Skewness, Fund Flows and Hedge Fund Performance

Transcription

1 Skewness, Fund Flows and Hedge Fund Performance Andrea J. Heuson a, Mark C. Hutchinson b and Alok Kumar a,* a University of Miami, 514 Jenkins Building, Coral Gables, FL 33124, USA b University College Cork, College Road, Cork, Ireland Abstract This paper examines the relationship between portfolio return skewness and subsequent fund flows and performance of money managers. Our results show that hedge fund returns exhibit significant skewness and investors in these funds have skewness preferences. Investors flows to hedge funds that earn positively skewed returns increase by 11.5% per annum relative to funds that earn negatively skewed returns. Evaluating hedge fund performance using a measure that reflects both skewness and risk adjustment leads to superior ex-ante fund selection. From 1994 to 2009 the average increase in out-of-sample performance is 2% per annum. This is particularly valuable during periods of economic crisis, when returns are more likely to exhibit skewness, where performance increases by an average of 4%. Keywords: Performance measurement, hedge funds, return skewness, performance persistence. JEL Classification: G10, G19, G20. * Corresponding author. akumar@miami.edu. Phone: Andrea Heuson can be reached at aheuson@miami.edu or Mark Hutchinson can be reached at m.hutchinson@ucc.ie or We are grateful to Vikas Agarwal, Sandro Andrade, Brad Barber, Liam Gallagher, Mila Getmansky-Sherman, Kyung-So Im, Bing Liang, Narayan Naik and Richard Taffler for helpful comments. Mark Hutchinson acknowledges the financial support of the Irish Research Council (IRC). 0

2 Skewness, Fund Flows and Hedge Fund Performance Abstract This paper examines the relationship between portfolio return skewness and subsequent fund flows and performance of money managers. Our results show that hedge fund returns exhibit significant skewness and investors in these funds have skewness preferences. Investors flows to hedge funds that earn positively skewed returns increase by 11.5% per annum relative to funds that earn negatively skewed returns. Evaluating hedge fund performance using a measure that reflects both skewness and risk adjustment leads to superior ex-ante fund selection. From 1994 to 2009 the average increase in out-of-sample performance is 2% per annum. This is particularly valuable during periods of economic crisis, when returns are more likely to exhibit skewness, where performance increases by an average of 4%. Keywords: Performance measurement, hedge funds, return skewness, performance persistence. JEL Classification: G10, G19, G20. 1

3 1. Introduction About 90% of hedge funds in the TASS database exhibit significant positive or negative skewness during the 1994 to 2009 period. Skewed fund returns can arise from managerialspecific skill such as superior security selection, dynamic use of leverage, or efficient risk management. Alternatively, systematic factors such as option-like positions on the market can skew hedge fund returns. 1 Skewed fund returns are also more likely to appear during periods of financial crisis since fund managers may exhibit a greater propensity to employ relatively more sophisticated investment and risk management strategies during those periods. 2 Furthermore, there is a known investor preference for positively skewed returns. 3 In this paper we test two hypotheses which follow from these observations. First, subsequent flows into and out of hedge funds should be a function of the historical skewness of specific fund returns. Second, incorporating skewness into the evaluation of the historical performance of the universe of hedge funds should lead to superior ex-ante fund selection. Investors who can choose between two assets that have identical means and standard deviations but different skewness levels will bid up the price of the asset that has positive skewness relative to the price of the asset that has negative skewness. This premium makes it more difficult for managers of funds who earn positively skewed returns to earn the same magnitude of returns as managers of negatively skewed funds. 1 See, for example, Fung and Hsieh (2001), Mitchell and Pulvino (2001) and Kosowski et al. (2007). 2 Jylhä et al. (2014) highlight the changing dynamics of hedge fund strategies in crisis periods. While in normal market conditions funds supply liquidity to the stock market, during these periods of market stress they demand liquidity. 3 See, for example, Markowitz (1952), Arrow (1971) and Kraus and Litzenberger (1976) for a theoretical justification. Studies of both mutual funds (Levy and Sarnat (1972)) and portfolio choice (Polkovnichenko (2005), Harvey and Siddique (2000)) provide empirical evidence that investors exhibit a preference for positive skewness. In other related work, Barberis and Huang (2008) show that investors may also exhibit a preference for positive idiosyncratic skewness. 2

