Mazi Kazemi and Ergys Islamaj. April 2014

Transcription

1 Board of Governors of the Federal Reserve System International Finance Discussion Papers Number D Returns to Active Management: the Case of Hedge Funds Mazi Kazemi and Ergys Islamaj April 2014 NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at This paper can be downloaded without charge from Social Science Research Network electronic library at

2 Returns to Active Management: the Case of Hedge Funds 1 Mazi Kazemi 2 and Ergys Islamaj 3 Abstract Hedge funds often change their exposure to market risk in response to market conditions and private information. Do more active portfolio managers perform better? Using a sample of 284 hedge funds covering , we study the relationship between activeness and various measures of performance. More specifically, we use dynamic estimates of exposure to market risk to construct a measure of activeness and examine the relationship with various measures of hedge fund performance. We find that more active managers tend to provide higher raw returns to their clients. However, once we adjust these raw returns for their riskiness, the relationship changes such that more active hedge fund managers do not earn higher risk-adjusted returns on their portfolios. Keywords: Hedge Funds, Fama-French, Active Management, Dynamic Trading JEL classifications: G11, G12, G14, G23 1 The views in this paper are solely the responsibility of the author(s) and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or of any other person associated with the Federal Reserve System. 2 The author is a Research Assistant in the Division of International Finance, Board of Governors of the Federal Reserve System, Washington, D.C U.S.A. 3 The author is an economist in the Department of Economics, Vassar College, Poughkeepsie, NY, 12604, U.S.A.

3 1 Introduction This paper investigates whether active portfolio managers perform better than those who are less active. Using a sample of 284 equity long-short hedge funds covering , we study the relationship between a constructed measure of activeness, calculated from estimates of funds dynamic exposures to risk factors, and various measures of performance, such as realized returns and risk-adjusted realized returns. We use the Fama-French-Carhart factors in both static and dynamic frameworks to construct performance benchmarks and to measure the level of activeness of each hedge fund. This measure is then employed to test our main hypothesis that there is no relationship between the level of activeness and the risk-adjusted performance of hedge funds. While more active funds tend to provide higher average raw returns, they do not provide higher risk-adjusted returns. Since 1997, the hedge fund industry s assets under management (AUM) has increased by more than 14 times, with AUM growing at an average pace of $100bn per year. 4 Hedge funds are defined as absolute return investment vehicles, seeking to generate some positive return in any market condition. They can take short positions and are not subject to the stricter charters that govern mutual funds. Having such freedom of investment puts extra emphasis on the importance of the hedge fund manager. The incentive fee structure employed by the hedge fund industry is supposed to align the interest of shareholders. 5 In addition, given that hedge fund managers receive a share of their funds profits in the form of incentive fees, it is argued that the industry attracts the most skilled asset managers. 6 Numerous academic studies have examined the performance of hedge funds and their managers. Generally, the primary goal of these studies has been to determine whether hedge funds are able to outperform a passive benchmark, such as the S&P 500 Index. 7 The evidence in the hedge fund literature is mixed. Some studies, such as Capocci (2001), found significant positive abnormal returns for a significant portion of hedge funds, whereas more recent papers, such as Ding and Shawky (2007), reported that the majority of hedge funds are not able to outperform buy-and-hold investment strategies on a risk-adjusted basis. To the degree that some hedge funds may provide positive abnormal returns, it would be instructive In addition, most hedge fund managers have a significant portion of their personal wealth invested in the fund, aligning their interests with those of their investors even further. 6 Incentive fees are typically 20% of a fund s profits above its previous high water mark. For instance, John Paulson, the founder of Paulson and Co, reportedly earned $5 billion in See 7 The anecdotal and academic evidence, at least for mutual funds, is fairly clear. For example, In 2011, 84% of actively managed U.S. equity mutual funds underperformed their benchmarks. For example, see Fama and French (2010), Wermers (2011), and underperformed-their-benchmark-in trail-over-3-year-period html. 1

