research paper mark hoaglund

AN ABSTRACT OF THE RESEARCH PAPER OF

Mark Hoaglund, for the Master of Science degree in economics, presented on August 14, 2008, at Southern Illinois University at Carbondale.

TITLE: Measuring the Performance of the Hedge Fund Market

MAJOR PROFESSOR: Scott Gilbert

The objective of this study was to determine some of the characteristics of the hedge

fund market and to compare the returns of the hedge fund market to the S&P 500 by

computing various statistical measures of performance for a representative sample of

hedge funds and imparting meaning to the results. In order to achieve the objective,

Capital Asset Pricing Models, polynomial regressions, variances, correlations, and mean

averages were computed and the results were analyzed. Finally, graphs were generated

as tests for heteroscedasticity and normality in the CAPM regressions, and plausible

interpretive meaning was suggested. The collective statistical analysis concluded that the

performance of hedge funds exceeds the market impressively. Specifically, the hedge

fund market was found to be far less volatile and more profitable than the S&P 500.

Moreover, those particular funds - as distinguished from the overall hedge fund market -

with higher Sharpe Ratios were found to be both less volatile and more profitable than

the S&P 500. Thus, within the hedge fund market, investment alternatives exist which

are characterized by an overall improvement to the index fund.

i

ACKNOWLEDGEMENTS

I’d like to thank Professor Scott Gilbert for helping me throughout the process of

developing this study.

ii

TABLE OF CONTENTS

ABSTRACT ……………………………………………………………..i

ACKNOWLEDGEMENTS ….......................................................................................ii

LIST OF TABLES ……………………………………………………………iv

LIST OF FIGURES …......................................................................................vi

TEXT ……………………………………………………………..1

REFERENCES …………………………………………………………..123

VITA …………………………………………………………..124

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LIST OF TABLES

TABLE PAGE

Table 1…..........................................................................................................................6

Table 2…………………………………………………………………………………...11

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LIST OF FIGURES

FIGURE PAGE

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Figure 23…………………………………………………………………………………32

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Introduction

The purpose of the following study was to examine various measures of performance

of the hedge fund market, to compare the hedge fund market to the broader stock market

by way of the S&P 500 index, and to determine the implications of the hedge fund

market performance from the perspective of considering all the investigative results

collectively. The source of data used in the analysis of hedge funds was

www.hedgefund.net which is a service owned by Channel Capital Group Incorporated

that provides hedge fund news and proprietary performance data on approximately 8000

hedge funds.1 The hedge fund data were drawn by conducting a search for funds

according to the Sharpe Ratio in descending order and then selecting the performance

data from 30 hedge funds using an algorithm. By arranging the funds in terms of the

Sharpe Ratio, a sample of data more representative of the overall hedge fund market was

obtained because the data accounted better for the full spectrum of both risk and return of

the funds. Many interesting statistics began to emerge once the data was arranged in

Excel and analyzed.

The literature contained information that shared a complementary relationship with

the findings of this study, but also, that information yielded some cautionary reservations

that must be noted with respect to this study’s performance findings of hedge funds. In

an article by John Morgan on July 7, 20082, a warning was issued that the Securities and

Exchange Commission (SEC) is poised to initiate tighter regulation of the hedge fund

market depending on the political persuasions of those elected in the impending

xiii

http://www.hedgefund.net/

presidential election. If these regulatory prospects materialize, then access might be

further restricted to investors, and fewer funds may form as a result of an inability of

smaller firms to raise capital. Perhaps the lack of smaller, unstable firms might actually

improve the statistical performance results, such as those that are found in this study,

because there would be fewer firms that collapse and pull the performance data of the

hedge fund market down. However, an October 2004 publication by Burton G. Malkiel3

extensively studied many ways that hedge fund performance data artificially inflate the

true returns of the hedge fund market. For example, hedge funds that are about to close

stop reporting their performance data during the last months of their existence, and

because hedge funds, unlike mutual funds, do not have to report their performance data to

the SEC, a hedge fund only begins offering its data to a database when the fund has

established some sustainable measure of success so that the initial performance remains

unreported. Nevertheless, if a hedge fund were to be chosen judiciously, such as the

selection of one with low volatility and a proven track record, then surely the integrity of

the results will be intact since the investor would not have to be as concerned about the

hedge fund folding. An additional concern is also noted in a September 11, 20064 article

by Pascal Botteron regarding the inflated perception of hedge fund performance.

Namely, the fact that hedge funds tend to have low volatility is only true insofar as the

fund itself is solvent and viable. For example, the volatility of stocks in a company

reflects broadly disseminated reports about the welfare of the company itself, but a hedge

fund is not required to produce such information, so an imperative for wise investment is

the process of thoroughly vetting a fund. These reservations about the hedge fund market

performance must be taken into context and temper any understanding about the results.

xiv

Models and Variables

Employed in the study of the hedge fund market were a number of statistical variables

and models which will be defined and explained next.