4 We first show that flows into and out of the funds in the TASS database reflect investor preferences for more positively skewed funds. Specifically, the difference in flows between funds that show positive and negative historical skewness is a statistically significant 11.5% per annum. While both Agarwal et al. (2009) and Fung et al. (2008) study hedge fund capital flows they do not consider skewness. To our knowledge, this is the first evidence in the literature showing the skewness-hedge fund flow relationship. We next show that portfolio allocation decisions based on historical performance in the face of traditional risk factors generate significant positive alphas over the entire sample period, that are a combination of larger alphas during non-crisis periods and significant negative alphas during times of crisis. An alternative decision rule that allocates capital to hedge funds based on return measures that also incorporate skewness is then shown to improve future performance relative to the traditional measure that is more limited in scope. Specifically, during the 1994 to 2009 period, the average annual increase in out-of-sample performance from using a skewness consistent metric is 2%. 5 Furthermore, we find that the improvement in overall return is attributable to less negative returns during periods of economic crisis, which is when skewness should be most important. In these periods performance improves in excess of 4% per annum by allocating based on a historical return measure that allows for skewness relative to a return measure that ignores it. In doing so, we build upon related research which developed methods other than OLS to provide better estimates of hedge fund performance. 6 For example, Kosowski et al. (2007) and Avramov et al. (2011) use a Bayesian approach and demonstrate that forward looking portfolios 5 We compare skewness consistent and standard alpha estimates using both Fung and Hsieh (2004) and Agarwal and Naik (2004) factor model specifications and obtain qualitatively similar results. 6 Our performance measurement framework is also motivated by the findings in studies such as Chan and Lakonishok (1992), Barber and Lyon (1997), Knez and Ready (1997), and Dell'Aquila et al. (2003), which show that estimating financial models using methods that explicitly control for distributional deviations from normality can significantly improve the accuracy of the empirical results. 3

5 formed using their more precise estimates of historical alpha outperform standard alpha portfolios by a considerable margin. Similarly, Buraschi et al. (2014) focus on second moment information, finding large differences in skill estimates when corrected for hedge fund endogenous risk taking, and improved out-of-sample performance. Jagannathan et al. (2010) use weighted least squares to reduce measurement errors in estimated alphas and develop a GMM model to assess the persistence of managerial over- or under-performance. They find significant relative performance persistence for the top hedge funds but their model loses predictive power when economic conditions are adverse for the hedge fund industry. The hedge fund literature acknowledges that fund returns exhibit skewness and kurtosis, (e.g., Gupta and Liang (2005), Agarwal et al. (2009), Liang and Park (2010), Agarwal et al. (2013)), but evidence on the impact of higher moments on performance has been mixed. Specifically, Agarwal et al. (2009) find dispersion in performance when hedge funds are sorted on exposure to higher moments, but Bali et al. (2012) show that skewness and kurtosis in individual hedge funds returns do not have predictive power. Our evidence supports Agarwal et al. (2009) but differs in several ways (in addition to our new evidence on the skewness-fund flows relationship). We use a measure of performance that reflects both skewness and traditional risk factors when analyzing fund returns and use skewness-consistent metrics in subsequent portfolio allocation decisions. We also perform a series of robustness tests to show that the improvement is due to the inclusion of skewness in the assessment of hedge fund performance rather than to idiosyncrasies in the administrative nature of hedge funds. Recent studies have developed improved performance measures that explicitly account for non-normality in hedge fund returns. In particular, Gupta and Liang (2005) document evidence of non-normality in hedge fund returns and propose value-at-risk type risk measures to 4

6 account for this non-normality. Further, Liang and Park (2010) show that risk measures that account for potential non-normality in hedge fund returns are better able to predict hedge fund failure. 7 Agarwal et al. (2015) look at both the returns and portfolio holdings of hedge funds and find that tail risk, measured as a function of negative co-skewness, is important in explaining the future cross section of hedge fund returns. Our study compliments Agarwal et al. (2015) as we are interested in both positive and negative skewness and how it affects future hedge fund flows and performance. While not focusing on hedge funds, Kadan and Liu (2014) demonstrate the importance of including higher moment information when evaluating the performance of private equity, mutual funds and momentum strategies We extend this line of research and show that hedge fund performance evaluation can be improved considerably if information about return skewness is explicitly taken into account. In summary, our results provide the first link between the funds flow decisions of investors and historical skewness in fund returns. We then demonstrate that a decision rule incorporating skewness into historical performance measurement for future capital allocation purposes is rewarded by superior risk adjusted performance, especially during times of economic crisis. Together our findings provide strong new evidence on the importance of past skewness in predicting future flows and performance persistence for hedge funds. The remainder of the paper is organized as follows. Section 2 describes the data and demonstrates that most hedge fund returns in the Lipper/TASS database exhibit skewness while Section 3 documents the significant difference in flows into funds whose historical returns are positively skewed and out of funds whose historical returns are negatively skewed. Section 4 7 While Kadan and Liu (2014) do not focus on hedge funds and take a very different methodological approach, ranking funds based upon two riskiness measures incorporating higher moment information (Aumann and Serrano (2008) and Foster and Hart (2009)), they have similar findings. Portfolios formed on active equity mutual funds with a higher ranking based on their measure exhibit outperformance and lower tail risk out-of-sample. 5

