alternative investments for institutional investors: risk

Alternative Investments for Institutional Investors: Risk Budgeting Techniques in Asset Management and Asset-Liability

ManagementJanuary 2009

An EDHEC Risk and Asset Management Research Centre Publication

Sponsored by

Foreword ...........................................................................................................................2

Abstract ..............................................................................................................................5

1. Introduction ........................................................................................... 7

2. Modelling Return and Inflation Dynamics .........................................13

3. Data and Model Specification ...........................................................19

4. Inflation-Hedging Properties of Various Assets and Portfolios ...25

5. Implication for Risk Budgeting in Asset-Liability Management ..31

6. Conclusions and Directions for Future Research ............................35

Appendix ........................................................................................................................ 39

References ..................................................................................................................... 59 About the EDHEC Risk and Asset Management Research Centre .............. 64

About Morgan Stanley Investment Management ........................................... 69

Table of Contents

Printed in France, January 2009. Copyright EDHEC 2009.The opinions expressed in this survey are those of the authors and do not necessarily reflect those of EDHEC Business School.

3An EDHEC Risk and Asset Management Research Centre Publication

Alternative Investments for Institutional Investors: Risk Budgeting Techniques in Asset Management and Asset-Liability Management — January 2009

The present publication is the first to be drawn from the EDHEC/Morgan Stanley Investment Management research chair on Financial Engineering and Global Alternative Portfolios for Institutional Investors.

This chair, which corresponds to a three-year partnership between Morgan Stanley Investment Management and the EDHEC Risk and Asset Management Research Centre, adapts risk budgeting and risk management concepts and techniques to the specificities of alternative investments, both in the context of asset management and asset-liability management. The research is led by Professor Lionel Martellini, Scientific Director of the EDHEC Risk and Asset Management Research Centre.

In the current context of a short- and probably medium-term downturn in the financial markets, our research seems to be of particular relevance for long-term investors. Our results suggest that real estate and commodities have particularly attractive inflation hedging properties over long-horizons, which justify their introduction in pension funds' liability-matching portfolios. We show that novel liability-hedging investment solutions, including commodities and real estate in addition to inflation-linked securities, can be designed so as to decrease the cost of inflation insurance for long-horizon investors.

I would like to thank my co-authors, Lionel Martellini and Volker Ziemann, for the extensive work that they have done in this area. We hope that you will find our analysis and conclusions interesting and will continue to monitor and contribute to our research in this area.

Finally, we would like to extend our warmest thanks to our partners at Morgan Stanley Investment Management for their commitment to this research chair and their close involvement with our research.

Wishing you an enjoyable and informative read,

Foreword

Noël AmencProfessor of FinanceDirector of the EDHEC Risk and Asset Management Research Centre

4 An EDHEC Risk and Asset Management Research Centre Publication


About the Authors

Noël Amenc is Professor of finance and Director of Research and Development at EDHEC Business School, where he heads the Risk and Asset Management Research Centre. He has a Masters degree in Economics and a PhD in finance and has conducted active research in the fields of quantitative equity management, portfolio performance analysis, and active asset allocation, resulting in numerous academic and practitioner articles and books. He is Associate Editor of the Journal of Alternative Investments and a member of the scientific advisory council of the AMF (French financial regulatory authority).

Lionel Martellini is Professor of Finance at EDHEC Business School and Scientific Director of the EDHEC Risk and Asset Management Research Centre.Lionel has consulted on risk management, alternative investment strategies, and performance benchmarks for various institutional investors, investment banks, and asset management firms, both in Europe and in the United States.His research has been published in leading academic and practitioner journals, including the Journal of Mathematical Economics, Management Science, Review of Financial Studies, the Journal of Portfolio Management, Financial Analysts Journal, and Risk. He sits on the editorial board of the Journal of Portfolio Management and the Journal of Alternative Investments. Lionel has co-authored and co-edited reference texts on fixed-income management and alternative investment such as the much-praised Fixed-Income Securities: Valuation, Risk Management and Portfolio Strategies (Wiley Finance) and is regularly invited to deliver presentations at leading academic and industry conferences. He holds graduate degrees in business administration, economics, statistics, and mathematics, as well as a PhD in finance from the Haas School of Business at UC Berkeley.

Volker Ziemann is a Senior Research Engineer at EDHEC Risk and Asset Management Research Centre. He holds Master’s degrees in economics and statistics and a PhD in finance. His research focus is on the econometrics of financial markets and optimal asset allocation decisions involving non-linear payoffs.

Abstract

5An EDHEC Risk and Asset Management Research Centre Publ icat ion



This paper presents an empirical analysis of the benefits of alternative forms of investment strategies from an asset-liability management perspective. Using a vector error correction model (VECM) that explicitly distinguishes between short-term and long-term dynamics in the joint distribution of asset returns and inflation, we identify the presence of long-term cointegration relationships between the return on typical pension fund liabilities and the return of various traditional and alternative asset classes. Our results suggest that real estate and commodities have particularly attractive inflation hedging properties over long-horizons, which justify their introduction in pension funds' liability-matching portfolios. We show that novel liability-hedging investment solutions, including commodities and real estate in addition to inflation-linked securities, can be designed so as to decrease the cost of inflation insurance for long-horizon investors. These solutions are shown to achieve satisfactory levels of inflation hedging over the long-term at a lower cost compared to a solution solely based on treasury inflation-protected securities (TIPS) or inflation swaps. Overall our results suggest that alternatives are very useful ingredients for institutional investors facing inflation-related liability constraints.

Abstract

1. Introduction




A recent surge in worldwide inflation has increased the need for investors to hedge against unexpected changes in price levels. In the most recent forecasts, global consumer price index (CPI) inflation has been revised up more than a percentage point, to 5.0%, for calendar year 2008, and by 0.7 percentage points, to 3.7%, in 2009, a trend that, given the long-term increased pressure on food and energy resources, is likely to continue, despite the current crisis. The CPI inflation peak has been forecasted to be 4.1% in the euro area and 5.5% in the US, and the direct impact of higher food and energy costs is estimated to account for 2.5 percentage points and 3 percentage points, respectively, of these rates.1

Inflation acceleration in emerging markets will likely be greater than it is in developed countries, a reflection of the much greater importance of food in the basket of consumer goods in these markets and of their generally higher rates of growth. As a result of these trends, inflation hedging is now of critical importance not only for private investors, who consider inflation a direct threat to their purchasing power, but also, and perhaps more importantly, for pension funds, which may have to make pension payments that are indexed (conditional or full indexation) to consumer price or wage indices.

This focus on inflation hedging is consistent with the heightened focus on liability-risk management that has emerged as a consequence of the 2000-2003 pension crisis. A number of so-called liability-driven investment (LDI) techniques have been promoted over the past few years by several investment banks and asset management firms, which advocate the design of a customised

liability-hedging portfolio (LHP), the sole purpose of which is to hedge away as effectively as possible the impact of unexpected changes in risk factors affecting liability values, and most notably interest rate and inflation risks. This LHP complements the traditional performance-seeking portfolio (PSP), the composition of which is not impacted by the presence of liabilities. Within the aforementioned LDI paradigm, a variety of cash instruments (treasury inflation-protected securities, or TIPS) as well as dedicated OTC derivatives (such as inflation swaps) are typically used to tailor customised inflation exposures that are suited to particular institutional investor’s liability profile. One outstanding problem, however, is that such solutions generate very modest performance. In fact, real returns on inflation-protected securities, negatively impacted by the presence of a significant inflation risk premium, are usually very low. In other words, while these solutions offer substantial risk management benefits, the lack of performance makes them costly options for pension funds and their sponsors. In addition, the inflation-linked securities market does not have the capacity to meet the collective demand of institutional and private investors, while the OTC inflation derivatives market suffers from a perceived increase in counterparty risk.

In this context, it has been argued that other asset classes, such as stocks and nominal bonds, as well as real estate or commodities, could provide useful, albeit imperfect, inflation protection at a lower cost than TIPS do. In the short term, equity investments are relatively poor inflation

Introduction

1 - See Barclays Capital Global Outlook 2008, Implications for financial markets.



hedging vehicles. Indeed, empirical evidence suggests that there is in fact a negative relationship between expected stock returns and expected inflation (Fama and Schwert 1977; Gultekin 1983; Kaul 1987), which is consistent with the intuition that higher inflation leads to less economic activity and thus depresses stock returns (Fama 1981).2

Higher future inflation, however, leads to higher dividends and thus higher returns on stocks (Campbell and Shiller 1988), so equity investments should offer significant inflation protection over longer horizons, as has been confirmed by a number of recent empirical academic studies (Boudoukh and Richardson 1993; Schotman and Schweitzer 2000). This property is particularly appealing for long-term investors such as pension funds, which need to match increases in prices at the horizon, but not necessarily on a monthly basis. Obviously, different kinds of stocks offer different inflation-hedging benefits, and it is in fact possible to select stocks or sectors on the basis of their ability to hedge against inflation (hedging demand), as opposed to selecting them for their outperformance potential (speculative demand). For example, utilities and infrastructure companies usually have revenues that are heavily correlated with inflation, and as a result they tend to provide better-than-average inflation protection. Similar inflation-hedging properties are expected for bond returns. Indeed, bond yields may be decomposed into a real yield and an expected inflation component. Since expected and realised inflation move together over the long term (Schotman and Schweitzer 2000), we expect a positive long-term correlation between

bond returns and changes in inflation. In the short-term, however, expected inflation may deviate from actual realised inflation, leading to low or negative correlation. There again, an investor willing and able to relax short-term constraints to focus on long-term inflation hedging properties will find that investing in nominal bonds can provide a cost-efficient alternative (or complement) to investing in inflation-linked securities.

Moving beyond traditional investment vehicles such as stocks and bonds, recent academic research has also suggested that alternative forms of investment offer attractive inflation-hedging benefits. Commodity prices, in particular, have been found to be leading indicators of inflation in that they are quick to respond to economy-wide shocks to demand. Commodity prices are generally set in highly competitive auction markets and consequently tend to be more flexible than prices in general. Moreover, the rise in the prices for agricultural, mineral and energy commodities has been behind much of the recent rise in inflation. Gorton and Rouwenhorst (2006) find that, over the 1959-2004 period, commodity futures were positively correlated with inflation, unexpected inflation, and changes in expected inflation. They also find that inflation correlations tend to increase with the holding period and are larger at return intervals of one and five years than at the monthly or quarterly frequency. In the same spirit, it has also been found that commercial and residential real estate provide at least a partial hedge against inflation, which implies that portfolios that include real estate allow enhanced

Introduction

2 - This finding is also consistent with the so-called "Fed model", which is used by many investmentprofessionals to generate signals about the relative attractiveness of stock prices relative to bond prices. The model assumes that bonds and equities compete for space in investment portfolios; if bond yields increase, then stock yields must also rise in order to remain competitive. Thus, the Fed model relates the yield on stocks (as measured by the ratio of dividends or earnings to stock prices) to the yield on Treasury bonds and to the relative risk premium of stocks versus bonds. In the long-run, the Fed model posits that the actual yield on stocks will revert to a normal yield level given by the bond yield plus the risk premium. Historically, the rate of inflation has been a major influence onnominal bond yields. Therefore, the Fed model implies that stock yields and inflation must be highlycorrelated. Campbell and Vuolteenaho (2004) review stock market performance between 1927 and 2002, examining the impact of risk premiums and inflation on stock yields and find strong support for the Fed model.



inflation-hedging benefits (Fama and Schwert 1977, Hartzell et al. 1987; Rubens et al. 1989). This effect seems to be particularly significant over long horizons. Hence, Anari and Kolari (2002) examine the long-run impact of inflation on homeowner equity by investigating the relationship between house prices and the prices of non-housing goods and services, rather than return series and inflation rates, and infer that house prices are a stable inflation hedge in the long run. When it comes to securitised forms of real estate investment, the situation is less clear, even though there is evidence of a long-term connection that suggests that REITs could neutralise part of the inflation risk in the long run (Westerheide 2006).

