()1()))((( ))1((0
0 cIxrwc eEbexIrWxWUE −+−−++= (23)
)()1()))((( )())1((0
0 xxcIxIxrwc eEbexIrWxWUE −−++−−++= (24)
The Taylor series expansion of this expression around m yields:
)241
61
211())1())(( 443322)1(
00
xxxercW KIcSIcVIcbexIrWWUE
xcI
+−+−++=−+−
(25)
where"2 )(,)( θθθθ −=−= ESEV xx and
4)( θθ −= EK x .
361
From (12), we get the risk measure xR , for a standard unit of wealth (normalized
to)
xxxx KCCSVR 2
241
61
21
+−= (26)
where 0WIcC ≡
is the product of the (intrinsic) risk perception coefficient, c, and
the (wealth-related) proportion of risky investment 0/WI .
This risk measure accounts for volatility, asymmetry and fat tails. The level of C
depends on the appetite for risk of the investor. Based on experiments on a sample of
40 students, we consider three representative levels. C=10 for a dynamic investor that
does not put much weight on the extreme risks, C=35 for an average investor and C=60
for a very protective investor who mostly fears the tail event of a distribution.
Our spanning test is performed as follows. For each frontier, we identify the
tangency portfolio, i.e. the efficient portfolio where the adapted Capital Market Line or
CML (defined, as in the CAPM, as the locus attainable combinations of the risk free rate
and this risky portfolio) and the efficient frontier are tangent, and draw the adapted CML
with the risk-free rate. Then we fix a value of the risk measure and test the difference in
the returns achievable before looking at the slope of the two capital market line (one
362
with hedge funds and one without) for that measure of risk. Our main challenge is to
estimate the slope of the adapted CML because, as risk is not measured with the
variance, this function is not a straight line.
The underlying idea is illustrated in Figure 11. The capital market line reported
seems to be classic. The only particularity to this Figure is that the risk measure used is
no more the standard deviation of the returns but the extended risk measure as defined
in formula 26.
Figure 12 illustrates the test performed. We first consider a risk level X and we let
a CML containing only mutual funds through point A and another including hedge funds
and mutual funds through point B. Both called “average CML” are in dotted lines in
Figure 12. Secondly, we plot in bold a CML go through the 95% percentile and we add
(in bold again) another CML that goes through the 5% percentile for the portfolio
containing hedge funds and mutual funds. We plot point s C and D Plot points C and D at
another risk value Y.
In our example, at X the test is fully conclusive since hedge funds and mutual
funds do significantly better than mutual funds alone and mutual funds alone do
significantly worse than hedge funds and mutual funds, while at Y the test is partly
conclusive. The portfolio of hedge funds and mutual funds do significantly better than
mutual funds alone, but mutual funds alone do not significantly worse than hedge funds
plus mutual funds.
363
Figure 11: Illustration of the adapted Capital Market Line
2.4 Estimation methodology
The term “bootstrapping” due to Efron (1979), is an allusion to the expression
“pulling oneself up by one’s bootstraps” – in this case, using the sample data as a
population from which repeated samples are drawn. It is a general approach to
statistical inference based on building a sampling distribution for a statistic by
resampling from the data. In the simpliest form of bootstrapping, one repeatedly
analyses subsamples of the data. Each subsample is a random sample with replacement
from the full sample.
Return
Efficient Frontier
Capital Market Line
Risk Measure
364
Figure 12: Illustration of the test of the adapted Capital Market Line
Three sets of funds are taken from a database: hedge funds, equity mutual funds
and bond mutual funds described below. The algorithm that makes the calculations was
written in FORTRAN and C# and was compiled with the Microsoft.net framework.
On the basis of the algorithm construct sets of portfolios having the required
characteristics with regard to the proportion of funds of each type (for example 20 %
hedge funds, 40 % equity mutual funds and 40 % bond mutual funds). All the funds
from the three sets are randomly selected, constructing portfolios each with ten funds
and we repeat the process as many times as required. For each portfolio the algorithm
determines two elements: 1) as a first step the CML generated from the funds included
D
B
A
CML (HF+MF)
CML (MF)
C CML95% (MF)
X Y Risk measure
Return
CML5% (HF+MF)
365
in this portfolio and 2) a series of ten slopes for each CML, each slope corresponding to a
particular value of tR .
The calculation of the CML is carried out point by point. The iterative process
establishes a series of risk levels whose maximum required return must be calculated.
At each step the algorithm implements an optimization problem with the required return
as objective function and the risk function as constraint. The curve is then estimated
with the locus of these risk/return pairs79.
The calculation of the objective is worked out in accordance with the classical
CAPM. The benchmark index return br for the beta calculations is S&P 500 and the risk
free rate Rf is 2.78%.80
))((),,( 110010 fmnnfn RRxxRxxE −++= −−− ββ KK (27)
for a portfolio ∑=
=n
iiip rwr
1
The calculation of the various centred moments lpm , appearing in the risk
function is carried out using the following general formula:
79 The specificity of this pair in comparison with the classical risk/return pair is that the risk measure
has been improved by the including of skewness and kurtosis.
80 This 2.78% risk free rate is the level of the 3-month T-bill rate from Ibbotson and associates such
as the one used by Fama and French (1993).
366
∑ ∑=++ =
−−++
=)..... ,...,(
1111
1,
11
11 )...()(...1...!
lkktskk
T
t
knnt
kt
kn
k
nlp
nn
nn rrrrwwTkk
lm (28)
And the optimization problem is:
iwww
RmCCmmR
rE
in
bpppp
pww n
∀≥=++
=+−≡
0 ,1... 241
61
21 s.t.
)(max
1
4,2
3,2,
,...,1
λ
(29)
where λ is the target proportion of the (fixed) risk measure of the benchmark
portfolio bR .
These elements imply that we have to solve a linear problem with non-linear
constraints. The selected resolution method is the SQP (Sequential Quadratic
Programming, see Schittkowski, 2002) and is based on an iterative reformulation of the
non-linear problem into a problem of quadratic programming which is solved by the
quadratic approximation of the Lagrangian of the objective function, and the
367
linearization of the constraints. The resulting quadratic problem is then solved for every
iteration.
The main interest with this method lies in its “non-feasible way”: the progression
towards an optimum solution is achieved on the basis of the “feasible” but also the “non-
feasible” intermediate points near the field of the constraints. Therfore, contrarily to
many methods where the constraints are verified at each iteration, the SQP method
requires only the final solution to respect the constraints.
Our procedure for the calculation of the CML does not give us an analytical
expression of this one which would enable us to use its derivative for the calculation of
the slopes and the returns. Thus a set of risk values, summarized with values of
parameter λ, is selected within the whole range of the risk values. For each of these
values the expected yield value is calculated for ε−pR and for ε+pR with 81 −= Eε
in accordance with the above procedure. The slope is then given by bp RRp
p
RRE
λ=∆
∆ )(
.
In order to determine the reference p-value at the any confidence level, we
estimate the returns and slope of 2,000 CML (using bootstrapping), rank the slopes or
the returns depending on the case considered by decreasing values for each value of
risk, and select the level of confidence corresponding to the numerical p-values. We
perform 2,000 estimations for 5 different levels of lambda (5 different levels of allocation
to the risk free rate - 20%, 40%, 60%, 80% and 100%). Then, we perform the same
algorithm including various levels of hedge funds (10%, 20%, 50% and 100%) and
separate directional, undirectional and fund of funds that do not have the same
objectives and distribution characteristics. Practically, we estimate the 95% percentile
368
returns and slopes for a portfolio consisting of mutual funds only81 and we compare
these levels with the mean82 return or slope of the results obtained when hedge funds
are added.
81 We made the estimation for the 90%, 95% and 99% confidence levels but we only report the 95%
level. Complete tables are available.
82 We make the same estimation using the median. The results are not reported because they are
perfectly in line. Tables are available upon request.
369
III The database
We attempt to determine if adding hedge funds in a classical portfolio can
enhance the utility of an investor that is invested in stock and bond mutual funds. For
hedge funds, we use the Hedge Fund Research, Inc database. Following Amin and Kat
(2003), we concentrate on the 431 funds that exist during the entire January 1996-May
2006 period. 83 Note that our sample includes the period 1997-1998 which includes
crises in Asia and Russia and the subsequent collapse of LTCM. This particular period
was especially difficult for hedge funds along with the Nasdaq bubble of Srping 2000 and
the enuing bear market of 2000-2002. For mutual funds, we use data from Micropal. We
use monthly performance data from 2,418 surviving equity mutual funds and 1,308
surviving bond mutual funds. We report the descriptive statistics of our databases in
Table 54.
