Gambling or De-risking: Hedge Fund Risk Taking vs. Managers Compensation. Chengdong Yin and Xiaoyan Zhang * January Abstract

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1 Gambling or De-risking: Hedge Fund Risk Taking vs. Managers Compensation Chengdong Yin and Xiaoyan Zhang * January 2017 Abstract Hedge fund managers risk-taking choices are determined by their compensation. Managers derisk when the management fee becomes more important in total compensation, potentially to protect their existing assets and fee incomes. When funds are below their high-water marks, managers increase risk taking to recover past losses. Managers also take more risk when funds are above their high-water marks, possibly to further increase their compensation. During the recent financial crisis, managers herded more with their styles and decreased fund-specific risk. Finally, when fund managers take more risk, they do not generate better future performance and thus do not benefit investors. Key Words: Hedge Fund, Risk Taking, Incentive Fee, Management Fee, High-water Mark. JEL Classification: G23 * Chengdong Yin is with the Krannert School of Management at Purdue University. Xiaoyan Zhang is with the Krannert School of Management at Purdue University, and PBC School of Finance at Tsinghua University. We would like to thank Lu Zheng, Martijn Cremers, Neng Wang, Mitchell Johnston and participants at Krannert School Alcoa Workshop and Wabash River Finance Conference for helpful comments and suggestions. All remaining errors are ours. Electronic copy available at:

2 Media articles routinely associate hedge funds with aggressive risk taking, namely gambling or betting. 1 According to these news articles, hedge fund managers speculate on movements of all types of financial assets, such as stocks, currencies, interest rates, commodities, and even exotic ones like lawsuits. 2 These suspicions are not completely unfounded. Unlike traditional investment vehicles, such as pension funds and mutual funds, hedge funds are significantly less regulated. Hedge fund managers have the freedom to use all weapons in the investment armory, including the highly risky ones, such as leverage, derivatives, and short selling. Meanwhile, the compensation structure for hedge fund managers is highly nonlinear and resembles a call option. Because the value of an option increases with uncertainty, hedge fund managers compensation structure encourages them to take more risk. Thus, it is reasonable for the public to worry that hedge funds may take excessive risk. The landscape for the hedge fund industry clearly changed after the most recent global financial crisis. With more regulation and less stellar returns in recent years, some hedge funds have started to de-risk, that is, take less risk. 3 One purpose of de-risking is to increase survival probabilities, which is essential during and after the recent financial crisis. There is another important reason for de-risking, which has not received enough attention. As discussed in Yin (2016), because most hedge funds suffer from diseconomies of scale, that is, fund performance decreases with fund size, the management fee becomes the more important part of managers total compensation when funds grow large. 4 At the same time, because hedge fund investors are more sophisticated, they are sensitive to past performance and withdraw their money when fund performance falls. 5 This return-chasing behavior of hedge fund investors clearly motivates 1 See for instance Hedge fund manager circus isn t investing it s gambling from the Guardian on May 8, 2014 ( 2 See for instance Hedge Fund Betting on Lawsuits Is Spreading from Bloomberg on March 18, 2015 ( 3 See for instance Hedge fund derisk by January Month End from Hedge Fund Insight on February 6, In our sample, the management fee on average accounts for more than 70% of total compensation. 5 See, for example, Naik, Ramadorai, and Stromqvist (2007), Fung et al. (2008), Getmansky et al. (2015), and Yin (2016) for a discussion of the flow-performance relation in the hedge fund industry. 1 Electronic copy available at:

3 managers of large funds to risk little to retain fund size and keep collecting fees. That is, hedge funds might take less risk and behave similarly to mutual funds when they grow large. Conceptually, no matter whether gambling or de-risking, hedge fund managers choose their optimal levels of risk taking to maximize their own compensation. In this article, we empirically investigate how hedge fund managers risk-taking behavior is related to their compensation. The optimal risk-taking choice for a hedge fund manager has been studied extensively in the literature, both theoretically and empirically, but there are still many unanswered questions. Because of different assumptions, models in theoretical studies have quite different predictions. For example, Hodder and Jackwerth (2007) show that hedge fund managers take more risk when fund value falls below the high-water mark by assuming power utility and a finite time horizon, while Lan, Wang, and Yang (2013) argue that fund managers reduce risk taking to increase survival probabilities by assuming risk-neutral managers with an infinite horizon. To have a general view on the complicated interplay between managers risk taking and their compensation, it is important to compare and test the predictions of various models on real data, and that is one focus of this study. Meanwhile, previous empirical papers on risk taking, such as Aragon and Nanda (2011) and Kolokolova and Mattes (2014), mainly focus on risk shifting within a calendar year, or the socalled tournament behavior. That is, hedge fund managers might take more risk in the second half of a year when they perform poorly in the first half. We, instead, document the general pattern of hedge fund managers risk-taking behavior, and link the risk-taking choices to managers compensation as well as various other potential explanatory variables. In addition, we examine how the risk-taking choices affect fund performance in the future and how investors react to those choices. Our results can help investors better manage their portfolios risk and can shed light on future compensation contract design. We use fund level data from the Lipper TASS database over the period from 1994 to 2015 to examine the relation between risk taking and managers compensation. Hedge fund managers compensation comes from the management fee and the incentive fee. Most hedge funds adopt the high-water mark (HWM) provision, which requires fund managers to make up any previous losses 2

4 before they can collect the incentive fee. The combination of the incentive fee and the high-water mark provision makes hedge fund managers compensation nonlinear and resemble a call option. To capture the effect on risk-taking choices, we focus on two important aspects of managers compensation, that is, the percentage of the management fee in the total compensation, and the distance between fund value and the high-water mark. 6 Previous literature mostly focuses on the incentive fee rather than the management fee. There is one exception. Lan, Wang, and Yang (2013) show that the management fee is the majority part of managers total compensation, and thus motivates managers to take less risk to increase survival probabilities when their funds perform poorly. Consistent with Lan, Wang, and Yang (2013), our data show that, even when funds are above water, on average 70-80% of managers compensation comes from the management fee. That is to say, the management fee is the majority part of managers total compensation. Therefore, we use the percentage of the management fee in total compensation as a key variable in this study. Following Buraschi, Kosowski, and Sritrakul (2014), we measure hedge fund risk taking using fund return volatility, style beta, and style residual volatility. Return volatility is a natural measure for uncertainty, and is directly driven by fund managers decisions on risk taking. We compute style beta and style residual volatility by regressing fund returns on hedge fund index returns. Style beta measures the uncertainty caused by co-movement with a hedge fund style index, or intuitively, style beta represents hedge fund risk caused by style strategies. Residual volatility is the standard deviation of the error term and measures the fund specific risk taking. Our first empirical finding is somewhat surprising. Hedge fund managers de-risk, or reduce risk taking, when the contribution of the management fee to their total compensation increases. Why? According to the intuition in Yin (2016), when funds grow large and the management fee becomes more important, managers tend to take less risk so that they can retain fund assets and keep collecting the management fee. 6 To make sure both aspects are relevant for fund managers compensation, we initially restrict our sample to funds with both high-water mark provisions and non-zero fees. This excludes 27% of the hedge funds that meet our other criteria. In the robustness check, all main results remain without this sample restriction. 3