In order to assess the inflation-hedging potential of the various asset classes within a united framework, we follow the literature on predictability of asset returns (see Kandel and Stambaugh 1996; Campbell and Viceira 1999; Barberis 2000). As such, our analysis is closely related to that of Hoevenaars et al. (2008), who construct optimal mean-variance portfolios with respect to inflation-driven liabilities based on model-implied forward-looking variances and expected returns. Their basic finding is that alternative asset classes add value to the investor's portfolio and command signficant positive allocation in the optimal mean-variance portfolio. The authors further stress that the allocations in alternative asset classes are higher within the optimal asset-liability portfolio as opposed to the optimal asset-only portfolio. In what follows, we extend this existing literature in several directions. First, we note that modelling

returns with a vector auto-regressive (VAR) model on log-returns, as was common in previous research on the subject, omits any information on price dependencies and long-term equilibria to focus purely on short-term effects in return series. In order to address this shortcoming of the VAR model, we include cointegration relationships in the model and assess sensitivities of model-implied dynamics with respect to these additional factors that capture price dependencies in addition to return dependencies. The resulting error correction form of the vector-autoregressive model (VECM), or cointegrated VAR model, has the striking advantage, as compared to the standard VAR representation, that it explicitly distinguishes between short-term and long-term dynamics in the joint distribution of asset returns and inflation. While error correction forms of the vector-autoregressive model have been extensively used in the macroeconomic literature in order to distinguish between trends and business cycles and thus between stationary and non-stationary components in consumption and wealth dynamics (see Lettau and Ludvigson 2004 or Beaudry and Portier 2006 for recent studies), this approach is relatively new in the finance literature. It has been used in modelling price and return dependencies of financial securities (e.g. Blanco et al. 2005 or Durre and Giot 2007) and, more recently, in inflation hedging contexts (Westerheide 2006 or Hoesli et al. 2007).

To the best of our knowledge, our paper is the first to provide a comprehensive VECM model for the formal analysis of inflation-hedging properties of various traditional and alternative classes. We derive econometric forecasts for model-

Introduction



implied volatilities and correlations, and we find that the results strongly deviate from what is obtained with a standard VAR model (see sections 3 and 4). Using the VECM model that explicitly distinguishes between short-term and long-term dynamics in the joint distribution of asset returns and inflation, we identify the presence of long-term cointegration relationships between the return on typical pension fund liabilities and the return of various traditional and alternative asset classes. Our results suggest that real estate and commodities have particularly attractive inflation-hedging properties over long horizons. Subsequently, we use the VECM fitted parameters to perform a simulation-based analysis of the impact on ALM risk budgets of various portfolio allocations. More precisely, the paper suggests a structural form of the model that incorporates i.i.d. innovations, which allows for the generation of a stochastic Monte Carlo analysis in a straightforward manner. The afore mentioned findings suggest that novel long-term liability-hedging investment solutions can be designed so as to decrease the cost of inflation insurance from the investor's perspective. In particular, it is possible to construct enhanced versions of inflation-hedging portfolios including inflation-linked securities, as well as commodities and real estate, so as to achieve satisfactory levels of inflation hedging over the long-term at a cost lower than that of versions that rely solely on inflation swaps. The intuition behind our results is rather straightforward. The increasedexpected return generated by making commodities and real estate in addition to TIPS part of the LHP allows a reduced

overall allocation to the PSP while meeting overall performance expectations, which in turn allows better risk management properties.

The rest of this paper is organised as follows. In section 2, we present the econometric framework and motivate the introduction on an error correction extension of the standard VAR model. In section 3 we describe the database as well as preliminary statistical tests that are used for model selection purposes. In section 4, we assess the inflation hedging potential of various traditional and alternative asset classes, and construct different versions of enhanced liability-hedging portfolios that contain real estate and commodities in addition to TIPS. Section 5 analyses the impactin terms of risk budget improvements of the introduction of such enhanced liability hedging portfolios. Section 6 concludes.

Introduction



Introduction

2. Modelling Return and Inflation Dynamics




The first key challenge that needs to be met for the analysis of the benefits of alternative investment strategies from an asset-liability perspective is the design of an appropriate econometric model for the joint distribution of asset returns and inflation. As recalled in the introduction, the bulk of the literature on stock return predictability and return dynamics modelling (e.g., Campbell and Shiller 1988) has relied on vector-autoregressive (VAR) models. The calibration of a VAR model is generally performed on asset return series corresponding to asset classes of interest and a set of potentially predictive economic variables that are introduced in order to enhance the explanatory power of the model. In the context of VAR models, the choice of using return series as opposed to price series is either non-motivated, or motivated by the stylised fact that return series are stationary while asset price series are not. The important consequence of stationarity follows from the Wold's Decomposition Theorem that states that stationary processes can be expressed as a moving average process (cf. Hamilton 1994, p. 108), which in turn allows for the derivation of analytical expressions for shock responses, expected return and forward-looking variances. Secondly, non-stationarity leads to unstable, explosive and unbounded forward-looking variances and covariances, which makes the model non-tractable and non-suited for portfolio selection purposes (Lütkepohl 1993). As a consequence, most econometric financial applications are based on return series or log-return series that are proven to be stationary, while price series tend to be integrated of order 1 at least. More formally, a process yt is integrated of order d (written: yt ~ I(d)) if Δdyt is stationary

while Δd-1 is not stationary (see Lütkepohl 1993).

One outstanding question, however, is whether taking first differences and removing information related to price dependencies is too restrictive. The main concept behind the cointegration framework, introduced by Engle and Granger (1987), is precisely that integrated variables may exhibit common trends that account for the non-stationary pattern in the system. Thus, linear combinations of non-stationary variables may turn out to be stationary. Formally, a process is said to be cointegrated of order (d, i) with d, i > 0, or yt ~ CI(d, i), if yt is integrated of order d (yt ~ I(d)) and there exists a linear combination β'yt such that β'yt ~ I(d-i). In particular, if price series are I(1), we are interested in linear combinations of these price series that are I(0) and thus stationary. The next section introduces the error correction version of the VAR model, known as VECM model, which incorporates both levelled and difference series. In other words, the model uses systematic relationships of both cross-sectional return dynamics and cross-sectional price dynamics.

2.1 The econometric modelLet us first consider the standard vector-autoregressive (VAR) model of order p:

yt = c + A1yt-1 + … + Apyt-p + ut

where yt represents a n x 1 vector of endogenous variables, c is a constant, Ai are n x n coefficient matrices and ε is the innovation process. If the process is stable,3

it may be rewritten as a finite moving


3 - A process yt is stable if its reverse characteristic polynomial has no roots in or on the unit circle:det (I - A1-…¡Apzp) = ∀|z|<1.



average process:

(2)

where Φ0 is the identity matrix and the Φs are recursively given as:

(3)

with Aj =0 for all j > p.

Moreover, stability implies stationarity, meaning that expected returns, variances and covariances are time-invariant. This is a critical point for financial applications where the econometric model is used for forecasting purposes and for deriving analytical expressions for expected returns, variances and correlations. In the case of non-stationary processes, variances would be unbounded and time-variant, which in turn leads to unbounded confidence intervals of the forecasted variables.

In order to infer whether a time series is stationary or not, various so-called unit root tests are available. The most commonly used test is the Augmented Dickey-Fuller (ADF) test (Greene 2003). If the test of unit roots cannot be rejected for all endogenous variables in y, the VAR process is integrated or cointegrated. As outlined above, if the variables are I(1), writing the VAR model (1) on first-differenced variables generates a stationary process:

Δyt = c + Γ1Δyt-1 + … + ΓpΔyt-p + ut (4)

The unfortunate consequence of using the first-differenced variables is that any information regarding price dynamics is

lost, which could prove detrimental to the predictive power of the model. For example, in an early economic study on the relationship between log consumption and log income, Davidson et al. (1978) have found that information on the deviation from a long-term equilibrium enhances the explanatory power of the predictive model. To account for the presence of long-term relationships in price series, the VAR model can be generalised through the following error correction form (henceforth, VECM):

Δ yt = c + αzt-1 + Γ1Δyt-1 + … + ΓpΔyt-p + ut (5)

where z represents the deviation from the long term equilibrium. Subsequently, this representation has been used to define the cointegration framework. Indeed, if a long-term equilibrium relationship exists, it implies that z is a stationary variable. Assuming that the long-term equilibrium can be expressed as a linear combination of the endogenous variables, we can rewrite (5) as:

Δ yt = c + Πyt-1 + Γ1Δyt-1 + … + ΓpΔyt-p + ut (6)

with the reduced rank matrix Π = αβ'. Its rank r<n determines the number of linearindependent long-term equilibrium relationships and is also called cointegration rank. In other words, there are r independent linear combinations of the lagged endogenous variables that define the cointegration relationships constituting r stationary variables β'y. Accordingly, α and β are nxr matrices and β hosts the cointegrating vectors so that β'yt. is stationary and reflects the long-term




equilibrium relationships of the variables while α hosts the corresponding adjustment parameters, that is, the parameters that determine the reversion speed to this long-term equilibrium. It is important to note that α and β are not unique due to the reduced rank of Π. Accordingly, additional restrictions are needed to ensure that α and β are just identified. A set of restrictions that has been accepted as a standard procedure in the econometric literature is to define the upper part of β as the rxr identity matrix. Then, it can be shown that the estimated coefficient matrices are asymptotically unbiased (Lütkepohl 1993, p. 358). Two particular cases are worth mentioning. First, if r=0, then there are no linear combinations of the original variables that form a stationary process, and only first-differencing may lead to a stationary system. Secondly, if r = n, yt has a stable VAR(p) representation.

Note that we specify all entries in y as the log of the index level values. This is mainly done because economic and financial time series are often shown to have exponential trends. Writing linear regression models such as the VAR or the VECM on the log of these variables is therefore consistent with the economically assumed dynamics since taking the log of exponential process linearises the processes. Log-returns are also convenient because they directly add up across time-intervals.

2.2 Structural model and impulse-response functionsIn the context of cointegrated processes, the dynamics of the underlying variables may be separated in short-run and long-run dynamics. Short-run dynamics

are driven by the structural responses to lagged innovations captured by Γi in (5). The cointegration relationship vector β and the reversion speed vector α govern the long-run dynamics. More precisely, Π=αβ' induces instantaneous shocks to the system if it deviates from the long-term equilibrium. As outlined earlier, if the system is cointegrated, cross-sectional responses to shocks may be non-transitory or persistent as the time-series "hang together". This section introduces a modelling approach that uses long-run and short-run restrictions in order to identify the structural shocks of the system. The structural form of the model is characterised by i.i.d. innovations εt,i, as opposed to the correlated original innovation process ut,i. For this, we search for the transformation matrix B such that: ut = Bεt (7 )

From the structural assumption we know that the covariance matrix of the i.i.d innovations ε (Σε) is diagonal. Without any loss of generality we postulate Σε to be the identity matrix. Therefore, the original innovation covariance matrix may be written as Σu = BB'. The transformation matrix B hosts nxn parameters that need to be identified. Since Σu is symmetric, only n(n + 1)/2 independent equations are available from Σu = BB'. For the parameters to be just identified we need n(n - 1)/2 additional restrictions. One way to do this is to use the Cholesky decomposition. Then, the contemporaneous impact matrix B is given as a lower triangular matrix. As a matter of fact, the matrix B is not unique and the ordering of the variables determines the dynamics of the structural shocks.




