Hedge Fund Benchmarks: A Risk-Based Approach

Transcription

1 Volume 60 Number , CFA Institute Hedge Fund Benchmarks: A Risk-Based Approach William Fung and David A. Hsieh Following a review of the data and methodological difficulties in applying conventional models used for traditional asset class indexes to hedge funds, this article argues against the conventional approach. Instead, in an extension of previous work on asset-based style (ABS) factors, the article proposes a model of hedge fund returns that is similar to models based on arbitrage pricing theory, with dynamic risk-factor coefficients. For diversified hedge fund portfolios (as proxied by indexes of hedge funds and funds of hedge funds), the seven ABS factors can explain up to 80 percent of monthly return variations. Because ABS factors are directly observable from market prices, this model provides a standardized framework for identifying differences among major hedge fund indexes that is free of the biases inherent in hedge fund databases. The new millennium marked an end to the Internet bubble and closed another investment cycle in which the simple buyand-hold strategy dominated all other strategies. Investors search for alternative investments naturally intensified in the ensuing market decline. As a result, hedge funds have received increased interest from a broad base of investors. The opaqueness of hedge fund operations, however, and a lack of performance-reporting standards make it hard to formulate expectations for hedge fund performance that reflect the current economic outlook. In addition, the relatively short history of hedge fund returns makes assessing their long-term performance difficult. In short, investors do not have an easy time determining the appropriate amount of exposure to hedge funds in their portfolios. Existing hedge fund indexes, although helpful in providing investors with an idea of the current progress of the industry on average, offer few clues to answer investors questions. Conventional models for constructing asset class indexes rest on the assumption that the underlying assets are reasonably homogeneous and that the dominant investment strategy being used is to buy the asset and hold it. Hedge funds, however, William Fung is visiting research professor at the Centre for Hedge Fund Education and Research, London Business School. David A. Hsieh is professor of finance at the Fuqua School of Business, Duke University, Durham, North Carolina. are diverse in the makeup and performance of their underlying assets, have dynamic investment styles, and may take highly levered bets. These characteristics, together with the lack of standardized reporting of historical performance, greatly limit the information content of hedge fund indexes that are constructed by using conventional methods. And at times, using conventional hedge fund indexes can even produce misleading results. In this article, we explore the flaws of existing hedge fund indexes, propose an alternative approach to benchmarking hedge fund returns by using asset-based style (ABS) factors in a model of hedge fund risks, apply the model to discover what the ABS factors can reveal about the typical hedge fund portfolio, and carry out an out-of-sample check on the usefulness of the risk-factor model in explaining significant return differences among major hedge fund indexes. Drawbacks in Peer-Group Averages A standard method of modeling hedge fund risk is to use a broad-based index of hedge funds. 1 Indexes constructed from averaging individual hedge funds, however, can inherit errors that were in the hedge fund databases. These problems have been noted by previous researchers (e.g., Brown, Goetzmann, and Ibbotson 1999; Fung and Hsieh 2000; Liang 2000). The remainder of this section provides a summary of the problems. September/October

2 Data Biases. Hedge fund data are prone to selection bias, survivorship bias, and instant history bias. Using funds of hedge funds (FOF) data, however, can reduce or even eliminate the effects of the biases. Selection bias. Unlike mutual funds, hedge funds are not required to make public disclosure of their activities. In addition, no hedge fund industry association exists (comparable to the Investment Company Institute for mutual funds) that could act as a central depository of fund information. Hedge fund data are generally collected by data vendors and sold, with the consent of the hedge fund manager, to accredited investors. Selection bias can arise if the sample of funds in the database is not a representative sample of the universe of hedge funds. The cause may be that entry to a database is a voluntary decision. Because hedge funds are prohibited from public solicitation, they can be marketed only through word of mouth. And one way of spreading information about a fund is by belonging to a database purchased by interested investors. Therefore, to the extent that the performance of funds seeking investors is different from the performance of funds not seeking investors, the database will be plagued by selection bias. Survivorship bias. Most hedge fund databases provide information only on operating funds. Funds that have stopped reporting information or ceased operation are regarded as uninteresting to investors and are purged from the database. The result is survivorship bias because the performance of disappearing funds is typically worse than the performance of surviving funds. This type of bias is well known in mutual funds (see, for example, Brown, Goetzmann, Ibbotson, and Ross 1992). Instant-history bias. When a fund enters a database, its past performance history (prior to the entry date) is appended to the database, which creates instant-history bias. Many new funds start with an incubation period to accumulate a track record. If the performance is good, they enter a database to seek new investors. If the performance is bad, they cease operation. Thus, when a data vendor backfills the fund s performance, the average return in the database is biased (upward). When hedge