Table 54 indicates that the bulk of the hedge funds in the database are funds of
funds, equity hedge and CTAs (almost 60% on aggregate). The best performers over the
period under review have been directional funds led by emerging markets, equity non-
hedge and equity hedge managers providing net annualized returns of 21.8%, 18.2%
and 15.5% respectively. The lower return providers have been equity market neutral,
83 Obviously, this introduces survivorship bias. As this bias favors the performance of the surviving
funds, our conclusions are very likely to embellish the risk-return trade-off of hedge funds, and should
be considered with caution. There is no simple way to mitigate this problem though. Note, also that a
similar bias is likely to hold for our sample of mutual funds as well. A way to mitigate this problem
would be to replace a fund from the dataset when it is dissolved (of before it exists) by another fund
that exists at this moment. This would be the next step in such an analysis. A large number of
estimations are required and we therefore postpone this step.
370
merger arbitrage and convertible arbitrageurs that provided net returns of 7.85%,
9.34% and 9.47% respectively. In terms of volatility, as one could expect, a large
majority of the directional strategies have been the most volatile. Pure arbitrage
strategies have offered the most stable returns.
The minimum and maximum monthly returns range range from -25.4% for
emerging markets to -2.1% for convertible arbitrage and from 2.5% for relative value to
33.4% for short sellers respectively. Next, we report skewness and kurtosis for each
strategy as well as the minimum and maximum skewness and kurtosis obtained for
individual funds in each strategy and globally. The results interestingly show that even if
skewness reported per strategy is close to zero, there is a diversification effect and the
individual skewness reported has a large range, which is illustrated in Figure 13. These
results confirm that at least for some strategies (event driven, equity market neutral,
fixed income arbitrage, fund of funds and relative value) skewness tends to be negative.
The same analysis on kurtosis indicates that kurtosis is always positive for hedge funds
and that it is largely positive in most cases as indicated by Figure 14.
Table 54 : Descriptive statistics of the hedge fund (Panel A)
and of the Equity and Bond Mutual Funds (Panel B)
N % Mean Ann. Return Std. Dev. Sharpe Ratio
DIRECT. 245
DS 11 2,6% 12,90% 5,30% 2,07
EM 19 4,4% 21,90% 20,60% 0,96
ENH 20 4,6% 18,20% 12,70% 1,27
EH 81 18,8% 15,50% 9,40% 1,44
ED 25 5,8% 11,70% 7,80% 1,24
MAC 18 4,2% 13,20% 7,10% 1,59
SEC 13 3,0% 13,80% 10,60% 1,12
SS 1 0,2% 10,40% 36,10% 0,23
CTA 54 12,5% 13,30% 11,60% 0,97
MT 3 0,7% 14,20% 11,20% 1,09
UNDIR. 70
MA 8 1,9% 9,30% 3,70% 1,96
RV 12 2,8% 11,00% 3,10% 2,94
EMN 14 3,2% 7,90% 3,10% 1,91
FIA 17 3,9% 10,20% 5,10% 1,6
CB 19 4,4% 9,50% 3,30% 2,25
FOF 116 26,9% 11,70% 5,10% 1,88
GLB 431 100% 13,10% 6,00% 1,86
Panel A: Hedge Fund Descriptive Statistics (1/1996-5/2006)
372
Min Max Skewness Kurtosis
DIRECT.
DS -4,80% 7,80% 0,01 0,01
EM -25,40% 19,00% 0,09 0,06
ENH -13,70% 8,00% 0,03 0,02
EH -9,50% 9,60% 0,04 -0,01
ED -10,20% 7,60% 0,02 0
MAC -3,40% 7,70% 0,01 0,01
SEC -14,90% 7,50% 0,04 -0,02
SS -21,80% 33,20% -0,06 0,19
CTA -6,90% 9,20% -0,02 0,02
MT -6,60% 11,60% 0,02 -0,01
UNDIR.
MA -5,20% 3,90% 0,02 0,02
RV -3,10% 2,60% 0,02 0,01
EMN -2,80% 3,10% 0,02 0,01
FIA -4,70% 4,80% 0,01 0,01
CB -2,10% 3,40% 0,01 0,01
FOF -5,20% 6,60% 0,02 0,01
GLB -5,70% 5,80% -0,16 1,02
Panel A (continued): Hedge Fund Descriptive Statistics (1/1996-5/2006)
373
N Mean Ann. Return Ann. Std. Dev. Sharpe Ratio (2%)
Eq MF 2 418 9,60% 19,30% 0,39
Bd MF 1 308 4,85% 7,68% 0,37
Min Max Skewness Kurtosis
Eq MF -16,5% 16,5% -0,22 0,98
Bd MF -4,2% 7,2% 0;62 0,51
This table reports the descriptive statistics of our database. Our database covers 431 hedge funds, 2418 equity mutual funds and 1308 bond funds over the January 1996 to May 2006 period. CB = convertible arbitrage, DS = distressed securities, EM = emerging markets,EqLong = equity long biaised and equity long only, ELS= equity long/short, EqShort = equity short, ED = event driven, MAC = macro, Multi = mutli-strategy, SEC = sector funds, Others = other strategies, EMN = equity market neutral, MA = merger arbitrage, StatArb = statistical arbitrage, FI = fixed income strategies, FoF = fund of funds and HF = global database. DIR.= directional strategies; UNDIR.=undirectional strategies.
Panel B: Mutual Fund Descriptive Statistics (1/1996-5/2006)
374
On the mutual fund side, the net mean annualized return is at 9.6% for equity
funds with volatility at 19.3%. Such returns are relatively low when compared to hedge
funds with a high volatility. The skewness figures (more particularly the minimum and
maximum skewness) indicate a positive skewness trend. Kurtosis column indicates the
presence of fat tails. Bond mutual funds offer much lower returns with a relatively limited
volatility, positive skewness and positive kurtosis.
These results indicate that hedge funds seems to offer attractive risk-return trade-
offs but that the asymmetry in their return distribution and the presence of large fat tails
may impede their attractiveness when all these aspects are taken into consideration.
375
Figure 13: Repartition of the skewness of individual funds
-4
-3
-2
-1
0
1
2
3
4
HF CB DS EM
EqLon
gELS
EqSho
rt EDMac
Multi
SECOthe
rsEMN MA
StatArb FI
FoF
This figure reports the repartition of the skewness of individual funds. Our database
covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the
January 1996 to May 2006 period. CB = convertible arbitrage, DS = distressed securities,
EM = emerging markets,EqLong = equity long biaised and equity long only, ELS= equity
long/short, EqShort = equity short, ED = event driven, MAC = macro, Multi = mutli-
strategy, SEC = sector funds, Others = other strategies, EMN = equity market neutral,
MA = merger arbitrage, StatArb = statistical arbitrage, FI = fixed income strategies, FoF
= fund of funds and HF = global database. DIR.= directional strategies;
UNDIR.=undirectional strategies.
376
Figure 14: Repartition of the kurtosis of individual funds
-6
-4
-2
0
2
4
6
8
10
12
HF CB DS EM
EqLon
gELS
EqSho
rt EDMac
Multi
SECOthe
rsEMN MA
StatArb FI
FoF
This figure reports the repartition of the kurtosis of individual funds. Our database covers
431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January
1996 to May 2006 period. CB = convertible arbitrage, DS = distressed securities, EM =
emerging markets,EqLong = equity long biaised and equity long only, ELS= equity
long/short, EqShort = equity short, ED = event driven, MAC = macro, Multi = mutli-
strategy, SEC = sector funds, Others = other strategies, EMN = equity market neutral,
MA = merger arbitrage, StatArb = statistical arbitrage, FI = fixed income strategies, FoF
= fund of funds and HF = global database. DIR.= directional strategies; UNDIR.=
undirectional strategies.
377
IV Results
The objective of this study is to test if the inclusion of hedge funds in a diversified
portfolio of stock and bond mutual funds enables investors to attain a significantly higher
level of return for the same risk level.
We start this section by explaining how we determine the levels of the p-values,
that is, the level over which the inclusion of hedge funds in a portfolio enables the
investor to significantly improve his satisfaction. Then, we report the results of the
estimation increasing the allocation to hedge funds from 0 to 100% for three types of
investor risk profiles and for the five different levels of allocation to the risk-free asset.
4.1 Significance level
We want to ascertain if the inclusion of hedge funds in a portfolio of stocks and
bonds enables an investor to significantly improve the level of return he gets for a
predetermined maximum level of risk. We first have to determine the significance levels,
then we estimate the p-values by calculating the value corresponding to the 95%
percentile of a portfolio consisting of mutual funds only (50% equity mutual funds and
50% bond mutual funds) for each value of lambda. This 95% confidence level is obtained
by estimating 2,000 capital market line for each level of lambda, by ranking them to
extract the level of confidence (95% corresponding to the 1900th estimation).