Given the specific context of the VECM and the fact that some shocks are persistent, we follow Breitung et al. (2004) and impose restrictions on short-run dynamics of theshocks as well as on the long-run impact matrix. According to Granger's representation theorem (Johansen 1995, theorem 4.2), this matrix is given by (see Vlaar 2004 for details):

Ξ = β⊥[α'⊥(I—Γ)β⊥]-1 α'⊥B (8)

with α⊥ and β⊥ such that:

α'⊥ α = β'⊥β (9)

The rank of this matrix is n-r since r cointegrating relationships form stationary combinations, meaning that r shocks have only transitory impacts and disappear in the long run. As can be seen from (3), the long-run impact matrix of the structural shocks is ΞB. This matrix also has reduced rank equal to n-r. Hence, at most r columns of ΞB can be zero columns since at most r structural innovation can have transitory effects and at least n-r shocks must have persistent effects to the system. Given its reduced rank, each column of zeros in ΞB accounts for n-r restrictions. As shown in Gonzalo and Ng (2001), the remaining restrictions split up into r(r - 1)/2 restrictions on the transitory shocks (B) and into (n - r)((n - r) - 1)/2 additional restrictions on the permanent shocks (ΞB). We set the identifying restrictions through:

RΞBvec (ΞB) = rl and RBvec (B) = rs (10)

while we restrict rl and rs to vectors of zeros. The long-run restrictions may also be written as Rlvec(B)=rl with

Rl =RΞB(In ⊗Ξ). The matrix B can accordingly be estimated by the maximum likelihood method. Following Breitung et al. (2004), the corresponding log-likelihood function is given by:4

(11)

Once the transformation matrix is identified, we can write the structural VECM(1) (SVECM(1)) in its reduced form:

Δyt = c + Πyt-1 + ΓΔyt-1 + Bεt (12)

This representation allows us to conduct structural impulse-response analyses, that is, to analyze the impact of isolated independent structural shocks εt as opposed to the correlated innovation process ut in the reduced VECM form (5). To illustrate this, we write the model in its level variables form:

yt = c + A1yt-1 + A2yt-2 + Bεt (13)

with:

A1 = In + Γ + αβ' and A2 = —Γ (14)

Accordingly, the VAR model structure allows us to write structural impulse-response functions as Ξs = ΦsB (15)

with Φs as in (3). The elements in Ξs

illustrate the impacts of unit structural shocks that occurred at time t on the endogenous variables at time t+s. The kl-th element of Ξs, for instance, depicts the impact of a unit structural shock to


4 - More details on distributional assumptions and asymptotic properties of the estimation methodcan be found in Lütkepohl (2008).



variable l at time t on variable k at time t+s. As a result, this analysis allows us to measure the impact of inflation shocks on the various asset classes through time and to analyse short-run inflation-hedging potential, in addition to the long run dynamic analysis captured by the cointegration relations and the long-run dynamics given by Ξ∞. Confidence intervals for impulse-response functions are computed based on the bootstrap procedure described in Brüggemann (2006). In other words, we can assess co- or counter-movements between the inflation index and asset returns, and subsequently analyse horizon-dependent inflation hedging capacities for the various asset classes. It is also worth mentioning that the impulse response functions converge towards the long-run impact matrix ΞB.

As a direct application of the structural VECM, section 5 uses the i.i.d. innovationprocess property to perform a Monte Carlo analysis based on the fitted model. The generated scenarios will be subsequently exploited in a portfolio construction context.


3. Data and Model Specification




Our empirical analysis focuses on a set of traditional and alternative asset classes. Stock returns are represented by the CRSP value-weighted stock index. Commodities are proxied by the S&P Goldman Sachs Commodity Index (GSCI). Real estate investments are represented by the FTSE NAREIT real estate index, which is a value-weighted basket of REITs listed on the NYSE, AMEX and NASDAQ. We thus limit the opportunity set to liquid and publicly traded assets. Finally, we add the Lehman Long US Treasury Index, as well as the one-month Treasury bill rate.5 Following the evidence from the extensive literature on return predictability (see Stock and Watson 1999 among others), we also add potential predictive economic variables to the set of endogenous variables. We introduce the dividend yield (Campbell and Shiller 1988; Hodrick 1992; Campbell and Viceira 2002), the credit spread (computed as the difference between Moody's seasoned Baa corporate bond yield and the ten year Treasury constant maturity rate), as well as the term spread (obtained from the difference between the ten year Treasury constant maturity rate and the one month T-bill rate). The dividend yield data is obtained from CRSP and all other economic figures were obtained from the US Federal Reserve Economic Database.6 Our analysis is based on quarterly returns from Q1 1973 through Q4 2007.

Regarding the liability side, we include an inflation proxy represented by the consumer price index (CPI). As in Hoevenaars et al. (2008), we assume that the fund is in a stationary state as would be the case in a situation where the age cohorts and the built-up pension rights per cohort

are constant through time. Under this assumption, and further assuming that liability payments exhibit unconditional inflation-indexation, the return on the liability portfolio can be proxied as the return on a constant maturity zero-coupon TIPS with a maturity equal to the duration of the liability cash-flows.7 We construct the time-series for such constant maturity zero-coupon TIPS in accordance with the methodology described in Kothari and Shanken (2004), which states that the nominal return on a real bond is given as the sum of a real yield plus realised inflation. The real yield is in turn obtained as the difference of the nominal yield and the sum of expected inflation plus the inflation risk premium. As in Kothari and Shanken (2004), we assume the inflation risk premium to be equal to zero.8 We simplify the computation of expected inflation by taking it as the 60-month moving average inflation. As a result, we obtain the returns on liabilities as:

rL,t = yield(τ) - Et(π) (16)

where the upper index τ indicates the duration of the liabilities, which we have arbitrarily chosen in what follows to be equal to twenty years.9 In appendix A.2, we provide a detailed derivation of the pricing scheme for inflation-indexed liabilities.

3.1 Model selectionWe begin our empirical analysis with a number of preliminary tests that help us select the appropriate econometric model. Table 1 presents the results of Augmented Dickey-Fuller (ADF) tests for level, differenced and twice differenced


5 - The series is downloadable from Kenneth French's web site (borrowed from Ibbotson Associates).6 - See http://research.stlouisfed.org/fred2.7 - Incorporating additional features such as actuarial uncertainty and inflation indexation would notimpact the main message of the paper, which focuses on the inflation-hedging properties of real assets.8 - Note, that Kothari and Shanken (2004) also considered the case of a 50bps per annum inflationpremium.9 - Hoevenaars et al. (2008) use seventeen years as the duration of the liability portfolio. To avoid having to rely on interpolation, we rather use observable interest rate series from the FED, which are exclusively available for maturities of one, two, three, five, six, seven, ten and twenty years (see http://research.stlouisfed.org/fred2).

t




series. The results clearly show that all price series (level series) are non-stationary and thus integrated of at least order 1. The results further indicate that some economic variables are I(1), while other variables are I(2) as illustrated by the ADF tests on first and second differences. In fact, for all log asset return series as well as for the credit and term spread series, we reject the hypothesis of a unit root. The corresponding price series are therefore integrated of order 1 and denoted by I(1)-variables. Other predictive economic variables (dividend yield, ten-year yield, CPI) and the T-bill rate exhibit the pattern of I(2) variables since taking second differences of the original price series is needed to eliminate the non-stationarity in the variables.

The presence of I(2) integrated variables is a concern since it implies that the cointegrating relations may still exhibit unit roots. As defined in Lütkepohl (1993), the system is said to be integrated of order 2, which we denote by yt ~ I(2), since the highest order of integration among the set of variables is 2. In order to address I(2) processes, the VECM model a priori needs to be extended to polynomial- or multi-cointegration frameworks, meaning that second differences, linear combinations of first differenced variables and linear combinations of level variables are included in the econometric model (see Johansen 1995 for more details on the methodology). Two approaches have been proposed in the econometric literature in order to circumvent the problem caused by such an increase in the model complexity. A first approach consists of transforming the I(2) variable into I(1) variables without loss of information. The idea is to choose a control variable among the I(2) variables that is supposed

to move homogeneously with the remaining I(2) variables. Subtracting this variable from the others transforms the variables from I(2) into I(1) variables since the common trend is eliminated. A convenient choice for the control variable in our setup is the price index since subtracting it from the series means that the remaining I(2) variables will accordingly be transformed from nominal to real variables. Additionally, the control variable itself, in our case the price index, needs to be replaced by its first difference. This nominal-to-real transformation has been studied in Juselius (2007) and is inspired by preceding studies such as Engsted and Haldrup (1999), who consider various settings where some variables are I(2) and show that adding their first differences as regressors to the model leads to consistent stationary expressions for the long-run equilibrium. A drawback of this approach is that it supposes price-homogeneity for the economic variables and thus a common trend in the price level and the corresponding nominal variables, a rather strong assumption that needs to be empirically justified. A second possibility to circumvent the problem of I(2) variables is to find cointegrating relationships, that is, linear combinations of I(1) and I(2) variables that are stationary. Then, the system is said to be cointegrated of order (2; 0), yt ∼ CI(2; 0), meaning that there exists a cointegration matrix β such that β'yt ∼ I(0). This is also referred to as direct cointegration (Haldrup 1998). This approach is consistent with the recommendations in Hansen and Juselius (1995), who argue that ex-ante cointegration rank tests should be accompanied with ex-post analysis of the cointegrating vectors. Accordingly, we will first specify the cointegration rank r and then try to find r linear combinations that




form stationary variables. It is important to note that, because of the normalisation in the cointegration matrix β (see section 2.1), different orderings of the variables lead to different cointegrating relationships.

Table 2 presents the results of the Johansen trace test for the cointegration rank. The results suggest that the cointegration rank is either six or seven. We proceed as follows: for each permutation of the order of variables, we estimate the reduced form VECM withcointegration ranks r=6 and r=7 and extract the time-series across the cointegrating vectors β'yt. Next, we perform ADF unit root tests in order to test for stationarity of the cointegrating vectors. The "best" ordering is evaluated as the one that leads to the smallest p-values associated with the unit root tests. Tables 3-5 yield the estimation results for the "best" specification of the model measured by stationarity analyses on the cointegrating vectors. The p-values associated with this order of variables range from 0 to 5.98% for the six vectors, which are reasonably low values.

Table 4 presents information regarding the estimated cointegrating vectors. As evidenced by the results, all six equilibrium relationships are quite similar with respect to the relevant, non-normalised parameters. In fact, for each of the six first variables (liabilities, long bond, stocks, CPI, Yield [10Y] and T-bills) the remaining variables enter through a similar linear equilibrium relationship. While the loading on commodities and real estate is negative within the equilibrium relationship, credit spread, term spread and dividend yield enter the long-term relationship positively. Accordingly, the interpretation of the impact of the cointegrating relationship on the

return dynamics depends merely on the adjustment speed parameters displayed in table 5. The next section presents model-implied volatilities, correlations and impulse-response functions. In addition to the VECM estimates, we also estimate for comparison purposes the standard VAR(1) model on quarterly returns. Indeed, our goal is to show that explicitly accounting for the presence of cointegration relationships leads to significantly different results from what is obtained from the standard benchmark VAR model used in previous literature.