5 Regarding the incentive fee and the high-water mark, most prior theoretical work, such as Hodder and Jackwerth (2007), Panageas and Westerfield (2009), and Buraschi, Kosowski, and Sritrakul (2014), predicts that when funds are below their high-water marks, fund managers increase their risk taking to boost performance and make up past losses. When funds are above their high-water marks, fund managers take constant risk. Our empirical results are consistent with the theoretical prediction that fund managers take more risk when fund value is below the highwater mark. Unexpectedly, we find that when the fund value is above the high-water mark, fund managers actually take more risk rather than constant risk. Why do our findings differ from theoretical predictions? One possible reason is that many models assume an infinite horizon for hedge fund managers. In real practice, however, hedge funds only survive a few years. When fund value is far enough above the high-water mark, fund managers would take more risk to further enhance their compensation, rather than reduce risk taking to lock in their gains. We further examine managers risk-taking behavior during the recent financial crisis. During this period, many hedge funds suffered huge losses and fell below their high-water marks. Managers of these funds face a dilemma, that is, whether increase risk to make up the losses or reduce risk to enhance survival probabilities. One interesting finding is that fund managers increased style beta but reduced residual volatility during the crisis period. In other words, managers herded more with other funds in the same style to increase survival likelihood. How managers risk-taking choices affect fund performance and fund flows? We find that more risk taking seemly improves hedge funds future after-fee raw returns, but not their styleadjusted returns, or the style alphas. This seems to indicate that investors do not benefit from increased risk taking. Are investors aware of managers risk-taking behavior and investing accordingly? Our analysis suggests that investors are smart and avoid funds with high risk-taking. Finally, we test whether other variables documented in the literature would influence hedge fund risk taking, as indicated in Lan, Wang, and Yang (2013), Drechsler (2014), and Kolokolova and Mattes (2014). We find that fund managers take more risk when funds are not near termination, when their outside options are low, when their strategies are scalable, and when their compensation is volatile. More importantly, after controlling for these variables, we still find that fund managers 4

6 take more risk when fund value falls below and grows above the high-water mark and they reduce risk taking when the management fee becomes more important. Overall, we comprehensively test predictions of theoretical research related to hedge fund risk taking. Our study delivers four new empirical findings to the literature. First, to our best knowledge, we are the first study to empirically examine the impact of the management fee on hedge fund risk taking. Consistent with Lan, Wang, and Yang (2013), we find that the management fee is the majority part of hedge fund managers total compensation. More importantly, we find that managers take less risk when the management fee contributes more to their total compensation, possibly to retain fund size and lock in gains. Second, we find that fund managers take more risk not only when fund value falls below the high-water mark, but also when funds grow above their high-water marks. The latter part differs from most of the theoretical predictions. Third, we provide an explicit analysis of hedge fund risk taking during the recent financial crisis. We find that style betas increased, yet fund-specific return volatilities decreased. In other words, hedge funds herded more with their style peers during the crisis period. Finally, extra risk taking only boosts raw returns, but not style-adjusted returns. Our study complements the large body of literature regarding hedge funds behavior and thus can help investors better understand hedge fund risk taking. The rest of our article is organized as follows. In Section I, we provide a literature review and develop our hypotheses. We define key variables and describe the data in Section II. Section III presents basic empirical relation between managers compensation and risk taking. We conduct robustness checks and examine other potential variables related to hedge fund risk taking in Section IV. Section V concludes. I. Literature Review and Hypotheses Development How hedge fund managers compensation structure influences fund managers risk taking has been studied theoretically in many papers. However, the assumptions and focuses of these studies vary, and as a result, these studies reach mixed conclusions regarding fund risk taking. In this section, we review six previous studies in the order of publication time, and we compare each 5

7 study s main assumptions and conclusions. Building on these previous studies, we develop our testable hypotheses. One of the earliest work is Goetzmann, Ingersoll, and Ross (2003), which examines the costs and benefits of high-water mark provisions in hedge fund managers compensation contracts. The authors extend their model to test whether fund managers take excess risk because of the convex payoff structure when fund value is below the high-water mark. Based on the assumption that fund managers maximize the present value of their fees, the authors show that fund managers should reduce volatility when fund value is near liquidation to increase survival probabilities, and adopt larger volatility at higher asset levels to increase the value of the incentive fee. Hodder and Jackwerth (2007) assume that fund managers have a finite time horizon, and they maximize power utility of terminal wealth with constant relative risk aversion (CRRA). Based on these assumptions, fund managers increase risk taking when fund value falls below the highwater mark, and the model defines an endogenous shutdown barrier. When fund value is above the high-water mark, fund managers allocate a constant proportion of fund capital to the risky asset, that is, the Merton s constant. Merton (1969) shows that investors with constant relative risk aversion (CRRA) would allocate a constant proportion of their wealth to the risky asset, and this constant is referred to as the Merton s constant. Panageas and Westerfield (2009) develop a model in which fund managers with CRRA risk preference maximize the present value of their compensation. The authors argue that managers risk taking depends on the time horizon. With an infinite horizon, fund managers allocate a constant fraction of capital to the risky asset. However, with a finite horizon, fund managers opt for unbounded volatility as they approach the termination time. Over the most recent couple of years, we collect three almost contemporaneous papers. Lan, Wang, and Yang (2013) focus more on funds survival. They find that a risk-neutral manager becomes endogenously risk-averse and decreases leverage following poor performance to increase the fund s survival likelihood. In their model, fund managers have an infinite time horizon and try to maximize the present value of total fees (i.e., both the incentive fee and the management fee). In their setting, the management fee becomes the more important part of managers total 6

