INVESTING IN HEDGE FUNDS WHEN THE FUND S CHARACTERISTICS ARE EXPLOITABLE JUHA JOENVÄÄRÄ AND HANNU KAHRA

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1 INVESTING IN HEDGE FUNDS WHEN THE FUND S CHARACTERISTICS ARE EXPLOITABLE JUHA JOENVÄÄRÄ AND HANNU KAHRA Centre for Hedge Fund Research, Risk Management Laboratory Imperial College Business School Working Paper 08 Date: 6/2010

2 Investing in hedge funds when the fund s characteristics are exploitable Juha Joenväärä and Hannu Kahra y University of Oulu First version March 2009, this version February 2010 Abstract In this paper we form hedge fund investment strategies that exploit optimally fund characteristics using the Brandt, Santa-Clara, and Valkanov (2009) approach. We exploit economically well motived fund characteristics based on managerial incentives, share restrictions, and the fund size. The optimal portfolio weight of a speci c hedge fund can be seen as a ranking between funds. The results suggest that small funds with high managerial incentives and long notice periods obtain the highest rankings. Our ndings suggest that the proposed characteristics-based strategy delivers significant outperformance for a real-time investor. The results are robust across a wide range of performance measures even after controlling for underlying redemption and subscription impediments associated with investment decisions. JEL Classi cations: G11, G12, G14, C31. Keywords: hedge fund performance, portfolio optimization, fund s characteristics, share restrictions, managerial incentives y We thank Robert Kosowski, Antti Petajisto, Markku Rahiala, and seminar participants at the Pohjola Asset Management, 22nd Australasian Finance and Banking Conference 2009, University of Oulu for helpful comments and suggestions. Both authors are grateful nancial support from OP-Pohjola Group Research Foundation. Corresponding author: Juha Joenväärä, University of Oulu, Department of Finance. juha.joenvaara@oulu.. Hannu A. Kahra, University of Oulu, Department of Finance. hannu.kahra@oulu.. 1

3 1 Introduction The aim of the paper is to form optimal investment strategy based on hedge fund characteristics. We form optimal hedge fund portfolio strategies using the Brandt, Santa-Clara, and Valkanov (2009) approach. We parameterize portfolio weights as a function of the fund s characteristics based on managerial incentives, share restrictions and the fund s size. Brandt, Santa-Clara, and Valkanov (2009), instead, optimize a large portfolio of equities by exploiting the well-known value, momentum and size e ects. Their empirical results suggest that the approach delivers superior performance for a real time investor who invests in equities. Hence, it is interesting to examine whether the Brandt, Santa-Clara, and Valkanov (2009) approach can be successfully applied in forming real time hedge fund investment strategies. Investing in hedge funds di ers fundamentally from investing in equities. A typical fund of hedge funds portfolio includes hedge funds, while a well-diversi ed equity portfolio may contain thousands of stocks. In addition, hedge funds impose share restrictions on investors redemptions, and it is not possible to sale short funds. Therefore, we rank funds based on their optimal portfolio weight, and we then evaluate the performance of portfolios formed using these rankings. We argue that the Brandt, Santa-Clara, and Valkanov (2009) approach is particularly well-suited for constructing hedge fund investment strategies. First, the approach provides several conceptual advantages that are especially favorable in case of hedge funds. Given the large cross-section of hedge funds relatively short histories, it is extremely di cult to model the joint distribution of hedge fund returns and characteristics. By focusing directly on portfolio weights, one avoids the estimation errors in the rst and second moments of returns, which are well-known problems in the traditional mean-variance approach. 1 Hence, we obtain a robust investment strategy that is not based on erroneously estimated funds expected returns, variances and covariances, but solely on funds characteristics that are related to funds future return distributions. The approach also inherently accommodates 1 Brandt (2004) provides a comprehensive survey that discusses the role of estimation error in the context of the Markowitz (1952) approach, while Brandt (1999), Aït-Sahalia and Brandt (2001), and Brandt and Santa-Clara (2006) propose approaches that focus directly on optimal portfolio weights. 2

4 a varying number of hedge funds through time. This implies that optimal portfolios also contain information about hedge funds that are liquidated, merged or closed. Therefore, we obtain portfolio weights that are relatively free from survivorship bias. Finally, the results of Carlappi, DeMiguel, and Uppal (2007) suggest that when the number of assets is large, which is exactly the case with hedge funds, information contained in cross-sectional characteristics plays a major role in delivering superior performance. Second, hedge funds are characterized by unique characteristics that are related to the cross-sectional variation of hedge fund risk-adjusted returns. These characteristics provide important implications to investors, since they may alleviate investors in making allocations to hedge funds. Related to this line of research, our paper takes the rst attempt to examine whether hedge funds characteristics can be employed in forming optimal hedge fund portfolio strategies or rankings. In particular, three speci c fund characteristics, based on economic phenomena, arise from prior literature. Consistent with agency theory, Agarwal, Daniel, and Naik (2009) nd that hedge funds with higher managerial incentives tend to deliver superior performance. Aragon (2007) nds that hedge funds with severe share restrictions characterized by longer lockup, notice and redemption periods are able to earn an illiquidity premium. Teo (2009) provides robust evidence that there is a negative and convex relation between fund size and future alphas. Hence, consistently with Berk and Green (2004), hedge fund performance su ers once the funds grow beyond a certain optimal size. 2 In our empirical application, we evaluate hedge fund performance by forming optimal portfolio strategies using parameterization based on (i) managerial incentives measured by the manager s option delta, (ii) the length of the notice period, and (iii) the fund s size. 3 Given that the proposed strategy exploits the information contained in the funds characteristics to predict hedge fund performance, we term the strategy characteristics-based. We motivate the use of these three characteristics by their association with economic phenomena and robust empirical evidence. This indicates that the relationships between the fund 2 Fung, Hsieh, Naik, and Ramadorai (2008) and Boyson (2008) test the implications of the Berk and Green (2004) model in the context of the hedge fund industry. 3 Agarwal, Daniel, and Naik (2009) propose the use of hedge fund manager s delta to measure the fund s managerial incentives. 3