7 compares traditional and skewness-sensitive performance persistence overall and during periods of market crisis. Section 5 covers robustness tests while Section 6 concludes. 2. Hedge fund data, summary return statistics and skewness tests 2.1 Hedge fund data We evaluate hedge funds using monthly net-of-fee returns of live and dead funds in the Lipper/TASS database. Our sample runs from January 1994 to September This period includes several extreme market conditions, including the LTCM collapse in 1998, the dot-com crash in 2000 and 2001 and the sub-prime and credit crises in 2007 and As of the final quarter of 2009, the TASS database contains 5,897 live and 8,058 dead funds, including funds of funds. Hedge fund returns are self-reported to TASS which may lead to some inaccuracies. 9 In order to minimize the potential for mis-representation, we remove funds with less than two years of returns data, funds that report only gross returns and funds that do not report monthly returns or investment style information. We group funds according to the TASS classifications: Convertible Arbitrage (CA), Event Driven (ED), Equity Market Neutral (EMN), Emerging Markets (EM), Fixed Income Arbitrage (FIA), Fund of Funds (FoF), Global Macro (GM), Long Short Equity Hedge (LSEH), Managed Futures (MF) and Multi Strategy (MS). 10,11 Our final sample consists of 2,237 live 8 TASS does not keep information on funds that died before December 1993, which may lead to survivorship bias so we do not start our sample of fund returns until January See Brown et al. (1999) for a discussion on survivorship bias in hedge fund performance estimates. 9 Recent evidence suggests that in some cases funds may misreport returns to the database vendors (see, for example, Bollen and Pool (2009) and Agarwal et al (2011)). 10 Lipper/TASS do not include Madoff funds in our version of the database, so our results are not driven by the discovery of the Madoff fraud in November We do not report separate results for the Dedicated Short Bias style because there are only 39 of those funds in the sample. However, they are included in the full sample results. 6

8 hedge funds and 3,876 dead hedge funds. We also report results for 1,747 live and 2,020 dead funds of funds. 2.2 Summary return and skewness statistics Table 1 contains summary return statistics for the funds in our sample. The table lists the number of funds and the equal-weighted cross sectional mean of each fund s mean monthly return, standard deviation, Sharpe ratio, skewness, and kurtosis. Altogether, ninety-two percent of the funds can be classified as having significantly negatively- or positively-skewed returns. Funds are further categorized into the following six segments based on the significance level of their sample skewness t-ratio statistics: (i) live negative-skewness (1,251 funds), (ii) live noskewness (172 funds), (iii) live positive-skewness (814 funds), (iv) dead negative-skewness (1,979 funds), (v) dead no-skewness (446 funds), and (vi) dead positive-skewness (1,451 funds). Among the various fund groups, Convertible Arbitrage, Event Driven, Equity Market Neutral, Emerging Markets, Fixed Income Arbitrage and Multi-Strategy funds have more negative-skewness than positive-skewness while Long Short Equity Hedge and Global Macro funds are more balanced. Further, more Managed Futures funds exhibit positive skewness than exhibit negative skewness. 3. Skewness and fund flows If hedge fund investors have skewness preferences then flows in the industry should respond to this characteristic of hedge fund returns. Following Sirri and Tufano (1998), we first construct the quarterly net flow of capital into each of the funds in our sample as (1) 7