We then compare the mean return obtained for portfolios including hedge funds
with p-value in order to determine if hedge funds significantly add value to the initial
portfolio. We test if the mean returns obtained for each level of risk are higher than the
95% level of confidence of a mutual funds only portfolio when hedge funds are added.
A further analysis is based on the slope of the capital market line estimated and it
test the inverse relation whereby the p-values are estimated the same way. The p-values
378
for the slope analysis are estimated for mutual fund portfolios only and are then ranked.
For inverse relations, we estimate the p-values for a portfolio consisting of only hedge
funds and compare this level with the mean returns obtained when mutual funds are
added to the portfolio.
4.2 Including hedge funds in mutual funds portfolio
As previously stated, we consider three categories of investors: average,
protective and progressive. We report the results obtained for the three categories of
investors separately. For each estimation we report a Table that provides comparison and
figures that illustrate the results.
a. Average investor
The first line of Table 56 reports the p-value for the 95% confidence level for a
portfolio of mutual funds only. Panel A reports the mean returns when only directional
hedge funds are added; Panel B the same results when undirectional hedge funds are
added. Finally Panel C the mean returns when funds of hedge funds are added to the
portfolio.
The p-value line indicates that 95% of the time, a portfolio consisting of equity
mutual funds and bond mutual funds would have offered a return lower than 5.4%
annualized if 20% of the assets were allocated to the risky asset. For an allocation of
40% to the risky asset, the mean annualized return would have been lower than 8.3%
annualized 95% of the time. A full exposure to the risky asset would have yield returns
as high as 16%, 5% of the time.
379
The first line of Panel A indicates that the addition of 10% of directional hedge
funds would not enable the investor to reach a higher mean return. This result holds for
any level of allocation to the risky asset. This result should be explained by the fact that
directional strategies are exposed to the market and adding only 10% of directional
strategies to a directional portfolio does not enable the investor to attain significantly
higher levels of returns.
The second line of Panel A shows that results are mitigated for an allocation of
20% to directional hedge fund strategies. For low levels of allocation to the risky asset
and for high allocation to the risky asset, the levels of return achievable are lower than
the corresponding p-values. For allocation to the risky asset between 40% and 60%
however, the inclusion of hedge funds helps for medium risks levels. This indicates a first
inflection point whereby depending on the risk appetite and the allocation to the risky
asset, some investors can reach significantly higher level of return when 20% of their
portfolio is allocated to directional hedge funds.
The next two lines report 50% and 100% levels of allocation to hedge funds. They
clearly indicate that large allocations to directional hedge funds enable investors to reach
significantly higher levels of returns for the same level of risk. The 100% directional
hedge fund line confirms that on a stand alone basis directional hedge funds are more
attractive than a diversified portfolio of mutual funds.
The first column of Panel A indicates that as they tend to be risky, directional
hedge funds do not enable the investor to attain the risk level corresponding to the 20%
lambda.
Table 55: Mean return estimation for average investors
20% 40% 60% 80% 100% All
P-value (95%) 50% 50% 0% 5,4% 8,3% 11,5% 14,4% 16,0% 14,6%
PANEL A: DHF
Mean Return 45% 45% 10% 4,7% 7,9% 10,4% 12,5% 13,7% 11,5%
Mean Return 40% 40% 20% 5,1% 9,2% 12,0% 14,2% 15,6% 13,0%
Mean Return 25% 25% 50% 5,3% 10,9% 14,1% 16,5% 18,3% 15,3%
Mean Return 0% 0% 100% NA 12,7% 16,3% 18,7% 20,6% 17,5%
PANEL B: UHF
Mean Return 45% 45% 10% 5,9% 8,7% 10,4% 11,7% 12,6% 10,8%
Mean Return 40% 40% 20% 6,8% 9,8% 11,5% 12,4% 13,2% 11,5%
Mean Return 25% 25% 50% 8,2% 11,6% 12,9% 13,6% 14,1% 12,4%
Mean Return 0% 0% 100% 9,1% 13,0% 14,6% 15,4% 16,3% 13,6%
LambdasEMF BMF HF
20% 40% 60% 80% 100% All
PANEL C: FOF
Mean Return 45% 45% 10% 5,4% 9,5% 11,1% 12,3% 13,2% 11,5%
Mean Return 40% 40% 20% 5,9% 10,5% 12,2% 13,3% 14,2% 12,5%
Mean Return 25% 25% 50% 6,3% 12,0% 13,6% 14,6% 15,7% 13,5%
Mean Return 0% 0% 100% 8,2% 13,3% 14,8% 16,0% 17,6% 14,9%
LambdasEMF BMF HF
This table reports the mean return obtained for various allocation to hedge funds and for various level of allocation to the risky asset for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure defined as
xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the return distribution and xK = the kurtosis of the
return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when including directional hedge funds in the initial portfolio, Panel B reports the result obtained when including undirectional hedge funds in the initial portfolio and Panel C reports the result obtained when including funds of hedge funds in the initial portfolio. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
382
Panel B reports a different pattern. The first three of Panel B indicate that the
addition of undirectional hedge funds to a portfolio of mutual funds enable investors to
reach higher levels of returns for allocation to the risky assets up to 60%. For higher risk
allocation, undirectional strategies do not help diversifying. The last line of Panel B
however indicates that a 100% allocation to undirectional hedge funds is however more
attractive than a 100% mutual fund portfolio.
Panel C reports exactly the same pattern as Panel B. Adding only 10% of a
portfolio to funds of hedge funds enables an investor to reach significantly higher levels
(for allocation to the risky assets up to 60%). These results are in line with our
expectations. Undirectional strategies and funds of funds are low risk profile investments
with return distribution completely different from the equity markets and to a certain
extent to directional hedge funds that are exposed to the market. The difference is
however that allocating 50% to funds of hedge funds can enable the investor to
significantly improve his returns when 80% of the portfolio is allocated to risky
strategies, indicating that funds of hedge funds are marginally more attractive than
unidirectional strategies.
This first analysis interestingly and clearly indicates that hedge funds can help an
investor to reach a higher level of returns for any level of risk depending on his appetite
for risk and its allocation to the risky asset. Low risk allocation can significantly improve
the returns offered while adding low levels (10-20%) of undirectional hedge funds or
funds of funds while higher risk level should give high allocation to directional strategies.
Figures 15 to 17 report the same results visually. Figure 15 confirms that a small
allocation to directional hedge funds does not enable the investor to reach significantly
higher returns while higher allocation do, particularly for higher risk level.
383
Figure 15: Directional Hedge Funds - Mean
Percentile Return
10%DHF20%DHF
50%DHF100%DHF
Lam
bda
20%
Lam
bda
40%
Lam
bda
60%
Lam
bda
80%
Lam
bda
100%
All la
mbd
as
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
This figure reports the difference between the mean hedge fund return and the critical value obtained for various levels of allocation to directional hedge funds (0%, 10%, 20%, 50% and 100%) and for various levels of allocation to the risk-free asset (20%, 40%, 60%, 80% and 100%) for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure defined as
xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of
the return distribution and xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). P-values are reported in the 0% allocation to hedge funds part of the Figure. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). The 0% hedge fund portfolio is divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
384
Figure 16 shows that including undirectional hedge funds enable investors to earn
higher returns, particularly for low values of lambda. The lambda 20% series of values
increases monotically with the inclusion of undirectional hedge funds confirming that
allocating 10% of the portfolio to undirectional hedge funds strategies enables investors
to obtain significantly higher returns. For higher allocation to the risky asset large
exposure to undirectional hedge funds have to be considered to be as attractive as the
classical portfolio of stock and bond mutual funds.
As indicated by Figure 17, funds of hedge funds offer the same characteristics as
undirectional hedge funds, and enable investors to attain higher returns for the same
level of risk for low allocation to the risky asset (lambda up to 60%) even when only
10% of the portfolio is allocated to hedge funds. For higher allocation to the risky asset,
integrating 10% or 20% of funds of funds does not help the investor to attain higher
returns. More than 20% of the portfolio has to be allocated to hedge funds.
b. Protective & progressive investors
By definition, a protective investor does not like riskand he would put more weight
to an investment that enables him to diversify the risk of its portfolio away. A progressive
investor does not care as much about the risk but is focused on returns that can be
attained. Results are reported in Table 57 and Table 5884.