8 compensation, and thus survival is more important for fund managers. Therefore, hedge fund managers choose to de-risk when fund value is below the high-water mark. Drechsler (2014) examines the optimal risk choice of fund managers who maximize the present value of total fees with an infinite horizon. The author argues that hedge fund risk taking depends not only on the ratio of fund assets to the high-water mark, but also on other factors. When a manager s outside option value is low, investors termination policy is strict, or the management fee is high, negative returns would induce the manager into de-risking. Otherwise, the fund manager engages in gambling. Finally, Buraschi, Kosowski, and Sritrakul (2014) focus more on the endogenous choice of hedge fund leverage and its impact on performance evaluation. In their model, fund managers have a finite time horizon and maximize the utility of terminal wealth with constant relative risk aversion. The authors argue that hedge fund managers face several nonlinear incentives, such as the combination of the incentive fee and the high-water mark provision (call option) and the combination of investors redemption options and prime brokers options allowing for forced deleverage when funds are under water (put option). Therefore, the optimal leverage is statedependent, and the traditional alpha measure can be seriously biased. They find a concave relation between risk taking and fund value when funds are below their high-water marks. Fund managers increase risk taking when fund value falls below the high-water mark but decrease risk taking when funds are near termination. Based on the extant literature, which is more explicit on the incentive fee and the highwater mark rather than on the management fee, we first examine the relation between risk taking and fund value relative to the high-water mark. Although the incentive fee contract and the highwater mark provision make hedge fund managers compensation look like a call option, Lan, Wang, and Yang (2013) and Drechsler (2014) show that the option-like compensation design does not necessarily lead to more risk taking. Thus, it is important to empirically study hedge fund managers behavior when fund value is below the high-water mark. 7 Therefore, our first hypothesis is: 7 One interesting scenario is the recently financial crisis, during which many hedge funds suffered huge losses and fell below their high-water mark. We are going to examine the crisis period in Section III.C. 7

9 H1: When hedge fund value falls below the high-water mark, managers will take less risk. At the same time, hedge fund risk taking when fund value is above the high-water mark either is neglected in previous studies or appears to be constant in the models. However, taking constant risk seems to be a strong assumption. Because fund value is commonly above the highwater mark in our sample, it is also important to examine managers behavior when their optionlike compensation is in the money. To be more specific, our second hypotheses is: H2: When hedge fund value grows above the high-water mark, managers will take constant risk. The importance of the management fee has been slowly recognized by both academics and practitioners over recent years. 8 The management fee increases with fund size and is a more reliable source of compensation for fund managers. When funds grow large, the management fee may become the more important part of managers total compensation. As a result, fund managers may want to reduce risk to increase survival probabilities so that they can keep collecting the management fee. In other words, we want to test the following hypothesis. H3: Hedge funds managers take less risk when the contribution of the management fee is high. As discussed in the literature, funds with different characteristics may behave differently. Lan, Wang, and Yang (2013) argue that managerial ownership is important, Drechsler (2014) states that the termination policy plays an important role, and both studies show that managers outside options influence their risk-taking behavior. For managerial ownership, many hedge fund managers are required to invest in their own funds with the purpose of aligning managers incentives with investors best interests. Thus, it is expected that fund managers will take more risk to boost fund performance when managerial ownership is high. For the fund termination policy, termination is costly for fund managers because they cannot continue to collect fees and not every manager can start a new fund later. When investors are more likely to leave, fund managers may take less risk to increase survival probabilities. Finally, when fund managers have outside options, 8 See Hedge Fund AUM: Why Assets Matter to Family Offices and Other Investors ( among others. 8