9 where are the flows for a fund i in quarter q, expressed as a percentage of prior period Assets Under Management (AUM), is the AUM of fund i in quarter q, and is the return of fund i in quarter q. Following Fung et al. (2008), each quarter we winsorize the quarterly flows across all funds at the 1st and 99th percentile to reduce the effect of outliers. Summary statistics on overall and annual for hedge funds with positively and negatively skewed 24-month prior returns are reported in Table 2. Next we rank funds at the beginning of each year on skewness t-statistics computed using the prior 24 months of returns and divide the funds into quintiles. The top (bottom) skewness funds are categorized as the positive-skewness (negative-skewness) group. We then compare the capital inflows and outflows for these fund groups each year and over the full sample to see how investors skewness preferences relate to actual investment flows. Figure 1 confirms that there is indeed a dramatic difference in the cumulative flows into positive-skewness funds and out of negative skewness funds. These cumulative flows are calculated by compounding the out of sample, equally weighted average flow observations for each group of hedge funds. By September of 2009 the cumulative flow into positive-skewness funds is 399%, whereas the cumulative flow into negative-skewness funds is 0%. Table 3 reports the equally weighted average annual flow into positive-skewness and negative-skewness fund groups in the year following their classification. On average, positiveskewness funds generate a statistically significant inflow of 11.5% per annum in the year following classification while the flow into negative-skewness funds is not statistically different from zero. There are also important differences between the two groups in individual years. Table 3 shows that positive-skewness funds experienced statistically significant inflows in every year except 1996 and Negative skewness funds suffered outflows following LTCM in 8

10 1999, and again beginning in 2005, before accelerating with the onset of the sub-prime crisis in 2007 and the consequent global financial crisis in 2008 and Comparing flows between both groups of funds, flows into positive skewness funds were greater than those to negative skewness funds in twelve of fourteen years and the difference is statistically significant at the 10% level in eleven of those years. To ensure that these flows are not due to return chasing behavior such as that documented for beta-only funds by Fung et al. (2008), we estimate the following regression model (2) where,, is the quarterly flow measure for funds classified in group g for quarter q expressed as a percentage of end-of-previous quarter AUM, and is the return of funds in group g for quarter q -1. As before funds are classified each year into two groups, positiveskewness funds and negative-skewness funds, based on their previous 24 monthly returns. The results reported in Table 4 are for the full sample, (Panel A), for the eight quarters following the three structural breaks previously identified (LTCM, the Dotcom crash and the onset of the sub-prime crisis), (Panel B) and for quarters representing more benign market conditions (Panel C). 12 For all three samples investors in positive-skewness funds are influenced by past flows but not by past performance, (the coefficient on lagged returns is not statistically significant). Flows into negative-skewness funds do exhibit return chasing behavior, however. These results affirm our conclusion that flows into investment vehicles that have demonstrated positively skewed returns are due to investor preferences for that skewness. 12 In total the structural break flows period represents twenty two quarters as there is overlap between LTCM and the Dotcom crash. 9

11 4. Skewness in fund returns and performance persistence 4.1 Traditional hedge fund performance measurement The skill of hedge fund managers is typically measured by the alpha coefficient in a regression where the independent variables were benchmark factors chosen to capture the systematic risk in hedge fund strategies and the coefficients are estimated without considering the distribution of the errors. Given the variety of strategies used by hedge fund managers, it is quite difficult to choose factors that can accurately characterize the return generating process across the universe of hedge funds. We focus on two factor models that have been shown to perform particularly well in characterizing hedge fund returns: Fung and Hsieh (2004) and Agarwal and Naik (2004). The general equation we estimate to compute a manager s risk-adjusted performance is:, (3) where r is the net-of-fees excess return on hedge fund i at time t, α is the estimated abnormal performance of the hedge fund, is the estimated factor loading of hedge fund i on risk factor k, F, is the return of factor k in month t, and ε is the estimated residual. The Fung and Hsieh (2004) model specifies three trend-following risk factors, including Bond (PTFSBD), Currency (PTFSFX) and Commodity (PTFSCOM). This set is augmented by the following two equityoriented risk factors: SNPRF, i.e., the excess total return on the Standard & Poor s 500 index, and SCMLC, i.e., the size spread factor (Wilshire Small Cap 1750 Wilshire Large Cap 750 monthly total return). The model also contains two bond-oriented risk factors: BD10RET, the monthly change in the 10-year treasury constant maturity yield (month end-to-month end), and 10