4 to find out whether these funds share some common characteristics. For example, Boyson (2008) reports that smaller and younger funds display better and more persistent performance. 8 However, none of the previous studies have examined whether those funds who display positive abnormal are relatively more active in managing their portfolios. In other words, even if the majority of hedge funds may not be able to outperform buy-and-hold investment strategies, it is of interest to determine whether those who outperform their peers do so because they are unusually active in managing their portfolio allocations does active hedge fund management mean skilled management? The contribution of this paper is to test for a relationship between activeness and performance. The activeness measure is constructed from dynamic risk exposure estimates. Papers, such as Monarcha (2009), Roncalli and Tieletche (2007), and Bollen and Whaley (2009) have employed dynamic regression models with time-varying coeffi cients to explain hedge funds abnormal returns. As will be discussed later, dynamic regressions allow the researcher to better capture the hedge fund manager s reallocations into different risk factors. These changes can be in response to macro-economic conditions, like the Great Recession, arbitrage opportunities, costs of leverage, and varying performance of equity indices (Patton and Ramadorai (2010)). We apply the Kalman Filter methodology to a dynamic version of the model first proposed by Carhart (1997) and use the estimated time-varying hedge fund risk-exposures to generate a measure of activeness for each fund. We also employ various cross-sectional regressions and find that more actively managed funds tend to provide higher raw returns to their clients. However, after adjusting for riskiness, the relationship changes such that more active hedge fund managers do not earn higher risk-adjusted returns on their portfolios. 2 Literature Review The key question that we wish to study in this paper is whether more actively managed hedge funds are able to generate higher returns. According to the effi cient market hypothesis (EMH), asset prices reflect all available information, and, therefore, actively managed portfolios should not outperform passive investments on a risk adjusted basis. 9 However, this does not imply that investors should be indifferent between passive investment products (e.g., index funds) and those that are actively managed (e.g., hedge funds). If markets are effi cient, the returns on actively managed portfolios will be lower by the amount of fees and transaction costs. 8 Boyson (2008) contains numerous references to papers on varying aspects of hedge funds performance persistance, which is beyond the scope of this paper. 9 For a discussion of the EMH see Bodie, et al (2011). 2

5 We conduct a returns-based analysis to evaluate performance. 10 Wermers (2011) warns of three potential problems when conducting returns-based analysis. First, in determining a performance model, one must have an accurate measurement of the risk exposures of the managers. That is, one must have the correct benchmark. Second, one must be aware of the difference between idiosyncratic and systematic risks in the fund s holdings. Finally, one should have a good understanding of the return distribution, which may deviate from the normal distribution. This paper concentrates on hedge fund managers who invest in U.S. equity markets, and we construct a model that reflects the risks they take. This is the model developed in Carhart (1997). Second, the model differentiates between systematic and idiosyncratic risks. Finally, while we assume that hedge fund returns are normally distributed, we correct our results for potential heteroskedasticity when estimating the relationship between performance and the measure of activeness. The development of the Capital Asset Pricing Model (CAPM) in the 1960 s provided a testable model of risk for financial assets. Jensen (1968) was one of the first to use this new tool to evaluate fund performance. An econometric representation of the CAPM to model the ex post returns would be, R jt R ft = α j + β j (R mt R ft ) + µ jt, j = 1,..., J, t = 1,..., T, (1) where α j is the intercept of interest and µ jt is a random error term with expected value equal to zero. The interpretation of α j is the average excess return on portfolio j. Thus, this is the average return on a portfolio that can be attributed to the manager s investment skills. This variable is colloquially known in the financial literature as Jensen s alpha. If managers are consistently generating returns in excess of those predicted by their risk-factor exposures, it would appear that managers are extracting economic rents by trading on certain information. Jensen selected a sample of 115 open-end mutual funds covering Only 13 intercepts are positive and significant at the 5% level. 11 One of the shortcomings of the CAPM is that it only includes one risk factor to model returns. Many researchers have expanded the CAPM to create multi-factor models. Fama and French (1992, 1993, 1996) develop a widely employed model of risk and 10 There are two broad categories of performance analysis used to study both hedge funds and mutual funds: portfolio holdings and returns-based analysis. The former involves obtaining information regarding the portfolio structure of each fund. This is not feasible for hedge funds since, unlike mutual funds, most hedge funds are not required to disclose their holdings on a regular basis and when they do, they report only their long positions. However, for hedge funds, the latter method offers the possibility of obtaining estimates of portfolio holdings as well as risk-adjusted performance. 11 Jensen (1968) states, The model implies that with a random selection buy and hold policy one should expect on average to do no worse than α = 0. Thus it appears from the preponderance of negative ˆα s that the funds are not able to forecast future security prices well enough to recover their research expenses, management fees and commission expenses. (pg. 22). 3