84 We do not report the figures for the sake of brevity but they are available.
385
Figure 16: Undirectional Hedge Funds - Mean Percentile
Return
10%UHF20%UHF
50%UHF100%UHF
Lam
bda
20%
Lam
bda
40%
Lam
bda
60%
Lam
bda
80%
Lam
bda
100%
All la
mbd
as
-0,04
-0,03
-0,02
-0,01
0,00
0,01
0,02
0,03
0,04
0,05
This figure reports the difference between the mean hedge fund return and the critical value obtained for various levels of allocation to undirectional hedge funds (0%, 10%, 20%, 50% and 100%) and for various levels of allocation to the risk-free asset (20%, 40%, 60%, 80% and 100%) for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure defined as
xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of
the return distribution and xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). P-values are reported in the 0% allocation to hedge funds part of the Figure. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). The 0% hedge fund portfolio is divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
386
Figure 17: Funds of Hedge Funds - Mean Percentile Return
10%FOF
20%FOF
50%FOF100%FOF
Lam
bda
20%
Lam
bda
40%
Lam
bda
60%
Lam
bda
80%
All la
mbd
as
S6
-0,04-0,03-0,02-0,010,000,010,020,030,04
0,05
0,06
This figure reports the difference between the mean hedge fund return and the critical value obtained for various levels of allocation to funds of hedge funds (0%, 10%, 20%, 50% and 100%) and for various levels of allocation to the risk-free asset (20%, 40%, 60%, 80% and 100%) for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure defined as
xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of
the return distribution and xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). P-values are reported in the 0% allocation to hedge funds part of the figure. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). The 0% hedge fund portfolio is divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
Table 56: Mean return estimation for protective investors
20% 40% 60% 80% 100% All
P-value (95%) 50% 50% 0% 5,3% 8,3% 11,5% 14,5% 16,3% 14,7%
PANEL A: DHF
Mean Return 45% 45% 10% 4,7% 8,1% 10,5% 12,6% 13,9% 11,7%
Mean Return 40% 40% 20% 5,0% 9,1% 11,9% 14,0% 15,4% 12,9%
Mean Return 25% 25% 50% 5,5% 10,9% 14,1% 16,4% 18,0% 15,1%
Mean Return 0% 0% 100% NA 12,7% 16,2% 18,7% 20,5% 17,5%
PANEL B: UHF
Mean Return 45% 45% 10% 6,0% 8,6% 10,4% 11,6% 12,6% 10,7%
Mean Return 40% 40% 20% 6,9% 9,8% 11,3% 12,4% 13,2% 11,4%
Mean Return 25% 25% 50% 8,0% 11,5% 12,8% 13,5% 14,1% 12,3%
Mean Return 0% 0% 100% 9,2% 13,0% 14,5% 15,2% 16,1% 13,4%
LambdasEMF BMF HF
20% 40% 60% 80% 100% All
PANEL C: FOF
Mean Return 45% 45% 10% 5,3% 9,4% 11,1% 12,4% 13,4% 11,6%
Mean Return 40% 40% 20% 5,7% 10,5% 12,1% 13,3% 14,2% 12,4%
Mean Return 25% 25% 50% 6,8% 12,0% 13,5% 14,5% 15,5% 13,5%
Mean Return 0% 0% 100% 8,5% 13,1% 14,6% 15,8% 16,9% 14,7%
LambdasEMF BMF HF
This table reports the mean return obtained for various allocation to hedge funds and for various level of allocation to the risky asset for a protective investor. A protective investor is defined as an investor with a C value of 60 in our extended risk
measure defined as xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the return
distribution and xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when including directional hedge funds in the initial portfolio, Panel B reports the result obtained when including undirectional hedge funds in the initial portfolio and Panel C reports the result obtained when including funds of hedge funds in the initial portfolio. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
Table 57: Mean return estimation for progressive investors
20% 40% 60% 80% 100% All
P-value (95%) 50% 50% 0% 5,4% 8,2% 11,2% 14,3% 16,9% 14,6%
PANEL A: DHF
Mean Return 45% 45% 10% 4,7% 7,9% 10,3% 12,5% 13,9% 11,5%
Mean Return 40% 40% 20% 5,1% 9,1% 11,7% 14,0% 15,6% 12,9%
Mean Return 25% 25% 50% 5,7% 11,0% 14,1% 16,4% 18,3% 15,2%
Mean Return 0% 0% 100% NA 12,7% 16,3% 18,8% 20,8% 17,6%
PANEL B: UHF
Mean Return 45% 45% 10% 6,1% 8,7% 10,4% 11,7% 12,7% 10,8%
Mean Return 40% 40% 20% 7,0% 9,8% 11,4% 12,4% 13,4% 11,5%
Mean Return 25% 25% 50% 8,3% 11,6% 13,1% 13,6% 14,5% 12,5%
Mean Return 0% 0% 100% 9,2% 13,0% 14,7% 15,5% 16,7% 13,6%
LambdasEMF BMF HF
20% 40% 60% 80% 100% All
PANEL C: FOF
Mean Return 45% 45% 10% 5,2% 9,4% 11,0% 12,3% 13,2% 11,5%
Mean Return 40% 40% 20% 5,7% 10,5% 12,2% 13,3% 14,1% 12,3%
Mean Return 25% 25% 50% 6,5% 11,9% 13,6% 14,8% 15,7% 13,6%
Mean Return 0% 0% 100% 8,4% 13,2% 14,8% 16,1% 17,8% 14,9%
LambdasEMF BMF HF
This table reports the mean return obtained for various allocation to hedge funds and for various level of allocation to the risky asset for a progressive investor. A progressive investor is defined as an investor with a C value of 10 in our extended
risk measure defined as xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the
return distribution and xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when including directional hedge funds in the initial portfolio, Panel B reports the result obtained when including undirectional hedge funds in the initial portfolio and Panel C reports the result obtained when including funds of hedge funds in the initial portfolio. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
391
The results obtained for progressive and protective investors are very close to
those obtained for an average investor. The results indicate that it is the level of lambda
(the global risk level) that has the most importance and the main impact on our results.
Depending on the global risk level and the kind of investor considered, the investor
should decide if he will use directional, undirectional hedge funds or funds of funds, and
to what extent they should be used to achieve higher levels of satisfaction.
d. Slope comparison
Table 59 reports the same analysis based on the slope of the capital market line
as a tool to measure investor satisfaction rather than simply using returns85. The use of
the slope as a tool to measure satisfaction can be justified by the fact that it can be
viewed as an adapted Sharpe ratio with the extended risk measure as denominator as
defined hereafter:
Adapted Sharpe ratio: Riskturn /Re (30)
With the risk measure defined asxxxx KCCSVR 2
241
61
21
+−= (31)
85 We report the results for average investors. Corresponding Tables for protective and progressive
investors are available upon request.
Table 58: Slope estimation for average investors
20% 40% 60% 80% 100% All
P-value (95%) 50% 50% 0% 0,078 0,038 0,020 0,004 0,002 0,022
PANEL A: DHF
Mean Return 45% 45% 10% 0,068 0,024 0,009 0,002 0,001 0,007
Mean Return 40% 40% 20% 0,079 0,028 0,008 0,003 0,001 0,008
Mean Return 25% 25% 50% 0,118 0,038 0,008 0,003 0,001 0,010
Mean Return 0% 0% 100% NA 0,033 0,008 0,003 0,001 0,009
PANEL B: UHF
Mean Return 45% 45% 10% 0,088 0,017 0,005 0,002 0,001 0,008
Mean Return 40% 40% 20% 0,006 0,008 0,009 0,010 0,010 0,009
Mean Return 25% 25% 50% 0,155 0,013 0,003 0,001 0,001 0,020
Mean Return 0% 0% 100% 0,161 0,012 0,003 0,001 0,001 0,031
LambdasEMF BMF HF
20% 40% 60% 80% 100% All
PANEL C: FOF
Mean Return 45% 45% 10% 0,099 0,019 0,005 0,002 0,001 0,007
Mean Return 40% 40% 20% 0,160 0,020 0,004 0,001 0,001 0,008
Mean Return 25% 25% 50% 0,286 0,016 0,003 0,001 0,001 0,009
Mean Return 0% 0% 100% 0,507 0,014 0,003 0,001 0,001 0,008
LambdasEMF BMF HF
This table reports the mean slope obtained for various allocation to hedge funds and for various level of allocation to the risky asset for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure
defined as xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the return distribution and
xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of mutual funds for any level of lambda and taking the 95% percentage level value. P-values estimated with a mutual fund portfolio divided equally between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when including directional hedge funds in the initial portfolio, Panel B reports the result obtained when including undirectional hedge funds in the initial portfolio and Panel C reports the result obtained when including funds of hedge funds in the initial portfolio. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
394
Table 59 reports mitigated results. Results requires careful analysis when returns
are not the only measure considered as a measure of investor wealth for a specific level
of risk level. Two remarks, first, the slope decreases as we increase the risk level. This is
perfectly in line with the visual aspect of an efficient frontier. An investor who accepts
higher risks with the objective of higher returns will see risk/return ratio decrease as the
risk increase more rapidly than the return, the curve drawn will be concave. Second, the
lambda 100% column indicates that for high allocation to the risky asset, the slope is low
on absolute terms and close to zero indicating that we are close to the flat tangent.