fund indexes are created from hedge fund databases, they inherit all the instanthistory biases. Some index providers take care to correct these errors to the extent possible, but to what extent these errors can be mitigated through data manipulation techniques alone is unclear. FOF indexes. One method to reduce some of these data biases is to use the returns of funds of hedge funds. We have argued (Fung and Hsieh 2000) that FOF data are less prone to selection, survivorship, and instant-history biases. If a fund of hedge funds invests in a fund that does not report to any database, the performance of that hedge fund is still reflected in the performance of the fund of hedge funds. Thus, FOF returns have less selection bias than those of individual funds. If a fund of hedge funds invests in a fund that later ceases operation, the performance of that fund remains as part of the historical return of the fund of funds. Thus, survivorship bias is reduced. When a fund of hedge funds invests in a fund, the previous history of that hedge fund is not included in the historical return of the fund of funds. This aspect reduces instant-history bias. Sampling Differences. Sampling differences exist among the various hedge fund databases. For example, a recent study by Agarwal, Daniel, and Naik (2004) examined the composition of hedge funds in the TASS Research, Hedge Fund Research (HFR), and Zurich Capital Markets (ZCM/MAR) databases and concluded that as of December 2000, there were 1,776 funds in operation. 2 TASS had 983 funds that were in operation, HFR had 1,063, and ZCM/MAR had 828. However, only 309 funds were in all three databases. TASS contained 348 funds that were not in the other two databases. Similarly, HFR had 395 funds and ZCM/MAR had 244 funds that were not in the other databases. Sample differences can lead to divergent returns from different hedge fund subindexes. For example, the HFR index for equity market-neutral hedge funds (the HFRI Equity Market Neutral Index) was reported to have returned 1.57 percent for the month of January 2001 whereas the CSFB/ Tremont Index for equity market-neutral hedge funds returned 2.13 percent for the same month. The high degree of return correlation between broadbased peer-group averages from different databases, however, indicates that there may be only a small number of common hedge fund risk factors. Short History. Another drawback to using hedge fund indexes, either based on individual funds or funds of hedge funds, is that reliable data on hedge funds begin only in the 1990s. This sample period coincides with one of the greatest bull markets in U.S. history, with only a few years of market decline. It does not provide a sufficiently long history to allow determination of how hedge funds perform in a variety of market environments. Later, we propose a method of constructing hedge fund risk factors that can circumvent this problem. Lack of Transparency. Another disadvantage of using hedge fund indexes is the lack of transparency. As private investment vehicles, , CFA Institute

3 Hedge Fund Benchmarks: A Risk-Based Approach hedge funds do not disclose their activities. Consequently, other than historical return statistics that are of dubious quality, analysts have few ways to determine the equity or bond content of a hedge fund portfolio and to assess the content s impact in an overall asset-allocation framework. Issues in the Choice of Index Weights. Typically, each conventional asset class transacts in a different market from the other classes and can easily be distinguished by the way an asset is securitized. An index of a conventional asset class is usually an average (equally weighted, price weighted, or value weighted) of the underlying assets in that class. Consequently, an asset class index resembles a broad-based index for the particular market in which the constituent assets are traded. As an investment portfolio, an investable asset class index is passive and its constituents change only according to explicitly defined rules governing index rebalancing. The rebalancing rules themselves implicitly assume particular portfolio strategies. For instance, an equally weighted index implicitly assumes a contrarian approach, in which the better-performing assets are sold in exchange for the underperforming assets at index rebalancing points to maintain equal weighting. A valueweighting scheme assumes a momentum strategy, in which winners are permitted to exert increasing influence on the portfolio s (index s) total return. When these assumptions are applied to hedge funds, certain problems occur. A well-known facet of hedge fund investing is that the distribution of assets among hedge fund managers is skewed toward the top funds. Fewer than 25 percent of the funds manage, in aggregate, more than 75 percent of the industry s capital. Therefore, an equally weighted index s returns will not reflect this phenomenon. Also, an equally weighted scheme biases the index toward newly minted funds, where the instant-history bias is at its maximum. Using assets under management as weights in a hedge fund index also has problems. First, the quality of the data in historical series of assets managed by hedge fund managers is much less reliable than that of the historical series of conventional asset class returns. Second, most hedge fund strategies have finite capacity. So, a large, successful hedge fund manager might choose to close the fund to new capital and stop reporting performance to index providers, resulting in distortions to the index return series. Third, an index of hedge funds should reflect the return experience of risk capital used to generate the performance, but leverage can distort this experience. On the one hand, the dollar return of any strategy, and of the hedge fund industry in general, ultimately depends on the market environment. The rate of return, on the other hand, involves one more factor the degree of leverage used by the hedge fund manager. To assume that all hedge fund managers operate at optimal leverage