The Sharp Ratio, mentioned in the introduction, is defined as where E(Ri)

is the expected return of fund i, Rf is the risk free rate of return as measured by treasury

bonds, and σ is the standard deviation of the excess return as given by the entire

numerator. The Sharpe Ratio is considered a measure of the tradeoff between excess

return and risk from volatility.

The variance is a measure of the spread of the values of a random variable around the

expected value. The variance can be defined, in its most abstract sense, as

var(X) = E(X – μ)2 where X is a random variable and μ = E(X), the expected value of X.

The coefficient of correlation is a measure of the degree of association between two

variables. The coefficient always lies in the interval [-1, 1] where a high positive value

means that the two variables move closely together whereas a low negative value means

that the two variables move in opposition to each other. The coefficient of correlation is

defined differently for a population of data and a sample of data.

xv

2

The definition of the population coefficient of correlation in its most abstract is

ρ = where X and Y are random variables and the rho values in the

denominator are their respective population standard deviations.

The definition in its most abstract form of the sample coefficient of correlation is

r = where X and Y are random variables and the s values are their sample

standard deviations. However the definition in a form best suited for interpretation in

terms of simple regression is

r = where X and Y are random variables and

n is the number of pairs observed.

A point of clarification must be addressed in preparation for the body of the study. In

conducting the analysis of the hedge fund market, the tables for the coefficient of

correlation values were computed for a population of data in Excel because the only

Excel function available to compute correlations uses the formula for populations of data.

The only difference between the correlation formulas for populations and samples of data

is that the sample standard deviation is divided by n-1 whereas the population standard

deviation is divided by n. Consequently, the denominator of the population correlation is

smaller than the denominator of the sample correlation, so the population correlation is

larger than the sample correlation when both the sample correlation and population

correlation are applied to the same set of data. In truth, the populations of data were

3

known in this study, but these populations were often treated as samples in order to

project future trends, so whether the population correlation or sample correlation is more

desirable is a matter of interpretation. Also, the reader must know that the regressions are

based on the sample correlation formula when the discussion about the r2 = R2 values is

encountered later in the study.

The coefficient of determination, r2, is a measure of how well a regression line fits the

data. In other words, the coefficient measures the percentage of the regression that can

be explained by the regression where the remaining percentage can only be accounted for

by random error. In regression involving more than one explanatory variable, that is, in

multiple regression, the term used by convention for the coefficient of determination is

R2, and in regression involving only one explanatory variable, that is, in simple

regression, the term used is r2. However, R2 is often used interchangeably for both simple

regression and multiple regression. Since Excel used the R2 term for the simple

regressions discussed later, the reader must be aware that r2 = R2.

Average Returns

For both the S&P 500 and the individual hedge funds, each month of percentage

returns was annualized by multiplying each monthly return by 12. For the period of

January, 1995 – April, 2008, the mean average of the annualized monthly returns for the

S&P 500 index was 9.21515%. The mean average of the annualized monthly returns for

each hedge fund was obtained similarly, but care must be taken to note that many of the

hedge funds did not span the same number of months as the time period stated above that

was chosen for the S&P 500. Regardless, when these averages for the individual hedge

4

funds were themselves averaged, the result was 13.11473%, which is substantially higher

than the return for the S&P 500. Moreover, the hedge fund performance data was also

approached somewhat differently by first averaging, for any given month, across all 30

hedge funds so that, for example, in September of 1995, the average annualized monthly

performance across all the hedge funds was 37.2%. When these monthly annualized

averages were themselves averaged, the result was 16.9934%, which was even higher

than the 13.114% figure. Therefore, the average returns of the hedge fund market yielded

much higher returns than the general stock market.

Correlations

The correlations between the annualized S&P 500 monthly market returns and each of

the 30 hedge fund monthly performances were computed to determine how closely hedge

fund investments behave like the market. The correlations are shown below in

descending order of the Sharpe Ratio as explained in the introduction.