5 characteristics and performance may not be an artifact in the data. This paper adds to the existing literature on hedge fund performance evaluation by examining a hedge fund portfolio strategy that uses information contained in the fund s characteristics. Our ndings suggest that it is optimal for hedge fund investors to invest in smaller funds with higher managerial incentives and longer notice periods. Speci cally, by sorting on past portfolio weights, which can also be interpreted as a ranking among hedge funds, we document an annual Fung-Hsieh (2004) alpha spread between the top and bottom quintiles ranging from 2.7 to 4.0 percent. We test further whether the proposed strategy contains additional information over the naïve strategies that are based on the single sorts based on the t-statistics of the Fung-Hsieh (2004) alpha as well as the fund s characteristics that are used in forming the characteristics-based strategy. We nd that our strategy contains relevant information over these simple strategies. Finally, we nd that by double sorting on the highest ranking based on our strategy and the t-statistics of the alpha, a real time investor is able to earn annually a Fung-Hsieh (2004) alpha of percent over the ve-year out-of-sample period. The performance of the characteristics-based strategy remains economically signi cant, even high, also after controlling for the impact of share restrictions on the performance of the strategy. We tackle this issue by forming a strategy that takes into account each fund s share restrictions, the lockup and notice periods as well as the redemption and subscription frequencies, in such a way that investors are able to apply the proposed strategy in real time. 4 Hence, our ndings provide important implications for hedge fund investors such as pension funds, high-net wealth individuals, and funds-of-hedge funds. We expect that our results provide important advice to hedge fund investors when they allocate wealth to hedge funds and select managers for their portfolios. The rest of the paper is organized as follows. Section 2 motivates the choice of fund s characteristics and discusses the related literature. Section 3 reviews the methodology. In 4 We were unable to control for the impact of suspension clauses on the performance of the characteristicsbased strategy, because the HFR database does not contain any material information on these clauses. However, we expect that this is a minor problem, since hedge funds have applied suspension clauses extremely rarely during our out-of-the sample period. 4

6 Section 4, we present the empirical results. Section 5 gives the conclusion. 2 Fund s characteristics and related literature Academics have made signi cant e orts to examine hedge fund performance and its persistence. Our results are consistent with the recent evidence on the value of active management in the hedge fund industry. Using a robust bootstrap procedure and the Bayesian approach, Kosowski, Naik, and Teo (2007) nd that top hedge fund performance cannot be explained by luck, and hedge fund performance persists at annual horizons. 5 Fung, Hsieh, Naik, and Ramadorai (2008) examine the performance of funds of hedge funds. Their ndings suggest that the subset of funds of funds consistently delivers alpha, but consistently with Berk and Green (2004) these funds experience relatively greater and steadier capital in ows, which decreases their future performance. Jagannathan, Malakhov, and Nokikov (2010) nd significant performance persistence among superior funds even after controlling for various hedge fund database biases. Our results are comparable with Avramov, Kosowski, Naik, and Teo (2010), who form hedge fund portfolio strategies that incorporate predictability in managerial skills, fund risk loadings, and benchmark returns. They nd that the major source of investment pro tability is due to predictability in managerial skills. In our case, predictability in hedge fund returns is due to the fund s characteristics that are related to the hedge fund return distributions. We contribute to existing literature by showing that the characteristics-based strategy delivers alpha even when the role of hedge funds share restrictions are taken into account. We choose the fund s characteristics on the basis of economic phenomena and robust empirical evidence. Three speci c fund characteristics arise, (i) the managerial compensation structure, (ii) share restrictions imposed by the fund manager, and (iii) the fund s assets under management. First, agency theory predicts that hedge funds with better managerial incentives should 5 Their bootstrap procedure is based on Kosowski, Timmermann, Wermers, and White (2006), while the Bayesian approach is proposed by Pástor and Stambaugh (2002). 5