at any time may be unreasonable. Using an assets-under-management weighting scheme will thus bias the index return toward underlevered managers and, at the extreme, will overemphasize the performance of asset gatherers. In the absence of explicitly specified portfolio objectives, there is no optimal way to determine how hedge fund managers should be combined to form an index that is suitable for all investors. A more flexible method for constructing hedge fund benchmarks is clearly called for. Return-Based and Asset-Based Style Factors Hedge fund managers typically transact in the same markets as traditional fund managers. Yet, evidence shows that hedge fund returns have different characteristics from those of traditional fund managers. For example, we found (Fung and Hsieh 1997a) that hedge fund returns have much lower correlations with standard asset returns than mutual fund returns do. One interpretation is that hedge fund managers have more skills than traditional fund managers. This view is inconsistent, however, with the evidence that hedge funds typically perform poorly when asset markets perform very poorly. An alternative interpretation is that hedge funds are exposed to risks as mutual funds are but hedge fund risks are different from mutual fund risks. In this article, we use asset-based style factors (see Fung and Hsieh 2002a) to create hedge fund benchmarks that capture the common risk factors in hedge funds. The process of developing the ABS factors was as follows. First, we extracted common sources of risk in hedge fund returns. Second, we linked these common sources of risk to observable market prices. We used these explicitly identified ABS risk factors to construct a hedge fund risk-factor model similar to an APT (arbitrage pricing theory) model, in which the factor loadings (betas) are permitted to vary over time. The payoff of this model can be significant. Consider the analogy with equities. Equity risk factors can be modeled by using the capital asset pricing model (CAPM) or APT. The models separate the return (or risk) of an equity investment into two September/October

4 parts systematic and idiosyncratic. The systematic part is the common source of return. In the CAPM, it is simply the market portfolio; with APT, it is typically the market portfolio together with a few other sources, such as interest rate spreads. The idiosyncratic part of the return is unique to the equity and unrelated to other equities. This decomposition allows investors to diversify away idiosyncratic risk by holding a large portfolio of equities. At the portfolio level, investors need be concerned with only the common sources of equity risk. This type of risk model was successfully applied by Sharpe (1992) to model equity mutual fund styles. Our hedge fund risk-factor model similarly helps investors identify the common sources of risk expressed in a familiar setting by using conventional asset prices hence, the notion of ABS factors. This approach creates the critical link between hedge fund investments and conventional asset classes and allows hedge fund investments to be managed within the framework of an overall portfolio. To avoid the data biases in hedge fund databases, we constructed benchmarks based on asset returns rather than on hedge fund returns. The approach we advocate is to link common components of hedge fund returns to observable market risk factors. We extracted common components of hedge fund returns by using a statistical procedure called principal components analysis, and we call these common components return-based style factors. Whenever return-based style factors can be linked to models that involve only observable market risk factors, we consider the factors to be asset-based style factors. We extracted common components of hedge fund returns in two ways. In Fung and Hsieh (1997a), we analyzed all hedge funds and commodity funds with at least two years of monthly performance data. We used the idea that if two funds trade similar assets in a similar manner, their returns should be highly correlated. The correlated part of their returns is, therefore, a common return component. By grouping funds with correlated returns, we could extract their common components. We found that the five most important common components accounted for roughly 50 percent of the covariation among these funds. Applying a variation of this method allowed us to extract common return components from subgroups of hedge funds that were classified by data vendors to have similar styles, without having to verify their classification method (Fung and Hsieh 2001, 2002b). This approach is in line with the philosophy of checking what hedge managers do instead of taking what they say they do at face value. The next phase of our approach was to explicitly identify these common return components by using observable market risk factors. This process is illustrated for four subgroups of hedge funds and commodity funds. Trend-Following Funds. In Fung and Hsieh (1997b), we extracted a common return component from trend-following funds. In Fung and Hsieh (2001), we modeled this common return component as a portfolio of lookback straddles. 3 The model extended the insight from the pioneering work of Merton (1981). We asserted that trend followers are betting on big moves. Similar to option buyers, they make money when markets are volatile. We thus constructed five portfolios of lookback options from exchange-traded options. We showed that these option portfolios have high correlations with and return characteristics similar to the returns of trend-following funds. Subsequently, we showed (Fung and Hsieh 2002a) that this analysis continued to hold beyond the sample period of the original analysis. The out-of-sample results from January 1998 to the end of 2002 are depicted in Figure 1. The dotted line is the average monthly return of trendfollowing funds as measured by the Zurich Trend- Following Index. This line depicts the return-based style factor for trend-following funds. The solid line is the predicted monthly return of the portfolio of lookback straddles based on the parameter estimates in Fung and Hsieh (2001), which used data through the end of This line depicts the assetbased style factor for trend-following funds. Figure 1 shows that the replicating portfolio of straddles can mimic the returns of the average trendfollowing fund. Modeled in this way, the trendfollowing ABS factor highlights an interesting feature of the strategy: Trend-following strategies thrive when conventional asset markets are distressed, which provides a valuable diversifying source of return to portfolios of conventional assets. 