10 that is, the opportunity to start a new fund, they may be more willing to take more risk. In summary, we test the following hypothesis regarding other variables documented in the literature. H4: Hedge fund managers take less risk when managerial ownership is low, the termination policy is strict, or outside options are low. II. Data We collect data from the Lipper TASS database. Following the literature, we only keep funds that report monthly net-of-fee returns in US dollars (USD). Because our key compensation measures involve the high-water mark and the management fee, we require all funds in our sample to have high-water mark provisions and charge positive incentive fees and management fees. 9 Fund-month observations with missing information about fund returns, assets under management, or investment styles are deleted. We exclude Fund of Hedge Fund style because funds in this style invest in other hedge funds rather than directly invest in securities, and the risk-taking behavior of funds of hedge funds can be different from that of regular hedge funds. Finally, the Option Strategy style is also excluded because only a few funds belong to this style, and this style only starts around To minimize the survivorship bias, we include defunct funds in our sample. Because TASS provides data on defunct funds dating back to 1994, the sample period in this study is from January 1994 to December To mitigate backfill bias, we exclude observations before the dates when funds were added to the TASS database. If the add dates are not available, we exclude the first 18 months of data. In addition, we require each fund to have at least $5 million under management and 24 months of observations. A. Managers Compensation: High-water Mark, Incentive Fee, and Management Fee 9 This restriction makes sure both measures are relevant to the funds in our sample. It excludes 27% of hedge funds that meet other criteria from our sample. Our robustness tests with all data available show that the main findings can be extended to the whole sample. 9

11 We are interested in two key variables of hedge fund managers compensation that might affect their risk-taking decisions. The first variable is the fund value relative to the high-water mark, and the second one is the contribution of the management fee to managers total compensation. We measure how far a fund is from its high-water mark using the distance between fund value and the high-water mark at the end of each quarter, DDDDDDDD2HHHHHH iiii = NNNNNN iiii 1, (1) HHHHHH iiii where NAV is the quarter-end net asset value of fund i. A similar measure is used in Buraschi, Kosowski, and Sritrakul (2014). When Dist2HWM is negative, the fund is under water, and the more negative it is, the more distressed the fund is. When Dist2HWM is positive, the fund is above water, and the more positive it is, the better off the fund is. We compute the contribution of the management fee to manager s overall compensation, MgmtFee%, at the end of each quarter as below, MMMMMMMMMMMMMM% iiii = MMMMMMMMMMMMMMMMMMMM FFFFFF iiii TTTTTTTTTT CCCCCCCCCCCCCCCCCCCCCCCC iiii, (2) where the management fee and managers total compensation are in absolute dollar terms. When the fund is below water, all managers compensation comes from the management fee, and MgmtFee% is equal to 100%. This is a less interesting case. When the fund is above water, managers compensation comes from both the incentive fee and the management fee, and MgmtFee% is between zero and 100% and can differ across time and across funds. Therefore, we only examine the influence of the management fee on risk taking when fund value is above the high-water mark in the following analysis. One potential concern is that both measures clearly depend on the value of the high-water mark, which is not directly observable. In this study, we assume that hedge funds reset their highwater marks at the end of each year, and therefore the high-water mark is the historical highest year-end NAV as in Yin (2016). We also perform robustness tests with a rolling high-water mark as in Li, Holland, and Kazemi (2014) in Section IV.A. 10