7 deliver superior performance. Several papers propose theoretical models on hedge funds optimal incentive contracts. For example, Goetzmann, Ingersoll, and Ross (2003) provide a closed-form solution to the high-water mark contract under certain conditions. Their results suggest that managers have an incentive to take excess risks, since the value of the manager s contract is increasing in portfolio variance due to the call option-like feature of the incentive contract. On the other hand, because of the long horizon contact, Panageas and Wester eld (2009) nd that even risk-neutral managers will not place unboundedly large weights on the risky assets, despite the option-type features of the contract. Their results suggest that managers will place a constant fraction of assets in a mean-variance e cient portfolio and the rest in the riskless asset, similar to investors with constant relative risk aversion. Pioneering literature such as Ackerman, McEnally, and Ravenscraft (1999), Edwards and Caglayan (2001) and Liang (1999) examine the relation between the incentive fee rate and the risk-adjusted performance of hedge funds. Their ndings are mixed. However, the recent study of Agarwal, Daniel, and Naik (2009) argues that all of these papers measure managerial incentives by an incentive fee rate, which does not take into account how far the fund is relative to its high-water mark. Therefore, they propose that managerial incentives can be measured more precisely using the manager s option delta, which represents the expected dollar increase in the manager s compensation for one percent increase in the fund s netasset-value. Their ndings suggest that funds with higher delta deliver superior performance. Hence, we also opt to measure managerial incentives using manager s option delta. Second, the asset pricing theory predicts that investing in illiquid asset should be associated with illiquidity premium. 6 In case of hedge funds, the ndings of Aragon (2007) suggest that funds with stringent share restrictions in the form of longer lockup, notice and redemption periods, are capable of earning illiquidity premium. Joenväärä and Tolonen (2008), however, nd that the notice period, not the lockup period, is associated with investing in illiquid assets. Indeed, their ndings suggest that the notice period is the most important share restriction variable related to illiquidity premium. Furthermore, they argue that the 6 Amihud, Mendelson, and Pedersen (2006) provide a comprehensive survey that discusses the role of liquidity in the context of the asset pricing theory. 6

8 notice period is the only share restriction variable that provides speci c information concerning the timing and the amount of investors redemptions, indicating that funds with longer notice periods can manage their illiquid assets e ectively. Therefore, we opt to measure the level of share restrictions using the length of notice period. Finally, there are several papers including Liang (1999), Agarwal, Daniel, and Naik (2005) and Getmansky (2004), which touch on the relation between hedge fund size and future performance. Teo (2009) focuses solely on this issue by showing that the relation between the fund size and future alphas is negative and convex. This is consistent with the theoretical model proposed by Berk and Green (2004). The model predicts that performance su ers once the fund grows beyond a certain threshold. Taken together, we construct our characteristics-based strategy using the manager s option delta, the notice period and the fund s size as characteristics. We hypothesize that it is optimal to invest in smaller funds with greater managerial incentives and longer notice periods. The paper is also related to other branch of performance evaluation literature that uses additional information in estimating fund performance measures more precisely. Commonly, hedge fund performance is measured using alpha that is the return that cannot be explained by the fund s exposure to the systematic risk factors. Unfortunately, identifying and forecasting alpha is not a trivial task. As Kosowski, Naik, and Teo (2007) point out, there are several explanations why hedge fund performance is so di cult to measure. Hence, standard performance measures based on ordinary-least-squares (OLS) estimation are often measured imprecisely. To measure the fund s performance more accurately, recent studies use information provided by the longer histories of benchmark assets and the other assets that are not contained in the benchmark model. Kosowski, Naik, and Teo (2007) examine the role of prior information in evaluating hedge fund performance by using an approach proposed by Pástor and Stambaugh (2002). 7 They estimate hedge fund alphas by using information contained in (the) longer time-series of hedge fund strategy returns. On the other hand, 7 Busse and Irvine (2006) predict mutual fund performance using the Bayesian approach proposed by Pástor and Stambaugh (2002). 7

9 by pooling funds cross-sectionally, the precision of estimates increases especially when the fund s performance measure is estimated based on the time-series average of short series of returns. For example, Jones and Shanken (2005) and Huij and Verbeek (2007) incorporate learning across funds to examine mutual fund performance and its short-run persistence. The information contained in the holdings of other funds can also be used to estimate the fund s performance more precisely. Cohen, Coval, and Pástor (2005) judge the mutual fund manager s skill based on the similarities in portfolio holdings and trades with other managers. Their simulation and empirical results support their judgement that the mutual fund manager s skill can be estimated more precisely using information contained in other managers holdings. Cremers and Petajisto (2007) propose a measure that captures the share of portfolio holdings that di ers from the benchmark index. Their ndings suggest that the most active mutual funds outperform their benchmarks even after expenses. Given the secretive nature of the hedge fund industry, funds holdings, especially short positions, are rarely available to investors. Therefore, only very few papers utilize funds holdings. 8 Our paper is closely related to these studies that develop new performance measures that exploit the information contained in the fund holdings or in the returns of other funds. Our study, however, di ers from the previous ones, because we exploit information contained in the hedge fund s characteristics to predict hedge fund performance more precisely. Our paper takes the rst attempt to measure hedge fund performance by applying a statistical estimator that exploits optimally the information content of a large cross-section of hedge funds, instead of only the time-series of hedge fund returns. 3 Methodology This section introduces the characteristics-based investment strategy, which exploits hedge funds characteristics to estimate the optimal portfolio weights or the ranking of funds. The approach is closely related to Brandt, Santa-Clara, and Valkanov (2009), who form optimal 8 Notable exceptions are Gri n and Xu (2008), who evaluate hedge fund performance using their holdings, and Brunnermeier and Nagel (2004), who examine the behavior of hedge funds during the dot-com bubble. 8

