Hedge Funds, Funds-of-Funds, and Commodity. Trading Advisors

Transcription

1 Hedge Funds, Funds-of-Funds, and Commodity Trading Advisors Bing Liang Weatherhead School of Management Case Western Reserve University Cleveland, OH Phone: (216) Fax: (216) This Draft: September 2002 The author acknowledges a research grant from the Foundation for Managed Derivatives Research. I would like to thank Dick Oberuc for his comments. I am grateful to Zurich Capital Markets Inc. for providing the data.

2 Abstract In this paper, we study performance, risk, and fund characteristics for alternative investment vehicles such as hedge funds, funds-of-funds, and commodity trading advisors (CTAs). We have several interesting findings. First, funds-of-funds underperform hedge funds over the period from 1994 to 2001, probably due to the double fee structure of funds-of-funds. The diversification effect and services provided by fundsof-funds do not justify the fees they charge. Second, hedge funds and funds-of-funds follow similar investment strategies when they are analyzed in an asset class factor framework. This is consistent with the fact that funds-of-funds invest in the underlying hedge funds. Third, CTAs underperform both hedge funds and funds-of-funds, making them poor stand-alone investments. However, CTAs have low correlations with hedge fund styles or funds-of-funds and they also follow different investment strategies from those of hedge funds and funds-of-funds. When adding CTAs to the hedge fund portfolio or the fund-of-funds portfolio investors can marginally benefit from the risk return tradeoff. Fourth, we indicate that funds within the same style are less correlated; making a style index less useful than one expects. Finally, CTAs differ from the other investment vehicles by having a survivorship bias as high as 6.2% on an annual basis. 1

3 Alternative investments differ from traditional investments in low correlation with traditional asset classes, managers involvement in their personal wealth, dynamic trading strategies, and use of a wide range of techniques and instruments. Due to these features, alternative investment vehicles have gained popularity lately. For example, one hedge fund data vendor alone traces over 4,000 hedge funds although we don t know precisely how big the total population is. 1 Alternative investments include, but are not limited to, hedge funds, fund of hedge funds, commodity trading advisors (CTAs), private equity, partnerships, and venture capital. In this paper, we focus on three major alternative investment vehicles: hedge funds, funds-of-funds, and CTAs. In fact, major data vendors such as TASS Management Ltd. and Zurich Capital Markets Inc. (Zurich) collect data for all three categories. 2 With rapid growth in the hedge fund industry, funds-of-hedge funds become more and more popular. A fund-of-funds invests in underlying hedge funds and serves the purposes of diversifying fund specific risk, relieving burdens on investors to select and monitor managers, and providing asset allocation in dynamic market environments. In addition, funds-of-funds usually require less initial investment so they are more affordable to investors than the regular hedge funds. Funds-of-funds do tend to have lower investment minimums. As such they may provide the only way a small investor can invest in the hedge fund arena. These smaller investors may be willing to suffer the double fees in order to participate. 1 See 2 Previously, the data was known as Managed Accounts Reports (MAR) data. 2

4 Previous studies in the area of hedge funds have pooled hedge funds with funds-offunds (see Ackermann, McEnally, and Ravenscraft (1999), Brown, Goetzmann, and Ibbotson (1999), and Liang (1999)). Combining hedge funds with funds-of-funds would not only cause a double counting problem but also would hide the difference in fee structures between hedge funds and funds-of-funds (see Brown, Goetzmann, and Liang (2002)). A hedge fund charges a management fee and incentive fee while a fund-of-funds not only charges these fees at the fund-of-fund level but also pays at the hedge fund level. Returns are usually reported on an after fee basis. After fee returns will certainly be affected by how fees are paid. Underlying hedge fund fees will be passed to fund-offunds investors no matter whether the fund-of-funds makes a profit or not. As a result, total fees from a fund-of-funds can exceed the total realized return on the fund. Brown, Goetzmann, and Liang (2002) propose an alternative fee arrangement for funds-of-funds, under which funds-of-funds managers will absorb the underlying hedge funds fees and establish their own incentive fees at the fund-of-fund level. This will provides a better incentive for fund-of-fund managers and reduce the dead-loss costs for investors. Because of the above issues, we need to separate funds-of-funds from hedge funds and address the differences in performance and risk. Studies like the above can provide investors and managers with useful information in this fast growing area. Previous studies have also pooled hedge fund data with CTAs (see Fung and Hsieh (1997a)). Although there are certain similarities between the two groups, such as management and incentive fee structures, high initial investment requirements, use of leverage and derivatives, systematic differences can also exist. For example, hedge funds are involved in varieties of dynamic trading strategies using different financial 3