Table 1. Fund Correlations With the S&P 500__________________________________

Fund #1 -0.173464524 Fund #2 0.649193451

Fund #3 -0.044247993 Fund #4 -0.0714241

Fund #5 -0.207737278 Fund #6 0.497261555

Fund #7 0.414375015 Fund #8 0.470509021

Fund #9 0.253269275 Fund #10 0.486760127

Fund #11 0.601120061 Fund #12 -0.190548726

5

Fund #13 0.407577199 Fund #14 0.44922268

Fund #15 0.570891982 Fund #16 0.620327411

Fund #17 0.298016148 Fund #18 0.45629676

Fund #19 0.262008673 Fund #20 0.409339549

Fund #21 0.781050409 Fund #22 0.514196748

Fund #23 0.744336757 Fund #24 0.202843746

Fund #25 0.421641744 Fund #26 -0.585642472

Fund #27 0.582170503 Fund#28 0.35064364

Fund #29 0.65484412 Fund #30 -0.083269169

________________________________________________________________________

Upon inspection, the only detectable pattern in the behavior of the correlations is that, as

the fund number increases, that is, as the Sharpe Ratio decreases, the correlation between

the given fund and the market tends to grow larger. The increase in the correlation could

indicate that many of the fund selections, especially those with decreased Sharpe Ratios

that more closely resemble the volatility of the stock market, might be characterized by

investments intentionally designed to mimic the behavior of the market. In fact, the time

plots comparing the excess market returns with the excess fund returns corroborate the

suspicion that many of the selected funds were designed thusly. Consider the following

6

selected examples shown below.

Figure 1. Fund 2 Performance Comparison_____________________________________

Figure 2. Fund 6 Performance Comparison_____________________________________

7

Figure 3. Fund 10 Performance Comparison____________________________________


8



9

Similarly, many of the funds appear to move negatively with the market by construct, and

the remainder, of course, appear to move neither with the market nor against the market,

and there are a significant number of these graphs seemingly unconnected to the market

movement in the 30 funds selected. The reader can observe the graphs for himself on

page 74.

Variances

Interestingly, of all the first 10 hedge funds, the average annualized monthly return

exceeded that of the market, yet, as the reader can quickly verify from the time plots, the

variances are extremely small for most of the first 10 hedge funds compared to the

variance of the market. Thus, the hedge fund investments with high Sharpe Ratios

offered both exceptionally-lower risk and higher returns than the market. Consider the

raw variance data for the first 10 hedge funds and the average hedge fund:

Table 2. Fund Variance and Average Return____________________________________

Market Variance: 2415.999957 Average Market Return: 9.21525

Ave. Fund Variance: 753.2803166 Ave. Fund Return: 16.99337751

Fund #1 Variance: 11.70683544 Average Return: 8.890983447





10






________________________________________________________________________

Notice that for the average over the entire Sharpe Ratio spectrum of funds, the variance is

only 753 compared to 2415 for the S&P 500. Such a comparatively low variance

reinforces the position that the entire hedge fund market, even when fledgling hedge

funds with low Sharpe Ratios are included in the analysis, remains far less volatile than

the stock market. Another significant characteristic of this data is that, despite the low

variability compared to the market, the average annualized monthly return for these funds

with the highest Sharpe Ratios are typically higher than those latter 20 with the lower

Sharpe Ratios. Although the fact that all but fund one of the top ten Sharpe Ratio funds

exceeded the average market return of 9.21525 could be the result of a coincidental

selection of funds, a trend seems more likely that most funds in the market with favorable

Sharpe Ratios do not merely compromise high returns with excessively low volatility.

Hence, the evidence supports the hypothesis that the hedge fund market in general forms

a powerful apparatus for generating inordinate returns.

11

Regressions

Regressions of the excess annualized monthly fund returns on the excess annualized

monthly market returns were performed for all 30 hedge funds with the intention of

examining the results for the overall volatility of the hedge fund market as measured

against the stock market and the degree to which the overall hedge fund market moves

with the stock market when, in fact, the hedge fund market actually does move with the

stock market.

The regressions revealed that the volatility of the hedge fund market and the degree to

which the hedge fund market moves with the S&P 500 depend on the perspective from

which the regression results are considered. By averaging the excess returns across each

month and then regressing those average monthly returns on the excess S&P 500 returns,

results were determined for the general hedge fund market. Consider the graph of that

regression as shown below as an overview of the data.

12

Figure 7. Regression of the Average Fund Return on the S&P 500__________________

The regression equation demonstrates that the degree of movement in the hedge fund

market is not very responsive to the S&P 500. Specifically, an increase or decrease in

S&P 500 returns of 1% corresponds to an increase or decrease, respectively, of

only .3576% in the hedge fund market. The observation must be noted that the R2 value

is .428, which means that only 42.8% of the variation in the hedge fund market is being

explained by the regression. Furthermore, examining each of the hedge fund regressions

individually yields more perspective by revealing some potential hazards, but also some

detectable trends.

13

Inspection of the regressions shows that some patterns emerge. The funds with the

highest Sharpe Ratios tend to have, in terms of absolute value, the smallest beta

coefficients because low risk implies lower volatility. The following regression graph

illustrates the effect.