10 equity portfolio strategies that exploit the stock s cross-sectional characteristics. Suppose that there are M managers, i = 1; : : : ; M; which share K common characteristics, k = 1; : : : ; K; speci c to each hedge fund. The speci cation of the fund s characteristics must be somewhat arbitrary, but the chosen characteristics have to be associated with hedge fund return distributions and should be based on a speci c economic phenomenon. The data snooping biases may be mitigated by requiring that a speci c fund s characteristic is associated with economic phenomena. Consider the portfolio choice at time t of an investor who maximizes the expected utility of wealth at date t+1. Throughout the paper we use constant relative risk aversion (CRRA) preferences over investor s wealth W : u (W ;t+1 ) = (W t+1) 1 1 ; (1) where is the relative risk aversion coe cient, which is assumed to be equal to three. The rationale behind this decision is based on two facts. Goetzmann, Ingersoll, Spiegel, and Welch (2007) show that standard performance measures such as alpha and Sharpe ratio can be gamed using, for example, time-varying leverage and speci c option strategies. Furthermore, they show that there are conditions under which performance measures cannot be manipulated. Based on the utility independence and the fact that the power utility is an increasing and concave function, these manipulation-proof conditions are valid in the case of power utility function. Finally, Brandt, Santa-Clara, and Valkanov (2009) discuss that power utility preferences nest implicitly higher moments in asset returns, which is especially important in hedge fund portfolio optimization, since it is a well-known fact that hedge fund returns do not follow normal distribution. Let r i;t+1 be a return on hedge fund i from date t to t+1 associated with fund characteristic y i;t observed at date t. Given the CRRA preferences the level of initial wealth does not matter; thus, the investor solves the portfolio weights w i;t that maximize the conditional expected utility of the resulting portfolio s return r p;t+1 : 9

11 max E t [u (r p;t+1 )] = E t "u fw i;t g M t i=1 XM t i=1 w i;t r i;t+1!# : (2) Following Brandt, Santa-Clara, and Valkanov (2009), the optimal weight of hedge fund i at date t is modeled as the weight _ w i;t in the benchmark portfolio plus a linear function of the hedge fund i s characteristics : w i;t = _ w i;t + 1 M t > by i;t ; (3) where is a vector of coe cients to be estimated, and by i;t is a vector of hedge-fund speci c cross-sectionally standardized characteristics with zero mean and unit standard deviation across all funds at date t. Hence, the rst term in (3) corresponds to a constant and it determines the weight in the benchmark portfolio, while the second term optimizes the deviations from the benchmark weights. The term 1=M t is a normalization that allows for an arbitrary and time-varying number of hedge funds. The characteristics are standardized for two reasons. The raw characteristics may be nonstationary by construction, but the cross-sectional distributions of the standardized characteristics are stationary through time. Second, the standardization implies that the crosssectional average of T by i;t is zero, indicating that the deviations of the optimal weights from the benchmark weights sum to zero, and consequently the optimal portfolio weights always sum to one. There are several ways to standardize hedge funds characteristics. The pioneering work of Fung and Hsieh (1997) and Brown and Goetzmann (2003) nds that hedge funds tend to be diverse in their trading strategies, while Brown, Goetzmann, Liang, and Schwarz (2008) and Brown, Fraser, and Liang (2008) discuss the role of the operational risk in the hedge fund industry. We try to clean out systematic behavior due to operational di erences across hedge fund strategies by subtracting the cross-sectional mean of the characteristics of the hedge fund strategy rather than the cross-sectional mean of the hedge fund universe. The standardization is implemented by following the modi ed classi cation proposed by Agar- 10

12 wal, Daniel, and Naik (2009), in which hedge funds are classi ed into ve broad strategies: directional traders, relative value, security selection, managed futures, and multiprocess. In our case, the portfolio weight function is w i;t = _ w i;t + 1 M t ( size log (size i;t ) + delta delta i;t + notice notice i;t ) ; (4) where w _ i;t is the equally-weighted benchmark, size i;t is the size of the hedge fund, delta i;t is the manager s option delta measuring managerial incentives, and notice i;t is the length of the notice period measuring the level of share restrictions imposed by the hedge fund. The rst component of the model captures the idea that a priori all hedge fund managers are expected to perform equally. One can also interpret the results so that the optimized portfolio weights provide a ranking of funds. The ranking of a speci c fund depends on its characteristics relative to other funds. Cohen, Coval, and Pástor (2005) propose a new performance measure that contains information on other mutual funds holdings. Analogously, we use information contained in other hedge funds characteristics by applying a statistical estimator that exploits other funds characteristics optimally. The exibility of the Brandt, Santa-Clara, and Valkanov (2009) approach also allows us to exploit information contained in defunct hedge funds. This implies that we obtain relatively survivorship bias-free portfolio weights or rankings when defunct funds are also included in the sample. The combined dataset of both alive and defunct funds may well contain information that cannot be obtained by using only alive funds. 9 Following Brandt, Santa-Clara, and Valkanov (2009), we assume that the estimated coe cients are constant across hedge funds and through time, indicating that the optimal portfolio weight of each fund is related only to the fund s characteristics but not to the fund s historical returns. In other words, we assume that return distribution is constant over 9 The unreported results suggest that the parameter estimates di er signi cantly when only alive funds are taken into account, indicating more aggressive allocation towards smaller funds, which may be associated with high liquidation probability. 11