6 return where they describe a set of three risk factors, which was used to analyze stock returns. Fama and French (2009) apply their model to 1,308 equity mutual funds with monthly data from January 1984 to September The estimated annualized alpha was Carhart (1997) combines the three-factor model, developed by Fama and French (1992, 1993, 1996), and the momentum factor, developed by Jegadeesh and Titman (1993). 13 Equation (3) represents the four-factor Fama-French-Carhart model: r pt = α + β(rmrf t ) + s(smb t ) + b(hml t ) + u(umd t ) + ε t, t = 1,..., T. (3) Here r pt and the Fama-French factors are as before, and UMD t is the excess return of the stocks that were winners in the past period over those that were the losers, and ε t is white noise. Carhart showed that funds that had a positive performance in one year tended to perform above average the following year. However, in subsequent years this abnormal return vanished. Studies of hedge funds performance have approached the subject in a similar fashion. 14 Table 1 of the Appendix summarizes the results of some of the papers on the topic. Capocci (2001) uses 198 monthly returns ( ) for 2,154 hedge funds to test the viability of the CAPM as a performance metric for hedge funds. The author finds an estimated monthly alpha of 0.65% and estimated beta of Both of these estimates are significantly different from zero. 15 Then, the author applies Carhart s (1997) four-factor model (equation (3)) to hedge funds. The author shows that in a sample of 2,154 funds the estimated monthly alpha is 0.66%, and the estimated betas are 0.23, 0.05, and 0.03 for SMB t, HML t, and UMD t, respectively. Only the coeffi cient on the momentum factor is not significantly different from zero. The data indicated that the hedge fund managers abilities are significant and positive. Asness, Krail, and Liew (2001) also use the CAPM with lagged market returns to analyze hedge fund performance. The authors consider a sample of 656 funds with data spanning from 1994 to For long short equity funds, the authors find a value of alpha equal to 3.82% and beta equal to However, neither of these values are significantly different from zero at the 12 They estimate model (2) below. r pt = α + β(rmrf t) + s(smb t) + b(hml t) + ε t, t = 1,..., T. (2) Here r pt is the excess return in month-t of the portfolio over the T-Bill, RMRF t is the excess return of the market in month-t, SMB t is the excess return of small cap stocks over large cap stocks in month-t, HML t is the excess return of value stocks over growth stocks in month-t, and ε t is white noise. Since the authors were examining equity funds, the coeffi cient on the market beta was close to one, 0.98, and the coeffi cients on SMB t and HML t were close or equal to zero, 0.18 and 0.0, respectively. 13 Aptly refered to as the four-factor Fama-French-Carhart model. 14 For a discussion of hedge funds see Lhabitant (2006). 15 The small beta coeffi cient implies that hedge funds do not have much exposure to traditional market risk. This motivates the use of extended models to evaluate hedge funds performance. 4

7 5% level. Brown, Goetzmann, and Ibbotson (1999) consider hedge fund performance for the years 1988 to However, they divide their analysis into each individual year, for instance, , , etc. The authors find positive significant alphas in the years and However, they also find negative and significant alphas for the years and In recent years, the performance of hedge funds has suffered. Some argue that because of significant inflows of capital into this industry, sources of excess return have gradually disappeared. Recent papers on the performance of hedge funds seem to support this hypothesis. These studies have reported zero or even negative alphas for hedge funds using the four-factor Fama-French-Carhart model. Agarwal and Naik (2004) add non-linear variables to the fourfactor model and show that hedge funds had significant risk exposures to both the non-linear and the original four factors. The authors also compare long-run hedge fund returns to their recent performances and find that in the long-run, returns are lower, volatility is higher, and tail-losses are higher. This evidence suggests that hedge fund returns fluctuate over time and across different samples. The models mentioned make a central assumption that is frequently violated in real life: They assume constant parameter values. However, as new information becomes available to fund managers, they are likely to make material changes to the fund s composition. For instance, they may take on more leverage or change their allocations to securities. A basic solution for this dynamism is to partition the sample and test for structural shifts. This was presented by Bollen and Whaley (2009) who show that they could apply these tests to basic linear models by using the change-point regression of Andrews, et. al. (1996). 16 The above method suffers from the fact that the researcher must have some prior knowledge as to when this structural break occurs. Hasanhodzic and Lo (2006) also recognize that non-dynamic regression coeffi cients could be problematic. The authors use a rolling-window regression as an alternative. In their paper, the window is 24 months. While this methodology offers more insights into the fluctuations of returns over time, there is still some ambiguity in choosing the window size. Also, shifts and 16 Consider rewriting the single-factor return model as, r t = α 1 + β 1 x t + ε t, t = 1,..., T 1 r t = a 2 + α 1 + (β 2 + β 1 )x t + ε t, t = T 1 + 1,..., T. Once the above models are estimated, then one would proceed to test the null hypothesis, H 0 : β 2 = α 2 = 0. 5