3.2 Model implied variances, correlations and impulse responsesBased on the estimated structures, we derive for both the VECM and the VAR(1) model implied properties of the return dynamics. In figure 1, we plot annualised volatilities for returns on liabilities and asset classes for different investment horizons according to the equations derived in appendix A.1. A particular focus of the graphs is on the difference between VAR-implied volatilities (dashed lines) and VECM-implied volatilities (solid lines). The difference between the two econometric methodologies turns out to be rather significant for bonds, stocks and commodities, with VECM-implied volatilities proving to be significantly lower than VAR-implied volatilities for these classes. Liability, T-bill and real estate returns show only minor differences between the VAR and the VECM approaches. The difference in implied volatility estimates is due to the equilibrium reverting character of the additional part αβ'yt-1. As explained above, while β'yt-1 establishes the equilibrium relationship, α determines the instantaneous impact of a deviation from



this equilibrium on Δyt. In an attempt to shed light on this discrepancy between VAR- and VECM- implied characteristics for stocks and commodities, it is worthwhile to refer to the credit spread variable. First, credit spread is highly significant as a predictive variable for both stocks and commodities. Secondly, credit spread enters positively into all cointegrating vectors with t-statistics ranging between eight and ten. Given that stock (respectively, commodity) returns depend positively (respectively, negatively) on changes in credit spread (see table 3) and given that (according to table 5) the highest adjustment parameter values are negative (respectively, positive) the long-term dynamics partly offsets the short-term dynamics, which in turns reduces the volatility. For real estate and liabilities, this offsetting effect is less pronounced, as evidenced by the balanced set of adjustment parameters in table 5, meaning that some are positive while others are negative, which eventually cancels much of the overall long-term impact on the corresponding return dynamics.

A second remarkable effect is that VAR-implied volatilities seem to indicate that assets become more risky as the investment horizon increases, while VECM volatilities have differing implications for the various assets. Liabilities, T-bills and real estate investments appear to be riskies in the long run, while bonds, stocks and commodities exhibit a downward sloping volatility structure, especially from very short to medium-term horizons. It should be noted at this stage that a mean-reversion effect is already present in the VAR model, and is due to a mean-reversion effect induced by the predictive power of specific lagged

variables and negative relationships for instantaneous covariances, as explained in Campbell and Viceira (2005). For instance, stock returns exhibit some shown of predictability through lagged dividend yields as evidenced by positive coefficients in tables 3 and 9. At the same time, contemporaneous innovations are negatively correlated (see table 6). As a result a positive shock in t on dividend yields goes (on average) along with a negative shock on stock returns in t and, through the autoregressive link, a positive shock on stock returns in t+1. The offsetting effect may be interpreted as mean-reversion, which in turn lowers the volatility of compounded stock returns. However, our findings suggest that this predictability-induced mean-reversion effect is small compared to the mean-reversion effect induced by the long-term co-integration relationships.10

Next, figure 2 displays horizon-dependent correlation coefficients between liability returns and the return on various asset classes. The plots clearly suggest that bond, stock and real estate returns are negatively correlated with liabilities in the short run, and that the correlation coefficient exhibits an upward pattern as the investment horizon increases. Bond returns and stock returns start to become positively correlated with liability returns after about sixty quarters (fifteen years) and end up with a significant positive correlation of roughly 0.4 with a thirty-year investment horizon. Again, the result allows us to identify significant discrepancies between VAR and VECM models, especially for commodities and real estate. Commodity returns are positively correlated with liability returns in both


10 - It should be noted that Campbell and Viceira (2005) have found with a VAR model a steeper downward sloping volatility term structure for stock returns, but their analysis is based on real return series, while we explicitly analyse the nominal returns, and its inflation component.



cases, but the VECM implies a significantly higher and more stable correlation than the VAR. Model-implied correlations between real estate and liability returns, on the contrary, are significantly higher in the VAR model than in the VECM. This may be due to the fact that commodities are part of all six long-term equilibrium relationships, a result of the normalisation process of the matrix β and the variable order permutation procedure described above. The next section evaluates the impact of these model-implied moments and co-moments from a liability-hedging portfolio perspective.

Impulse-response functions (figure 3) indicate that with the sole exception of commodities all responses to a structural liability shock are higher when implied by the VECM. This is mainly intrinsic to the model, as some shocks are persistent which cannot be the case in VAR model-implied shocks, an important restriction of the latter class of models.


4. Inflation-Hedging Properties of Various Assets

and Portfolios




Allocation decisions dependent on the investment zone have been widely studied in the literature over the last decade. Brandt (2005) and Campbell and Viceira (2005) discuss the differences between short-term or myopic and intertemporal asset allocation decisions. The term structure of risk, driven solely by the presence of mean-reversion effects, with different speeds of mean reversion (Lettau and Wachter 2007), also plays a central role in asset allocation decisions in the presence of liabilities (see Campbell and Viceira 2005 for the notion of term structure of risk). This section uses VECM model-implied dynamics to assess inflation hedging potential across different investment horizons.

Consistent with the portfolio separation theorem, we will study the liability- hedging portfolio (LHP) separately from the performance seeking portfolio (PSP). In a framework where liabilities are indexed with respect to inflation, and when short-term liability risk hedging is the sole focus, the optimal LHP allocation consists of investing 100% in the inflation-indexed bond portfolio (TIPS portfolio), which unfortunately leads to very limited upside potential. Consequently, the investor needs a relatively sizable allocation to the PSP to meet the return requirements, which in turn generates a relatively high funding risk. Intuitively, one would expect that relaxing the constraint of a perfect liability fit for the LHP at the short-term horizon would allow one to include alternative asset classes in the LHP, which in turn leads to increased upside potential. Overall, this would allow an investor to reduce his/her allocation to the PSP, which leads to a reduced surplus risk. To formalise

this intuition, we perform a scenario-based analysis to derive the funding ratio distribution at various investment horizons. The data generating process is described by the vector error correction model (VECM) introduced in section 2.1. We further use the structural model so as to disentangle the correlated innovation process and transform it into i.i.d. innovations. We draw i.i.d. random variables from the multivariate standard normal distribution for the structural innovations εs (s = 1 … S) and obtain the modelled returns by:

Δys = c + Πys + Γys + Bεs (17)

for a total of S = 5,000 simulated paths. The first variable in ys represents the liability return. We evaluate the different portfolios in terms of the funding ratio (FR) distribution. The funding ratio at t in scenarios s is accordingly given by:

FRs = exp ((w' - ι)ys ) (18)

where ι denotes the n x 1 vector containinga 1 in the first position and zeros elsewhere, and ω is the portfolio vector. We first analyse the potential of stand-alone inflation-hedging portfolios before constructing optimal portfolios.

4.1 Stand-alone hedging potentialThis section assesses the inflation hedging potential of the various asset classes on a stand-alone basis. The analysis follows the methodology previously described, that is, all conclusions are drawn from the funding ratio distributions over the 5,000 simulated scenarios based on the fitted VECM dynamics (cf. previous section).

4. Inflation-Hedging Properties of Various Assets and Portfolios

t

t t-1 t-1 t

t

t t



We compare investments in the perfect liability-hedging portfolio (TIPS) to investments in traditional assets (bonds and stocks) and to investments in alternative investments (commodities and real estate). Various investment horizons from three through thirty years are considered.

Table 10 presents the relevant indicators for the funding ratios assuming a 100% investment in the corresponding traditional or alternative asset class. The first column of the table refers to the liability- hedging portfolio that is obtained by a 100% investment in an inflation-indexed security that has the same maturity as the liabilities.11 In this simplified setting, this 100% TIPS liability hedging portfolio in fact proves to be a perfect match for the liability, and therefore mean funding ratios are equal to 1 with a 100% probability for all time horizons.12 The mean funding ratios for other classes in panel A are higher than 1, which indicates that all assets have, on average, higher returns than the liability stream. This is consistent with the observed historical values that have been used to calibrate the data generating process described in the previous section. On the other hand, these asset classes involve the introduction of some liability risk, as evidenced by the number in panel B and panel C. The shortfall probabilities in panel B illustrate the time-horizon characteristics of the assets with respect to the liabilities. Indeed, shortfall probabilities systematically decrease as the investment horizon increases. This is consistent with results obtained for the model-implied volatilities and correlations with the liabilities (see figures 1 and 2). The correlation between bonds, stocks and real

estate with the liabilities increases with the time horizon. Additionally, volatilities decrease with the investment horizon for bonds, stocks and commodities, and slightly increase, in relative terms, for real estate, while the model-implied volatilities of liability returns sharply rise as the investment horizon increases. Furthermore, the superior returns of the assets explain a part of the observed downwards sloping shortfall probabilities since they translate into a steeper positive trend in the numerator than in the denominator of the funding ratio. The strong decrease in shortfall probability for stocks is also explained by the structural relationship between liability shocks and aggregated responses to stock returns (see figure 3). Indeed, the persistence of liability shocks is much more pronounced for stocks than for other assets. As far as commodities are concerned, the response to liability shocks is immediate but not persistent, which explains why shortfall probabilities decrease less sharply than in the case of stocks. Real estate, on the other hand,reacts negatively in the short run but "recovers" as the liability shocks lead to persistently positive shocks to future real estate returns.

Overall, these shortfall probabilities are quite high in the short run, with numbers ranging from 37% (stocks and real estate) to 47% (long bond) and fall, at least for stocks and real estate, which suggests that moving away from TIPS, if it allows for better performance (mean funding ratios greater than 1), involves significant short-term liability risk. On the other hand, these values eventually decrease in the long run for stocks and real estate (with shortfall probabilities equal to 10%


11 - Note that in reality such portfolios may be unavailable as TIPS are issued for a small number of maturities. For instance, in the US, only TIPS with maturity up to ten years are available. Notefurther that we omitted statistics for T-bill portfolios from these tables. In fact, even though T-billsare well correlated with the liability returns, they exhibit a significant lack of relative performance due to the term spread risk premia contained in the liability return. As a result, T-bills underperformliabilities significantly and are not a natural candidate for the liability-hedging portfolio.12 - In practice, the presence of non-financial sources of risk, e.g., actuarial risk, implies that there is some remaining funding risk even with a solution invested 100% in inflation-hedging instruments with maturities matching the maturity dates of the pension payments.



and 15% respectively), while they remain high for commodities (25%) and the long bond (38%).

In panel C we present the probabilities that the asset portfolio value falls "severely" short of the liability portfolio value.13 For short investment horizons, these severe or extreme shortfall probabilities are alarmingly high with numbers greater than 20%. Additionally, for the long bond, extreme shortfall probabilities do not seem to decrease in the long run (26% for three and for thirty years with even higher numbers in the medium term).

As far as commodities are concerned, one obtains a modest decrease from 26% (three to seven years) to 20% (thirty years). On the other hand, stocks and real estate exhibit similar significantly downwards sloping patterns as in the case of shortfall probabilities (panel B).Across all four assets, we observe that the level of severe shortfall probabilities (panel C) is only slightly below the level of standard shortfall probabilities (panel B), which would obviously be of great concern to investors such as pension funds.