12 B. Hedge Fund Risk Taking Hedge fund risk taking can be measured in many different ways. Volatility is commonly used in the literature. For instance, theoretical work such as Lan, Wang, and Yang (2013) and Drechsler (2014) combine the volatility of risky assets and leverage to measure hedge fund risk taking. Empirical studies, such as Aragon and Nanda (2011) and Kolokolova and Mattes (2014), also use volatility to measure hedge fund risk taking. Therefore, our first measure of risk taking is the volatility of fund i s monthly returns computed over a one-year period as follows, where μμ ii is the average return over this one-year period. vvvvvv ii,(tt+1,tt+12) = 1 12 (rr 11 kk=1 ii,tt+kk μμ ii ) 2, (3) Hedge fund return volatility is highly related to their style strategies. For example, hedge funds that bet on the direction of asset prices, such as Dedicated Short Bias style, would have higher volatility than funds that aim to minimize market exposure, such as Fixed Income Arbitrage style. 10 In fact, previous studies, such as Brown and Goetzmann (2003), find that hedge fund return dynamics are well described by their styles indices. To further decompose hedge fund risk taking into style-related component and fund-specific component, we estimate the following specification for fund i in style j, rr ii,tt = αα ii + ββ ii SSSSSSSSSSSSSSSSeeeeeeeeeeeeeeee jj,tt + εε ii,tt. (4) We estimate the above regression for each fund using a rolling 12-month of data. For the style index, we use the indices provided by Credit Suisse, as in Buraschi, Kosowski, and Sritrakul (2014). Credit Suisse Hedge Fund indices can be directly observed by investors and perfectly match the ten hedge fund styles from the TASS database. 11 Style alpha is the intercept, αα ii, from equation (4), 10 During our sample period, the standard deviation of Credit Suisse Fixed Income Arbitrage index return is 1.52%, and the standard deviation of Credit Suisse Dedicated Short Bias index return is 4.73%. 11 The Credit Suisse index universe is defined as funds with a minimum of U.S. $50 million assets under management, a minimum one-year track record, and current audited financial statements. Funds within the Credit Suisse Hedge Fund Index are separated into ten primary subcategories based on their investment strategy. The Credit Suisse Hedge Fund Index in all cases represents at least 85% of the AUM in each respective category of the index universe. The index is asset-weighted. Fund weight caps may be applied to enhance diversification and limit concentration risk. The index is calculated and rebalanced monthly. Funds are reselected on a quarterly basis as necessary. For more detail, 11

13 and is normally interpreted as the style-adjusted return. Style beta, ββ ii, is the coefficient on the style index returns and measures risk taking of a hedge fund caused by the nature of its style strategy. We compute the fund-specific volatility, or residual volatility, as the standard deviation of the error term, εε ii,tt, which measures the fund-specific risk taking. Style beta and residual volatility provide more insight into hedge fund risk taking, that is, whether a hedge fund s risk taking comes from the style or from the specific managers behavior. C. Fund Performance and Fund Flows To measure fund performance, we mainly rely on after-fee raw returns, rr ii,tt, and the styleadjusted return, αα ii, defined above. In addition, we use fund capital flows to examine how investors react to managers risk-taking behavior. Following Sirri and Tufano (1998), we calculate capital flows over a one-year period as, FFFFFFFF ii,(tt+1,tt+12) = AAAAAA ii,tt+12 AAAAAA ii,tt (1+CCCCCCCCCCCCCCCCCCCC RRRRRRRRRRRR ii,(tt+1,tt+12) ) AAAAAA ii,tt, (5) where AAAAAA ii,tt is assets under management of fund i in month t. D. Summary Statistics Table I reports the summary statistics of our sample. To eliminate reporting errors and outliers, we winsorize fund returns, capital flows, and Dist2HWM at the 1% and 99% level. Our sample includes about 31,000 fund-quarter observations. [Insert Table I about here] The mean of Dist2HWM across all funds and all quarters is 0.07%, suggesting that hedge funds are on average slightly above their high-water marks. However, the large standard deviation of 15.94% and the inter-quartile range of 12.75% both indicate that there is a large variation in Dist2HWM. In other words, while some funds are very successful and above water, many others are deep under water. The mean and median of MgmtFee% are 75.35% and 82.69%, respectively. please refer to the index documents at Credit Suisse Hedge Fund Indexes website ( ). 12