5 instruments in different markets while CTAs mainly consist of technical trading strategies in commodity and financial futures markets. Investing in different instruments from different markets can result in differences in risk and returns. In addition, CTAs must register with the Commodity Futures Trading Commission (CFTC) while hedge funds and funds-of-funds are largely exempt from government regulations. Most importantly, correlations among various hedge fund styles are very high while correlations among CTAs and hedge fund styles are almost zero. In this paper, we study the similarities and differences in terms of performance, risk, and fee structures of hedge funds, funds-of-funds, and CTAs. We study them not only on a stand alone basis, but also on a basis of portfolio of investment. As far as we know, this is the first paper to comprehensively evaluate all three alternative investment vehicles together. Analyzing these interesting investment vehicles can provide not only a contribution to the literature but also guidance to the investment community. In this paper, we find several interesting results. First, funds-of-hedge funds are highly correlated with each hedge fund style; both being linked to some common asset class factors. This is consistent with the notion that funds-of-funds invest in different hedge fund styles. However, funds-of-funds underperform their hedge fund components, probably due to the double fee structure and incomplete coverage (hence ineffective diversification) of the hedge fund universe. 3 Some superior hedge funds may be closed to investment so funds-of-funds will not be able to access them. Because of these, investors who invested in funds-of-funds will face inferior risk-return trade-off than that of hedge funds. Secondly, CTA styles are slightly or negatively correlated with hedge fund styles or funds-of-funds. Asset class factor analysis also indicates that CTAs follow very 3 Our survey indicates that an average fund-of-funds invests in only 13 hedge funds. 4

6 different trading strategies from those of hedge funds or funds-of-funds. Fourth, we indicate that funds within the same style are less correlated; making a style index less useful than one expects. Finally, adding CTAs to the hedge fund portfolio or fund-offunds portfolio can marginally benefit investors in the mean variance efficient world. The rest of the paper is organized as follows. Section I describes the data. Section II compares performance, risk, and fee structures of hedge funds, funds-of-funds, and CTAs on a stand alone basis. Section III analyses correlations of these different investment vehicles and consider them in a portfolio framework. Section IV concludes the paper. I. Data The data is provided by Zurich Capital Markets Inc. (Zurich). As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (including 349 live and 248 dead), and 1,510 CTAs (294 live CTAs and 1216 dead CTAs). Zurich classifies CTAs into live CTAs and dead CTAs and defines a hedge fund or a fund-of-funds dead if it fails to report to the data vendor in three consecutive months or more. Table 1 reports the basic statistics of the data. The median management fees for hedge funds, funds-of-funds, and CTAs are 1%, 1%, and 2%, respectively. Apparently, hedge funds charge the least amount of management fees, compared with funds-of-funds and CTAs. Note that a fund-of-funds invests in different hedge funds and hence charges two-tier fees: a fee that is indirectly paid to the individual hedge fund (1% on average) in which the fund-of-funds invests and a fee that is paid directly to the fund-of-funds (1% on average). The two-tier fees are all borne by investors. All things being equal, returns 5