8 changes that occur within the window can be lost. The shortcomings of the above two dynamic methods can be overcome through the use of the Kalman Filter methodology. The Kalman Filter uses observable data (hedge fund returns) to provide the best estimate for an unobservable stochastic random variable (hedge funds exposures to various risk). For mutual funds, Mamaysky, et al (2004) show that a dynamic regression using the Kalman Filter does a better job of fitting historical mutual fund returns data and provides a better forecast of the out-of-sample returns than the static OLS models. For hedge funds, Monarcha (2009) compares the explanatory power of a mutli-factor model using a dynamic regression with the Kalman Filter with those of a static linear model. The author uses a sample of 6,716 funds with monthly data from January 2003 to December Monarcha finds that the mean adjusted R 2 rises from 0.60 for the static linear model to 0.72 for the dynamic case with the Kalman Filter. Even a linear static model with non-linear variables yields an adjusted R 2 of only Roncalli and Teiletche (2007) compare the dynamic regression applied to hedge funds with the Kalman Filter to rolling window OLS estimates. They find that the Kalman Filter produces smoother estimates of the funds sensitivity to different indexes and reacted to new information much quicker than either the 12 month, 24 month, or 36 month rolling window techniques. Bollen and Whaley (2009) also comment on the use of a dynamic regression with stochastic betas, using the Kalman Filter to estimate these betas, as an effective way to capture the time-dynamics of hedge fund allocations. Table 1 in the Appendix summarizes the three key performance measuring results mentioned above The Model Since we are considering a sample of U.S. long-short equity hedge funds, it makes sense to select a multi-factor model whose risk-factors are equity-related. The goal is to estimate hedge funds exposures, or weights, to these factors and, in the spirit of Sharpe style analysis, create a benchmark for each manager. 18 Consider the general case of the excess return on a portfolio: r p,t r f,t = n ω i,t 1 (r i,t r f,t ) p = 1,..., K (4) i=1 In equation (4), r p,t is the hedge fund s portfolio returns at time t, r f,t is the risk-free rate at time t, ω i,t 1 is the weight on asset i decided at time period t 1, and r i,t is the return on 17 The Table includes our results as well. These were calculated by taking the mean weighting on each risk-factor across all time periods and managers. Further details on my model will be discussed later. 18 Since the Fama-French-Carhart factors are in excess returns form, we do not need to impose a restriction that the weights have to add up to one. Further, since hedge funds can take long and short positions, we do not need to impose the restriction that the weights should be positive. 6

9 asset i. The weight on risk-free rate in the portfolio is given by (1 n i=1 ω i,t 1). The above expression is, in fact, an economic identity, as it describes how the excess return on a portfolio is simply a weighted average of the excess returns of securities that constitute the portfolio. In practice, one does not know the exact composition of the portfolio and thus the weights have to be estimated using available returns on a set of asset classes or risk factors that approximate the investment universe considered by the portfolio manager. We employ the four-factor Fama-French-Carhart model as described in equation (3). 19 Thus, the econometric representation of the model is equation (5) below. r p,t r f,t = w p,t 1f t + ε p,t p = 1,..., K, t = 1,..., T. (5) The weights w p,t, a 5 1 vector, will be estimated by the Kalman Filter. f t is a 5 1 vector of Fama-French Carhart factors (including the constant term, alpha). The error term is represented by ε p,t. The weights are assumed to follow the following autoregressive process. w t = w t 1 + µ t, t = 1,..., T. The variance of the error terms, ε t and µ t, is described as follows. V ar [( ε t µ t ) f t, t = 1,..., T ] = [ Q Σ εµ R Σ εµ ]. Note that we have assumed that the weights could change through time. As the portfolio manager receives new information at time (t 1), the portfolio weights are adjusted and then the time t realized returns on the risk factors will determine the return on the portfolio. Having estimated the parameters of equation (5), we then attempt to measure the variation in the weights, which will represent the degree of activeness of each fund. We use the sum of absolute changes in w i,t 1 to measure the activeness of each portfolio. In particular, we define, φ p = 4 T 1 w i,t w i,t 1, p = 1,.., K, (6) i=1 t=1 as the measure of activeness of fund p. 20 Once the measure of activeness is obtained, we focus on investigating our question of 19 For a description of all the risk-factors see 20 One possible approach is to use the average standard deviation of the time-series of the estimated weights. We decided not to use this approach because it will not adequately capture the degree of activeness of a portfolio where the weights are trending in a predictable way. 7