As a first result, we find that both commodities and real estate exhibit potentially interesting features in an asset-liability management context. Both outperform the liability on average, and exhibit inflation-hedging potential that increase in the long run. In fact, real estate exhibits shortfall probability figures that are as competitive as stocks and that sharply decrease with the investment horizon (from 37% for three years to 15% for thirty years). Commodities substantially

outperform bonds in terms of average funding ratio and shortfall probabilities. So we expect significant gains from adding commodities and real estate to the pure liability-hedging portfolio invested in TIPS.

4.2 Liability-hedging portfoliosThe results from the previous section suggest that introducing commodities and real estate, in addition to TIPS, in a pension fund LHP would allow for upside potential while limiting shortfall probabilities to a reasonably low level, at least from a long-term perspective. In what follows, we quantify the trade-off between a deviation from the perfect liability match and the resulting return upside potential, which in turn will have the welcome side effect of decreasing the required contributions. The consequences in terms of ALM risk budgets of introducing alternative asset classes so as to design enhanced liability-hedging portfolios with improved performance will be quantitatively analysed in section 5.

To analyse the characteristics of LHPsthat are enhanced by commodities and real estate assets, we proceed in two steps. First, we find the optimal portfolio mix of commodities and real estate and secondly, this portfolio is added to TIPS in various proportions so as to form the enhanced liability hedging portfolio (henceforth enhanced LHP). The first step is addressed by finding the portfolio of commodities and real estate that minimises the tracking error volatility with the TIPS portfolio. Figure 4 shows the resulting portfolios as a function of the investment horizon.


13 - Throughout this study, severe shortfalls are defined as a situation with a funding ratio lower than 90%.



As evidenced by the graph, the portfolio is well balanced between the two assets, and the position in commodities increases with the investment horizon.

Table 11 presents funding ratio statistics for the enhanced LHP. Various portfolios,ranging from 0% to 50% of alternative investments (AI) with the remainder in TIPS, are studied. The mean funding ratio of the enhanced LHP is a simple linear combination of the individual mean funding ratios and the interpretation is straightforward. In particular, panel A of table 11 shows that the upside potential is an increasing function of the percentage allocated to alternative assets within the LHP portfolio. On the other hand, the more the investor allocates to the alternative assets, the higher the risk of falling severely short of the liabilities is.However, the results suggest great gains when stepping from stand-alone alternative asset classes to alternative investment portfolios in terms of shortfall probabilities. Indeed, at all investment horizons, the shortfall probabilities are significantly lower for various versions of the enhanced LHP than those obtained for the stand-alone assets (table 10). For instance, for investment horizons of ten years, shortfall probabilities are as low as 17%, compared to 27%-35% on the stand-alone basis.14 For twenty-year horizons, these probabilities fall to as low as 9% (19-29% on the stand-alone basis). More importantly perhaps, panel C indicates that the decrease in severe shortfall probability is substantial. Even for a substancial allocation to the AI portfolio of 50%, severe shortfall probabilities are only 6% in the short-runand 2% for long investment horizons.

For modest allocations to the AI portfolio (0-15%), the severe shortfall probability even decreases to 0%, meaning that none of the 5,000 simulated paths yields a funding ratio lower than 90%, whatever the investment horizon. Overall, these results suggest that the introduction of alternative investment vehicles may lead to increased upside potential for the LHP without severely increasing the shortfall risk.


14 - Note that shortfall probabilities depend solely on the investment horizon and not on the fraction allocated to the AI portfolio. This result is intrinsic to the buy-and-hold methodology and the fact that the TIPS portfolio exhibits non-stochastic funding ratios equal to 1.

5. Implication for Risk Budgeting in Asset-Liability

Management




This section attempts to study the impact of the introduction of real estate and commodities to the LHP on the level of expected funding ratio over various time horizons.

5.1 Risk budgeting with LDI solutionsIn terms of risk budgets, the implementation of LDI solutions depends on the attitude towards risk. It is typically understood that high risk aversion leads to a predominant investment in the LHP, which in turn implies low extreme funding risk (zero risk in the complete market case), as well as low expected performance and therefore high contributions. On the other hand, low risk aversion leads to a predominant investment in the PSP, which implies high funding risk as well as higher expected performance, and hence lower contributions. To formalise this intuition, one may compare the initial contribution that is needed to generate a 100% funding ratio at the horizon when the investor's portfolio is fully invested in TIPS (the perfect LHP) versus the initial contribution needed to generate an average 100% funding ratio at the horizon when risky asset classes such as stocks and bonds are introduced. Figure 6 presents a graphical representation of this effect for different investment horizons. For instance, for an investment horizon of twenty years years, an allocation of 40% to the PSP (which is so far assumed to contain stocks and bonds in a proportion that generates the maximum Sharpe ratio—see figure 5) and 60% in the liability hedging portfolio fully invested in TIPS allows one to reduce the initial contributions by almost 20% compared to a 100% investment in TIPS LHP. Of course, this contribution-saving

effect comes at the cost of introducing funding risk at the global portfolio level. As can be seen from panel B in table 12, shortfall probabilities show a significant increase in the allocation to the PSP, even though the magnitude of this effect decreases with the time horizon.

5.2 Improving ALM risk budgets through the introduction of real estate and commodities to the LHPWe now analyse the impact on ALM risk budgets of the introduction of real estate and commodities to the LHP. We first make a comparison between the option that consists of investing 100% in the LHP but enhancing the LHP with the introduction of real estate and commodities, and the option that consists of leaving the LHP fully invested in TIPS and seeking to add performance potential through the introduction of the PSP, as discussed in the previous sub-section. A comparison of the results in panels B and C of table 11 and the results in panels B and C of table 12 clearly indicates that introducing alternatives to the LHP (option 1) systematically leads to an increase in risk indicators lower than that of traditional asset classes through the PSP (option 2). For example, the probability of a shortfall greater than 90% at the twenty year horizon is 2.1% when the investor's portfolio is invested 60% in TIPS and 40% in the combination of real estate and commodities that allows for the best liability hedge (see panel C of table 11), while it reaches 5.92% when the investor's portfolio is invested 60% in TIPS and 40% in the combination of stocks and bonds that allows for the maximum Sharpe ratio (see panel C of table 12).

5. Implication for Risk Budgeting in Asset-Liability Management



In the same spirit, figure 7 shows the relative contribution savings as a function of the allocation to the PSP when the LHP is enhanced by 10% alternative investments. In comparison to figure 6, the graph suggests that for comparable allocations to the PSP, contribution savings are greater when the enhanced LHP rather than TIPS LHP alone is used. Consequently, the target contribution savings can now be reached with a lower allocation to the PSP portfolio. Figures 8 and 9 illustrate this effect for LHPs that are enhanced by the introduction of 5%, and 10% of alternative investments (represented again by the portfolio of real estate and commodities that minimises the tracking error with respect to the liability portfolio). For instance, with an LHP that is composed of 90% TIPS and 10% alternative assets (figure 9), an allocation of only 27% to the PSP leads to the same mean funding ratio, or, equivalently, to the same contribution savings, as an investment of 40% in the PSP when the LHP is invested solely in TIPS.

Table 13 presents the corresponding ALM risk indicators , with numbers that can becompared to the results in table 12. We observe that (for a given allocation to the PSP) enhanced LHPs lead not only to higher mean funding ratios but also to shortfall probabilities (see panel B of table 13) lower than those of the non-enhanced (i.e., pure TIPS) LHP (panel B of table 12). This is obviously related to portfolio diversification effects between traditional assets in the PSP and alternative assets in the LHP. Severe shortfall probabilities (see panel C of table 13) also decrease substantially when compared to the case where the LHP was represented by the

TIPS portfolio (see panel B of table 12).

Figure 10 combines the risk and return perspectives by plotting the reduction in the probability of a deficit and probability of a severe deficit indicators when shifting from the standard LHP (100% TIPS) to the enhanced LHP while maintaining the mean funding ratio. In this analysis, we consider a base case of 40% investment to the PSP and 60% to TIPS, and show the reduction of the required PSP allocation obtained by an investor willing to substitute the enhanced LHP (when either 5% alternative investments or 10% alternative investments are introduced) to the pure 100% TIPS LHP. For instance, we find that when the investment horizon is twenty years enhancing the LHP by introducing 5% (10%) of the real estate + commodities portfolio allows one to reduce the allocation to the PSP by 14% (31%) while maintaining the mean funding ratio at the same level as with the non-enhanced LHP. The graphs further show the resulting percentage reduction in shortfall probability and expected shortfall. Again for an investment horizon of twenty years, the introduction of 5% of alternatives (real estate and commodities) to the LHP leads to a 19% reduction in shortfall probability. The reduction in the probability of severe shortfall, a spectacular 42%, is even greater; when the real estate + commodities portfolio is bumped up to 10% there is a 39% reduction in the probability of shortfall and 78% in the probability of extreme shortfall.


6. Conclusions and Directions for Future

Research




We have studied the relationship between inflation-driven liabilities and asset returns on bonds, stocks, commodities and real estate at various horizons. We have used the error correction form of the vector autoregressive model (VEC model or VECM) that allows for incorporating price and return dependencies, as opposed to the standard form of VAR models that solely focuses solely on the dynamics of returns. As a result, long-term dependencies between asset and liability values may be better captured, based on a larger fraction of the information contained in the data. We have used the VEC model-implied return dynamics to construct horizon-dependent volatilities and asset-liability correlations. Our empirical analysis suggests that explicitly accounting for long-term cointegration relationships leads to significant differences in forecasted properties of asset returns in terms of their term structure of risk and correlations with the liabilities. In particular, we have foundthat VECM-implied volatilities are significantly lower than VAR-implied volatilities for stocks, bonds and commodities, an effect particularly pronounced in the long-term. This is due to the fact that mean-reverting properties of asset returns are accounted in a more satisfactory manner when the econometric procedure explicitly allows for the modelling of long-term dependencies between asset returns and predictive state variables. We have also found that VECM-implied correlations between asset returns and liability returns to be significantly different from the VAR-implied correlations. In particular, the liability-hedging potential of commodities seems to be understated by the VAR estimation

procedure compared to the case when the presence of long-term cointegration relationships is explicitly accounted for.

We have used the structural form of the VEC model to perform a Monte Carlo simulation exercise and generate a large number of simulated scenarios for asset and liability returns in order to analyse the distribution of funding ratios of various portfolios at different time horizons. We have found that various alternative asset classes exhibit attractive inflation-driven liability-hedging properties. For instance, investing in commodities leads to very low shortfall probabilities at virtually all investment horizons. While investing in real estate leads to higher shortfall probabilities in the short and medium term, significantly lower probabilities are obtained in the very long run (>thirty years). These results suggest that novel liability-hedging investment solutions, including commodities and real estate in addition to inflation-linked securities, can be designed so as to decrease the cost of inflation insurance for long-horizon investors. These solutions are shown to achieve satisfactory levels of inflation hedging over the long-term at a lower cost than that of a solution based solely on TIPS or inflation swaps. The increased expected return generated through the introduction of commodities and real estate in addition to TIPS in the LHP allows a reduced global allocation to the PSP while meeting overall performance expectations, which in turn allows better risk management. For example, for an investment horizon of twenty years, the introduction of 5% of alternatives (real estate and commodities) to the LHP leads to a 19% reduction in shortfall probability.