Panel A reports the slopes of the capital market line obtained when directional
hedge funds are added to the portfolio. Directional hedge funds enable average investors
to improve their satisfaction (as measured by the slope) by giving high allocation to
directional hedge funds for low levels of risky assets (lambda 20%). Results are however
completely different when we go further to the right and consider higher risk allocation.
Directional hedge funds do not enable investors to reach higher levels of satisfaction.
These results have to be mitigated because we are looking at very small numbers on
absolute terms.
Panel B and C report the same pattern for undirectional hedge funds and for funds
of hedge funds. The main difference is that the inclusion of high levels of undirectional
hedge funds and funds of funds increases rapidly the slope in absolute and relative
bases.
We obtain exactly the same pattern for protective and progressive investors,
confirming that hedge funds enable investors to reach significantly higher levels of
satisfaction (as measured by the ratio of return to risk) when the risk level is low, but the
results are unclear for higher levels of risk since figures reported are very low in absolute
terms.
395
4.3 Including mutual funds in hedge fund portfolios
We perform the inverse test as a complementary analysis, by starting with a
portfolio of hedge funds and test if the inclusion of mutual funds in this portfolio enables
the investor to reach a significantly higher level of satisfaction. We perform this test for
average, protective and progressive investors as well as use mean returns as a measure
of satisfaction and slope.
a. Average investors
Table 59 interestingly indicates that in some cases the inclusion of mutual funds in
a hedge fund portfolio may enable investors to reach higher returns. In the case of
directional hedge funds, the investor can reach higher level of returns for any level of risk
when 50% of the portfolio is allocated to mutual funds (half equity and half bon mutual
funds). When higher allocation are made to mutual funds, returns are less attractive
indicating that high allocation should be made to directional hedge funds when investors
are considering directional hedge funds a diversification tool to mutual funds.
For directional hedge funds, the results are even more interesting. Adding mutual
funds to hedge fund portfolio is attractive. Up to 80% of the portfolio can be allocated to
mutual funds and the portfolio would still offer attractive returns for low level of risks
(lambda up to 40%). For higher level of risks, the returns offered remains attractive even
for low allocation to hedge funds. This result is in line with the underlying characteristics
of undirectional strategies. Such strategies are low risk strategies by definition. To offer
riskier returns, such strategies should be diversified with directional high risk strategies.
Results are more controversial with funds of funds. The inclusion of mutual funds
in a fund of hedge funds portfolio is only attractive for relatively low levels of allocation to
mutual funds (up to 50%). Over this level, the returns offered for each level of risk are
more attractive when only funds of funds are considered. For high risk portfolio however,
396
this is not true. This result is logical since funds of hedge funds are low risk investments
that should be diversified to be considered risky.
b. Protective and progressive investors86
The results obtained for protective and progressive investors are the same as
those obtained for average investors. Adding mutual funds in portfolio of hedge funds
can be attractive mainly for high risk investors and the inclusion of mutual funds in a
undiversified portfolio of hedge funds is attractive for relatively low levels of allocation to
mutual funds.
86 Complete results are available upon request.
Table 59: Mean return estimation for average investors (including mutual funds in a
hedge fund portfolio)
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% NA 9,6% 13,2% 14,9% 15,8% 11,8%
Mean Return 25% 25% 50% 5,3% 10,9% 14,1% 16,5% 18,3% 15,3%
Mean Return 40% 40% 20% 5,1% 9,2% 12,0% 14,2% 15,6% 13,0%
Mean Return 45% 45% 10% 4,7% 7,9% 10,4% 12,5% 13,7% 11,5%
Mean Return 50% 50% 0% 4,5% 6,8% 8,9% 11,0% 12,3% 10,2%
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% 6,3% 10,0% 10,5% 10,7% 11,1% 7,7%
Mean Return 25% 25% 50% 8,2% 11,6% 12,9% 13,6% 14,1% 12,4%
Mean Return 40% 40% 20% 6,8% 9,8% 11,5% 12,4% 13,2% 11,5%
Mean Return 45% 45% 10% 5,9% 8,7% 10,4% 11,7% 12,6% 10,8%
Mean Return 50% 50% 0% 5,9% 8,7% 10,4% 11,7% 12,6% 10,8%
Panel A: DHF
LambdaEMF BMF UHFPanel B: UHF
EMF BMF HFLambda
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% 6,7% 11,3% 12,6% 13,2% 13,5% 11,7%
Mean Return 25% 25% 50% 6,3% 12,0% 13,6% 14,6% 15,7% 13,5%
Mean Return 40% 40% 20% 5,9% 10,5% 12,2% 13,3% 14,2% 12,5%
Mean Return 45% 45% 10% 5,4% 9,5% 11,1% 12,3% 13,2% 11,5%
Mean Return 50% 50% 0% 4,5% 6,8% 8,9% 11,0% 12,3% 10,2%
Panel C: FoFLambda
EMF BMF FOF
This table reports the mean return obtained for various allocation to mutual funds and for various level of allocation to the risky asset for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure
defined as xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the return distribution and
xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of hedge fund for any level of lambda and taking the 95% percentage level value. The allocation to mutual fund is equally weighted between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when the initial portfolio consists of directional hedge funds, Panel B reports the result obtained when the initial portfolio consists of unidirectional hedge funds and Panel C reports the result obtained when the initial portfolio consists of hedge funds of funds. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
399
c. Slope comparison
As reported in Table 61, the results obtained using the slope as a measure of
satisfaction are in line with the previous one based on mean return for any specific
lambda. Mutual funds may enable hedge fund investors to significantly increase their
level of satisfaction.
Table 60: Slope estimation for average investors (including mutual funds in a hedge
fund portfolio)
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% NA 0,0694 0,0138 0,0053 0,0027 0,0335
Mean Return 25% 25% 50% 0,1178 0,0375 0,0077 0,0026 0,0012 0,0099
Mean Return 40% 40% 20% 0,0791 0,0284 0,0079 0,0025 0,0011 0,0082
Mean Return 45% 45% 10% 0,0684 0,0235 0,0088 0,0024 0,0011 0,0074
Mean Return 50% 50% 0% 0,0520 0,0197 0,0095 0,0022 0,0011 0,0065
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% 0,3578 0,0273 0,0067 0,0023 0,0013 0,1807
Mean Return 25% 25% 50% 0,1551 0,0131 0,0028 0,0011 0,0006 0,0197
Mean Return 40% 40% 20% 0,0055 0,0078 0,0091 0,0098 0,0104 0,0091
Mean Return 45% 45% 10% 0,0884 0,0170 0,0046 0,0017 0,0008 0,0079
Mean Return 50% 50% 0% 0,0520 0,0197 0,0095 0,0022 0,0011 0,0065
Panel B: UHF
Panel A: DHF EMF BMF HFLambda
EMF BMF HFLambda
20% 40% 60% 80% 100% All
Percentile 5% 0% 0% 100% 1,6006 0,0315 0,0059 0,0025 0,0014 0,0238
Mean Return 25% 25% 50% 0,2858 0,0158 0,0033 0,0014 0,0007 0,0093
Mean Return 40% 40% 20% 0,1598 0,0198 0,0038 0,0014 0,0007 0,0077
Mean Return 45% 45% 10% 0,0985 0,0190 0,0048 0,0015 0,0008 0,0068
Mean Return 50% 50% 0% 0,0520 0,0197 0,0095 0,0022 0,0011 0,0065
Panel C: FoF EMF BMF FOFLambda
This table reports the mean slope obtained for various allocation to mutual funds and for various level of allocation to the risky asset for an average investor. An average investor is defined as an investor with a C value of 35 in our extended risk measure
defined as xxxx KCCSVR 2
241
61
21
+−= with xV =the variance of the return; xS = the skewness of the return distribution and
xK = the kurtosis of the return distribution. P-values are obtained by estimating 2,000 CML for a portfolio of hedge fund for any level of lambda and taking the 95% percentage level value. The allocation to mutual fund is equally weighted between equity mutual funds (EMF) and bond mutual funds (BMF). Panel A reports the result obtained when the initial portfolio consists of directional hedge funds, Panel B reports the result obtained when the initial portfolio consists of unidirectional hedge funds and Panel C reports the result obtained when the initial portfolio consists of hedge funds of funds. Lambda is the level of allocation to the risk free rate (20%, 40%, 60%, 80% and 100%). Our database covers 431 hedge funds, 2,418 equity mutual funds and 1,318 bond funds over the January 1996 to May 2006 period. Numbers in the table are annualized mean returns.