7 from hedge funds will be higher than returns from funds-of-funds since lower management fees are charged. Apart from the management fee, the median incentive fees for hedge funds, funds-of-funds, and CTAs are all 20%. Again, a fund-of-funds may deliver lower after fee returns than a hedge fund due to the two-tier fee structure. The median minimum investment for hedge funds, funds-of-funds, and CTAs are $300,000, $250,000, and $250,000, respectively. They are all designed for accredited investors or institutional investors. As of December 2001, the median fund assets for hedge funds, funds-of-funds, and CTAs are $ 36 million, $34 million, and $13 million, respectively. Hence, most funds or CTAs are relatively small. It seems that the average size for a CTA is smaller than those of hedge funds or funds-of-funds. Consistent with the small asset base, Table 1 also indicates that on average a CTA has only four employees. The median fund ages (of both live and dead funds) for the three portfolio groups are 44 months, 52 months, and 46 months. Fund-of- funds has the longest average life because of the diversification effect across different hedge fund components. If one or more hedge funds die in the fund-of-funds portfolio, other hedge funds can still remain in the portfolio and fund-of-funds managers can easily switch to other hedge funds to replace the dead ones. II. Performance, risk, and fee structures A. Survivorship bias We define survivorship bias as the return difference between two portfolios: the survived fund portfolio and the entire portfolio including. The survived portfolio contains funds with returns from inception (or the time when the first return data is recorded, whichever 6

8 is latter) all the way to the current reference date, and the entire portfolio has included all funds (both live and dead funds). Funds may drop off the database because of different reasons such as mergers and acquisitions, closure or liquidation, and voluntary withdrawal. However, Liang (2000) indicates that poor performance is the main reason for a fund to die. In this paper I reproduce Figure 1 from Liang (2000). Figure 1 clearly indicates that dead fund returns decline toward the date of fund exit. Poor performed funds lose assets over time, triggering margin calls and increasing leverage hence risk due to reduction in equity. Table 2 displays survivorship biases over a 17-year period from 1985 to In Panel A, the average survivorship bias for hedge funds is 0.126% per month or 1.52% per year. The 1.52% bias is almost the same as the 1.5% bias reported by Fung and Hsieh (1997b) and consistent with the 2.2% bias reported by Liang (2000). The survivorship bias for funds-of-funds is reported in Panel B. The 17-year average is only 0.058% per month or 0.7% per year. Consistent with our previous argument, a fund-of-funds contains more than a single hedge fund and poor performance or death of one or more hedge funds should not materially affect the others in the fund-of-funds. Therefore, the attrition rate for funds-of-funds should be much lower than that of the hedge funds and hence the survivorship bias is lower. Panel C reports the bias for CTAs. Surprisingly, over the 17- year period, the average survivorship bias is 0.504% per month or 6.22% per year. This is much higher than the 3.54% bias reported by Fung and Hsieh (1997b) over a 7-year period from 1989 tot Differences can be explained by different time periods and different data used. 7

9 In summary, CTAs have the highest survivorship bias; hedge funds the second, and funds-of-funds the lowest. The difference in the magnitude of survivorship bias can affect the performance analysis in the next section. Excluding dead funds can significantly inflate the performance numbers. Therefore, we will include all funds both live and dead in our following analysis. B. Returns, Standard deviations, and Sharpe ratios Table 3 reports performance and risk for hedge funds, funds-of-funds, and CTAs. The table reports raw returns, standard deviations, and Sharpe ratios over an eight-year period from 1994 to There are several interesting findings in Table 3. First, hedge funds outperform funds-of-funds in seven out of eight years (six of them are significant at the 1% level) when performance is measured by raw returns. This proportion falls to five out of eight years (two are significant at the 5% level) when Sharpe ratio is used. Hence, we have some evidence that hedge funds outperform funds-of-funds during this eight-year period. We can attribute the outperformance to the two-tier fee structure of funds-offunds, which reduces the after fee performances. Although a fund-of-funds offers diversification but it comes with a cost: the fees may not justify the diversification effect. Second, hedge funds also outperform CTAs during the same time period. When raw return is used, hedge funds earn higher returns than CTAs in four out of eight years (all are significant at the 1% level) while CTA is the winner in only one out of eight years (significant at the 10% level only). When Sharpe ratio is used, the result is more dramatic: CTAs underperform hedge funds in seven out of eight years (five are significant at the 5% level, one at the 5%, and one at the 10% level). We may attribute 8