14 The calculation of the MgmtFee% actually includes funds under their high-water marks, which have MgmtFee% of 100% by definition. If we only consider funds above their high-water marks, the mean and median for MgmtFee% are 71.23% and 73.08%, respectively. Either way, the management fee is clearly an important part of managers overall compensation. During our sample period, the average volatility of hedge fund returns is 3.08% per month (or 11.15% per year), which is below the market volatility of 4.30% per month (or 14.90% per year). This suggests that hedge funds do hedge and provide some protection against market fluctuation. The style beta in our sample has a mean of 0.87 and a standard deviation of This result implies that, although hedge funds in the same style category share some commonality with an average style beta close to one, there is a large dispersion in managers behavior. This can also be seen in residual volatility. Average residual volatility of 2.38% per month (or 7.97% per year), compared to average volatility of 3.08% (or 11.15% per year), indicates that most of hedge fund volatility is fund specific. In terms of fund performance, the average cumulative return is 7.90% per year. The annualized style alpha has a mean of 1.31% and a median of 1.73% per year. The positive mean and median of style alpha suggest that smaller funds have better performance than the style index, because Credit Suisse indices are calculated using returns of large hedge funds. During our sample period, the average flow is positive at 14.57% with a negative median of -1.14%. This indicates that overall fund flows over the past 20 years have been large and positive, yet the majority of funds do not receive positive flows, potentially due to the global financial crisis and its aftermath. We also report summary statistics on many important fund characteristics. Hedge funds typically charge a management fee between 1% and 2% and an incentive fee of 20%. Although the average fund size is above $200 million, the median size is only around $60 million. Thus, hedge funds are relatively small compared to traditional investment vehicles such as mutual funds. Furthermore, hedge funds are short-lived, given that the median fund age is only 72 months. Share restrictions are common in the hedge fund industry. Most hedge funds have a redemption frequency between 30 and 90 days and a notice period of 30 days. However, lockup periods are not commonly used, given a median of zero months. In our sample, 34% of all funds have 13

15 investment from their own managers and 66% use leverage. The high minimum investment requirements and low average of Open to Public suggest that only qualified investors can invest in hedge funds. III. Hedge Fund Managers Compensation and Risk Taking In this section, we examine the general pattern between hedge fund risk-taking behavior and managers compensation. We start in Section III.A with a preliminary analysis. In Section III.B, we provide rigorous analysis using piecewise regressions. We take a close look at the recent financial crisis in Section III.C. How hedge fund risk taking affects their future performance is investigated in Section III.D. A. Preliminary Analysis To get a heuristic understanding of the impact of managers compensation on hedge fund risk taking, we start by plotting the relation between managers compensation and funds subsequent year risk-taking. Taking Dist2HWM as an example. Each quarter, we first rank funds into ten groups based on their quarter-end Dist2HWM (five groups below the high-water mark and five groups above), then we calculate the average risk taking of the ten groups over the next oneyear period. That is, we would like to observe how Dist2HWM affects a hedge fund s risk taking over the next year. The results are presented in Figure 1 Panel A. The relation between hedge fund risk taking and funds distance to their high-water marks is convex rather than straight, which indicates a linear regression would be mis-specified. To the left, when fund value falls below the high-water mark, all three measures of risk taking increase with distance. This is consistent with Hodder and Jackwerth (2007), Panageas and Westerfield (2009), and Buraschi, Kosowski, and Sritrakul (2014). The intuition is that when funds are below their high-water marks, fund managers would take more risk to make up the losses and be profitable again. When fund value exceeds the high-water mark, to the right of the graph, we find that hedge funds reduce their risk slightly at first but then significantly increase their risk taking with distance. According to Hodder and Jackwerth (2007) 14