402
V Conclusion
Hedge funds exhibit abnormal returns. This is the basic reason why traditional
tools like the mean-variance efficient frontier analysis should not be used to analyse
alternative assets such as hedge funds. In this paper we develop the idea of an adapted
capital market line in an extended risk-return framework that includes not only volatility
as a measure of risk but also higher moments. Our methodology is based on the Taylor’s
extension of the linex utility function developed by Bell (1988, 1995).
This new methodology opens a new field in portfolio analysis research. It enables
investors to determine if they should include alternative investments in their portfolio
depending on their level of risk aversion. When the risk measure is limited to volatility,
hedge funds exhibit an attractive risk/return profile, however this result needs careful
care when higher moments are considered.
Our results indicate that directional hedge funds should be considered separately
from undirectional hedge funds and fund of hedge funds. On one hand adding small
allocations to directional hedge funds does not significantly change the risk-return profile
of the global portfolio but this changes when we attain 20% an allocation of 20% to
directional hedge funds. This result in a significant improvement of satisfaction for
diversified portfolios. Over a 50% allocation to directional hedge funds provides a
significantly more attractive returns in all cases.
On the other hand, undirectional hedge funds and fund of funds can be grouped
together because they have the same pattern. Adding undirectional hedge funds or fund
of funds to a classical portfolio enables investors to reach higher levels of returns for low
and medium risk levels for allocation as low as 10% to hedge funds. For high allocation
to the risky asset undirectional strategies do not help diversifying and reaching higher
return levels. This result is in contrast with the one obtained for directional hedge funds
403
and confirms the need to differentiate directional from unidirectional hedge funds.
Undirectional strategies and funds of funds are low risk profile investments and should be
used as such.
A complementary analysis on the impact of the insertion of mutual funds in hedge
fund portfolios confirms that mutual funds do not significantly diversify hedge fund
portfolios when an extended risk measure is considered.
The new adapted efficient frontier opens new doors for asset allocators. Based on
the clients’ objective and the market conditions, it determines if hedge funds must be
added to the existing portfolio and in the future we should be able to determine what
hedge fund strategy should be favoured.
The next step will be first to distinguish between hedge fund strategies while
determining the impact of inserting hedge funds on the adapted efficient frontier.
Second, the identical tests should be performed on various analysis period to determine
what kind of fund should be favoured in specific market conditions. Another important
future step would be to go into more precision regarding the estimation of the aversion
to risk in order to enable investors to precisely determine if or not they should use hedge
funds.
General Conclusion
405
General Conclusion
Hedge funds have attracted the attention of many academicians over the last
decade. Almost every aspect of the hedge fund world has been studied from performance
decomposition, to risk analysis, strategy explanation, regulatory aspects, and so on. The
purpose of this doctoral thesis is clearly established: to understand hedge fund strategies
by looking at the number produced. Our contribution is on the quantitative analysis of
hedge fund strategies. We divide this Thesis in three complementary parts.
Our first objective is to clearly understand hedge fund managers and to explain
how they create alpha over time. To extract pure alpha we develop, test and improve an
extended multi-factor performance analysis model in order to understand hedge fund
performance on the one hand, while on the other to develop and adapt a methodology to
determine whether there is any persistence in hedge fund returns. Three studies cover
this aspect of the analysis (Analysis of Hedge Fund Performance, Hedge Fund
Performance and Persistence in Bull and Bear Markets and Sustainability in Hedge Fund
Performance: New Insights).
We analyse hedge fund returns, understand how manager create performance
over time and if the extracted is consistent over time. Globally, our results confirm that
some hedge fund managers do create pure alpha over time and persistently do so
independently of the market conditions considered and of the performance decomposition
model considered. Depending on the period under review and on the strategy considered
between 20% and 50% of the individual managers do outperform classical indices. This
result indicates that hedge funds have been attractive investments in various market
conditions. With these results in hand, we looked for a systematic way of investing in
406
hedge funds that would enable the investor to consistently and significantly outperform
the classical markets over time. Our first persistence analysis based exclusively on
performance showed that around half of the funds create significant and persistent alpha
over time and that these funds tend to be low volatile funds with a limited exposure to
the equity market. Then, we performed a further analysis that uses other tools than
simply returns (like the Sharpe ratio, standard deviation, alpha, beta, skewness, kurtosis
and an adapted Sharpe ratio ) as a way of determining if hedge funds offer consistence in
alpha creation. We find a consistent, systematic way of creating pure alpha using a
simple classification methodology based on basic statistics: risk-return trade-off measure
(the Sharpe score), volatility and to a lesser extent, the beta exposure appear to be the
best and most stable way of classifying hedge funds in order to detect persistency in the
returns. Funds offering the highest Sharpe score, funds with a limited volatility and/or
funds with a limited exposure to the equity market consistently and significantly
outperform equity and bond markets. These results hold not only for a full market cycle,
but also when separating bull and bear market conditions.
This analysis is of particular interest because it clearly proves that some funds
consistently and significantly outperform classical markets. The important element used
to detect these funds is the methodology by which they are classified. The hedge fund
industry may in attractive and outperform classical markets if the investors select the
good managers.
The second objective analysed is clearly linked to the first. We perform a specific
analysis on the most represented strategy: market neutral funds. By definition, market
neutral funds have a limited relative exposure to the equity market. We check for this
neutrality and analyse what kind of funds consistently outperform over time: the pure
market neutral funds, market timers or funds with a more directional bias. This aspect is
analysed in part 2 (Analysis of Hedge Fund’s Market Exposure).
407
The core of the study is based on a methodology that uses classical exposure
measures like the beta in an original way. Our analysis of market neutral funds indicates
first that the betas obtained are low on an absolute term but significantly positive and
that the more volatile funds tend to have the highest market exposure. Second,
individual fund analysis results indicate that around one third of the funds have been
significantly exposed to the market while two thirds of the alphas have been significantly
positive. Finally, sub-period analysis confirm that market neutral funds tend to have a
higher exposure to the markets in market turmoil and no exposure in strong bull markets
even if they are some exceptions. This result confirms that the correlation of market
neutral fund tend to increase when the market in going down even if there may still be
alpha creation depending on the sub-strategy considered. On the other hand, they were
few funds significantly positively exposed to the market during the bullish period. This
relation is not what investors are looking for but as many market neutral funds continue
to create significant alpha there is a trade-off between the increase in the beta
(unwanted added risk) and value creation (significantly positive alpha). Another time,
fund selection remains the central point.
Finally, the third complementary objective of the thesis is to determine whether
hedge fund strategies should be included in a classical portfolio of stocks and bonds. In
Part three, Diversifying Using Hedge Funds: A Utility-Based Approach, we analyse the
inclusion of hedge funds in a portfolio of stocks and bonds. The main originality of this
study centres upon the development of a new efficient frontier, based not only on
volatility but also on higher moments (skewness and kurtosis) and on a utility function
that more closely corresponds to that of the investor without normality or other strong
assumption. We develop a adapted capital market line that includes not only the volatility
in the risk measure but that integrates the asymmetry of returns and the fat tails in
order to determine if investors should include hedge funds in their portfolio once almost
408
the whole hedge fund return distribution characteristics are taken into account. Our
results confirm that hedge funds are attractive investment tools for almost any kind of
investors but that investors specific needs have to be considered in order to determine
what kind of funds should be used and what allocation should be given to hedge funds.
Hedge funds can be good investments on a stand alone basis and as a
diversification tool but everything depends on the way of investing in hedge funds and on
the quality of the selection of the underlying hedge fund managers.