13 time, i.e., there is no time varying investment opportunities. This assumption means that all aspects of the joint distribution of returns are captured by the fund s characteristics. Hence, two funds with similar characteristics should obtain weights that are close to each other even if their sample returns are very di erent. Consequently, the maximizing the investor s conditional expected utility at date t is essentially equivalent to maximizing the investor s unconditional expected utility for all dates. Hence, one can rewrite the conditional optimization problem (2) with respect to the portfolio weights w i;t using the following unconditional optimization with respect to the coe cients : max E [u (r p;t+1 )] = E " u XM t i=1 _ w i;t + 1 M t > by i;t r i;t+1!# : (5) Thus, rather than estimating one weight for each hedge fund, we estimate weights as a single function of characteristics that applies to all hedge funds. Hence, the portfolio choice problem can be transformed into a statistical estimation problem. The coe cients can be estimated by maximizing the corresponding sample analogue: max 1 XT 1 T t=0 u (r p;t+1 ) = 1 XT 1 u T t=0 = 1 XT 1 u T t=0 XM t i=1 XM t i=1 w i;t r i;t+1! _ w i;t + 1 M t > by i;t r i;t+1! : (6) The formulation is numerically robust and parsimonious, since our estimation procedure consists of only three parameters, 1 ; 2 and 3. The property reduces the risk of in-sample over tting since the coe cients will only deviate from zero if the respective characteristics are able to provide a sensible combination of return and risk consistently across hedge funds and through time. As Brandt, Santa-Clara, and Valkanov (2009) point out, the maximum expected utility estimate ^ satis es the rst-order conditions of the portfolio optimization problem with a linear portfolio weight function indicating that one can interpret it as a method of moment 12

14 estimator such as 1 XT 1 h (r p;t+1 ; y t ; ) = 1 T T t=0 XT 1 u 0 (r p;t+1 ) t=0 1 by t > r i;t+1 = 0: (7) M t Hansen (1982) shows that the asymptotic covariance matrix of this estimator is: AsyV ar [] = 1 T G > V 1 G 1 ; (8) where G 1 T XT (r p;t+1 ; y t ; t=0 = 1 XT 1 u 00 (r p;t+1 ) T t=0 T 1 1 by t > r i;t+1 by t > r i;t+1 ; (9) M t M t and V is the consistent estimator of the covariance matrix (r; y; ) : If one assumes that marginal utilities are uncorrelated, this implies that V can be constituently estimated by 1 XT 1 T t=0 h r p;t+1 ; y t ; ^ ^ T h r p;t+1 ; y t ; : (10) However, this assumption may be unrealistic, because it implies that one has to specify the portfolio weight function without error. To overcome this problem, the covariance matrix V can be estimated using the autocorrelation-adjusted estimator of V proposed by Newey and West (1987). Another alternative is to apply bootstrapping to estimate the covariance matrix of coe cients: Brandt, Santa-Clara, and Valkanov (2009) implement bootstrapping in their empirical application and argue that the advantage of bootstrapping is that it does not rely on asymptotic results and it takes into account potentially non-normal features of the data. 13

15 4 Empirical results 4.1 Data and the benchmark model We evaluate the performance of the characteristics-based strategy using one of the largest commercial hedge fund databases provided by the Hedge Fund Research (HFR). The initial HFR database contains 7,999 hedge funds over the time period from January 1978 to October We use data from January 1995 to December 2006 to avoid the database bias related e ects. 10 We examine only individual hedge funds, which report their returns on a monthly basis, in US dollars and net-of-fees. We minimize the back lling and self-selection biases by excluding the rst 12 observations for each fund. 11 In addition, Titman and Tiu (2008) argue that back ll bias is likely to be prevalent among small hedge funds. Following their procedure, we exclude funds that never exceed $20 million assets under management limit. In practical point of view, the funds below this limit may also be too small for institutional investors. The nal dataset contains 2,824 individual hedge funds from 1,343 di erent money management rms, of which 1,627 are alive, and 1,197 are defunct. Table 1 presents hedge fund classi cation into ve broad strategies: directional traders, relative value, security selection, multiprocess, and managed futures. The classi cation is based on the pioneering work of Fung and Hsieh (1997) and Brown and Goetzmann (2003). Their ndings suggest that hedge fund returns are exposed to only a few distinct factors. As we discussed above, the classi cation plays an important role in controlling for operational di erences among hedge fund strategies. [Insert Table 1] The HFR database provides information on the funds characteristics that we apply in forming the characteristics-based strategy. The HFR provides the hedge fund s assets 10 Ackerman, McEnally, and Ravenscraft (1999), Liang (2000), and Fung and Hsieh (2000) discuss the role of the survivorship bias when the database contains only alive funds. The post-1994 HFR database contains also defunct hedge funds, indicating that it should be relatively free from survivorship bias. 11 According to Kosowski, Naik, and Teo (2007) the back lling bias can be mitigated by excluding the rst 12 return observations. 14