4 Merger Arbitrage Funds. Mitchell and Pulvino (2001) created an asset-based style factor for merger arbitrage funds. Merger arbitrage (also known as risk arbitrage) is a strategy that buys the stock of the target and shorts the stock of the acquirer. The bet is that the announced merger transaction will be completed. Mitchell and Pulvino simulated the return of a rule-based merger arbitrage strategy by using all announced stock and cash merger transactions from 1968 through They showed that this ABS factor for merger arbitrage has return characteristics that are similar to those of merger arbitrage funds , CFA Institute

5 Hedge Fund Benchmarks: A Risk-Based Approach Figure 1. Trend Followers Average Return: Actual vs. Predicted, Monthly Return (%) 15 Actual 10 Predicted /98 7/98 1/99 7/99 1/00 7/00 1/01 7/01 1/02 7/02 12/02 Mitchell and Pulvino also discovered the interesting result that is illustrated in Figure 2. The vertical axis is the monthly return of the HFR Merger Arbitrage Index, which is an average of the returns of merger arbitrage funds in the HFR database. Figure 2 shows that the returns of merger arbitrage funds in this period had low correlations with the S&P 500 Index returns except when the S&P 500 experienced a large decline. A sharp decline in the S&P 500 coincided with the worst performance of merger arbitrage funds. In other words, the deal risk that merger arbitrageurs are exposed to can be proxied by a short position in an out-of-the-money put option on the S&P 500. This conclusion is reasonable. The systemic risk in merger arbitrage is that many transactions will be canceled at the same time. In normal market conditions, risks of individual deals are idiosyncratic and can be diversified. But if the market declines sharply, merger transactions may be called off or postponed irrespective of their individual merit, creating a systemic loss for merger Figure 2. Merger Arbitrage Returns vs. S&P 500 Returns, Monthly Return of HFR Merger Arbitrage Index (%) Monthly Return of S&P 500 Index (%) September/October

6 arbitrage funds. In this case, the ABS factor, in the form of a short put, helps highlight a systemic source of risk in merger arbitrage beyond the risk in individual deals. Fixed-Income Hedge Funds. In analyzing fixed-income hedge funds (Fung and Hsieh 2002b), we found that these funds are typically exposed to yield spreads. The reason is that fixed-income funds typically buy bonds with lower credit ratings and/or less liquidity and then hedge the interest rate risk by shorting U.S. T-bonds, which have the highest credit rating and are more liquid. The difference between the yields on the two bonds is the yield spread. Because yield spreads tend to move together, especially during times of market distress, fixedincome funds can be modeled as being exposed to credit risk or credit spreads. In addition, fixedincome arbitrage positions are often highly levered. So, the cost of financing the positions will also depend on the overall liquidity of the marketplace, which is also reflected in the credit spread variable. Therefore, both the nature of the bets and the way positions are funded are sensitive to credit spread as the common risk factor. The following regression of the HFR Fixed Income: Arbitrage Index on changes in the credit spread is a good illustration: HFR Fixed-Income Arb = (Change in credit spread), where the credit spread is measured as the difference between the yield on Moody s Investors Service Baa bonds and the yield on the 10-year constant-maturity T-bond. The regression states that a 1 percent increase (decrease) in the credit spread will lead to a 5.37 percentage point decline (increase) in the return of the average fixed-income arbitrage fund. When data from 1990 until 1997 were used, the R² of this regression was This regression is useful in an examination of the history of the credit spread in Figure 3. The 1990s were a relatively benign period for the credit spread: It generally declined, and it remained low relative to the 1970s or 1930s. As a result, based solely on the funds returns, we cannot answer the question of how fixed-income arbitrage hedge funds would have performed in the credit market conditions of the 1970s. The beta of these funds with respect to the credit spread does, however, provide a good idea of what might have happened. A rise of 2 percent in the spread, which was not experienced in the 1990s, would have led to a loss of 10.7 percentage points for these funds. That conclusion cannot be drawn from the hedge fund data alone. But by identifying and using the relevant ABS factor, we can assess the risk of a given fixedincome hedge fund strategy over a much longer history and a span of different economic cycles than the actual fund has experienced. Equity Long Short Hedge Funds. The original concept of a hedge fund, ascribed to A.W. Jones, was founded on strategies similar to the modern equity long short fund. Fung and Hsieh (forthcoming 2004) show that equity long short hedge funds have exposure to the stock market and to the spread Figure 3. The Credit Spread, Credit Spread (%) Note: Dates are as of December , CFA Institute