10 this underperformance to high attrition rate and survivorship bias, high fees, relatively less diversified positions, and high leverage of CTAs. Third, CTAs even underperform the fund-of-funds portfolio. When Sharpe ratio is used, CTAs underperform funds-offunds in seven out of eight years (six are significant at the 1% level) although CTAs wins only in The results from raw return are mixed. In summary, according the risk return analysis, we rank hedge funds the highest, funds-of-funds are the second, and CTAs the lowest on a stand alone basis. This ranking order may have to do with the fee structures of these different investment vehicles. We know that hedge funds charge less fees than those of funds-of-funds and CTAs. C. Asset Class Factor Model For performance attribution and evaluation of these investment vehicles, we adopt a multi-asset class factor model and regress asset returns on several asset class factors. Similar kinds of analyses have been conducted by Sharpe (1992), Fung and Hsieh (1997a), Ackermann, Ravenscraft, and McEnally (1999), and Liang (1999). Since these investment portfolios may span varieties of asset classes, we apply seven different asset class factors to cover these asset classes. We use Morgan Stanley Capital International s (MSCI) developed country index for developed equity markets, MSCI emerging market index for emerging markets, Salomon Brothers world government bond index and Salomon Brothers Broad Investment Grade (BIG) index for government bond and broad bond markets, Federal Reserve Bank trade-weighted dollar index for currency, gold price for commodities, and one-month US dollar deposit for cash. The asset class factor model can be expressed as: 9

11 R t 7 = α + β k Fkt + ε t. (1) k = 1 Table 4 reports the regression results. For hedge funds, returns are significantly related to MSCI developed country index, MSCI emerging market index, Salomon Brothers world government bond index, and the BIG index. Simply speaking, hedge funds profit from up developed equity markets and emerging equity markets, down government bond market and up broad bond markets. We know that many hedge funds have net long equity positions which will benefit from up equity markets. Note that the coefficients on the two bond factors are only marginally significant and the signs are opposite; we can interpret the reverse signs as something such as fixed income arbitrage: long the investment grade bonds and short sell government bonds. This is based on the bet on that the credit spread between the two will converge, which is a popular bond trading strategy during that time period. The model can explain about 71% hedge fund return variability, which is reasonably high. The regression results for funds-of-funds are similar to those for hedge funds although the regression is not as strong: the model picks up similar asset class factors and the estimates have the same signs as those for hedge funds. This is not surprising because funds-of-funds invest in different hedge funds, they should cover similar investment styles on average. The adjusted R-squared for the fund of fund-of-funds regression is 58%, lower than that of the hedge funds. In a strong contrast, the model has almost no explanatory power for CTA returns. The adjusted R-squared is only 4.13%. The cross group comparison indicates that CTAs follow very different investment strategies from hedge funds or funds-of-funds. The signs of factor loadings are very different from those of the other two groups. It is well known that CTAs mainly invest in futures markets and often are used for hedging equity market 10

12 risk. This can be reflected from the negative and significant sign of the MSCI developed market index. In addition, CTAs are long and short timers in commodities or financial futrues, which may result in no correlation with the commodity index since long and short positions can cancel each other out. This can explain why the coefficient on factor Gold is insignificant. Once again, we can see that hedge funds outperform the other two groups: the intercept term or the unexplained return from the asset class factor model is 0.81% per month and significant at the 5% level for hedge funds, the intercept term for funds-of-funds is 0.59% per month and significant at the 10% level while the intercept term for CTAs is not significantly different from zero. III. Correlations and analysis in a portfolio framework A. Correlation In Table 5, we report correlation coefficients within hedge fund styles and CTA styles. We also report the cross correlation among hedge funds, funds-of-funds, and CTA styles. For hedge fund styles, we observe two things: First, all styles are highly correlated, with coefficients ranging from a low of to a high of All 45 coefficients are significant at the 5% level. This can be explained by two possible reasons: aggregation at each style level reduces variability of individual fund and different funds have more or less net long positions in the equity markets. Styles will be 4 Other studies such as Ackermann, McEnally, and Ravenscraft (1999) and Liang (1999) have found much lower correlations. The difference comes from different datasets and different time periods used. For example, based on Zurich data, the average positive correlation coefficient during the and periods are and , respectively, compared with in the period. It seems that there is an increasing trend for correlation among hedge fund styles. 11