12 BAAMTSY, which is a credit spread factor (the monthly change in the Moody s Baa yield less 10-year treasury constant maturity yield (month end-to-month end)). 14 Rather than propose a single factor model for all hedge funds, Agarwal and Naik (2004) use a stepwise regression procedure to identify different combinations of market benchmarks and option-based factors. The option-based factors are constructed from European call and put options on the S&P500 composite index and are designed to capture the payoff from a range of hedge fund trading strategies. When we estimate the Agarwal and Naik (2004) model, we replace the three Fung and Hsieh (2004) trend-following factors in (3) with the Agarwal and Naik (2004) at-the-money call and put option-based factors. Table 5, Panel A contains summary statistics for the Fung and Hsieh (2004) and Agarwal and Naik (2004) factors we use to benchmark hedge fund returns. 15 The average excess returns of three of the factors (BD10RET, PTFSBD and PTFSCOM) are negative. SNPRF, the excess total return of the Standard & Poor s 500 index, has the highest Sharpe ratio (= 0.09). This value is less than the Sharpe ratios for all of the All Funds categories in Table 1, except for dead negative-skewness funds that have an average Sharpe ratio of only Overall, all but one of the six combinations of live and dead funds and negative, non-skewed, and positive skewness categories have better risk-adjusted performance than the risk factors chosen to measure that performance. Table 5, Panel B presents the correlation matrix for the various risk factors used in the analysis. These factors are only weakly correlated, with two exceptions. The two bond related 14 See Fung and Hsieh (2001) for details on the construction of the trend following factors. 15 We are grateful to Vikas Agarwal for providing the Agarwal and Naik (2004) option-based factor data. The PTFSBD, PTFSFX and PTFSCOM return series are obtained from David Hsieh s data library. The data to construct BD10RET and BAAMTSY come from the US Federal Reserve website. SNPRF and SCMLC are obtained from Data Stream. 11

13 factors have a correlation of 0.40, while the call and put option factors have correlations of 0.82 and 0.88 relative to the underlying equity index. 4.2 Allocating capital to hedge funds based on historical Fung and Hsieh (2004) and Agarwal and Naik (2004) alphas We measure the returns earned by investors who evaluate the performance of hedge fund managers based on Fung and Hsieh (2004) and Agarwal and Naik (2004) risk factors and then use that information in subsequent portfolio allocation decisions in Table 6, Panels A and B. Specifically, hedge funds, excluding Fund of Funds, are sorted on January 1 each year from 1996 to 2009 into decile portfolios based on their OLS alphas estimated over the previous twenty-four months. The Table reports the results of the rolling top decile portfolio based on annual resorting. Over the entire sample period the top historical alpha decile portfolio earns a significant positive alpha with respect to both Fung and Hsieh (2004) and Agarwal and Naik (2004) risk factors. The picture changes dramatically when we segment the sample into crisis and non-crisis periods, however. 16 It is evident that the overall return is formed by a combination of positive, significant alphas during normal market conditions and negative significant alphas during times of crisis. 4.3 Portfolio allocation decisions incorporating skewness in returns Given earlier evidence that most of the funds in our database exhibit significant skewness and that investors allocate capital from funds with negatively skewed returns into funds that earn positively skewed returns, we now seek to determine whether investors portfolio allocation decisions can be improved by including skewness in historical return measures. Our approach is 16 Crisis and non-crisis periods are classified following Billio et al (2011). 12

14 inspired by the well-established robust statistics literature (summarized most recently in Huber and Ronchetti (2009)), which demonstrates that the classical regression model s assumption of normally distributed error terms is inefficient when the underlying error distributions exhibit skewness. 17 We are also motivated by studies (see, for example, Chan and Lakonishok (1992), Barber and Lyon (1997), Knez and Ready (1997), and Dell'Aquila et al. (2003)), which show that controlling for distributional deviations from normality can significantly improve the accuracy of empirical results. Several estimators are available to provide efficient estimates when data are not drawn from a normal distribution. 18 We choose the residual augmented least squares (RALS) method of Im and Schmidt (2008) to account for skewness in individual hedge fund returns because it is an extension of OLS and it is relatively easy to implement using two-stage least squares. The RALS estimator is closely related to the GMM estimator (Hansen (1982)) because it is asymptotically equivalent to GMM (Im and Schmidt (2008)). It augments the linear factor model used for alpha estimation with two new factors that are functions of the OLS residuals derived from that factor model. These new factors reflect the skewness and kurtosis in fund returns and account for the presence of both idiosyncratic and systematic sources of non-normality Goetzmann et al. (2007) provide another rationale for our work. They show that performance measures estimated using standard statistical techniques inappropriately are at risk of manipulation by managers and cite hedge funds as a specific example of investments whose returns can deviate substantially from normality (p. 1505). 18 This set includes the M-estimators, the L-estimators, and the R-estimators. M-estimators are based on a generalized form of maximum likelihood estimation (Huber (1973)), the L-estimator class of models (e.g., the LAD estimator proposed by Bassett and Koenker (1978)) are based on linear combinations of order statistics, and the R- estimators are derived from rank tests. In addition, there are a number of variations within each of these classes. For example, Phillips et al. (1996) and Phillips and McFarland (1997) specify FM-LAD, a non-stationary form of the LAD regression procedure (Phillips (1995)) to model the relation between daily forward exchange rates and future daily spot prices. 19 Previous studies in finance have used RALS estimators but not in the context of performance measurement. For example, a test statistic based on RALS has been used to test for speculative bubbles in stock prices (Taylor and Peel (1998), Sarno and Taylor (1999)) and house prices (Garino and Sarno (2004)). In addition, Gallagher and Taylor (2000) use RALS to estimate the temporary and permanent component of stock prices. 13