7 Hedge Fund Benchmarks: A Risk-Based Approach between returns on large-capitalization stocks and returns on small-capitalization stocks. The ABS factors of these hedge funds can be seen in the following regression: HFR Equity Hedge Index = (S&P 500) (SC LC), where SC denotes returns on the Wilshire Small Cap 1750 Index and LC denotes returns on the Wilshire Large Cap 750 Index. Over the sample period of , the R² of this regression was This result is consistent with the observation that equity long short funds tend to have a small positive exposure to stocks and tend to be long the smaller-cap stocks and short the larger-cap stocks. Therefore, long short equity hedge funds are generally not an alternative source of investment to a conventional portfolio with significant equity exposure. The fund and the portfolio will overlap the U.S. equity market in directional exposure, and investing in the fund may increase a portfolio s tilt toward small-cap stocks. An interesting application of the ABS factor analysis would be to consider whether these systemic risk factors can be separately managed to modify the return profile of long short equity hedge funds so as to enhance their diversifying usefulness to conventional asset portfolios. Summary: Seven-Factor ABS Model. Thus far, research has found seven risk factors. Market risk and the spread between small-cap stock returns and large-cap stock returns are found in equity long short hedge funds. These two equity ABS factors are the major risk factors for a sizable portion of the industry. In the TASS database, out of 1,824 operating funds as of March 2003, 795 (44 percent) were classified as equity long short funds. In the HFR database, out of 1,911 operating funds as of July 2003, 550 (29 percent) were classified as equity hedge funds. 6 The change in 10-year Treasury yields and the change in the yield spread between 10-year T-bonds and Moody s Baa bonds are the fixed-income ABS factors, and they are the major risk factors for a small portion of hedge funds. For example, the TASS database contained only 88 such funds (5 percent of the database) as of March 2003 and the HFR database contained 34 (2 percent) as of July The portfolios of lookback straddles on bonds, on currencies, and on commodities are the trendfollowing (ABS) factors. These factors are the major risk factors for 5 10 percent of hedge funds; 161 funds (9 percent) were managed futures funds in the TASS database as of March 2003, and 121 funds (6 percent) were managed futures funds in the HFR database as of July In summary, these seven risk factors are found in 57 percent of the hedge funds in TASS and 37 percent in HFR. Research on additional hedge fund styles will probably discover other risk factors, although some of the yet-to-be-discovered risk factors may be correlated with the existing seven. For example, Fung and Hsieh (2002a) found that certain fixed-income hedge funds (convertible bonds, mortgage-backed securities) are correlated with the change in the credit spread. This crosscorrelation among risk factors is a primary reason we believe that seven risk factors are sufficient to explain a large portion of the risk in diversified portfolios of hedge funds. How Useful Are ABS Factors? Research on ABS factors has evolved by examining specific hedge fund strategies (or groups of strategies). Hedge fund investors, however, tend to diversify their investment through a portfolio of hedge fund strategies. Thus, an important question is how much of the risk of a typical hedge fund portfolio can be identified by using the seven risk factors. To proxy a typical hedge fund portfolio, we used the HFR Fund of Funds Index (HFRFOF). 8 We regressed its monthly return for on the seven hedge fund risk factors. We adopted a simple rule to select the 1994 start date for our analysis: that the fund universe should be at least 100 funds. 9 Table 1 reports the summary statistics of the regression. The first column of Table 1 shows that the regressions of the HFRFOF on the two equity ABS factors (S&P and SC LC) and the two fixedincome ABS factors (10Y and CredSpr) are highly significant for the full period. HFRFOF exposure to two of the trend-following factors (BdOpt and ComOpt) is statistically significant but exposure to FXOpt is insignificant for the full period. The adjusted R² of the regression is There is a statistically significant intercept term of approximately 48 bps a month. These observations suggest that, on average, hedge fund portfolios have systematic exposures to directional equity and interest rate bets as well as systematic exposures to long short equity and credit spread bets. Apparently, after adjusting for these risk factors, an investor can attain an average alpha of approximately 48 bps a month. However, to assume that investors asset allocations were static over this eight-year period is unrealistic. So, the question is: How stable are these conclusions? The period was marred by a number of stressful market events. During the early part of September/October

8 Table 1. Regression of the HFRFOF on Seven Hedge Fund Risk Factors (standard errors in parentheses) Factor 1/ /2002 1/1994 9/1998 4/ /2002 Intercept ( )** ( ) ( ) S&P ( )** ( )** ( )** SC LC ( )** ( )** ( )** 10Y ( )** ( ) ( )** CredSpr ( )** ( )** ( )* BdOpt ( )* ( ) ( ) FXOpt ( ) ( ) ( ) ComOpt ( )* ( )* ( )** R Notes: S&P = Standard & Poor s 500 stock return; SC LC = Wilshire Small Cap 1750 Wilshire Large Cap 750 return; 10Y = month-end to month-end change in the U.S. Federal Reserve 10-year constant-maturity yield; CredSpr = month-end to monthend change in the difference between Moody s Baa yield and the Federal Reserve s 10-year constant-maturity yield; BdOpt = return of a portfolio of lookback straddles on bond futures; FXOpt = return of a portfolio of lookback straddles on currency (foreign exchange) futures; ComOpt = return of a portfolio of lookback straddles on commodity futures. *Significant at the 5 percent level in a one-tailed test. **Significant at the 1 percent level in a one-tailed test. 1994, the U.S. interest rate rose abruptly, inflicting substantial losses on a number of hedge funds. The Long-Term Capital Management (LTCM) episode caused substantial volatility in hedge fund returns during the latter part of In addition, the Internet bubble burst circa March 2000, followed by yet another market disruption with the events of 11 September In 2002, the market had to absorb the unraveling of Enron Corporation and World- Com. With such a collection of market disruptions, most funds of hedge funds probably had to adjust their portfolios. These changes, in turn, should cause the betas in our risk-factor model to shift. HFRFOF Time-Varying Bets. To test the stability of the ABS factor betas, we devised a novel variation of the standard test of cumulative recursive residuals. We ran the regression backward starting in December 2002 and adding observations one month at a time. This approach is similar to running a Kalman filter with the time scale reversed. 