6. Conclusions and Directions for Future Research



The reduction in the probability of severe shortfall, a spectacular 42%, is even greater; when the real estate + commodities portfolio is bumped up to 10% there is a 39% reduction in the probability of shortfall and 78% in the probability of extreme shortfall. Overall our results suggest that alternatives are very useful ingredients for institutional investors facing inflation-related liability constraints. Our analysis of the benefits of alternatives in institutional portfolios can be extended in several directions, and in particular would ideally encompass other forms of alternative investment. While we have focused on real estate and commodities, institutional investors have recently shown an increasing interest in other alternatives such as private equity and infrastructure, for which intuition suggests that attractive inflation-hedging properties could also be obtained. The unavailability of time series of sufficient length and frequency for these asset classes is, however, a serious concern from the econometric perspective. One possible solution would involve the construction of liquid proxies for the returns on these assets based on publicly traded instruments with similar characteristics, but the adequacy between the proxy and the actual form of investment under consideration (private equity or infrastructure) would have to be carefully assessed. Other alternative forms of investment that have gained popularity in institutional portfolios are external hedge fund portfolios, and internal global tactical asset allocation (GTAA) strategies. While hedge funds and GTAA strategies are not expected to exhibit particularly attractive inflation-hedging properties, they are natural candidates for the performance-seeking portfolios because

of their focus on factor-neutral alpha generation. Here again, data availability is a serious concern since we have access neither to a time series that would represent the performance of an index of typical GTAA managers nor to a long history of return data.


Appendix




A.1 Model-Implied Returns, Variances and CorrelationsAs in continuous-time models, our econometric approach allows us to obtain analytical expressions for time-dependent variances, covariances and expected returns. To see this, we first write the model-implied forward looking returns for the first three dates as functions of the interim shocks and current values for yt and Δyt:15

Δyt+1 = Πyt +ΓΔyt + ut+1

Δyt+2 = Πyt+1 + ΓΔyt+1 + ut+2

= Π(yt + Δ Πyt+1 + ΓΔyt+1 + ut+2

= Πyt + (Π + Γ) (Πyt +ΓΔyt + ut+1)

+ ut+2

= Π (I + ΠΓ) yt + (Π + Γ) ΓΔyt

+ (Π + Γ) ut+1 + ut+2 (A.1)Δyt+3 = Πyt+2 + ΓΔyt+2 + ut+3

= Π(yt + Δyt+1 + Δyt+2) + ΓΔyt+2

+ ut+3

= [Π + Π2 + (Π + Γ) Π (I + Π + Γ)] yt + [Γ (Π + (Π + Γ)2)] Δyt

We subsequently obtain all finite forward- looking implied returns through iteration and denote:

(A.2)

These expressions may then be used to define model-implied expected returns, variances and covariances. Using yt+k =y0 + Δyt+1 + … + Δyt+k, it is straightforward to show that we obtain:

(A.3)

(A.4)

where Σu denotes the time-invariant covariance matrix of the innovation process u. Correlation coefficients may also directly be derived directly from relation (A.4).16

A.2 TIPS-PricingConsider a pension fund that faces inflation-indexed liability payments. Such inflation-linked cash-flows are formally similar to the payoff of a portfolio of zero-coupon treasury-inflation-protected securities (TIPS) with the corresponding face values and maturity dates. In what follows, we provide a closed-form expression for the price of this liability portfolio. Let us denote by Φ(t) the price index level at t. For each real dollar payment scheduled for date t, the pension fund will eventually pay Φ(t). Let us further denote Ψ(t) the stochastic discount factor or, put differently, the risk-neutral price of a unit real payment scheduled for t.

The current value of the liability (or equivalently TIPS) portfolio may then be written as:

(A.5)

with

(A.6)

where π(t) denotes expected inflation at t and rL(t) the risk neutral return of the liability portfolio at date t.17

Appendix

15 - We use a model with 1 lag as we will focus on this specification for our later numerical application. Further, as noted in Campbell and Viceira (2004) each Var(p) model may be transformed into a Var(1) model by adding a lagged version of the vector of endogenous variables as additional state variables.16 - Note that similar expressions may be obtained for the VAR(1) model on log returns. In this case,Ψ0

(s) is equal to 0 and ΨΔ(s) and

Ψu(s) simplify to ΨΔ

(s)= Ψu(s)= Φs

with Φs as in (3). It is obviousthat VAR(1) implied conditional moments are different from VECM(1) implied moments except if Π=0 and Γ=A. Note further that the non-stochastic constant term has been introduced as one ofthe endogenous variables for tractability of the formulas. Accordingly, assuming the first entry is the constant term, the first line and the first column of Σ solely contain zeros.17 - rL is typically a sum of three components: the real treasury bill rate, realized inflation and arisk premia that accounts for interest rate risk and (the absence of) inflation risk (Kothari andShanken 2004).



We obtain:

(A.7)

(A.8)

Assuming normally distributed residuals ut in (4) and (6) we use the expected value expression of log-normally distributed random variables: E(exp(X)) = exp [E(X) + 1/2 Var (X)] to obtain:

Finally, we use (A.3) and (A.4) and write risk-neutral price of the liability stream at initial date 0 as:

where μi(t)

i denotes the element in the vector E0(yt) that corresponds to variable i and Σi,j is the covariance-element in the matrix Var0(yt) that corresponds to variables i and j.

Appendix



Table 1 Unit-root tests (ADF)

Appendix

Table 2Johansen's trace test for cointegration order



Appendix

Table 3VECM parameter estimates (Γ)

Table 4Estimated cointegration relationship (β)



Appendix

Table 5Estimates for adjustment parameters (α)

Table 6VECM residuals—Correlation cœfficients



Appendix

Table 7Structural VECM—contemporaneous shocks (B)

Table 8Structural VECM—transitory shocks (ΞB)



Appendix

Table 9VAR parameter estimates (A)



Appendix

Table 10Stand-alone hedgers—ALM indicators



Appendix

Table 11Enhanced LHP—ALM indicators



Appendix

Table 12Global portfolio (LHP+PSP)—ALM indicators



Appendix

Table 13Global portfolio (enhanced LHP+PSP)—ALM indicators



Appendix

Figure 1Annualised volatilities

Annualised volatilities for asset and liability returns for various horizons are displayed. Dotted lines correspond to VAR-implied volatilities and solid lines to VECM-implied volatilities.



Appendix

Figure 2Correlation between liabilities and asset returns

Correlation coefficients between different asset returns and liability returns for various horizons are displayed. Dotted lines correspond to VAR-implied correlations and solid lines to VECM-implied correlations.



Appendix

Figure 3Aggregated responses to a structural liability shock

Aggregated impulse responses correspond to first column elements of matrices calculated via (15). Dotted lines correspond to VAR-implied correlations and solid lines to VECM-implied correlations.



Appendix

Figure 4Alternative LHP enhancers

The allocations correspond to those that minimise the tracking error with the TIPS, defined as the standard deviation between the portfolio and the TIPS return, for a given investment horizon. Optimisation is based on the 5,000 simulated scenarios.

Figure 5The PSP—Maximum Sharpe ratio allocation

The displayed allocations maximise the Sharpe ratio for a given investment horizon with the investment universe of stocks and bonds. The risk-free rate has been modelled through T-bills returns. Optimisation is based on the 5,000 simulated scenarios.



Appendix

Figure 6Contribution savings through introduction of a PSP

Contribution saving is defined as the potential reduction of initial investment when deviating from the perfect liability matching portfolio such that, on average, the pension plan is fully funded. Numbers are based on 5,000 simulated scenarios. The PSP contains stocks and bonds in proportions that depend on the investment horizon (see figure 5).

Figure 7Contribution savings through enhanced LHP

Contribution saving is defined as the potential reduction of initial investment when deviating from the perfect liability matching portfolio such that, on average, the pension plan is fully funded. Numbers are based on 5,000 simulated scenarios. The alternative investment (AI) portfolio contains commodities and real estate in proportions that depend on the investment horizon (see figure 4).



Appendix

Figure 8Return equivalents with 5% AI—PSP allocation reduction

The graph shows the impact of enhancing the LHP beyond TIPS. The enhanced LHP consists of 95% TIPS and 5% alternative investments (see figure 4). The graph yields the required allocations to the PSP so as to obtain on average the same amount of return as in the case of the traditional LHP (TIPS). Various non-enhanced portfolios are taken as benchmarks ((1 - ω) . TIPS + ω . PSP, ω ∈ {20%; 30%; 40%; 50%}).

Figure 9Return equivalents with 10% AI—PSP allocation reduction

The graph shows the impact of enhancing the LHP beyond TIPS. The enhanced LHP consists of 90% TIPS and 10% alternative investments (see figure 4). The graph yields the required allocations to the PSP so as to obtain on average the same amount of return as in the case of the traditional LHP (TIPS). Various non-enhanced portfolios are taken as benchmarks ((1 - ω) . TIPS + ω . PSP, ω ∈ {20%; 30%; 40%; 50%}).



Appendix

Figure 10Risk reduction through LHP enhancements

The graph shows the impact of enhancing the LHP beyond TIPS on various risk parameters. We considered the base case of an investment of 40% in the PSP and 60% in the traditional LHP and compared this portfolio to the case where the LHP is enhanced by 5%, respectively 10% of alternative assets (AI, i.e. estate and commodities). Enhanced and traditional portfolios are linked such that the portfolios exhibit the same mean funding ratios.



Appendix

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References



The choice of asset allocationThe EDHEC Risk and Asset Management Research Centre structures all of its research work around asset allocation. This issue corresponds to a genuine expectation from the market. On the one hand, the prevailing stock market situation in recent years has shown the limitations of active management based solely on stock picking as a source of performance.

40% Strategic Asset Allocation

3.5% Fees

11% Stock Picking

45.5 Tactical Asset Allocation

Percentage of variation between funds

Source: EDHEC (2002) and Ibbotson, Kaplan (2000)

On the other, the appearance of new asset classes (hedge funds, private equity), with risk profiles that are very different from those of the traditional investment universe, constitutes a new opportunity in both conceptual and operational terms. This strategic choice is applied to all of the Centre's research programmes, whether they involve proposing new methods of strategic allocation, which integrate the alternative class; measuring the performance of funds while taking the tactical allocation dimension of the alpha into account; taking extreme risks into account in the allocation; or studying the usefulness of derivatives in constructing the portfolio.

An applied research approachIn an attempt to ensure that the research it carries out is truly applicable, EDHEC has implemented a dual validation system for the work of the EDHEC Risk and Asset Management

Research Centre. All research work must be part of a research programme, the relevance and goals of which have been validated from both an academic and a business viewpoint by the Centre's advisory board. This board is made up of both internationally recognised researchers and the Centre's business partners. The management of the research programmes respects a rigorous validation process, which guarantees the scientific quality and the operational usefulness of the programmes.

To date, the Centre has implemented six research programmes:Asset Allocation and Alternative Diversification Sponsored by SG Asset Management and Newedge

The research carried out focuses on the benefits, risks and integration methods of the alternative class in asset allocation. From that perspective, EDHEC is making a significant contribution to the research conducted in the area of multi-style/multi-class portfolio construction.

Performance and Style AnalysisPart of a business partnership with EuroPerformanceThe scientific goal of the research is to adapt the portfolio performance and style analysis models and methods to tactical allocation. The results of the research carried out by EDHEC thereby allow portfolio alpha to be measured not only for stock picking but also for style timing.