13 connected through some common factors that affect equity markets or bond markets. This is confirmed by the significant equity market factor and bond market factor loadings in Table 4. Second, the style short sale is negatively correlated with other styles, indicating an opposite bet on the direction of asset price movement. For funds-of-funds, the portfolio is positively correlated with all hedge fund styles except for short sale. Again, this is consistent with the notion that funds-of-funds invests invest in different hedge funds. For CTAs, there are some correlations among diversified trading programs, currency trading programs, and financial trading programs. However, the remaining styles are not significantly correlated. Across hedge funds, funds-of-funds, and CTAs, there are some moderate correlations between CTA s stock trading program and hedge fund or fund of fund styles. Again, this can be caused by the common stock market factors. The other 40 correlation coefficients are either close to zero (36 of them) or slightly negative (6 of them). The low correlation between CTAs and hedge fund or fund-of-fund styles may have strong implications for portfolio managers investment decisions and asset allocation decisions: adding CTAs to hedge funds or funds-of-funds may increase the diversification effect hence improve the risk-return trade-off of an investor s portfolio. We will discuss this further in the next section. Since aggregation reduces individual fund variability, the true correlation structure may not be revealed at the aggregate level. Hence, we turn to examine correlations among different funds within the same style. Although correlations are high across different styles in Table 5, correlations among different funds within the same style could be very low. Table 6 reports these intra-style correlations. Under the style called market 12

14 neutral, the average correlation among different funds is only 0.11 (p-value<0.0001). Two randomly selected funds could be fairly independent from each other. There are two possible reasons: first, the instruments are very different across the two funds and, two, the timing to buy and sell are very different between the two managers. As a result, the long positions and the short positions in these market neutral portfolios are cancelled each other out. Similar situation happens to styles such as global macro and global international. The average correlations within these two styles are only 0.13 and 0.17, respectively. For the other styles, the average correlation ranges from 0.35 to Contrary to the traditional definition of hedge funds, many hedge funds are not hedged as that done by market neutral fund managers. As a result, the net long positions in equities will transfer to some moderate correlations among different funds through some common risk factors that are linked to equity markets. In Table 6, we also report correlations under different CTA styles. Similar to the results of hedge funds, these average correlations are also very low, indicating that long and short commodity/financial futures positions may cancel each other out. In Table 6, the highest correlation coefficient is 0.47 from funds-of-funds. Remember that a fund-offunds is aggregated hedge funds; aggregating can reduce volatilities and produce a similarly high correlation as those reported in Table 5. However, because of the limited numbers of hedge funds invested by each fund-of-funds, the 0.47 correlation is much lower than the numbers reported in Table 5, where aggregation is done by all funds under each style. The above low correlation structure within fund styles have important implications to constructing hedge funds indices. It is becoming more and more popular for hedge fund 13

15 consulting companies, data vendors, even investment banks to construct different style indices to meet the increasing demand from the investment community. These indices are built either from equally weighted 5 or value weighted averages 6 on hedge funds under the same style. The only exception from the above is the index from Zurich Capital Markets, who uses medians instead of weighted averages as the benchmarks. 7 Because of the low correlation among different funds within the same style, constructing a style index using hedge funds within each style may not be fruitful: aggregating may cancel long and short positions hence the index may not be representative for the funds that the index covers. The goal of a hedge fund index is to reflect fund performance under each style. If the funds within the same style behave differently because of different instruments and timing abilities involved, then it is not constructive to build the index by using the funds under the same style. Oberuc (2002) indicates that indices of financial CTAs, currency CTAs, bond arbitrage hedge funds, and international hedge funds do not represent the asset classes because two sub-samples of each asset class do not deliver similar index results. The difficulty of building a hedge fund index may be also reflected by the nature of hedge funds: they are absolute performers rather than relative performers. A relative performer compares its performance with a certain benchmark such as equity market index or bond market index while an absolute performer does not compare its performance with others. Most hedge funds have hurdle rates and high watermark provisions. Fund managers only need to cross the predetermined hurdle rate and assume 5 See and 6 See 7 See Zurich ranks each fund within the same style from high performance to low performance. The median is the 50 th percentile. If fund numbers are even, the median is then defined as the average of the two middle funds. 14