10 The logic behind this approach runs as follows. Given the tremendous growth in the hedge fund industry in the past decade, both the number of funds of hedge funds and the quality of their performance data have been rising. Thus, the information content of the return data is likely to decline with the age of the return observations. Looking for a sample breakpoint by running the Kalman filtering process backward implicitly allowed us to place more credence on recent returns without having to explicitly specify ad hoc schemes for weighing individual returns. By observing the behavior of the cumulative recursive residuals, we hoped to identify market events that triggered a violation of error bounds. Because these market events are exogenous to the regression equations, the result is an unbiased way of identifying sample breakpoints that are consistent with a change in the regression regime. Figure 4 plots the cumulative recursive residuals for the HFRFOF starting in December 2001 and working backward to December The two shaded lines represent 95 percent confidence bands. The crossing of the upper band by the cumulative recursive residuals in June 1999 indicates a sample break from a statistical viewpoint. The cumulative recursive residuals crossed back below the upper band in October 1998, again indicating a sample break around that time. The actual sample break is unlikely to have happened exactly at those times because the effect of the sample break shows up gradually in the regression. Therefore, we looked for market events around the time of the statistical sample breaks to pinpoint the culprit and the timing for the actual break. 11 Our search for sample breaks led us to identify March 2000 (the end of the Internet bubble) and September 1998 (the LTCM debacle) as the triggering market events. Accordingly, we chose two subperiods from the full sample period (January 1994 to September 1998 and April 2000 to December 2002) for our analysis. We left out the middle period (October 1998 to March 2000) because it is too short for statistical analysis based on monthly data. Table 1 reports the results for these periods in the second and third columns. Highly significant betas with respect to the two equity ABS factors are found in both subperiods, but in the period, the magnitude of the directional exposure to the S&P 500 is almost half of what it was in the earlier period. This result is consistent with the bear market conditions that prevailed during that period. Also consistent with the bear market effect is the increase in the beta with respect to the 10-year T-bond, which indicates an increase in bond market bets (a more negative beta indicates a larger exposure of the HFR- FOF to bonds because of the inverse price-to-yield relationship). In terms of exposure to credit spreads, , CFA Institute

9 Hedge Fund Benchmarks: A Risk-Based Approach Figure 4. Cumulative Recursive Residuals for the HFRFOF, Residual Upper Bound 10 5 HFRFOF Lower Bound Note: Dates are as of December. both the absolute value of the beta and the statistical significance level declined in the second period from results for the earlier period. This outcome also is consistent with portfolio HFRFOF bets reflecting a bear market environment. The same theme carries through to beta with respect to the trend-following ABS factor on commodities: In the later period, it increased in both magnitude and statistical significance. As pointed out in Fung and Hsieh (2001), this increase can be interpreted as a diversifying bet against potential stock market declines. Trend followers tend to benefit during stressful equity market conditions. Note that by separating the period according to the breakpoints in the regression, we found that the adjusted R² for both subperiods went up substantially from the 0.55 for the full period. The Vanishing Alpha. Perhaps the most troublesome change shown in Table 1 is in the intercept, or alpha, term of the regressions. For the first subperiod, both the magnitude and significance level for the intercept term drop dramatically from their values in the total period, indicating little to no added value from the average fund-of-funds manager beyond systematic bets. Although the second subperiod s intercept term is marginally better both in magnitude and significance than the first subperiod s, it is still less than half of the intercept term when the entire sample period was used. Prima facie evidence suggests that the full-period regression may create an alpha illusion, in that any apparent value added by the average fund-offunds manager beyond systematic bets took place during the bull market run of October 1998 to March This finding may be uncomfortable for institutional investors in hedge funds because bull market alphas are a redundant feature, at best, of an alternative investment. In conclusion, a properly structured risk-factor model clearly can reveal vital information about the risk profile of a hedge fund portfolio. In this case, it provided important clues as to where the average fund of hedge funds was placing its bets, how these bets varied over time, and whether the average fund added value beyond systematic bets on the ABS factors something that a simple index and its return statistics cannot convey. In the next section, we apply the same analysis to standard hedge fund indexes for insights into whether the time-varying bets we observed among funds of hedge funds is simply a derivative of systemic shifts in the underlying hedge funds or a consequence of the FOF portfolio strategies. Assessing Differences in Hedge Fund Indexes The primary difficulty in comparing existing hedge fund indexes is the lack of a common standard. In general, existing hedge fund indexes not only differ in construction methods but are also drawn from widely different data universes. Moreover, historical measurement errors in the data like those discussed September/October