15 Following Taylor and Peel (1998), Sarno and Taylor (1999), Gallagher and Taylor (2000) and Garino and Sarno (2004), we use a three-step procedure to estimate a fund s skewness sensitive historical performance. First, using OLS and the twenty-four previous months of return data for the fund, we estimate each of the hedge fund factor models for each available fund. Next, we create the RALS function using each fund s OLS residual. This function consists of two terms: (i), which relates to skewness, and (ii) 3, which relates to kurtosis. Here, is the OLS residual at time t, is the residual skewness, and is the OLS residual variance. Assuming 0, we then estimate the linear factor model augmented with and 3 (Taylor and Peel (1998), Sarno and Taylor (1999), Gallagher and Taylor (2000) and Garino and Sarno (2004) use an identical specification ). 20 The two new regressors essentially act as additional risk factors and are functions of the 3 rd and 4 th moments of the first-stage residuals constructed under the assumption that they are independent of the initial factors used to account for risk Finally, we estimate the risk factor model augmented with the RALS regressors for each fund to generate alpha estimates that are consistent in the presence of skewness in historical hedge fund returns. 23 Table 7, Panels A and B, summarizes the performance of the rolling top decile hedge fund portfolio when annual capital allocation decisions are based on skewness-consistent alphas estimated over the previous twenty-four months. As in Table 6, full sample alphas are significant and positive for both the Fung and Hsieh (2004) and Agarwal and Naik (2004) risk factors. In 20 If the RALS coefficient is invariant to skewness but will still be estimated more precisely than OLS (Im and Schmidt (2008)). 21 See Wooldridge (1993) for a discussion on the statistical improvement that can be obtained by adding orthogonal regressors to an estimation equation. 22 To demonstrate the results are robust to the assumption that the RALS residual functions are independent of the risk factors we repeat all the analyses in the paper for the subset of funds, which we are able to identify ex post as satisfying this assumption. The results, available from the authors, are stronger than those presented in the paper. It is not possible to identify these funds ex ante, however, and doing so ex post introduces look-ahead bias. 23 Please see the Appendix for a more detailed description of the statistical properties of the RALS estimator. 14

16 addition, alphas estimated during non-crisis periods are positive, significant and larger than the full sample alphas. Crisis period results are quite different across the two tables, however, in that the skewness-consistent alphas during crisis periods are still negative, but are much smaller than OLS alphas during the same crisis periods and are statistically insignificant. This suggests that ex-ante portfolio allocation decisions made on the basis of skewness-consistent alphas will provide superior overall performance for hedge fund investors. 4.5 Overall performance comparisons Table 8 reports the characteristics of both the skewness-consistent and OLS sorted top decile portfolios as well as the S&P500 using both Fung and Hsieh (2004) and Agarwal and Naik (2004) factor models. There are large differences in the performance estimates. When we consider the Fung and Hsieh (2004) risk factors the mean annual returns for the top-decile skewness-consistent and OLS alpha sorted portfolios are 12.9% and 11.6%, respectively, while the standard deviations are 11.6% and 13.2%, respectively. Consequently, the Sharpe ratio of the portfolio allocation is based on an alpha that allows for skewness in returns is larger (= 0.83) versus 0.63 for the OLS alpha portfolio and 0.25 for the S&P We also report the Goetzmann et al. (2007) manipulation-proof performance measures (MPPM 3 and MPPM 4 ) for each portfolio and find that they are both larger for the top-decile portfolio based on skewness consistent returns than for the top-decile OLS portfolio or for the S&P Direct performance comparisons of portfolio allocation strategies based on OLS and skewness consistent historical alphas 24 We follow Billio et al. (2011) and define crises periods as Asian (June January 1998), Russian and LTCM (August October 1998), Brazilian (January February 1999), Internet Crash (March May 2000), Argentinean (October December 2000), September 11, 2001, drying up of merger activities, increase in defaults, and WorldCom accounting problems (June October 2002), the 2007 subprime mortgage crisis (August January 2008), and the 2008 Global financial crisis (September November 2008). 15