Figure 8. Regression of Fund 1 on the S&P 500_________________________________

As can be seen, the beta coefficient indicates that a change of 1% in the stock market

corresponds to a change of only 0.01%. Such a small coefficient might simply reflect a

hedge fund which is volatile but which has data points that are more randomly dispersed

thereby representing a fund which is neither highly positively nor highly negatively

correlated with the S&P 500. There exist a few regressions matching that description for

which polynomial regressions were fitted to the data for somewhat better results in the

last part of this section, but for many of the regressions with extremely low beta

coefficients, the time plots confirm that the low coefficients reflect low volatility. In the

case of fund 1 shown above, the associated time plot is shown below.

14

Figure 9. Time Plot Returns Comparison Between Fund 1 and the S&P 500___________

An additional example pair of graphs is shown below for fund 3.

Figure 10. Regression of Fund 3 on the S&P 500________________________________

15

Figure 11. Time Plot Comparison Between Fund 3 and the S&P 500________________

Traversing the list of funds toward the funds with lower Sharpe Ratios leads to

regressions with beta coefficients increasing in absolute value. Ultimately, the purpose of

illustrating how the Sharpe Ratios affect the beta coefficients is to add interpretive

meaning to the average excess fund regression. For example, a citation of the .428 beta

coefficient would be remiss without attributing some of that coefficient’s meaning to the

Sharp Ratio’s effect. A few examples of the increased beta coefficients are shown below.

16

Figure 12. Regression of Fund 16 on the S&P 500_______________________________


17


Of greatest importance regarding the trend toward increasing beta coefficients is that,

with the exception of a single graph, the highest coefficient of any of the regressions

is .7875, and consequently, the hedge fund market is significantly less volatile than the

stock market. In order to facilitate the attainment of some sense of the extent to which

the hedge fund market trails the increases and decreases of the stock market, the top 15

correlations, in terms of absolute value, from the section entitled “Correlations” above,

have been juxtaposed below with their corresponding fund numbers and associated

regression beta coefficients.

18

Table 3. Fund Correlations and Beta Coefficients________________________________

Fund #21: Correlation: .781 Beta Coefficient: .7249






Fund #26: Correlation: -.58564 Beta Coefficient: -1.2199




Fund #6. Correlation: .49726 Beta Coefficient: .5249





________________________________________________________________________

19

The underlying assumption of analyzing these values is that the funds with the highest

correlations follow the market either naturally or by design such that the results of the

analysis can be used as predictors of the degree to which the broader market of hedge

funds that mimic the S&P 500 follows the stock market. A cursory overview of the data

shows that the beta coefficients are quite high in terms of absolute value, but none of

them, except fund #26, exceeds .8 indicating that hedge funds might actually be a safer

investment than the stock market.

The reader must be cognizant of some discrepancies in the regressions and data. First,

some of the regressions are based on a limited number of performance data. This

deficiency is attributable to the fact that many of the hedge funds that were selected have

not long been in existence, so the sum of 12 data points per year is not many points to

plot over the course of three or fewer years. Second, many of the regressions have very

low R2 values. The fact that so many of the regressions have these low values is

especially disturbing because there is no immediate, non-statistical way to account for the

proportion of the regression attributable to error. There is one statistical remedy,

however, that has been employed in the regression graphs on page 57: since many of the

graphs seemed to exhibit non-linear trends, polynomial curves were fitted to the data and

generated some improvement in the R2 values. Some of the scatter plots, however, were

so widely dispersed that even polynomials of orders five and six, which most uniquely

fitted the data, did not yield much improvement in R2. Moreover, interpretation of the

polynomial regressions becomes unwieldy at the higher powers. All of the polynomial

curves are only of order two, and in most of the regressions, the coefficient of the

variable raised to the first power is greater than the beta coefficient in the linear fit, and

20

the coefficients in the polynomial regressions are either both positive or both negative, so

the reader can interpret those results as meaning that a 1% increase or decrease in the

S&P 500 corresponds to at least an increase or at least a decrease of the coefficient of the

variable raised to the first power.

Heteroscedasticity

Scatter plots were derived by first obtaining the residuals from regressing each of the

funds on the S&P 500, squaring the residuals, and then plotting those squared residuals

against the S&P 500 for the purpose of determining the presence or absence of

heteroscedasticity. The reader can see the graphs and SAS regression tables on page 91.

An inspection of the graphs shows that the presence of heteroscedasticity is very weak.