10 whether more active funds are associated with higher returns. First, we divide the sample into the most active and least active funds and compare the alphas of the Fama-French-Carhart regressions for the two samples. Second, we use cross-sectional regressions to determine if there is a relationship between the average return on a hedge fund and its degree of activeness. That is, Z p = γ 0 + γ 1 φ p + ε p = 1,..., K (7) In equation (7), Z p represents the performance of hedge fund p. The hypothesis is that γ 1 = 0; i.e., higher activity does not lead to better performance. We use three different measures to represent the dependent variable Z p. First, we use the average return on each manager to represent Z p.this will determine if more active funds lead to higher average return. Of course, higher returns could come with higher risk. Thus, we use two different measures of risk-adjusted returns to determine if more active funds are able to provide higher risk-adjusted returns. First, we run the above regression using the manager s Sharpe ratio across the time period. With this metric, risk is measured as volatility, without any adjustment for systematic or idiosyncratic risk. Thus, second, we consider the above regression using the manager s mean alpha across the time period as our measure of risk. This method will allow us to consider the effect of activeness while considering returns adjusted for systematic risk specifically. 4 The Data The data is obtained from the Center for International Securities and Derivatives at the University of Massachusetts-Amherst (CISDM). We consider 284 hedge funds whose Morningstar category is listed as U.S. Long/Short Equity. These funds, as their name suggests, invest in U.S. stocks, taking both long and short positions. We have restricted the sample to equity funds to avoid the mistake of having misspecified risk factors. The factors in the four-factor Fama-French-Carhart model are appropriate risk factors to use, as suggested by the literature. The reported monthly returns are net of fees, calculated as percentage change in the net asset value. For each of the funds, we use 5 years of data, covering Since we consider funds that have survived for 5 years, the results might be impacted by survivorship bias. This means that considering only surviving hedge funds can lead to the overestimation of returns. However, the problem is mitigated a bit by the fact we are only comparing survivors to other survivors. Tables 2 and 3 below present summary statistics for the fund returns, and summary statistics for the risk-factor returns, respectively. Tables 2 and 3 Here 8

11 5 Results We begin by estimating the following static OLS regression (8) for 60 months across 284 funds. r pe,t = α p + w 1p (RMRF t ) + w 2p (SMB t ) + w 3p (HML t ) + w 4p (UMD t ) + ε tp (8) where r pe,t is the excess return on fund p. This regression is simply the standard four-factor Fama-French-Carhart model as was discussed in equation (3). We begin with the static model because it is the building block of the dynamic regression to follow. In addition, this allows us to compare our preliminary results with those reported in previous papers. We estimate regression (8) for each manager and then we average the estimated coeffi cients. These averaged estimates are presented in Table 4. Table 4 Here Note that most alphas are not significantly different from zero. In equation (8), the estimated mean abnormal return, α p, was 0.144% per month. Of all 284 funds, 31 had significantly positive alphas at the 5% level, and 15 had negative alphas significant at the 5% level. Since the funds in the sample are, by virtue of still existing, the most successful funds over the four year span, one would expect them to have better performance than an average fund selected at random from one of the time periods in the sample. 21 Keeping these results in mind, we now turn to the dynamic regression. Next, we estimate regression (8) with time-varying coeffi cients, using the Kalman Filter methodology. 22 Figure 1 displays the dynamics of the average estimated weights of the four factors. 23 As can be seen from the figure, the weights are indeed time-varying, suggesting that the managers have actively adjusted exposure to market risks across the period. Figure 1 Here 21 If this model were to be applied to all the funds that were available in 2007, the results would be different. One would most likely see alpha drop closer to 0, based on the evidence in the previous literature and by the EMH. 22 All empirical tests were carried out in MATLAB using the State Space Model toolbox developed by Peng and Aston (2011). 23 We ignored the first 10 observations of {w t} p, the sequence of weights on the risk-factors. The justification behind this is that the Kalman Filter is exceptionally volatile for the early observations, as it is still "learning" the trends in the data. 9