10 for individual indexes cannot be easily rectified by statistical means alone. In this section, we circumvent some of these difficulties by asking: What do various hedge fund indexes tell us about hedge fund risk and return? Applying ABS Factors to Indexes. Hedge fund indexes are constructed from various databases, with only a small overlap of funds. In fact, with a correlation coefficient of only 0.76, the HFR Composite Index (HFRI) and CSFB/Tremont Composite Index (CTI) would not be regarded as close substitutes as a proxy for the same universe of hedge funds. Thus, these two indexes can be expected to have significantly different risk characteristics. Table 2 reports the regression of the HFRI, the CTI, an equally weighted average return of all hedge funds in the TASS database (TASSAVG), and the equally weighted MSCI Hedge Fund Composite Index (MSCI) on the seven hedge fund risk factors for the period January 1994 through December The regressions show that the HFRI and the CTI have strong exposure to the two equity ABS factors. The CTI also has strong exposure to the two fixed-income ABS factors, but the HFRI does not. This difference is the first significant difference in risk characteristics between the two indexes. The second difference is the significant beta of the CTI trend-following ABS factor in bonds. Although trend-following funds have positive exposure to this risk factor, as shown in Fung and Hsieh (2001), some other hedge funds in the CTI must have negative exposure, leading to a net negative exposure at the index level. Both indexes have significant alphas in monthly returns (alpha characteristics are analyzed in the next section). The question is: How much of these risk differences is a result of different index construction methods? The HFRI is an equally weighted index for all hedge funds in the HFR database. The CTI is a value-weighted index for large hedge funds in the TASS database. To eliminate some of these differences, we created an equally weighted TASSAVG index by using the TASS database ending March 2003 excluding funds of hedge funds. Table 2 shows that the TASSAVG has equity ABS factor exposure similar to that of the CTI but smaller than the exposure to the fixed-income ABS factors. Thus, the TASSAVG risk profile is closer to that of the HFRI. The exposure of the TASSAVG to trend-following factors is also higher than the HFRI s exposure, which is consistent with the presence of commodity futures advisors (CTAs), who run managed futures programs, in the TASSAVG but not in the HFR indexes. In short, the CTI overweights fixed-income risks and underweights trend-following risks in comparison with the average of the universe of TASS funds from which it is taken. The CTI and the TASSAVG have similar levels of alpha. Table 2. Average Exposure of Indexes to the ABS Risk Factors, Data for (standard errors in parentheses) Factor HFRI CTI TASSAVG MSCI Intercept ( )** ( )** ( )** ( )** S&P ( )** ( )** ( )** ( )** SC LC ( )** ( )** ( )** ( )** 10Y ( ) ( )** ( )** ( )* CredSpr ( ) ( )** ( )* ( ) BdOpt ( ) ( )** ( ) ( ) FXOpt ( ) ( ) ( )** ( )** ComOpt ( ) ( )* ( )** ( )** R Note: Factor definitions in Table 1. *Significant at the 5 percent level in a one-tailed test. **Significant at the 1 percent level in a one-tailed test , CFA Institute

11 Hedge Fund Benchmarks: A Risk-Based Approach Finally, Table 2 also contains the average exposure of the MSCI hedge fund index. It has exposures similar to the HFRI and the TASSAVG. The equity ABS factor exposures of the MSCI are comparable to those of the TASSAVG, and both are lower than the HFRI exposure. Interestingly, the MSCI has no significant beta with respect to either of the fixed-income ABS factors. Its exposures to trend-following factors are similar to those of the TASSAVG. These results show how the risk-factor model can identify differences in the databases of standard providers of hedge fund data. Apparently, the HFR database is dominated by hedge funds with equityrelated bets. The TASS database has a better balance between equity-related hedge funds and funds that have interest-rate-related bets. Another point picked up by the risk factors is the presence of trend-following hedge funds in the TASS database but not in the HFR database. The MSCI database also has a larger presence of equity-related hedge funds than interest-rate-related hedge funds. But trend-following hedge funds are clearly present in the MSCI dataset. Thus, the risk factors can provide an alternative method for quantifying the hedge fund styles in vendor databases. Parameter Stability. We applied the same cumulative recursive residual technique in a reversed time scale to the hedge fund indexes to look for regime changes in the risk-factor model. Figure 5 plots the behavior of the cumulative recursive residuals for the four indexes. Generally, we found breakpoints to be similar to those in the analysis of the HFRFOF except for the CTI, for which no breakpoint is discernible. 12 Table 3 reports summary statistics of regressing three indexes HFRI, TASSAVG, and MSCI on the seven-factor model in the pre-breakpoint and post-breakpoint periods. The general conclusions about ABS factor betas for the HFRFOF regressions remain valid for these indexes. All three indexes have statistically significant betas for the two equity ABS factors. All three show lower equity ABS betas in the second subperiod, albeit less dramatic declines than in the case of the HFRFOF. Similar conclusions hold for the beta with respect to the 10-year Treasury factor except that none of the three indexes exhibit significant interest-raterelated exposure for the first subperiod. The bond bets of these three indexes appear to be a bear market phenomenon. As for the credit spread factor, the same behavior of declining magnitude and statistical significance occurs from period to period, reflecting the change to bear market sentiment, between the first and second subperiods. Figure 5. Cumulative Recursive Residuals for the HFRI, CTI, TASSAVG, and MSCI, Residual Note: Dates are as of December. MSCI HFRI CTI TASSAVG September/October