Two primary factors to explain why the variability in hedge fund performance is so

weakly related to the performance of the stock market are immediately suspects. First,

hedge fund investors are typically required to relinquish control over the money invested

for a period of six months or a year unless the investors are willing to accept a penalty for

withdrawing in the middle of that time interval, so whereas stock market investors may

invest and withdraw continually, hedge fund managers can continue their investment

strategy with impunity. Second, because access to hedge fund investing is extremely

limited, and because hedge funds are not required to report their performance to the SEC

and, by extension, the general public, hedge funds are not subject to the same nature of

stock market speculation as issuers of stock are subject to. These two aforementioned

possible reasons, however, imply only that hedge funds are facilitated, not coerced, to

lack a strong presence of heteroscedasticity with the stock market. For example, as will

be shown further into this section, if the nature of a hedge fund, perhaps by construction,

21

is to respond to the stock market, then some meaningful degree of predictive force of the

variability in a hedge fund might exist. Regardless, observation of the scatter plot for

the squared residuals associated with the average fund confirms that, although the

residuals are somewhat widely dispersed or that there are some outliers, depending on

how the graph is interpreted, there is simply no pronounced directional pattern of the

residuals other than strictly homoscedastic horizontal movement. Most of the individual

plots are constituted similarly to this average fund plot.

Before proceeding, the reader should consider the following table containing the betas

from regressing the squared residuals on the S&P 500 as discussed at the beginning of

this section. The funds, from which the residuals were originally obtained when the

funds were regressed on the S&P 500, are numbered in the left column, and the p-values

for the t-tests on the betas, obtained from regressing the squared residuals on the S&P

500, are in the rightmost column.

Table 4. Betas and p-values of Regressing the Squared Residuals on the S&P 500______

Fund #1: Beta: .02147 p-value: .3414

Fund #2: Beta: -.35204 p-value: .9110

Fund #3: Beta: -.95092 p-value: .0482

Fund #4: Beta: .29539 p-value: .9208

Fund #5: Beta: -14.92568 p-value: .0559

Fund #6: Beta: -11.25687 p-value: .3120

22

Fund #7: Beta: -.78789 p-value: .2328

Fund #8: Beta: 4.70992 p-value: .4046

Fund #9: Beta: 3.86371 p-value: .5341

Fund #10: Beta: -18.79702 p-value: .0031

Fund #11: Beta: -2.54423 p-value: .7317

Fund #12: Beta: -.31229 p-value: .7679

Fund #13: Beta: 1.80260 p-value: .9044

Fund #14: Beta: 1.99910 p-value: .9409

Fund #15: Beta: 12.07186 p-value: .5855

Fund #16: Beta: -13.25197 p-value: .1044

Fund #17: Beta: -7.80340 p-value: .6205

Fund #18: Beta: 8.00835 p-value: .2370

Fund #19: Beta: -2.39933 p-value: .1891

Fund #20: Beta: 4.56654 p-value: .5358

Fund #21: Beta: -6.43843 p-value: .0260

Fund #22: Beta: -22.24671 p-value: .0034

Fund #23: Beta: -2.16036 p-value: .3398

23

Fund #24: Beta: 3.1539 p-value: .1856

Fund #25: Beta: -.01672 p-value: .9693

Fund #26: Beta: -46.81454 p-value: .0245

Fund #27: Beta: -.02682 p-value: .9847

Fund #28: Beta: -32.74194 p-value: .1814

Fund #29: Beta: -4.2439 p-value: .2619

Fund #30: Beta: .33543 p-value: .8406

Average Fund:Beta: -3.41761 p-value: .0215

If the betas were consistently positive or consistently negative, then inference could be

made about the volatility of the hedge fund market when the stock market performed well

or poorly, but 30% of the hedge funds had positive betas which is a percentage too high

to conclude that there is a definitive trend. However, the absence of a trend in the

entirety of the hedge fund market does not imply such an absence in any individual fund,

and, in fact, fund 26 provides an excellent illustration. The graph is shown on the next

page. Fund 26 was chosen because it contains a sufficiently-large number of data points,

a large beta coefficient in terms of absolute value, and an R2 value relatively larger than

the other funds with similar numbers of data points: few data points can exaggerate the

regression results, a large beta indicates that the variability of the fund increases or

decreases with a movement in the stock market, and a higher R2 value suggests that more

24

of the changing variability in the fund is attributable to the stock market rather than

Figure 15. The Original Fund 26 Trend Line___________________________________

Figure 16. Performance Comparison For Fund 26_______________________________

25

random error. Now let the reader consider the time plot performance comparison

between fund 26 and the S&P 500. It is shown above. Whenever the S&P 500 is in a

state of decreasing, the performance of the fund tends to be extremely positive or

extremely negative. Thus, whereas the betas did not yield any trend, predicting the

variability in individual funds is possible.

Generally, the graphs tended to be homoscedastic. Some choice examples are given in

the graphs below.

Figure 17. Fund 13 Example of Homoscedasticity______________________________

26

Figure 18. Fund 15 Example of Homoscedasticity______________________________

Some of the graphs were less obviously homoscedastic for reasons that were common to

other funds with similar characteristics. Fund 24 below is the first example. There

Figure 19. Fund 24 Example of Aberrant Homoscedasticity_______________________

27

appear to be outliers present in this graph, but beware that this appearance is illusory,

because the scale on the vertical axis does not extend far compared to other graphs

suffering true outlier effects. Fund 6 below is the second example. Because there are so

Figure 20. Fund 6 Example of Insufficient Sample Size__________________________

few data points available, a solid homoscedastic or heteroscedastic trend simply cannot

be known.