16 responsibilities for making up previous losses. There is no need to compare themselves with other benchmarks. B. Benefit of adding CTAs to the portfolio The analysis in Section II only focuses on a stand alone basis: we don t mix one asset class with another. Poor stand alone performance from CTAs does not prevent them from becoming good additions to other investment portfolios, especially when CTAs and other portfolios have negative or low correlations. According to Elton, Gruber, and Rentzler (1987), a CTA should be added to an existing portfolio if, R CTA σ r CTA f > R P σ r P f ρ CTA, P (2) where R CTA is the expected return of the CTA, r f is the risk free rate, σ CTA is the standard deviation of the CTA, R P is the expected return of portfolio P, σ P is the standard deviation of portfolio P, and ρ CTA, P is the correlation coefficient between the expected return of the CTA and the existing portfolio P. The intuition of (2) is that the Sharpe ratio of the CTA should be greater than the product of the Sharpe ratio of portfolio P and the correlation coefficient between the CTA and portfolio P. In Table 7, the correlation coefficient between CTAs and hedge funds is only (with a p-value of 0.63) from 1994 to 2001, which is not significantly different from zero. Similarly, during this eight-year period, the correlation coefficient between CTAs and 15

17 funds-of-funds is only 0.05 (with a p-value of 0.60), again not significantly different from zero. Based on these zero correlations, equation (2) can be reduced to R r > 0 (3) CTA f Therefore, CTAs can be entered a hedge fund portfolio or a fund-of-fund portfolio only if the difference between the CTA return and the risk free rate (or the excess CTA return) is greater than zero. Empirically, testing the Sharpe ratios and correlations in (2) becomes testing the excess return in (3). Base on the data, from 1994 to 2001 the average excess CTA return is 0.39% on a monthly basis; the t-value is 1.70, which is significant at the 10% level. Therefore, adding CTAs to hedge funds or funds-of-funds portfolios can benefit investors on a marginal basis during this time period. IV. Conclusion We use a large database on hedge funds, funds-of-funds, and CTAs to study the issues of risk, return, and fee structures of these alternative investment vehicles. As far as we know, this is the first paper to comprehensively evaluate all these investment vehicles together. Our major findings are reported in the following: First, hedge funds and funds-of-funds invest in similar asset classes. Their performance can be attributed to similar asset class factors. These factors are MSCI developed country index, MSCI emerging market index, Salomon Brothers world government bond index, and Salomon Brothers BIG index. However, due to the double fee structure of funds-of-funds, there is some evidence that hedge funds outperform funds-of-funds during the time period of 1985 to

18 Second, on a stand alone basis, CTAs trail behind hedge funds and funds-of-funds during the same time period. This underperformance can be attributed to high management fees, high attrition rate and survivorship bias, under-diversified portfolio positions in futures markets, and high leverage in futures contracts. Third, although hedge fund styles and CTA styles are correlated among themselves, CTA styles are not or are only slightly correlated with hedge fund and fund-of-fund styles. This low correlation can lead to some marginal benefits to investors: adding CTAs to investors hedge fund portfolio or fund-of-funds portfolio can improve their risk return trade-off. Forth, although the correlations among different styles are high at the aggregate level, intra-style correlations among various funds within the same style are fairly low. This makes a style index less useful than one expects: the style index may not be representative for the asset class at all. Giving the increasing popularity of alternative investment vehicles, our study can contribute not only to the academic literature but also to the investment communities. 17