12 Having estimated the times series of each manager s exposures to the four equity factors, we are now prepared to use these estimates to create a measure of activeness for each fund manager. As described in equation (6), we construct a measure of activeness, φ p, for each fund. We normalize each manager s measure of activeness in following manner ρ p = φ p φ 1, where φ is the mean of measure of activeness across the sample. Therefore, ρ p represents how much more active fund p is, as a percentage relative to the mean. A value of 0 would indicate that a fund s amount of activity is average while a positive (negative) value means the manager is more (less) active than average. We first divide the sample into highly active and highly inactive funds and compare the Fama-French-Carhart alpha s coming from pooled OLS regressions. We use the top 40 percent most active and bottom 40 percent least active funds for these comparisons. 24 Table 5 shows the results. The second row of each group shows t-statistics. Our focus is on alpha, and examining the data suggests that the top 40 % most active funds have generated a higher Jensen alpha. Table 6 shows summary statistics for each group. Table 5 Here Table 6 Here To be able to make a more robust comparison across the two groups, we re-run the regression adding a dummy variable to identify firms in the top 40% of activeness, as follows: r pe,t = α p + w 1p (RMRF t ) + w 2p (SMB t ) + w 3p (HML t ) + w 4p (UMD t ) + +D p [α D + w 1D (RMRF t ) + w 2D (SMB t ) + w 3D (HML t ) + w 4D (UMD t )] + ε tp (9) where D p takes on a value of one if the observation comes from a top 40% manager and zero otherwise. The parameter of interest is D p α D, which is the upward "shift" in abnormal returns that come from being a member of the most active group. We find an estimated coeffi cient value of 0.13 with a t-statistics of This is just barely significant. Next, we re-run the four-factor OLS regression for each fund in the top and bottom 40% and calculate the percentage of funds with statistically significant positive and negative alphas 24 The results are similar when we use the 50 percentile benchmark to define different groups. 10

13 for each fund. Table 7 shows the results. The percentage of positive and statistically significant alphas is higher for the group of top 40% most active hedge funds (15.79% compared to 9.49% for the least active). This would suggest that most active funds perform better. But, the percentage of statistically significant negative alphas is also larger (6.14% vs. 4.31), suggesting that the higher percentage of alphas for the most active group may stem from higher risk taking behavior. Table 7 Here The results from OLS estimates for different groups are intriguing. To gain further insights, we consider three cross-sectional regressions using the constructed measure of activeness. In addition to serving as an alternative test, this allows us to also control for various measures of risk. First, we run the following cross-sectional regression: r p = γ 0 + γ 1 (ρ p ) + v. For p = 1,..., 284 (10) where, r p represents the mean excess return of fund p, and v is the error term. The regression employs White estimates of the variance covariance matrix of errors to correct for heteroskedasticity. 25 Table 8 presents the results of this regression. Table 8 Here We find that, γ 1, the coeffi cient on the measure of activeness is statistically significant and different from zero at the 5% level. The results indicate that activeness is associated with positive returns. It is important to point out that this result may be time period specific. The time span of the sample covers the financial crisis of the late Thus, much of the activity might be attributable to nimble managers who were able to shed toxic assets and avoid losses. However, the above regressions do not take into account the relationship between increased activeness and risk. That is, the managers who are more active may also be taking on riskier 25 Given an n n regressor matrix, X, and OLS residual u i for each observation, White s estimated variancecovariance matrix for ˆβ is, ] V ar [ˆβ = ( X X ) 1 X diag ( u u 2 ( n) X X X ) 1. 11