Although the scatter plots do not seem to assert the presence of heteroscedasticity, the

betas for funds 3, 10, 21, 22, and 26 and for the average fund were statistically significant

at the .05 level as computed in SAS. Every one of these funds, however, becomes

statistically insignificant when an outlier is removed. Fund 21 functions as an ideal

example. The fund 21 graph is below, and the outlier can clearly be seen in the upper left

corner. When the graph is recomputed without the outlier, not only does the beta become

statistically insignificant, but also the beta, R2, and intercept are changed dramatically.

28

Figure 21. Fund 21 Squared Residuals With the Outlier vs. S&P 500_______________

Figure 22. Fund 21 Squared Residuals Without the Outlier vs. S&P 500_____________

29

The results can be seen in the graph above. The table below has been prepared to show

relevant information and the t-statistics for the data sets excluding the outliers.

Table 5. t-Statistics and Other Relevant Information for the Modified Graphs________

Fund critical t new t df(n-2) new beta new intercept new R2

#3: 1.980 > .547058 68 -.77692 48.54227 .0327

#10: 2.021 > 1.65064 31 -9.034 730.2802 .0808

#21: 1.960 > .738383 144 1.509757 741.10505 .0038

#22: 1.960 > .613519 135 -3.56885 1614.52462 .0028

#26: 1.980 > 1.43195 65 -29.0355 4401.04655 .0306

Ave. 1.960 > .123604 150 .1486 373.7932 .0001

Because the betas all become statistically insignificant when an outlier is removed from

each of the funds, the p-values generated from the data sets including the outliers are

spurious detectors of heteroscedasticity, and the trend in the data does in fact appear to be

horizontal and homoscedastic in each of these funds in the table.

Normality

In order to test whether the assumptions of the classical regression model were

satisfied, a test of normality for the residuals was conducted by regressing all 30 of the

funds and the average fund on the S&P 500 and plotting the residuals into histograms.

The graphs can be seen on page 40. With the exception of funds 1, 6, 11, 14, 18, 23, and

30

24, all of the histograms conformed reasonably well to the normal curve, and in most of

those funds which did not readily conform, there were so few residual data that

concluding that the fund residuals were either normally distributed or not normally

distributed in future trends was premature. In particular, funds 1, 2, 14, and 18 are

represented by too few residuals. A normal fit for funds 6, 11, and 24 might actually be

deemed acceptable, but the shape isn’t as pronounced as it is for the other funds. Fund 23

is the only case for which there were a sufficient number of residuals available to exclude

an obviously normal fit. Most importantly, the average fund residuals appeared to

assume a very strong normal curve shape, and because many of the arguments presented

in this study have been embodied and buttressed by the results of the average fund

regression, the weights of those arguments are more securely anchored. Some sample

graphs depicting the strong tendency toward a normal curve shape, especially for the

average fund, are shown below.

Figure 23. Fund 7 Normal Shaped Residuals___________________________________

31

Figure 24. Fund 21 Normal Shaped Residuals__________________________________

Figure 25. Fund 27 Normal Shaped Residuals__________________________________

32

Figure 26. Average Fund Normal Shaped Residuals______________________________

Conclusion

When all the aspects of hedge fund performance are assessed collectively, the hedge

fund market dramatically outperforms the stock market. The average returns discussed in

the introduction show that, purely in terms of generating profit, the hedge fund market

outstripped the S&P 500. In terms of volatility, the hedge fund market performance

again defeated the market. Specifically, the variance data showed that most of the funds,

especially for high Sharpe Ratios, were far less variable and yielded greater returns than

the S&P 500. Moreover, the regression analysis confirmed that the hedge fund market as

a whole remained less volatile than the S&P 500 and that, for those funds highly

correlated to the stock market, the performance fluctuations were more dampened than

the stock market. In addition to the performance and volatility attributes, hedge funds did

33

not exhibit any heteroscedasticity which effectively translates into more stable

expectations on returns because of the independent nature of hedge fund operations. All

of these performance qualities affirm the superiority of the hedge fund market over the

stock market.

34

Descriptive Statistics

Complete tables of the statistical measures used in the study are given here for the

reader who wishes to gain comprehensive insight into the arguments that were proposed.