16 under management on a monthly basis. Table 2 shows that the mean (median) fund size is $146.4 ($48.0) million. Information on hedge funds share restrictions and the manager s compensation structure are reported in the form of a single updated snapshot. Hedge funds impose share restrictions in order to limit investor liquidity. A lockup restriction speci es the period during which investors are not allowed to withdraw their initial investment. Typically, hedge funds specify a redemption interval after which investors can withdraw their investment by giving an advance notice. Table 2 shows that hedge funds tend to impose a one-year lockup period and a 30-days notice period with quarterly redemptions. [Insert Table 2] The compensation of a typical hedge fund manager consists of a management fee, which is a xed percentage of assets under management and an incentive fee, which is related to the fund performance. The incentive fee is typically the subject of the hurdle rate and high water mark provisions. The hurdle rate provision implies that a manager has to exceed it, in order to earn the incentive fee. The high water provision indicates that each investor only pays an incentive fee when the value of their investment is greater than its previous maximum. Agarwal, Daniel, and Naik (2009) argue that the incentive fee rate does not fully capture managerial incentives, as two di erent managers that charge the same incentive fee rate could be facing di erent incentives in terms of dollars. Therefore, they measure managerial incentives using manager s option delta, which is de ned as the sensitivity of the manager s compensation to a one percent increase in the fund s net asset value. Unfortunately, the HFR database does not provide accurate information on hurdle rates. Following Klebanov s (2008) approach, which does not require any speci c information on hurdle rates, we estimate the manager s option delta. Speci cally, we estimate the manager s delta as = N(Z) AUM I 100 (11) Z = ln(1=l) + T (r + 2 =2) T 0:5 ; (12) 15

17 where is the manager s option delta measure in millions of dollars, N(:) de nes the cumulative distribution function for a standard normal distribution, AU M presents the fund s assets under management measured in millions of dollars, I is the fund s incentive fee expressed as a fraction, L is one plus the one year LIBOR rate, and r is the one year constant maturity Treasury bill rate. Finally, we assume that T time to maturity is equal to one. Table 2 shows that the sample mean (median) of the manager s delta equals $0.19 ($0.06) million, which is very similar to what is obtained by Agarwal, Daniel, and Naik (2009) and Klebanov (2008). Agarwal, Daniel, and Naik (2009) and Aragon (2007) suggest that managerial incentives proxies and hedge funds share restrictions are not associated with endogeneity related e ects, because share restrictions and fees are set at the inception of the fund and they extremely rarely change during the life of the fund. Hence, the manager s delta, the notice period and the fund s size can be used to forming the characteristics-based strategy for real time investors. We examine the performance of the characteristics-based strategy by estimating alphas, information and Sharpe ratios to the strategy. Throughout the analysis, we use the sevenfactor model proposed by Fung and Hsieh (2004b). The seven-factor model contains two stock factors, which are speci ed as the excess return on the S&P 500 index (SNPMRF) and the spread between the Wilshire small cap and large cap returns (SCMLC ). Fung and Hsieh (2004a) nd that these two factors are the most signi cant stock related factors explaining the time-series variation in the hedge fund returns. The model also contains two risk factors related to bond returns. The factors are speci ed by the change in the 10-year Treasury yields (BD10RET), and by the yield spread between the10-year Treasure bonds and Moody s Baa bonds (BAAMTSY ). To capture non-linearities in hedge fund returns, Fung and Hsieh (2001) construct three trend-following risk factors, de ned by the excess return on portfolios of lookback straddles on the bonds (PTFSBD), currencies (PTFSFX ), and commodities (PTFSCOM ). We obtain the data for two stock factors from the Data Stream and for the two bond factors from the Federal Reserve Board s H.15 reports. The three primitive trend 16

18 following factors are downloaded from the David Hsieh s webpage. The information ratio is estimated using the Fung-Hsieh seven-factor model. The ratio is de ned as a ratio between the alpha of the Fung-Hsieh seven-factor model and the standard deviation of monthly alphas. The advantage of the information ratio is that it is invariant to leverage. 12 We also report the Sharpe ratio, because it is independent of any benchmark model, in contrast with the alpha and the information ratio. Finally, we test whether the Sharpe (information) ratios of two strategies are statistically distinguishable using the approach proposed by Ledoit and Wolf (2008). Their approach extends the work of Jobson and Korkie (1981) by taking into account the time-series properties and nonlinearities in fund returns. Speci cally, we estimate standard errors for the di erence of two Sharpe (information) ratios by applying the Newey and West approach Performance of the characteristics-based strategy We evaluate the value of active portfolio management by forming a strategy that exploits the fund s characteristics. We test the performance of the strategy by analyzing its in- and out-of-the sample performance while controlling for the role of underlying share restrictions such as lockup, notice redemption, and subscription periods. Overall, parameter estimates displayed in Table 3 suggest that it is optimal to invest more heavily in small funds with better managerial incentives and longer notice periods. Hence, the signs are consistent with prior literature. Table 4 shows that the performance of the characteristics-based strategy is signi cant not only statistically but also economically, implying bene ts for a real time investor. First, we analyze the in-sample performance of the characteristics-based strategy. We estimate the parameters, size ; delta and notice ; using the whole sample from January 1995 to December Given annual holding periods, we also use annual optimization horizons. Annual rebalancing is justi ed, because hedge funds share restrictions usually impede more 12 Let K denote leverage, then the fund s information ratio is, IR = K=K " = = " : 13 As an unreported robustness check, we estimate standard errors using a bootstrap procedure provided by Ledoit and Wolf (2008). The main results remain unchanged. 17