19 References Ackermann, C.; R. McEnally; and D. Ravenscraft. The Performance of Hedge Funds: Risk, Return and Incentives. Journal of Finance, 54 (June 1999), Brown, S. J.; W. N. Goetzmann; and R. G. Ibbotson. Offshore Hedge Funds: Survival & Performance Journal of Business, 72 (Jan. 1999), Brown, Stephen J., William N. Goetzmann, and James Park, 1999, Conditions for Survival: Changing Risk and the Performance of Hedge Fund Managers and CTAs. Forthcoming, Journal of Finance. Brown, Stephen J., William N. Goetzmann, and Bing Liang, 2002, Fees on Fees in hedge Funds-of-Funds. Working paper, New York University. Chevalier, Judith, and Glenn Ellison, 1999, Are Some Mutual Fund Managers Better than Others? Cross-Sectional Patterns in Behavior and Performance. Journal of Finance, 54 (June 1999), Elton, Edwin J., martin J. Gruber, and Joel Rentzler, 1987, Professionally Managed, Publicly Traded Commodity Funds. Journal of Business, 60 (April 1987), Fung, William; and David. A. Hsieh. Performance Characteristics of Hedge Funds and Commodity Funds: Natural vs. Spurious Biases. Journal of Financial and Quantitative Analysis, 35 (September 2000), Empirical Characteristics of Dynamic Trading Strategies: The Case of Hedge Funds. The Review of Financial Studies, 10 (Summer 1997a),

20 . The Information Content of Performance Track Records: Investment Style and Survivorship Bias in the Historical Returns of Commodity Trading Advisors. The Journal of Portfolio Management, 24 (Fall 1997b), Liang, B. On the Performance of Hedge Funds. Financial Analysts Journal, 55 (July/Aug. 1999), Liang, B. Hedge Funds: The Living and the Dead. Journal of Financial and Quantitative Analysis, 35 (September 2000), Liang, B. Hedge Fund Performance: Financial Analysts Journal, 57 (Jan/Feb. 2001), Oberuc, Richard E., Alternative Investment Indices: Useful or Not? Laporte Asset Allocation System. Sharpe, W. F. Asset Allocation: Management Style and Performance Measurement. Journal of Portfolio Management, 18 (Winter 1992),

21 Table 1. Basic Statistics of Hedge Funds, Fund-of-Funds, and CTAs As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). Mfee is the management fee, Ifee is the incentive fee, staff is the number of staff for a CTA. Assets are in million dollars. Age is the number of months from a fund s reception or the time when the first monthly return is recorded (whichever is latter). Hedge Funds Fund-of -Funds CTA N Mean Std dev Median N Mean Std dev Median N Mean Std dev Median Mfee Ifee Min ,339 2,369, , ,798 1,955, , ,754 2,706, ,000 Staff N/A N/A Asset* Age *As of December

22 Table 2. Survivorship Bias As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). Survivorship bias is defined as the return difference between the portfolio without dead funds (live) and the one with dead funds (all). Panel A reports the bias for hedge funds, Panel B reports the bias for funds-of-funds, and Panel C reports the bias for CTAs. All returns are monthly numbers. N is the performance months of all funds. The averages in the last raw are simple averages over 17 years. Panel A: Hedge Funds Live Dead All Year N Mean Std dev N Mean Std dev Difference a N Mean Std dev Bias Average

23 Panel B: Fund-of -Funds Live Dead All Year N Mean Std dev N Mean Std dev Difference a N Mean Std dev Bias Average

24 Panel C: CTA Live Dead All Year N Mean Std dev N Mean Std dev Difference a N Mean Std dev Bias Average a The return difference between the live portfolio and the dead portfolio. 23

25 Table 3. Performance and Risk As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). Sharpe ratios are first calculated for each individual fund based on the data in that year only then averaged across all funds. Panel A: HF vs. FOF FOF HF Year No. Return Std dev Sharpe Std dev No. Return Std dev Sharpe Std dev t-return t-sharpe Panel B: CTA vs. HF CTA HF 4.59 *** 3.76 * 5.82 *** *** *** *** 2.22 ** 5.46 *** Year No. Return Std dev Sharpe Std dev No. Return Std dev Sharpe Std dev t-return t-sharpe * 2.66 *** 3.39 *** 4.87 *** 2.31 ** 3.30 *** 5.91 *** * *** 6.42 *** *** *** 24