35

Table 6. Performance Averages______________________________________________

S&P 500: 9.21525 Fund #1: 11.70683544

Fund #2: 26.14545455 Fund #3: 11.27661972

Fund #4: 14.82 Fund #5: 17.65830508

Fund #6: 19.965 Fund #7: 11.8096

Fund #8: 13.65818182 Fund #9: 19.17795918

Fund #10: 15.16941176 Fund #11: 15.28421053

Fund #12: 8.902702703 Fund #13: 21.87630252

Fund #14: 18.70909091 Fund #15: 19.87175258

Fund #16: 15.20047059 Fund #17: 14.57454545

Fund #18: 11.286 Fund #19: 7.771111111

Fund #20: 12.79418182 Fund #21: 12.28

Fund #22: 12.40956522 Fund #23: 9.06375

Fund #24: 7.451320755 Fund #25: 6.177391304

Fund #26: 12.76058824 Fund #27: 6.142702703

Fund #28: 8.341132075 Fund #29: 5.942608696

Fund #30: 5.215 Average Fund:16.99337751

36

________________________________________________________________________

Table 7. Variance_________________________________________________________

S&P 500: 2415.999957 Fund #1: 8.890983447

Fund #2: 726.1629818 Fund #3: 51.82846841

Fund #4: 453.5904889 Fund #5: 938.9087074

Fund #6: 1524.90216 Fund #7: 363.6100871

Fund #8: 653.8928485 Fund #9: 1908.131577

Fund #10: 1129.798794 Fund #11: 1126.69836

Fund #12: 193.7927049 Fund #13: 3808.637586

Fund #14: 3189.621818 Fund #15: 4362.841398

Fund #16: 2253.336476 Fund #17: 2108.215882

Fund #18: 993.25512 Fund #19: 250.9952252

Fund #20: 2125.89921 Fund #21: 2205.50663

Fund #22: 2575.932906 Fund #23: 985.9317532

Fund #24: 420.0005155 Fund #25: 137.1764503

Fund #26: 7179.599546 Fund #27: 254.4790703

Fund #28: 3352.015176 Fund #29: 555.4719747

37

Fund #30: 253.566817 Average Fund:753.2803166

________________________________________________________________________

Table 8. Fund Correlation with the S&P 500___________________________________

Fund #1: -0.173464524 Fund #2: 0.649193451

Fund #3: -0.044247993 Fund #4: -0.0714241

Fund #5: -0.207737278 Fund #6: 0.497261555

Fund #7: 0.414375015 Fund #8: 0.470509021

Fund #9: 0.253269275 Fund #10: 0.486760127

Fund #11: 0.601120061 Fund #12: -0.190548726

Fund #13: 0.407577199 Fund #14: 0.44922268

Fund #15: 0.570891982 Fund #16: 0.620327411

Fund #17: 0.298016148 Fund #18: 0.45629676

Fund #19: 0.262008673 Fund #20: 0.409339549

Fund #21: 0.781050409 Fund #22: 0.514196748

Fund #23: 0.744336757 Fund #24: 0.202843746

Fund #25: 0.421641744 Fund #26: -0.585642472

Fund #27: 0.582170503 Fund #28: 0.35064364

Fund #29: 0.65484412 Fund #30: -0.083269169

38

Average Fund: 0.654979938 __________________________________________

Residual Histograms

The residuals from regressing each of the funds on the S&P 500 were plotted and

placed into histograms as given here.

39

Figure 27. Fund 1 Residuals________________________________________________


40



41



42



43


Figure 36. Fund 10 Residuals_______________________________________________

44



45



46



47



48



49



50



51



52



53



54

Figure 57. Average Fund Residuals___________________________________________

55

Regressions

These graphs are the result of regressing each of the funds on the S&P 500 and then determining a regression line. In many of the graphs, polynomial regressions were also determined and plotted as curves.

56

Figure 58. Fund 1 Regression_______________________________________________

57



58



59



60



61

Figure 67. Fund 10 Regression______________________________________________


62



63



64



65



66



67



68



69



70



71


Figure 88. Average Fund Regression__________________________________________

72

Time Plots

These plots compare the performance of each of the funds and the S&P 500 over time.

73

Figure 89. Fund 1 Time Plot Comparison______________________________________

74



75



76



77



78

Figure 98. Fund 10 Time Plot Comparison_____________________________________

Figure 99. Fund 11 Time Plot Comparison_____________________________________

79

Figure 100. Fund 12 Time Plot Comparison____________________________________


80



81



82



83



84



85



86



87



88


Figure 119. Average Fund Time Plot Comparison_______________________________

89

Heteroscedasticity graphs and SAS output tables

In order to determine the regression graphs discussed and shown in the body of this

paper, each of the funds was regressed on the S&P 500. The SAS output tables in this

section are the result of squaring the residuals from those regressions, and then regressing

the squared residuals on the S&P 500 for the purpose of analyzing the p-values of the test

statistic for the betas. The graphs are the result of plotting the squared residuals vs. the

S&P 500.