17 We next compare the ex-post performance of the rolling top decile portfolio based on OLS and skewness consistent alphas directly in Table 9. Turning first to the top entry of each half of the table, using annual re-sorting based on performance over the previous 24 months the mean full-sample return of the top decile skewness-corrected portfolio exceeds the mean fullsample return of the top decile OLS portfolio by a statistically significant 1.23% per year with Fung and Hsieh (2004) risk factors and 2.48% per year with Agarwal and Naik (2004) risk factors. Cumulative returns for the January 1996 to September 2009 period for the skewnessconsistent and OLS top decile portfolios are displayed in Figure 2. Panels A and B report results for the Fung and Hsieh (2004) and Agarwal and Naik (2004) factor models, respectively. Cumulative total returns on the S&P500 are also included for comparison. Both hedge fund portfolio returns are high during our sample period and they track each other quite closely. Interestingly, divergences occur in late 1998, in early 2000, and, most strikingly, during 2007 and These are all well-known as periods of financial crisis and return volatility. 25 Given that economic crises are likely to be accompanied by increases in positively and negatively skewed returns an alpha estimator that allows for skewness and kurtosis in returns should perform particularly well in times of financial upheaval. To examine this possibility, we again split the estimation period into non-crisis and crisis periods in the middle and bottom entries of the panels of Table 9 respectively. As expected, the impact of allowing for fundspecific skewness in returns is more important during crisis periods. In this case, the alpha of a portfolio based on sorting funds by skewness-consistent historical alphas exceeds that of a portfolio based on sorting by OLS historical alphas by 4.4% per year with Fung and Hsieh 25 While the cumulative returns of the OLS and skewness-consistent hedge fund portfolios appear to track each other quite closely until 2007, it is notable that the volatility of the skewness-consistent portfolio is 1.6% lower, and consequently the Sharpe ratio is 3.1% larger. 16

18 (2004) risk factors and 4.63% per year with Agarwal and Naik (2004) risk factors. Both of these alpha differences are significant at the 5% level. 5. Robustness tests of the allocation strategy based on skewness-consistent alphas 5.1 Smoothing and backfill biases In Table 10, we repeat the analysis of Table 9 using the Getmansky et al. (2004) specification to unsmooth hedge fund returns (Panels A and C) and to control for the effects of backfill bias by removing the first twenty-four months of returns for each fund (Panels B and D). These results are almost identical to those reported in Table 9 with the exception that correcting for backfill bias indicates even more superior performance by a portfolio allocation strategy based on skewness-consistent historical alphas during crisis periods. This is evidence that the performance improvement gained by allocating capital to hedge funds based on alphas that are consistent in the presence of skewness in returns is robust to these two well-known statistical concerns. 5.2 Determinants of the spread between OLS and RALS alphas As a final test of our argument that skewness is an important component of hedge fund returns and a superior portfolio allocation strategy for hedge fund investors, we estimate fullsample cross sectional regressions to identify the determinants of the alpha spread. Specifically, we investigate whether skewness, kurtosis, or operational variables are the source of the alpha spread for a given fund. The first model we consider is:, (4) where 17

19 = the intercept of the skewness-consistent estimated time-series regression of fund i s returns against the Fung and Hsieh (2004) benchmark factors, and = the intercept of the OLS estimated time-series regression of fund i s returns against the Fung and Hsieh (2004) benchmark factors. Skew and kurt are the skewness and kurtosis estimates for fund i scaled by their standard errors to correct for outliers. We estimate skew and kurt using all available returns for each fund. The length of each fund return series varies from twenty four months to one hundred and ninety two months. Aragon (2007) demonstrates that six operational variables explain hedge fund performance: dlock, notice, min, notice 2, min 2 and dlock.notice. The variables dlock, notice, and min correspond to the lockup indicator, redemption notice period (in 30-day units), and minimum investment size (in millions of dollars). The variables notice 2 and min 2 allow for nonlinearity in the redemption and minimum investment relationships, while dlock.notice allows for interaction between the lockup and notice period restrictions. The extended regression model that considers all these determinants of the alpha spread is given by:, (5) where the vector C ji includes the set of operational variables from Aragon (2007). We expect that the skewness variable will be a strong determinant of the difference in alphas. The regression estimates using equations (4) and (5) are reported in Table 11. We first show the intercept (i.e. ) for live (Panel A) and dead (Panel B) negative- and positive- 18