12 Table 3. Changing Exposures of Hedge Fund Indexes to the ABS Risk Factor in Two Periods (standard errors in parentheses) Factor HFRI TASSAVG MSCI January 1994 September 1998 Intercept ( )** ( )** ( )** S&P ( )** ( )** ( )** SC LC ( )** ( )** ( )** 10Y ( ) ( ) ( ) CredSpr ( )** ( )** ( )* BdOpt ( ) ( ) ( ) FXOpt ( ) ( )* ( )** ComOpt ( ) ( )** ( )** R April 2000 December 2002 Intercept ( )** ( )** ( )** S&P ( )** ( )** ( )** SC LC ( )** ( )** ( )** 10Y ( )** ( )** ( )** CredSpr ( )* ( ) ( ) BdOpt ( ) ( ) ( ) FXOpt ( ) ( )** ( )** ComOpt ( )** ( )** ( ) R Note: Factor definitions in Table 1. *Significant at the 5 percent level in a one-tailed test. **Significant at the 1 percent level in a one-tailed test. The exposure of the indexes to the trendfollowing factor betas is less clear. Although the HFRI has no CTAs, it displays a significant beta with respect to the trend-following factor on commodities in the second period. We might infer that trend-following strategies on commodities were adopted by some of the hedge fund managers that were classified as having other styles, but more work is needed to fully explain this observation. The TASSAVG and the MSCI display increases in trend-following beta in the foreign exchange area in the second period. Colinearity between the trend-following factors may prevent a simple interpretation of these results. The adjusted R²s of the risk-factor equations are unusually high over 70 percent for the first subperiod for all three broad-based indexes. And for the second subperiod, the adjusted R²s rise. These high adjusted R²s are consistent with our assertion that only a limited number of risk factors are needed to capture the risk characteristics of large hedge fund portfolios. Unidentified factors remain a possibility, but whatever they are, it is hard to imagine they will add any dramatic improvement to the explanatory power of the model. Rediscovery of Alpha. To broaden the scope of the analysis, we added to the regressions the S&P Hedge Fund Index (SPHF), which started in 1998, for the second period. Table 4 provides the exposures of the HFRFOF, HFRI, TASSAVG, and MSCI for the two subperiods plus, in the second period, the exposures of the SPHF. Perhaps the most interesting result visible in Table 4 is the behavior of the intercept term the alphas. The three hedge fund indexes have significant alphas (at the 1 percent level) in both periods. All three also show a decline in the alpha value in the second period. Nonetheless, the magnitudes of these alphas are in stark contrast to the results from the HFRFOF regressions shown in Table 4. At this point, the reason is not clear. We can only surmise that there is a (statistically reliable) difference in alpha between the industry s average (as proxied by the broad-based indexes) and the average for funds of hedge funds (HFRFOF) after adjustments for systematic risk factors among hedge funds. Three explanations are possible. First, unrealistic index construction rules are creating pseudo alphas for the indexes. Second, managing a large hedge fund portfolio or fund of funds imposes structural costs that are not accounted for in the index returns. Third, poorly performing funds of hedge funds among the HFRFOF constituents drag the average alpha toward zero. First, index rebalancing rules can mislead investors as to the cost of replicating the index, but whether this aspect biases the index return upward relative to an actual portfolio of hedge funds is unclear. Still, investors need to acknowledge that artificial rebalancing rules assumed by hedge fund indexes give indexes an unrealistic cost advantage in portfolio rebalancing. Second, as for costs, managing large portfolios undoubtedly entails costs , CFA Institute

13 Hedge Fund Benchmarks: A Risk-Based Approach Table 4. Hedged Returns of Hedge Fund Portfolios in Two Subperiods (standard errors in parentheses) Factor HFRFOF HFRI TASSAVG MSCI SPHF February 1995 September 1998 Intercept ( )* ( )** ( )** ( )** S&P ( ) ( ) ( ) ( ) SC LC ( )* ( )** ( )** ( )** 10Y ( ) ( ) ( ) ( ) CredSpr ( )** ( ) ( )* ( ) BdOpt ( ) ( ) ( ) ( ) FXOpt ( ) ( ) ( )* ( )** ComOpt ( ) ( ) ( )* ( ) R April 2000 December 2002 Intercept ( ) ( )* ( )** ( )** ( ) S&P ( ) ( ) ( )* ( ) ( ) SC LC ( )** ( )** ( )** ( )** ( ) 10Y ( )** ( )** ( )* ( ) ( ) CredSpr ( ) ( ) ( ) ( ) ( ) BdOpt ( ) ( ) ( ) ( ) ( )* FXOpt ( ) ( ) ( )* ( )** ( )** ComOpt ( ) ( )* ( ) ( ) ( ) R Note: Factor definitions in Table 1. *Significant at the 5 percent level in a one-tailed test. **Significant at the 1 percent level in a one-tailed test. But the differences in alpha between the fund indexes and the HFRFOF are of a magnitude that cannot be easily explained away by the additional fees charged by funds of funds. Moreover, the costs should be part of the fund of hedge fund s fees, which cannot reasonably rise so high as to absorb the alpha differences. Third, therefore, the most likely explanation is the third one namely, the HFRFOF simply reflects too many inefficient funds of hedge funds. The HFR database contains more than 500 funds of funds. Consolidation and the emergence of investable hedge fund indexes will correct these problems over time. In the future, costs and returns can be estimated from the tracking errors of investable hedge fund indexes and should provide additional insight into these explanations. September/October