14 assets, leading to higher returns. It is, therefore, necessary to consider some risk-adjusted measures of return. Consider the definition of a portfolio s Sharpe ratio. SR = E[r p] σ p. Here r p is the excess return on a portfolio and σ p is the standard deviation of r p. 26 The Sharpe ratio can be thought of as a measure of effi ciency. In comparing managers, the ones with higher Sharpe ratios for their portfolios are able to extract higher returns for the same level of risk. In this context, risk is measured as volatility, which includes both systematic and idiosyncratic risks. Later, we will use the alpha from the four-factor model to only consider returns adjusted for systematic risk. Thus, we estimate regression (11), using White s approach. sr p = γ 0 + γ 1 (ρ p ) + µ. (11) The results of regression (11) are presented in Table 9. Table 9 Here The results indicate a negative relationship between activeness and the Sharpe ratio, but very close to zero. Higher activeness seems to be correlated to a lower ratio of reward to risk. The above results seem to indicate that there is, proportionally, more risk taken on than excess return achieved. To account for systematic risk of the manager, we examine the relationship between the mean alpha of each manager and the manager s activeness. α p = γ 0 + γ 1 (ρ p ) + ν. (12) Here α p is the mean value of {α t } p, sequence of risk-adjusted excess returns for fund p as estimated by the dynamic four-factor model. That is, this is the average of alpha for each fund across the entire sample time period. The motivation behind regression (12) is to adjust for systematic risk. The results are presented in Table 10. We use White s standard errors to correct for heteroskedasticity. Table 10 Here 26 For a discussion of the Sharpe ratio see Bodie, et al (2011). 12

15 Clearly, the results of the regression are not significant. The sign is negative, but the coeffi cients are not statistically different from zero. The results show that activeness is not associated with fund managers abnormal returns after adjusting for systematic risk. Given these results, why are certain managers more active than others, and why do investors allocate funds to these managers, if they are not generating alpha through their methods? The answer to this question is open for further research. A quick hypothesis is that it is diffi cult for investors or managers to recognize the relationship between active management and returns. Even the analysis presented above relies on the assumption that we have chosen the appropriate riskfactors in the regressions. Being able to separate the returns generated by activeness and those generated by luck can be very diffi cult. 6 Conclusion Do active portfolio managers perform better than their peers? The empirical evidence presented in this paper cannot reject the hypothesis that more active managers do not provide higher riskadjusted return for their investors. Using a sample of 284 U.S. equity long-short hedge funds covering , we find that while active hedge funds provide higher raw returns, their risk adjusted returns are, in fact, the same. Using a state space methodology, we estimated the exposures of these funds to the Fama- French-Carhart factors. We then developed a measure of activeness, which is used as an explanatory variable in a series of cross-sectional regressions. Three dependent variables were employed in these cross-sectional regressions. First, we examined the relationship between average unadjusted return on each manager and his/her degree of activeness. The results show that the estimated mean return is an increasing function of activeness. Therefore, active managers tend to outperform their peers when their returns are not adjusted for risk. Second, we used two different measures of risk-adjusted returns to determine if the above higher raw returns are associated with higher risk. The first measure of risk-adjusted return employed was the Sharpe ratio. As is well known, this measure does not distinguish between systematic and idiosyncratic risks. The results show that active managers have lower Sharpe ratios. This indicates that while active hedge fund managers are able to increase their returns by actively managing their portfolios, they are not able to do so without a substantial increase in return volatility. Finally, we considered using the fund managers mean alpha as a dependent variable. Each manager s alpha was derived from a dynamic regression model, and it accounted for the manager s exposures to systematic sources of risk, namely market, size, value, and momentum. The 13

16 results showed that there was no relationship between alpha and activeness. This indicates that the increase in an active manager s mean return is accompanied by an equivalent increase in the systematic risk of the portfolio. The results for pooled OLS regressions for the most active and least active groups of hedge funds are also not robust. While the alpha for the most active group is statistically different from zero and positive, we could not determine that the alpha s of the two groups were statistically different from each other. Furthermore, time series OLS regressions for each fund show that both the percentage of positive and negative statistically significant alphas was higher for the most active group of funds. Among the questions which this paper brings up is the issue of survival bias. All the funds in the sample were in existence in 2007 and were still in operation by the end of Since this period covers the financial crisis, it is safe to assume that these surviving funds were managed by rather skilled managers. 27 As a part of future research, we plan to examine the return to activeness for defunct hedge funds. The question would be whether less active funds were not able to survive the downturn. By the same token, future research should extend the results of this paper in two other directions. First, the methodology developed in this paper can be applied to other hedge fund strategies to determine if returns to activeness are different for other hedge fund strategies. 28 Next, the research could be applied to a larger database of hedge funds covering a longer time period. It is possible that results reported in this paper are time specific, and therefore return to activeness could be different during less turbulent times. 27 For example, a study by Liang and Park (2008) shows that for the period of , the attrition rate of hedge funds was about 8.7%. This rate is likey to be much higher during Other hedge fund strategies are: convertible arbitrage, merger arbitrage, fixed income arbitrage, distressed debt, event-driven, global macro and so on. 14