19 frequent rebalancing. 14 Unfortunately, there are only 14 independent annual observations. Therefore, we apply overlapping data in optimization. The use of overlapping data causes autocorrelation. Hence, we apply the Newey-West procedure with 12 lags to the standard errors of the estimates. The parameter estimates reported in Panel A of Table 3 suggest that it is optimal to invest in small funds, with high managerial incentives and long notice periods. The Wald test shows that the parameters, size ; delta and notice are jointly statistically highly signi cant, while the parameter estimates are individually statistically signi cant only at the 10% level. Consistently with prior literature, the parameter estimates are positive for the manager s delta and the notice period, but negative for the fund s size. The relative size of the coe cients implies that the notice period is marginally more important than the other characteristics. [Insert Table 3] Next, we examine the in-sample performance of the strategy. We interpret that portfolio weights provide a ranking of the funds. This simpli es the testing procedure. Each year, we sort the funds into quintile portfolios on the basis of the portfolio weights. Thereafter, we compute equally-weighted buy-and-hold returns for each quintile portfolio. We mitigate the look-ahead bias related e ects by estimating the return of equally-weighted portfolios without monthly rebalancing and assigning zero weight to funds that do not survive through the one-year holding period. 15 Panel A of Table 4 reports the parameter estimates of the Fung-Hsieh (2004) seven-factor model as well as various performance measures for quintile portfolios. The results show that the Fung-Hsieh (2004) model explains a signi cant part of the time-series variation in hedge fund returns, since the adjusted R 2 ranges from 66.3% to 73.8 % across quintile portfolios. The Fung-Hsieh (2004) alpha spread between the top and bottom quintiles is 4.2% with 14 Avramov, Kosowski, Naik, and Teo (2010) also apply annual rebalancing in their empirical application. 15 Baquero, Horst, and Verbeek (2005) and Horst and Verbeek (2007) discuss the e ects of the look-ahead bias by showing that it may lead to the overestimation of hedge fund performance. 18

20 t-statistics of furthermore, we test whether the mean returns as well as the Fung- Hsieh (2004) information and the Sharpe ratios of the top and bottom quintile portfolios are statistically distinguishable. For all of these measures, we nd that the di erence between the top and bottom quintile portfolios are statistically signi cant. Hence, the in-sample performance of the characteristics-based strategy is both economically and statistically highly signi cant. [Insert Table 4] The signi cant in-sample performance of the characteristics-based strategy is not surprising given the prior literature showing that the chosen fund s characteristics are related to hedge fund risk-adjusted returns. We address this concern by examining the out-of-the sample performance of the strategy. Our out-of-the sample testing begins roughly at the same time as the sample in Agarwal, Daniel, and Naik (2009) and Aragon (2007) ends. Our out-of-sample experiment complements Agarwal, Daniel, and Naik (2009) and Aragon (2007) by studying the bene ts of the real time investor who predicts hedge fund returns by exploiting the fund s characteristics. To perform the out-of-the sample experiment, we estimate the parameters using data from January 1995 to December Thereafter, the parameter estimates are used to determine optimal portfolio weights and quintile portfolios for the year We enlarge the sample by adding annual observations and re-estimate the model each subsequent year. Thus, we estimate the characteristics-based strategy in an increasing window and always test its performance in out-of the sample. Panel B of Table 3 shows that the optimization approach is robust, since the parameter estimates and their statistical signi cance are very similar as in-sample. For each estimation period, the Wald test suggests that the parameter estimates are jointly highly statistically 16 We estimate the standard errors of Fung-Hsieh seven-factor model using the Newey-West approach, which takes into account the time-series properties of hedge fund returns. We also estimate standard errors using the block bootstrapping technique that maintains the time-series dependence of the returns (e.g.,politis and Romano (1994)). The resulting inferences are quantitatively the same. 19

21 signi cant, but they are individually signi cant again only at the 10% level. The signs and the marginal importance of the estimates remain consistent in an out-of-sample analysis. The performance of the characteristics-based strategy remains signi cant in the out-ofsample period. Panel B of Table 4 presents the estimates of the Fung-Hsieh (2004) sevenfactor model as well as various performance measures for the quintile portfolios. The Fung- Hsieh alpha spread between the top and bottom quintile portfolios is 2.7% with t-statistics of The di erence between the mean returns as well as the information and the Sharpe ratios of the top and bottom quintile portfolios are signi cant for the mean returns and the information ratios, but not for the Sharpe ratios. However, we can conclude that the economic value of the characteristics-based strategy remains consistent also during the outof-sample period. Finally, to assess the bene ts of the characteristics-based strategy to investors, we must examine strategies that are feasible. At rst, we exclude funds that have a lockup restriction, and funds which do not provide redemptions and subscriptions at the end of the year. We estimate parameters, size ; delta and notice ; using information available in August in each year. Thus, previous year s fund characteristics available in August determine optimal portfolio weights for the next year. Therefore, we also have to exclude the funds, whose notice period is longer than 120 days. By forming the feasible strategy, we are able to control for the role of share restriction when we examine the performance of the characteristics-based strategy. Panel C of Table 3 reports parameter estimates of the feasible strategy. The statistical signi cance of parameter estimates is now striking, since they are not only jointly, but also individually highly signi cant. Results in the Panel of Table 4 suggest that the economic value of the characteristics-based strategy also remains consistent across performance measures. Speci cally, the Fung-Hsieh (2004) alpha spread between quintile portfolios is 3.0% per year with a t-statistics of 1.92, while the di erence of the top and bottom quintiles for the mean returns and the Fung and Hsieh (2004) information ratios are statistically distinguishable. Taken together, our ndings suggest that the real time investor can exploit the 20