20 skewness funds. 26 We find that the γ term is statistically significant in all four segments. However, adding the skewness and kurtosis variables (i.e., and in equation (7)) explains all of this error. The term is no longer significant, while and coefficient estimates are always significant. Next we add the administrative control variables and find that these variables are seldom significant, while both the skewness and kurtosis variables remain significant and explain most of the spread in alphas. 6. Summary and conclusions Prior theoretical and empirical evidence indicates that investors have a preference for positively skewed returns. The returns of most hedge funds in the TASS/Lipper database from 1994 to 2009 exhibit significant skewness. We link these two observations by showing that flows into and out of the funds in the TASS/Lipper database reflect investor preference for more positively skewed funds. Specifically, the difference in flows between funds that show positive and negative historical skewness is a statistically significant 11.5% per annum. To our knowledge, this is the first evidence in the literature showing the skewness-hedge fund flow relationship. We next show that portfolio allocation decisions based on historical performance in the face of traditional risk factors generate significant positive alphas over the entire sample period that are a combination of larger alphas during non-crisis periods and significant negative alphas during times of crisis. An alternative decision rule that allocates capital to hedge funds based on ex-ante return measures that also incorporate skewness is then shown to improve out-of-sample performance relative to the traditional measure that is more limited in scope. Furthermore, the 26 This error is not significantly different from zero for non-skewed fund returns. To save space we do not report the results for these funds here but they are available upon request. 19

21 improvement in overall return is attributable to less negative returns during periods of economic crisis, which is when skewness should be most evident. In these periods, performance improves in excess of 4% per annum by allocating based on a historical return measure that is consistent in the presence of skewness relative to a historical return measure that ignores it. We also perform a series of robustness tests to show that the improvement is due to the inclusion of skewness in the assessment of hedge fund performance rather than to idiosyncrasies in the administrative nature of hedge funds. In summary, our results first link the funds flow decisions of investors directly to historical skewness in fund returns. We then demonstrate that a decision rule incorporating skewness into historical performance measurement for future capital allocation purposes would have been rewarded by risk adjusted performance, especially during times of economic crisis. Together our findings provide strong new evidence on the importance of past skewness in predicting future hedge fund flows and performance. 20

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27 APPENDIX A: RALS methodology We start with a multivariate linear regression model (6) where: z t = (1, x t ), x t = a (k 1) x 1 vector of time series observed at time t, and = ( ) where is the intercept and is the (k 1) x 1 vector of coefficients on x t. Assume the following moment conditions hold: 0 (7) E x h y x'β H 0 (8) where (9) is the least squares moment condition, which asserts that x t and u t are uncorrelated, and (10) specifies the additional moment condition that some function of u t is uncorrelated with x t. h(.) is a J x 1 vector of differentiable functions and H is a J x 1 vector of constants. Therefore, there are k x J additional moment conditions. Skewness in the residual means the standardized third central moment is non-zero, so that: 0 (9) which implies that u 2 t σ 2 is correlated with u t but not with the regressors (since x t and u t are independent by assumption). Similarly, when the standardized fourth central moment of the series exceeds three the residuals exhibit excess kurtosis (10) 26

28 which implies that u t 3 3σ 2 u t is correlated with u t but not with the regressors (again, since x t and u t are assumed to be independent.) Im and Schmidt (2008) suggest a simple two stage estimator that can be estimated by the OLS model in equation (8) augmented with (13). 3 (11) where denotes the residual and denotes the standard residual variance estimate obtained from OLS applied to equation (8). The resulting estimator is the RALS estimator of, When both the dependent and independent variables are stationary, has an asymptotic distribution given by T β* β N 0, σ Var x (12) Im and Schmidt (2008) derive ρ*, a measure of the asymptotic efficiency gain from employing RALS as opposed to OLS. ρ* is constructed as (1 /σ 2 ), where σ 2 is the asymptotic variance of the OLS estimation of and σ is the asymptotic variance of the RALS estimator:, (13) where μ denotes the i-th central moment of u. The inclusion of the RALS terms that are functions of the first-stage OLS residuals generates a more efficient model estimate if the distribution of the OLS error term is non-normal. For normally distributed first-stage errors, OLS is efficient and the ratio equals one. can be estimated consistently by replacing the with the corresponding sample moments using OLS residuals, yielding. The covariance matrix for * can then be estimated consistently as 27