Indices and BenchmarkingSponsored by Af2i, Barclays Global Investors, BNP Paribas Investment Partners, NYSE Euronext, Lyxor Asset Management, and UBS Global Asset ManagementThis research programme has given rise to extensive research on the subject of indices and benchmarks in both the hedge fund universe and more traditional investment

About the EDHEC Risk and Asset Management Research Centre

EDHEC is one of the top five business schools in France.

Its reputation is built on the high quality of its faculty (110

professors and researchers from France and abroad) and

the privileged relationship with professionals that the school has been developing since its

establishment in 1906. EDHEC Business School has decided

to draw on its extensive knowledge of the professional

environment and has therefore focused its research on themes

that satisfy the needs of professionals. EDHEC is

also one of the few business schools in Europe to have received the triple

international accreditation: AACSB (US-Global), Equis

(Europe-Global) andAssociation of MBAs

(UK-Global).EDHEC pursues an active

research policy in the field of finance. The EDHEC Risk and Asset Management Research Centre carries out numerous research programmes in the areas of asset allocation and

risk management in both the traditional and alternative

investment universes.




classes. Its main focus is on analysing the quality of indices and the criteria for choosing indices for institutional investors. EDHEC also proposes an original proprietary style index construction methodology for both the traditional and alternative universes. These indices are intended to be a response to the critiques relating to the lack of representativeness of the style indices that are available on the market. In 2003, EDHEC launched the first composite hedge fund strategy indices.

Asset Allocation and DerivativesSponsored by Eurex, SGCIB and the French Banking FederationThis research programme focuses on the usefulness of employing derivative instruments in the area of portfolio construction, whether it involves implementing active portfolio allocation or replicating indices. “Passive” replication of “active” hedge fund indices through portfolios of derivative instruments is a key area in the research carried out by EDHEC. This programme includes the “Structured Products and Derivatives Instruments” research chair sponsored by the French Banking Federation.

Best Execution and Operational PerformanceSponsored by CACEIS, NYSE Euronext, and SunGard This research programme deals with two topics: best execution and, more generally, the issue of operational risk. The goal of the research programme is to develop a complete framework for measuring transaction costs: EBEX (“Estimated Best Execution”) but also to develop the existing framework for specific situations (constrained orders, listed derivatives, etc.). Research also focuses on risk-adjusted performance measurement of execution strategies, analysis of market

impact and opportunity costs on listed derivatives order books, the impact of explicit and implicit transaction costs on portfolio performances, and the impact of market fragmentation resulting from MiFID on the quality of execution in European listed securities markets. This programme includes the “MiFID and Best Execution” research chair, sponsored by CACEIS, NYSE Euronext, and SunGard.

ALM and Asset ManagementSponsored by BNP Paribas Investment Partners, AXA Investment Managers and ORTEC FinanceThis research programme concentrates on the application of recent research in the area of asset-liability management for pension plans and insurance companies. The research centre is working on the idea that improving asset management techniques and particularly strategic allocation techniques has a positive impact on the performance of asset-liability management programmes. The programme includes research on the benefits of alternative investments, such as hedge funds, in long-term portfolio management. Particular attention is given to the institutional context of ALM and notably the integration of the impact of the IFRS standards and the Solvency II directive project. It also aims to develop an ALM approach addressing the particular needs, constraints, and objectives of the private banking clientele. This programme includes the “Regulation and Institutional Investment” research chair, sponsored by AXA Investment Managers, the “Asset-Liability Management and Institutional Investment Management” research chair, sponsored by BNP Paribas Investment Partners and the "Private Asset-Liability Management" research chair, in partnership with ORTEC Finance.




Nine Research Chairs have been endowed:

Regulation and Institutional InvestmentIn partnership with AXA Investment Managers

The chair investigates the interaction between regulation and institutional investment management on a European scale and highlights the challenges of regulatory developments for institutional investment managers.

Asset-Liability Management and Institutional Investment ManagementIn partnership with BNP Paribas Investment Partners

The chair examines advanced asset-liability management topics such as dynamic allocation strategies, rational pricing of liability schemes, and formulation of an ALM model integrating the financial circumstances of pension plan sponsors.

MiFID and Best ExecutionIn partnership with NYSE Euronext, SunGard, and

CACEIS Investor Services

The chair looks at two crucial issues linked to the Markets in Financial Instruments Directive: building a complete framework for transaction cost analysis and analysing the consequences of market fragmentation.

Structured Products and Derivative InstrumentsSponsored by the French Banking Federation (FBF)

The chair investigates the optimal design of structured products in an ALM context and studies structured products and derivatives on relatively illiquid underlying instruments.

Financial Engineering and Global Alternative Portfolios for Institutional InvestorsSponsored by Morgan Stanley Investment Management

The chair adapts risk budgeting and risk management concepts and techniques to the specificities of alternative investments,

both in the context of asset management and asset-liability management.

Private Asset-Liability ManagementIn partnership with ORTEC Finance

The chair will focus on the benefits of the asset-liability management approach to private wealth management, with particular attention being given to the life cycle asset allocation topic.

Dynamic Allocation Models and new Forms of Target FundsIn partnership with Groupe UFG

The chair consists of academic research that will be devoted to the analysis and improvement of dynamic allocation models and new forms of target funds.

Advanced Modelling Techniques for Hedge Fund ReturnsIn partnership with Newedge

The chair involves a three-year project whereby academic research dedicated to hedge funds and to the analysis and modelling of their returns will be conducted.

Asset-Liability Management Techniques for Sovereign Wealth Fund (SWF) ManagementIn partnership with Deutsche Bank

The chair will introduce a formal dynamic asset allocation model that will incorporate the most salient factors in sovereign wealth fund management and propose an empirical analysis of the risk factors impacting the inflows and outflows of cash for various sovereign funds.




The EDHEC PhD in FinanceThe PhD in Finance at EDHEC Business School is designed for professionals who aspire to higher intellectual levels and aim to redefine the investment banking and asset management industries.

It is offered in two tracks: a residential track for high-potential graduate students who will hold part-time positions at EDHEC Business School, and an executive track for practitioners who will keep their full-time jobs.

Drawing its faculty from the world’s best universities and enjoying the support of the research centre with the most impact on the European financial industry, the EDHEC PhD in Finance creates an extraordinary platform for professional development and industry innovation.

Research for BusinessTo optimise exchanges between the academic and business worlds, the EDHEC Risk and Asset Management Research Centre maintains a website devoted to asset management research for the industry:www.edhec-risk.com, circulates a monthlynewsletter to over 200,000 practitioners, conducts regular industry surveys and consultations, and organises annual conferences for the benefit of institutional investors and asset managers. The Centre’s activities have also given rise to the business offshoots EDHEC Investment Research and EDHEC Asset Management Education.

EDHEC Investment Research supports institutional investors and asset managers in the implementation of the Centre’s research results and proposes asset allocation services in the context of a

core-satellite approach encompassing alternative investments.

EDHEC Asset Management Education helps investment professionals to upgrade theirskills with advanced risk and asset management training across traditional and alternative classes.




Industry surveys: comparing research advances with industry best practices EDHEC regularly conducts surveys on the state of the European asset management industry. They look at the application of recent research advances within investment management companies and at best practices in the industry. Survey results receive considerable attention from professionals and are extensively reported by the international financial media.

Recent industry surveys conducted by the EDHEC Risk and Asset Management Research Centre1/ The EDHEC European Investment Practices Survey 2008, sponsored by Newedge

2/ The Impact of IFRS and Solvency II on Asset-Liability Management and Asset Management in Insurance Companies, sponsored by AXA Investment Managers

3/ EDHEC European Real Estate Investment and Risk Management Survey, sponsored by Aberdeen Property Investors and Groupe UFG

EuroPerformance-EDHEC Style Ratings and Alpha League TableThe business partnership between France’s leading fund rating agency and the EDHEC Risk and Asset Management Research Centre led to the 2004 launch of the EuroPerformance-EDHEC Style Ratings, a free rating service for funds distributed in Europe which addresses market demand by delivering a true picture of alpha, accounting for potential extreme loss, and measuring performance persistence. The risk-adjusted performance of individual funds is used to build the Alpha League Table, the first ranking of European asset management companies based on their ability to deliver value on their equity management.www.stylerating.com

EDHEC-Risk websiteThe EDHEC Risk and Asset Management Research Centre’s website makes EDHEC’s analyses and expertise in the field of asset management and ALM available to professionals. The site examines the latest academic research from a business perspective, and provides a critical look at the most recent industry news.www.edhec-risk.com


Alternative Investments for Institutional Investors - Risk Budgeting Techniques in Asset Management and Asset-Liability Management - January 2009

Morgan Stanley Investment ManagementMorgan Stanley Investment Management (MSIM) is a client centric organization dedicated to providing investment and risk-management solutions to investors worldwide. Our global presence, thought-leadership, and breadth of products and services enable us to partner with clients to design solutions that are both flexible and tailored to meet the ever-evolving challenges of today’s financial markets.

With over three decades of asset management experience, our investment strategies span the risk/return spectrum across geographies, investment styles and asset classes, including equity, fixed income, alternatives and private markets. MSIM comprises a community of specialized investment boutiques, each with a unique talent pool of experienced investment professionals backed by the broad reach, access and resources of Morgan Stanley. With solutions ranging from strategic partnerships, portfolio architecture and risk modeling to beta management and portable alpha, our mission is to help investors worldwide make better investment decisions and manage their portfolios more efficiently.

A Diverse Community of Investment BoutiquesWe believe that diversity of ideas breeds the best investment solutions. That is why our community of investment boutiques, which integrates an assorted group of seasoned professionals located in every major market globally, is at the center of our business. Operating side by side, MSIM ’s boutiques leverage the Morgan Stanley platform, producing a wealth of

knowledge and perspectives, and fostering a creative environment for the generation of ideas and the selection of investment opportunities. While separately managed, all investment teams share the same core values of fiduciary responsibility and commitment to investment excellence that have been the hallmarks of MSIM for more than 30 years. Our investment professionals draw on Morgan Stanley’s global network of economists, strategists, research professionals and industry relationships, creating a flexible platform that optimizes resources and focuses on core expertise.

Global Investment Solutions for Investors WorldwideThe extensive range of MSIM ’s services and products reflects our continuous effort to provide solutions that meet the needs of investors worldwide. We partner with clients and consultants strategically to tackle a variety of challenges, from portfolio architecture, risk management and alternative-investment exposure to funded-status volatility management and increased portfolio efficiency. Through these strategic partnerships, we help clients develop comprehensive investment policies, implement original investment solutions and strive to enhance overall return potential. MSIM also designs structured products that take advantage of a full gamut of instruments available in the financial markets, from long-only strategies to long-short, event driven, global macro, global tactical asset allocation and portable alpha solutions. Additionally, our Global Portfolio Solutions (GPS) group gathers a team of professionals who combine practitioner and academic backgrounds to help clients conceive and implement

About Morgan Stanley Investment Management



targeted investment solutions in the areas of asset-liability management, liability-driven investing, risk management and modeling, and research and innovation.