22 fund s characteristics when making the allocation decision to hedge funds. 4.3 Naïve strategies vs. characteristics-based strategy Our ndings in the previous section suggest that hedge funds characteristics can be used in forming an investment strategy that adds value to a real time investor. Next, we examine whether the characteristics-based strategy contains information that is not contained in the naïve strategies based on sorting the funds by the t-statistics of the Fung-Hsieh (2004) alpha as well as the fund s size, the manager s delta, and the notice period. The results in Table 5 suggest that the characteristics-based strategy has extra explanatory information over the naïve strategies. We tackle the issue by performing a series of conditional sorts. For each year, we sort the funds into quintiles based on the t-statistics of the Fung-Hsieh (2004) alpha, and within each quintile, we sort the funds into quintiles based on the estimated portfolios weights. Table 5 reports the Fung-Hsieh (2004) alphas for resulting 25 portfolios, as well as for ve 5-1 spread portfolios that invest in funds with high portfolio weights and short funds with low portfolio weights within the given portfolio that is formed on the basis of the t-statistics of the Fung-Hsieh (2004) alpha. The cleanest measure for testing whether our strategy contains information beyond the naïve strategies is provided by the average of an equally-weighted portfolio that invests in the ve 5-1 spread portfolios. Controlling for e ects related to the t-statistics of the Fung-Hsieh (2004) alpha, Panel A of Table 5 shows that the average Fung-Hsieh (2004) alpha di erence between the top and bottom quintiles of funds ranked by portfolio weights ranges from 1.7% to 3.2% per annum. The result is robust across both in and out-of-sample testing and for the feasible characteristics-based strategy. Furthermore, Panel A shows that an investor is able to earn a Fung-Hsieh alpha ranging from 8.9% to 11.2% per annum by investing in the 25 portfolio, which contains the funds that have the highest t-statistics of the Fung-Hsieh (2004) alpha and portfolio weights The annual Fung-Hsieh alphas (0.089, and 0.112) are displayed in the elements (5,5) of the subtables having labels In-sample, Out-of-the sample and Feasible out-of-the sample. 21

23 [Insert Table 5] Finally, we examine how much information on future hedge fund risk-adjusted returns is contained in our strategy but not contained in the simple strategies based on sorting on the fund size, the manager s delta and the notice period. Speci cally, for each fund characteristics, except the notice period, we perform a similar procedure as for the t-statistics of the Fung-Hsieh (2004) alpha. The notice period does not t naturally in quintiles. Therefore, we form ve categories based on the length of the notice period. Results in Table 6 suggest that the characteristics-based strategy outperforms simple strategies. Our ndings suggest that even after controlling for e ects related to the fund s size, the manager s delta and the notice period, the average di erence of the Fung-Hsieh (2004) alpha between the top and bottom quintiles of hedge funds ranked by portfolio weights ranges from 1.0% to 3.3% per annum. The results are robust across both the in-the and out-of-sample analysis and the feasible characteristics-based strategy. Overall results in Table 6 suggest that the performance of the characteristics-based strategy remains signi cant even after controlling for the role of naïve strategies. 5 Conclusion This paper examines predictability in hedge funds returns and the value of active portfolio management in the hedge fund industry. Prior literature has documented that several hedge fund s characteristics based on economic phenomena are associated with hedge fund returns. Speci cally, we form optimal portfolio strategies using parameterization based on the (i) manager s option delta, (ii) notice period, and (iii) fund size by applying the approach proposed by Brandt, Santa-Clara, and Valkanov (2009). The approach is particularly wellsuited for hedge funds, because by focusing directly on optimal portfolio weights, one can avoid the well-known shortcomings of the traditional Markowitz approach that are related to an extremely di cult task, namely, to modeling the joint distribution of hedge fund returns and characteristics. 22

24 Our ndings suggest that the characteristics-based strategy allocates more heavily to small funds with better managerial incentives and longer notice periods. This is consistent with prior literature including Agarwal, Daniel, and Naik (2009), Aragon (2007) and Teo (2009). We nd that the performance of the characteristics-based strategy is signi cant not only statistically but also economically, indicating bene ts for the real time investor. The return predictability remains in and out-of-sample, even after controlling for the role of hedge funds share restrictions. Hence, we contribute to the existing literature by showing that the real time investor can use optimally the hedge fund s characteristics to predict hedge fund returns. We expect that our results provide important implications for hedge fund investors like pension funds, high-net-wealth individuals and funds-of-hedge funds. Given the exibility of the approach, investors can easily apply and extend it to real investment strategies. 23