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An Analysis of Hedge Fund Strategies – List of Figures
FIGURE 1: FOUR GLOBAL CATEGORIES OF HEDGE FUND ACADEMIC STUDIES .................................. 7
FIGURE 2: HEDGE FUND DATABASE UNIVERSE REPARTITION .................................................. 17
FIGURE 3: MONTHLY RETURNS FOR DEAD FUNDS TOWARDS THE DISSOLUTION DATE ...................... 65
FIGURE 4: HEDGE FUNDS DISSOLUTION FREQUENCIES ...................................................... 108
FIGURE 5: DECILE REPARTITION PER STRATEGY (RANKING BASE ON ALPHA) ............................ 226
FIGURE 6: STRATEGY REPARTITION IN THE ALPHA RANKING ............................................... 227
FIGURE 7: DECILE REPARTITION PER STRATEGY BASED ON BETA .......................................... 228
FIGURE 8: STRATEGY REPARTITION IN THE BETA RANKING................................................. 229
FIGURE 9: MINIMUM, MAXIMUM, MEDIAN AND MEAN INDIVIDUAL CORRELATIONS BETWEEN MARKET
NEUTRAL FUNDS AND THE EQUITY INDEX ................................................................ 292
FIGURE 10: LAGGED 12-MONTH DECILE DESCRIPTION ...................................................... 304
FIGURE 11: ILLUSTRATION OF THE ADAPTED CAPITAL MARKET LINE ...................................... 362
An Analysis of Hedge Fund Strategies – List of Figures
FIGURE 12: ILLUSTRATION OF THE TEST OF THE ADAPTED CAPITAL MARKET LINE ....................... 363
FIGURE 13: REPARTITION OF THE SKEWNESS OF INDIVIDUAL FUNDS ...................................... 375
FIGURE 14: REPARTITION OF THE KURTOSIS OF INDIVIDUAL FUNDS ....................................... 376
FIGURE 15: DIRECTIONAL HEDGE FUNDS - MEAN PERCENTILE RETURN .................................. 383
FIGURE 16: UNDIRECTIONAL HEDGE FUNDS - MEAN PERCENTILE RETURN ............................... 385
FIGURE 17: FUNDS OF HEDGE FUNDS - MEAN PERCENTILE RETURN ...................................... 386
An Analysis of Hedge Fund Strategies – List of Tables
TABLE 1: STUDIES SPECIFICITIES AND OBJECTIVES ............................................................. 4
TABLE 2: DATABASE COMPARISON............................................................................... 18
TABLE 3: BACKFILL BIAS AND SURVIVORSHIP BIAS ESTIMATION.............................................. 20
TABLE 4: HEDGE FUND INDICES COMPARISON ................................................................. 24
TABLE 5: MULTI-FACTOR PERFORMANCE DECOMPOSITION MODEL........................................... 31
TABLE 6: PERSISTENCE ANALYSIS STUDIES SPECIFICITIES, OBJECTIVES AND CONCLUSIONS............ 35
TABLE 7: NEUTRALITY OF MARKET NEUTRAL FUND SPECIFICITIES, OBJECTIVES AND CONCLUSIONS.... 37
TABLE 8: HEDGE FUND AS DIVERSIFICATION TOOLS SPECIFICITIES, OBJECTIVES AND CONCLUSIONS . 40
TABLE 9: SURVIVORSHIP BIAS IN HEDGE FUNDS .............................................................. 63
TABLE 11: ESTIMATION OF INSTANT RETURN HISTORY BIAS................................................. 69
TABLE 12: DESCRIPTIVE STATISTICS OF HEDGE FUNDS STRATEGIES AND PASSIVE INVESTMENT
STRATEGIES .................................................................................................. 71
TABLE 13: CORRELATION BETWEEN HEDGE FUNDS AND PASSIVE INVESTMENT STRATEGIES ............. 77
TABLE 14: PERFORMANCE MEASUREMENT USING THE CAPM, CARHART’S 4-FACTOR MODEL AND THE
COMBINED MODEL............................................................................................ 82
An Analysis of Hedge Fund Strategies – List of Tables
TABLE 15: PERFORMANCE OF HEDGE FUNDS IN DIFFERENT SUB-PERIODS ................................. 97
TABLE 16: HEDGE FUNDS PERSISTENCE BASED ON 12 MONTH LAGGED RETURNS....................... 101
TABLE 17: HEDGE FUNDS STRATEGY PERSISTENCE BASED ON 12 MONTH LAGGED RETURNS.......... 110
TABLE 18: DESCRIPTIVE STATISTICS OF HEDGE FUNDS STRATEGIES AND PASSIVE INVESTMENT
STRATEGIES ................................................................................................ 133
TABLE 19: DESCRIPTIVE STATISTICS OF HEDGE FUNDS STRATEGIES FOR THE BULLISH AND BEARISH SUB-
PERIODS..................................................................................................... 138
TABLE 20: CORRELATION AMONG HEDGE FUNDS, BETWEEN HEDGE FUNDS AND PASSIVE INVESTMENT
STRATEGIES, AND AMONG PASSIVE INVESTMENT STRATEGIES ........................................ 144
TABLE 21: SURVIVORSHIP BIAS IN HEDGE FUNDS............................................................ 149
TABLE 22: ESTIMATION OF INSTANT RETURN HISTORY BIAS ................................................ 152
TABLE 23: PERFORMANCE MEASUREMENT USING THE CAPM, CARHART’S 4-FACTOR MODEL AND THE
COMBINED MODEL.......................................................................................... 156
TABLE 24: PERFORMANCE OF HEDGE FUNDS DURING THE BULLISH AND BEARISH SUB-PERIODS........ 162
TABLE 25: HEDGE FUNDS PERSISTENCE BASED ON 12 MONTH LAGGED RETURNS ........................ 172
An Analysis of Hedge Fund Strategies – List of Tables
TABLE 26: HEDGE FUNDS PERSISTENCE DURING THE BULLISH AND BEARISH SUB-PERIODS............. 175
TABLE 27: HEDGE FUNDS PERSISTENCE FOR THE MARKET NEUTRAL STRATEGY .......................... 180
TABLE 28: CORRELATION BETWEEN THE OPTION FACTORS AND THE MARKET FACTOR .................. 198
TABLE 29: DESCRIPTIVE STATISTICS.......................................................................... 204
TABLE 30: HEDGE FUND STRATEGIES PERFORMANCE ANALYSIS (1/1994-12/2002) ................. 212
TABLE 31: HEDGE FUND PERSISTENCE IN PERFORMANCE (1/1995-12/2002)......................... 218
TABLE 32: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON THREE-YEAR DATA (1/1997-
12/2002).................................................................................................. 221
TABLE 33: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON THE SHARPE SCORE (1/1997-
12/2002).................................................................................................. 236
TABLE 34: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON THE STANDARD DEVIATION (1/1997-
12/2002).................................................................................................. 238
TABLE 35: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON THE ALPHA (1/1997-12/2002) .. 243
TABLE 36: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON BETA (1/1997-12/2002)......... 245
TABLE 37: PERSISTENCE IN PERFORMANCE ANALYSIS BASED ON THE SKEWNESS AND KURTOSIS
(1/1997-12/2002) ..................................................................................... 247
An Analysis of Hedge Fund Strategies – List of Tables
TABLE 38: PERSISTENCE IN PERFORMANCE ANALYSIS BASED AN ADAPTED SHARPE SCORE (1/1997-
12/2002).................................................................................................. 254
TABLE 39: SUMMARY OF ALPHA CREATION AND EQUITY EXPOSURE ....................................... 256
TABLE 40: KENDALL TAU ESTIMATION ........................................................................ 261
TABLE 41: DESCRIPTIVE STATISTICS AND DECILE DESCRIPTIVE STATISTICS.............................. 286
TABLE 42: CORRELATION BETWEEN MARKET NEUTRAL STRATEGIES AND EQUITY INDEX ................. 290
TABLE 43: BIRTH AND ATTRITION RATES...................................................................... 293
TABLE 44: SURVIVORSHIP BIAS ................................................................................ 297
TABLE 45: MARKET EXPOSURE ANALYSIS...................................................................... 301
TABLE 46: LAGGED 12-MONTH DECILE EXPOSURE ........................................................... 306
TABLE 47: INDIVIDUAL FUND MARKET EXPOSURE ............................................................ 309
TABLE 48 : INDIVIDUAL FUND MARKET EXPOSURE – MULTI FACTOR MODEL ............................. 310
TABLE 49: BULL AND BEAR BETA ESTIMATION ............................................................... 311
TABLE 50: EX-POST BETA ANALYSIS ........................................................................... 316
An Analysis of Hedge Fund Strategies – List of Tables
TABLE 51: INDICES AND DECILES SUB-PERIOD ANALYSIS ................................................... 320
TABLE 52: LAGGED 12-MONTH DECILE SUB-PERIOD ANALYSIS............................................. 324
TABLE 53: SUB-PERIOD INDIVIDUAL FUNDS RESULTS ....................................................... 328
TABLE 54: EX-POST BETA SUB-PERIOD ANALYSIS............................................................ 331
TABLE 55 : DESCRIPTIVE STATISTICS OF THE HEDGE FUND (PANEL A) AND OF THE EQUITY AND BOND
MUTUAL FUNDS (PANEL B) ............................................................................... 371
TABLE 56: MEAN RETURN ESTIMATION FOR AVERAGE INVESTORS .......................................... 380
TABLE 57: MEAN RETURN ESTIMATION FOR PROTECTIVE INVESTORS ...................................... 387
TABLE 58: MEAN RETURN ESTIMATION FOR PROGRESSIVE INVESTORS .................................... 389
TABLE 59: SLOPE ESTIMATION FOR AVERAGE INVESTORS ................................................... 392
TABLE 60: MEAN RETURN ESTIMATION FOR AVERAGE INVESTORS (INCLUDING MUTUAL FUNDS IN A HEDGE
FUND PORTFOLIO).......................................................................................... 397
TABLE 61: SLOPE ESTIMATION FOR AVERAGE INVESTORS (INCLUDING MUTUAL FUNDS IN A HEDGE FUND
PORTFOLIO)................................................................................................. 400
An Analysis of Hedge Fund Strategies – Detailed Table of
Contents
An Analysis of Hedge Fund Strategies - Abstract......................................................... i
An Analysis of Hedge Fund Strategies – Table of Contents ........................................... i
Acknowledgements ................................................................................................. i
Preface.................................................................................................................. i
Introduction and Purpose ....................................................................................... 1
Global Literature Review......................................................................................... 5
The Data Issue.................................................................................................... 14
Investing in Hedge Funds ..................................................................................... 26
Abstract Part One: The Persistence in Hedge Fund Performance ................................ 29
Abstract Part Two: The Neutrality of Market Neutral Funds ....................................... 36
Abstract Part Three: Hedge Funds as Diversification Tools ........................................ 38
Analysis of Hedge Fund Performance ............................................................... 45
I Introduction...................................................................................................... 46
II Literature Review ............................................................................................. 47
2.1 Performance Studies ............................................................. 47
2.2 Evolution in Performance Measurement ..................................... 49
III Performance Measurement Models .................................................................... 52
3.1 The Capital Asset Pricing Model ............................................... 52
3.2 The 3-factor Model of Fama and French (1993) and its international
version of Fama and French (1998) ............................................... 53
3.3 The 4-Factor Model of Carhart (1997) ....................................... 54
3.4 An Extended Multi-Factor Model ............................................... 55
IV Data .............................................................................................................. 57