17 References [1] Agarwal, Vikas, and Naik, Narayan Y., 2000, "Performance Evaluation of Hedge Funds with Option-Based and Buy-and-Hold Strategies." FA Working Paper No. 300 [2] Albrecht, F., 2005, "Time-Varying Exposure in Hedge Funds," Thesis for Master of Banking and Finance (MBF) HEC Lausanne [3] Andrews, et al., 1992, "Optimal Change Point Test for Normal Linear Regression." Journal of Econometrics, 70(1), 9-38 [4] Asness, Clifford, Krail, Robert, and Liew, John "Do Hedge Funds Hedge?" Journal of Portfolio Management, 28(1), 6-20 [5] Bodie, et al Investments. New York City: McGraw-Hill/Irwin. Print [6] Bollen, Nicholas P. B., and Whaley, Robert E "Hedge Fund Risk Dynamics: Implications for Performance Appraisal." Journal of Finance, 64(2), 985-1,035 [7] Boyson, Nicole M "Hedge Fund Performance Persistance: A New Approach." Financial Analysts Journal. 64(6), [8] Brown, Stephen J., Goetzmann, William N., and Roger G. Ibbotson "Offshore Hedge Funds: Survival & Performance ," Yale Working Paper Series [9] Capocci, Daniel P. J "An Analysis of Hedge Fund Performance " HEC - Université de Liège; Luxembourg School of Finance; Edhec Risk and Management Research Center Working Paper Series [10] Carhart, Mark M "On Persistence in Mutual Fund Performance." Journal of Finance, 52(1), [11] Ding, Bill, and Shawky, Hany A "The Performance of Hedge Fund Strategies and the Asymmetry of Return Distributions." European Financial Management, 13(2), [12] Elton, E., Gruber, M., Das, S., and Hlavka, M., 1993, "Effi ciency with Costly Information: A Re-Interpretation of Evidence from Managed Portfolios," Review of Financial Studies, [13] Fama, Eugene F., and French, Kenneth R "Common Risk Factors in the Returns on Stocks and Bonds." Journal of Financial Economics, 33(1), 3-56 [14] Fama, Eugene F., and French, Kenneth R "Luck Versus Skill in the Cross Section of Mutual Fund Returns." Journal of Finance, Forthcoming 15

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19 Tables and Figures Table 1: Studies on Hedge Fund Performance Study Model Data Betas α (%) RMRF t RMRF t 1 RMRF t 2 RMRF t 3 Capocci (2001) CAPM Asness, et al (2001) CAPM Asness, et al (2001) Lag CAPM Brown, et al (1999) CAPM α (%) RMRF t SMB t HML t UMD t Capocci (2001) 4-Factor This Paper 4-Factor α (%) RMRF t SMB t HML t GSCI t Agarwal & Naik (2004) Non-Linear Monarcha (2009) Kalman Filter increases R 2 Roncalli et al(2007) Kalman Filter smoother estimates than rolling window OLS Table 2: Average of Fund Monthly Returns (%) Mean Max Min Average of Return, Standard Deviation Skewness Table 3: Average of Risk-Factor Monthly Returns (%) Mkt-rf SMB HML MOM Mean Max Min Stand. Dev Skewness

20 Table 4: Results: Regression (8) Variable Mean Coeffi cient Value % t-stat sig. at 5% α p w 1p w 2p w 3p w 4p % F-stat sig. at 5% 88.7 Mean R Table 5: Pooled OLS Regressions for Top and Bottom 40% α RMRF SMB HML UMD R 2 F Stat T op Bottom Table 6: Summary Statistics for Returns Top 40% Bottom 40% Mean Standard Dev Skewness Kurtosis Table 7: Pooled OLS Regressions for Top and Bottom 40% α p Mean Coeffi cient %(+)ve sig. at 5% %(-)ve sig. at 5% T op 40% Bottom 40% Table 8: Regression (10) w/ 4-Factor Model Variable Estimated Value t-stat γ γ F stat R

21 Table 9: Results of Regression (11) Variable Estimated Value t-statistic γ γ F stat R Table 10: Results of Regression (12) Variable Estimated Value t-statistic γ γ F stat R Figure 1 Dynamics of the average factor loadings of the funds in our sample. 21