90

Table 9. Squared Residuals on Fund 1_________________________________________

The REG Procedure Model: MODEL1 Dependent Variable: squaredResidual

Number of Observations Read 79 Number of Observations Used 79

Analysis of Variance

Sum of Mean Source DF Squares Square F Value Pr > F

Model 1 70.77308 70.77308 0.92 0.3417 Error 77 5954.70142 77.33378 Corrected Total 78 6025.47451

Root MSE 8.79396 R-Square 0.0117 Dependent Mean 8.48215 Adj R-Sq -0.0011 Coeff Var 103.67613

Parameter Estimates

Parameter StandardVariable Label DF Estimate Error t Value Pr > |t|

Intercept Intercept 1 8.52905 0.99061 8.61 <.0001excess_market_return excess_market_return 1 0.02147 0.02244 0.96 0.3417

Figure 120. Squared Residuals against Fund 1__________________________________

91

Table 10. Squared Residuals on Fund 2________________________________________

Figure 121. Squared Residuals Against Fund 2__________________________________

92






Model 1 113937 113937 4.05 0.0482 Error 69 1942836 28157 Corrected Total 70 2056773

Root MSE 167.80060 R-Square 0.0554 Dependent Mean 51.70812 Adj R-Sq 0.0417 Coeff Var 324.51500

Parameter Estimates


Intercept Intercept 1 50.63853 19.92136 2.54 0.0133excess_market_return excess_market_return 1 -0.95092 0.47272 -2.01 0.0482


93








Parameter Estimates


Intercept Intercept 1 445.98346 129.06266 3.46 0.0009excess_market_return excess_market_return 1 0.29539 2.96242 0.10 0.9208



94







Parameter Estimates





The REG Procedure Model: MODEL1

95

Dependent Variable: squaredResidual






Parameter Estimates






96






Parameter Estimates


Intercept Intercept 1 295.03138 32.70554 9.02 <.0001excess_market_return excess_market_return 1 -0.78789 0.65758 -1.20 0.2328





97





Parameter Estimates




Table 17. Fund 9 Squared Residuals on the S&P 500_____________________________



98





Parameter Estimates



Figure 128. Fund 9 Squared Residuals Against the S&P 500_______________________

Table 18. Fund 10 Squared Residuals on the S&P 500____________________________




99




Parameter Estimates



Figure 129. Fund 10 Squared Residuals Against the S&P 500______________________






100



Parameter Estimates









Model 1 12574 12574 0.09 0.7679

101

Error 72 10313729 143246 Corrected Total 73 10326302


Parameter Estimates










102


Parameter Estimates










103


Parameter Estimates










Root MSE 10394 R-Square 0.0031 Dependent Mean 2911.99771 Adj R-Sq -0.0074

104

Coeff Var 356.93929

Parameter Estimates











105

Parameter Estimates











Parameter Estimates

106











Parameter Estimates

Parameter Standard

107

Variable Label DF Estimate Error t Value Pr > |t|










Parameter Estimates


108










Parameter Estimates



109









Parameter Estimates



110









Parameter Estimates



111









Parameter Estimates



112









Parameter Estimates



113







Model 1 56.50432 56.50432 0.00 0.9693 Error 90 3414573 37940 Corrected Total 91 3414629


Parameter Estimates



114









Parameter Estimates



115









Parameter Estimates



116









Parameter Estimates



117









Parameter Estimates



118









Parameter Estimates



119


Table 39. “Average” Fund Squared Residuals on the S&P 500_____________________







Parameter Estimates



120

Figure 150. “Average” Fund Squared Residuals Against the S&P 500_______________

References

1. http://www.hedgefund.net/marketing_index.cfm?template=aboutus.html

2. Hedge Funds Fear New SEC Regulations

Investment Management Weekly; 7/7/2008, Vol. 21 Issue 27, p6-11, 2p

John Morgan

3. Hedge Funds: Risk and Return

http://www.princeton.edu/~ceps/workingpapers/104malkiel.pdf

Burton G. Malkiel, Princeton University

4. Hedge funds: Ten years of private client investing — is it still time to invest?

Botteron, Pascal [email protected]

Derivatives Use, Trading & Regulation; 2007, Vol. 12 Issue 4, p301-313, 13p

http://www.hedgefund.net/marketing_index.cfm?template=aboutus.html

121

VITA

Graduate School

Southern Illinois University

Mark V. Hoaglund Date of Birth: June 5, 1977

203 West Jackson, Desoto, Il. 62924

Southern Illinois University at Carbondale

Bachelor of Science, Mathematics, May 2005

Research Paper Title:

Measuring the Performance of the Hedge Fund Market

Major Professor: Scott Gilbert

research paper mark hoaglund

Documents

table of contentsabstract

overall hedge fund market

hedge fund market wasfound

hedgefund market

index fund

performanceof hedge

scott gilbertthe objective

professor scott gilbert