4.1 Data Providers .................................................................... 57
4.2 Hedge Funds ....................................................................... 58
4.3 Risk-free Return and Market Performance .................................. 59
4.4 Biases in Hedge Funds Data .................................................... 60
V Data analysis ................................................................................................... 61
5.1 Survivorship bias ................................................................. 61
5.2 Instant Return History Bias .................................................... 64
5.3 Basic Performance ................................................................ 68
5.4 Correlation ......................................................................... 74
VI Hedge Funds Performance ................................................................................ 76
6.1 Performance Measurement using the CAPM ................................. 76
6.2 Performance Measurement using Multi-Factor Models .................... 80
6.3 Performance over Shorter Periods ............................................ 96
6.4 Comparison with other Studies ................................................ 99
VII Persistence in Performance............................................................................ 100
7.1 Persistence in One-year Return-Sorted Hedge Funds Portfolios ...... 100
7.2 Persistence over the Asian crisis ............................................. 106
7.3 Dissolution Frequencies ........................................................ 107
7.4 One-Year Persistence for Hedge Fund Strategies......................... 107
VIII Conclusion ................................................................................................. 115
Hedge Fund Performance and Persistence in Bull and Bear Markets .............. 120
Abstract ........................................................................................................... 120
I Introduction.................................................................................................... 121
II Performance Measurement Models ................................................................... 125
2.1 The Capital Asset Pricing Model .............................................. 125
2.2 The 4-Factor Model of Carhart (1997) ...................................... 126
2.3 The Composite Model ........................................................... 127
III Data............................................................................................................ 129
3.1 Database........................................................................... 129
3.2 Basic Performance ............................................................... 130
3.3 Analysis per Sub-periods ...................................................... 132
3.4 Correlations ....................................................................... 142
IV Analysis of biases .......................................................................................... 147
4.1 Survivorship bias ................................................................ 147
4.2 Instant Return History Bias ................................................... 151
4.3 Conclusion......................................................................... 154
V Hedge Funds Performance ............................................................................... 155
5.1 Performance Measurement using the CAPM ................................ 155
5.2 Performance Measurement using Multi-Factor Models ................... 160
5.3 Performance over bull ish and bearish sub-periods ....................... 161
VI Persistence in Performance ............................................................................. 168
6.1 Persistence over the total period ............................................ 168
6.2 Persistence over the sub-periods ............................................ 170
6.3 Analysis of the Market Neutral strategy .................................... 174
VII Conclusion................................................................................................... 186
The Sustainability of Hedge Fund Performance: New Insights ....................... 190
Abstract ........................................................................................................... 190
Introduction...................................................................................................... 191
I Methodology ................................................................................................... 195
II Database ...................................................................................................... 200
III Preliminary Analysis ...................................................................................... 203
3.1 Descriptive Statistics ........................................................... 203
3.2 Correlation Analysis ............................................................. 208
3.2 Survivorship Bias ................................................................ 209
IV Global Results: Market Analysis....................................................................... 210
4.1 Performance Analysis ........................................................... 210
4.2 Persistence in Performance - Returns ....................................... 216
4.3 Persistence in Performance – Three Years of Data ....................... 220
4.4 Persistence in Performance – Other Measures ............................ 223
V Further Analysis ............................................................................................. 263
5.1 Sub-Period Analysis ............................................................. 263
5.2 Date Impact....................................................................... 266
VI Frictions in the Real World .............................................................................. 267
VII Conclusion................................................................................................... 269
The Neutrality of Market Neutral Funds.......................................................... 273
Abstract ........................................................................................................... 273
Introduction...................................................................................................... 274
I Interest of the study ........................................................................................ 279
II Database ...................................................................................................... 282
III Descriptive statistics and attrition rates ........................................................... 283
3.1 Descriptive statistics ........................................................... 283
3.2 Correlation analysis ............................................................. 290
3.3 Birth and attrit ion rates........................................................ 292
IV Survivorship bias analysis............................................................................... 295
V Methodology .................................................................................................. 299
VI Strategy and decile analysis............................................................................ 303
VII Individual fund analysis................................................................................. 307
VIII Sub-period analysis ..................................................................................... 317
8.1 Market exposure ................................................................. 317
8.2 Individual funds .................................................................. 326
8.3 Ex-post beta sub-period analysis ............................................ 330
IX Conclusion.................................................................................................... 333
Diversifying using Hedge Funds: A Utility-Based Approach ............................ 339
Abstract ........................................................................................................... 339
Introduction...................................................................................................... 340
I Utility functions and Spanning........................................................................... 342
1.1 Uti l ity functions and the Bell function ...................................... 342
1.2 Spanning........................................................................... 348
II Methodology and data .................................................................................... 352
2.1 Classical portfolio selection approaches .................................... 353
2.2 Taylor approximation and risk measure .................................... 356
2.3 Risk Measure ..................................................................... 359
2.4 Estimation methodology........................................................ 363
III The database................................................................................................ 369
IV Results......................................................................................................... 377
4.1 Significance level ................................................................ 377
4.2 Including hedge funds in mutual funds portfolio ......................... 378
4.3 Including mutual funds in hedge fund portfolios ......................... 395
V Conclusion ..................................................................................................... 402
General Conclusion ............................................................................................ 404
References ....................................................................................................... 410
An Analysis of Hedge Fund Strategies – List of Figures ........................................... 424
An Analysis of Hedge Fund Strategies – List of Tables ............................................ 426
An Analysis of Hedge Fund Strategies – Detailed Table of Contents.......................... 431
An Analysis of Hedge Fund Strategies – Detailed Table of Contents.......................... 431
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© Copyright by Daniel Capocci 2007 All rights reserved
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Hedge Funds are relatively unknown investment vehicles. This PhD Thesis focuses on
analyzing hedge fund strategies and focuses more precisely on hedge fund returns. The
Thesis is divided in three parts. Part 1: The Persistence in Hedge Fund Performance
focuses on the explanation of hedge fund returns. Part 2: An Analysis of Hedge Fund
Market Exposure analyses the market exposure of so-called market neutral hedge funds
in depth. Finally, Part 3: Hedge Funds as Diversification Tools aims at determining if
investors should include hedge funds in a classical portfolio of stocks and bonds. We
develop an original methodology and present it and its application in details. Figures are
added when more illustrations are needed. This Thesis covers the whole analysis of
hedge fund returns.
Daniel Capocci, Ph.D.- Chartered Alternative Investment
Analyst, holds the positions of Senior Portfolio Manager at
Kredietbank Luxembourg. Daniel has been studying the
world of hedge funds for almost ten years and has worked
as a fund of hedge funds manager since the early 2000.
Daniel has published several papers in academic and
business journals such as the Journal of Empirical Finance,
the European Journal of Finance, Global Finance Journal,
l’Echo, Agefi, Haute Finance, aso. and he has contributed
to several hedge fund readers and presented his research
to several conferences. This Thesis is an aggregation of
his main research in the hedge fund area.