Sharing Knowledge, Empowering ClientsMSIM employs specialists dedicated to providing superior investment service to investors from the Americas, Europe, the Middle East, Africa and Asia Pacific. In addition to responding to client inquiries and providing timely portfolio analytics and commentary, MSIM strives to share knowledge with its clients by organizing proprietary conferences and webcasts, and distributing a wide array of publications and research papers highlighting intellectual capital, as well as educational and forward-thinking investment perspectives. We aim to empower our clients to become better fiduciaries and make informed, better investment decisions. The longevity of many of our client relationships testifies to our commitment to superior investment service and the productive partnerships we have cultivated throughout our history.

A Global LeaderAs of September 30, 2008, MSIM had more than 1,000 investment professionals worldwide who managed and supervised US$476 billion in assets for institutional and retail investors from around the globe. With 42 offices in 21 countries, we are able to provide indepth local knowledge and expertise while channeling the strengths of our global presence and resources to deliver targeted investment solutions. MSIM serves a diverse client base of institutional investors, including corporations, endowments, foundations,

central banks, government establishments, sovereign wealth funds, health-service organizations, financial institutions, public funds, and union and industry pension plans. We also serve a diverse group of intermediary and retail investors all over the world.

About Morgan Stanley Investment Management



EDHEC Risk and Asset Management Research Centre2008 Position Papers• Amenc,  N.,  and  S.  Sender.  Assessing  the  European  Banking  Sector  Bailout  Plans (December).

• Amenc, N., and S. Sender. Les mesures de recapitalisation et de soutien à la liquidité du secteur bancaire européen (December).

•  Amenc,  N.,  F.  Ducoulombier,  and  P.  Foulquier.  Reactions  to  an  EDHEC  Study  on the Fair Value Controversy (December). With the EDHEC Financial Analysis and Accounting Research Centre.

• Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou  non  :  un  débat  mal  posé  (December).  With  the  EDHEC  Financial  Analysis  and Accounting Research Centre.

•  Amenc,  N.,  and  V.  Le  Sourd.  Les  performances  de  l’investissement  socialement responsable en France (December).

• Amenc, N., and V. Le Sourd. Socially Responsible Investment Performance in France (December).

• Amenc, N., B. Maffei, and H. Till. Les causes structurelle du troisième choc pétrolier (November).

•  Amenc,  N.,  B.  Maffei,  and  H.  Till.  Oil  Prices:  the  True  Role  of  Speculation (November).

•  Sender,  S.  Banking:  Why  Does  Regulation  Alone  Not  Suffice?  Why  Must Governments Intervene? (November).

• Till, H. The Oil Markets: Let the Data Speak for Itself. (October).

• Amenc, N.,  F. Goltz,  and V.  Le Sourd. A Comparison of  Fundamentally Weighted Indices: Overview and Performance Analysis. (March).

• Sender, S. QIS4: Significant Improvements, but the Main Risk for Life insurance is Not Taken into Account in the Standard Formula. (February).      

2008 Publications• Amenc, N., L. Martellini, and V. Ziemann. Alternative Investments for Institutional Investors:  Risk  Budgeting  Techniques  in  Asset  Management  and  Asset-Liability Management (December).

• Goltz, F. and D. Schröder. Hedge Fund Reporting Survey. (November). 

• D’Hondt, C., and J.-R. Giraud. Transaction Cost Analysis A-Z: A Step towards Best Execution in the Post-MiFID Landscape. (November).

• Schröder. D. The Pros and Cons of Passive Hedge Fund Replication. (October). 

•  Amenc,  N.,  F.  Goltz,  and  D.  Schröder.  Reactions  to  an  EDHEC  Study  on  Asset-Liability Management Decisions in Wealth Management. (September).

• Amenc, N., F. Goltz, A. Grigoriu, V. Le Sourd, and L. Martellini. The EDHEC European ETF Survey 2008. (June).

EDHEC Position Papers and Publications from the last 3 years



•  Amenc,  N.,  F.  Goltz,  and  V.  Le  Sourd.  Fundamental  Differences?  Comparing Alternative Index Weighting Mechanisms. (April).

• Le Sourd, V. Hedge Fund Performance in 2007 (February).

• Amenc, N., F. Goltz, V. Le Sourd, and L. Martellini. The EDHEC European Investment Practices Survey 2008. (January).

2007 Position Papers• Amenc, N. Trois premières leçons de la crise des crédits « subprime » (August). 

• Amenc, N. Three Early Lessons from the Subprime Lending Crisis (August). 

•  Amenc,  N.,  W.  Géhin,  L.  Martellini,  and  J.-C.  Meyfredi.  The  Myths  and  Limits  of Passive Hedge Fund Replication (June).

• Sender, S., and P. Foulquier. QIS3: Meaningful Progress towards the Implementation of Solvency II, but Ground Remains to be Covered (June). With the EDHEC Financial Analysis and Accounting Research Centre.

• D’Hondt, C., and J.-R. Giraud. MiFID: the (In)famous European Directive (February). Hedge  Fund  Indices  for  the  Purpose  of  UCITS:  Answers  to  the  CESR  Issues  Paper (January).

•  Foulquier,  P.,  and  S.  Sender.  CP  20:  Significant  Improvements  in  the  Solvency  II Framework but Grave Incoherencies Remain. EDHEC Response to Consultation Paper n° 20 (January).

• Géhin, W.  The Challenge of Hedge  Fund Measurement:  a  Toolbox Rather  Than a Pandora's Box (January).

• Christory, C., S. Daul, and J.-R. Giraud. Quantification of Hedge Fund Default Risk (January).

2007 Publications•  Ducoulombier,  F.  Etude  EDHEC  sur  l'investissement  et  la  gestion  du  risque immobiliers en Europe (November/December).

• Ducoulombier,  F.  EDHEC European Real  Estate  Investment and Risk Management Survey (November). 

• Goltz, F., and G. Feng. Reactions to the EDHEC Study "Assessing the Quality of Stock Market Indices" (September).   

• Le Sourd, V. Hedge Fund Performance  in 2006: a Vintage Year  for Hedge Funds? (March).

• Amenc, N., L. Martellini, and V. Ziemann. Asset-Liability Management Decisions in Private Banking (February).

•  Le  Sourd,  V.  Performance  Measurement  for  Traditional  Investment  (Literature Survey) (January).

2006 Position Papers•  Till,  H.  EDHEC  Comments  on  the  Amaranth  Case:  Early  Lesson  from  the  Debacle (September).




• Amenc, N., and F. Goltz. Disorderly Exits  from Crowded Trades? On  the Systemic Risks of Hedge Funds (June).

• Foulquier, P., and S. Sender. QIS 2: Modelling That Is at Odds with the Prudential Objectives of Solvency II (with the EDHEC Financial Analysis and Accounting Research Centre) (November).

• Amenc, N., P. Foulquier, L. Martellini, and S. Sender. The Impact of IFRS and Solvency II  on  Asset-Liability  Management  and  Asset  Management  in  Insurance  Companies (with the EDHEC Financial Analysis and Accounting Research Centre) (November).  • Amenc, N., and F. Goltz. A Reply to the CESR Recommendations on the Eligibility of Hedge Fund Indices for Investment of UCITS (December).  2006 Publications• Amenc, N., F. Goltz, and V. Le Sourd. Assessing the Quality of Stock Market Indices: Requirements for Asset Allocation and Performance Measurement (September). • Amenc, N., J.-R. Giraud, F. Goltz, V. Le Sourd, L. Martellini, and X. Ma. The EDHEC European ETF Survey 2006 (October).   

EDHEC Financial Analysis and Accounting Research Centre2008 Position Papers•  Amenc,  N.,  F.  Ducoulombier,  and  P.  Foulquier.  Call  for  Reaction.  The  Fair  Value Controversy:  Ignoring the Real  Issue  (with the EDHEC Risk and Asset Management Research Centre) (December).

• Amenc, N., F. Ducoulombier, and P. Foulquier. Réactions après l’étude. Juste valeur ou non : un débat mal posé (with the EDHEC Risk and Asset Management Research Centre) (December).

• Escaffre, L., P. Foulquier, and P. Touron. The Fair Value Controversy:  Ignoring the Real Issue (November).

• Escaffre, L., P. Foulquier, and P. Touron. Juste valeur ou non : un débat mal posé (November).

• Sender,  S. QIS4:  Significant  Improvements, But  the Main Risk  for  Life  Insurance Is Not Taken into Account in the Standard Formula. EDHEC’s Answer to the Fourth Quantitative Impact Survey (February). With the EDHEC Risk and Asset Management Research Centre.

2007 Position Papers• Sender, S., and P. Foulquier. QIS3: Meaningful Progress towards the Implementation of Solvency II, But Ground Remains to Be Covered (June). With the EDHEC Risk and Asset Management Research Centre.

2006 Position Papers• Foulquier, P., and S. Sender. QIS 2: Modelling That Is at Odds with the Prudential Objectives  of  Solvency  II  (with  the  EDHEC  Risk  and  Asset  Management  Research Centre) (November).




• Amenc, N., P. Foulquier, L. Martellini, and S. Sender. The Impact of IFRS and Solvency II  on  Asset-Liability  Management  and  Asset  Management  in  Insurance  Companies (with the EDHEC Risk and Asset Management Research Centre) (November). 

EDHEC Economics Research Centre2009 Position Papers• Courtioux, P. Peut-on financer l’éducation du supérieur de manière plus équitable ? (January 2009)

2008 Position Papers•  Gregoir,  S.  Les  prêts  étudiants  peuvent-ils  être  un  outil  de  progrès  social  ? (October).

• Chéron, A. Que peut-on attendre d'une augmentation de l'âge de départ en retraite ? (June).

•  Chéron,  A.  De  l'optimalité  des  allégements  de  charges  sur  les  bas  salaires (February).

• Chéron, A., and S. Gregoir. Mais où est passé le contrat unique à droits progressifs? (February).

2007 Position Papers•  Chéron,  A.  Faut-il  subventionner  la  formation  professionnelle  des  séniors  ? (October).

• Courtioux, P. La TVA acquittée par les ménages : une évaluation de sa charge tout au long de la vie (October). 

• Maarek, G. La réforme du financement de la protection sociale. Essais comparatifs entre la « TVA Sociale » et la « TVA Emploi » (July). 

• Chéron, A. Analyse économique des grandes propositions en matière d'emploi des candidats à l'élection présidentielle (March).

• Chéron, A. Would a new form of employment contract provide greater security for French workers? (March). 

2007 Publications• Amenc, N., P. Courtioux, A.-F. Malvache, and G. Maarek. La « TVA emploi ». EDHEC publication (April).

•  Amenc,  N.,  P.  Courtioux,  A.-F.  Malvache,  and  G.  Maarek.  Pro-Employment  VAT. EDHEC publication (April).

• Chéron, A. Reconsidérer les effets de la protection de l'emploi en France. L'apport d'une approche en termes de cycle de vie (January).

2006 Position Papers• Chéron, A.  Le  plan national  d’action pour  l’emploi  des  seniors  :  bien, mais  peut mieux faire.



Alternative Investments for Institutional Investors - Risk Budgeting Techniques in Asset Management and Asset-Liability Management - January 2009

• Bacache-Beauvallet, M. Les  limites de  l'usage des primes à  la performance dans  la fonction publique (October)

• Courtioux, P., and O. Thévenon. Politiques familiales et objectifs européens : il faut améliorer le benchmarking (November).             

EDHEC Marketing and Consumption Research Centre – InteraCT2007 Position Papers•  Bonnin,  Gaël.  Piloter  l’interaction  avec  le  consommateur :  Un  impératif  pour  le marketing. EDHEC position paper (January).


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