26 Panel C: CTA vs. FOF CTA FOF Year No. Return Std dev Sharpe Std dev No. Return Std dev Sharpe Std dev t-return t-sharpe ***Significant at the 1% level. **Significant at the 5% level. *Significant at the 10% level *** ** ** 3.33 *** 2.17 ** 7.64 *** *** *** *** *** *** *** 25

27 Table 4. Asset Class Factor Regression As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). The dependent variable is the average monthly returns from The independent variables are MSCI developed country index, MSCI emerging market index, Salomon Brothers world government bond index and Salomon Brothers Broad Investment Grade (BIG) index, Federal Reserve Bank trade-weighted dollar index, gold price, and one-month US dollar deposit rate. HF FOF CTA variable estimate std error t-value estimate std error t-value estimate std error t-value Intercept ** * Developed ** ** Emerging *** ** Deposit Fed Gold Gov * BIG * N R Adj R ***Significant at the 1% level. **Significant at the 5% level. *Significant at the 10% level. 26

28 Table 5. Correlation Coefficients across Hedge Fund, Fund-of-Funds, and CTA Styles All hedge funds and futures funds have 36 consecutive monthly returns from January 1998 to December Strategy codes: Hedge funds or funds-of-funds EV: Event driven, MA: Global macro, EM: Global emerging market, ES: Global established markets, IN: Global international markets, LO: Long only, NE: Market neutral, SE: Sector, SH: Short sale, FF: Fund-of-funds. CTAs DIV: Diversified trading program, CUR: Currency trading program, AG: Agricultural trading program, STX: Stock trading program, FI: Financial trading program. Note that one of the hedge fund styles US opportunities dropped out since its latest available return date is September Ev Ma Em Es In Lo Ne Se Sh Ff Ag Cu Di Fi St Ev * 0.814* 0.868* 0.860* 0.820* 0.864* 0.856* * 0.923* * * 0.486* Ma * 0.856* 0.785* 0.802* 0.787* 0.806* * 0.880* * Em * 0.913* 0.747* 0.760* 0.750* * 0.894* * * 0.422* Es * 0.949* 0.817* 0.956* * 0.972* * In * 0.849* 0.752* * 0.917* * Lo * 0.957* * 0.919* * Ne * * 0.893* * 0.435* Se * 0.934* * * Sh * * Ff * Ag Cu * 0.514* Di * Fi St *Significant at the 5% level. 27

29 Table 6. Correlation Coefficietns within Investment Styles As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-of-funds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). We restrict funds having 36 consecutive monthly returns from 1998 to Correlations are calculated for each two fund pair and the average correlation is the average number across all independent pairs. Style Average corr t-value p-value Number of funds Number of corr Panel A: Hedge funds Event Driven < ,886 Global Macro < Global Emerging < ,45 Global Established < ,753 Global International < Long Only < Market Neutral < ,114 Sector < ,079 Short Sale < Panel B: Funds-of-funds Fund-of-funds < ,191 Panel C: CTAs Agriculture trading program Currency trading program < Diversified trading program < ,325 Financial trading program < ,378 Stock trading program

30 Table 7. Correlation Coefficients among Hedge Funds, Fund-of-Funds, and CTA Portfolios As of March 2002, there are 2,357 hedge funds (1,164 live funds and 1,193 dead funds), 597 funds-offunds (349 live and 248 dead), and 1,510 CTAs (294 live and 1216 dead). Every month, we calculate portfolio returns as the equally weighted average of all funds in the portfolio. From 1994 to 2001, 96 monthly observations are used for calculating the correlation coefficients. P-values are reported in the parentheses. Hedge funds Fund-of-funds CTAs Hedge funds (<0.0001) (0.6270) Fund-of-funds (0.6015) CTAs

31 Figure 1. Monthly Returns for Dead Funds towards the Death Date Return (%) Months to Death 30