16 and Buraschi, Kosowski, and Sritrakul (2014), when fund value is above the high-water mark, fund risk taking has a slightly positive slope but is bounded by Merton s constant. What we identify in the Figure 1 Panel A does not seem to be perfectly in line with previous studies. [Insert Figure 1 about here] Panel B of Figure 1 presents results based on the MgmtFee%. Similar to Panel A, every quarter, we rank funds above their high-water marks into five groups based on their MgmtFee% and then calculate their average risk taking for the next 12 months. When the MgmtFee% increases from 20% to 80%, we find that style beta decreases from 0.8 to 0.6. The total volatility first decreases from 3.77% to 1.98% but then slightly reverse back to 2.32%. The residual volatility follows a similar pattern as the total volatility. Overall, it seems that hedge fund managers slowly take less risk as the management fee becomes more important. B. Baseline Piecewise Regression To capture the nonlinear convex relation and control for fund characteristics more precisely, we use piecewise regressions, as in Buraschi, Kosowski, and Sritrakul (2014). Piecewise regressions allow us to examine fund managers behavior when fund value grows above and falls below the high-water mark separately. Our specification is as follows, RRRRRRRR TTTTTTTTTTTT ii,tt+1,tt+12 = ββ 0 + ββ 1 1 DDDDDDDD2HHHHHHiiii <0 DDDDDDDD2HHHHHH iiii + ββ 2 1 DDDDDDDD2HHHHHHiiii >0 DDDDDDDD2HHHHHH iiii +ββ 3 1 DDDDDDDD2HHHHHHiiii >0 MMMMMMMMMMMMMM% iiii + CCCCCCCCCCCCCC VVVVVVVVVVVVVVVVVV iiii + εε iiii. (6) Here 1 DDDDDDDD2HHHHHHiiii <0 equals one if fund value is below the high-water mark and zero otherwise, and 1 DDDDDDDD2HHHHHHiiii >0 is defined similarly. As discussed above, because MgmtFee% equals one when fund value is below the high-water mark, we only examine its influence on risk taking when managers can charge both the management fee and the incentive fee, that is, when Dist2HWMit>0. For control variables, we include fund size and fund age at time t, fund performance and capital flows over the past year, and fund characteristics such as fee structure and share restrictions. Following Petersen (2009), we cluster the standard errors at both fund and quarter level. 15

17 Table II presents regression results. When funds are below their high-water marks, the coefficient on Dist2HWM for predicting total volatility is with a t-statistic of In terms of magnitude, if the Dist2HMW value falls by one inter-quartile range, total return volatility would increase by 0.92% per month (or 3.19% per year). This increase is economically large, given that the overall volatility is only 3.08% per month (or 10.67% per year). The negative coefficient indicates that fund managers increase risk taking when their options to charge the incentive fee fall further out of the money. We find similar patterns using style betas and residual volatility. For instance, a one inter-quartile decrease in Dist2HWM leads to an increase in style beta by 0.30 and an increase in residual volatility by 0.67% per month (or 2.32% per year). Again, these are economically large, because the average style beta is 0.87 and the average residual volatility is 2.38% per month (or 8.24% per year). These findings are consistent with predictions in Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2014). [Insert Table II about here] When funds are above their high-water marks, the coefficient on Dist2HWM for total volatility is with a t-statistic of That is, a one inter-quartile increase in Dist2HWM leads to a 0.32% per month (1.11% per year) increase in total volatility. The coefficients on Dist2HWM for both style beta and residual volatility are also positive and significant. In terms of economic magnitude, a one inter-quartile increase in Dist2HWM leads to a 0.10 increase in style beta and a 0.27% per month (0.94% per year) increase in residual volatility. The significantly positive coefficients on Dist2HWM for all three risk-taking measures indicate that fund managers also take more risk when their funds are above water. Comparing with the corresponding coefficients when funds are below their high-water marks, the additional risk taking is less steep but is still economically large. This finding is unexpected, because models in Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2014) indicate constant risk-taking when funds are above their high-water marks. Why would managers take more risk when their funds are above water? One possible reason is that, as shown in Table I, hedge fund are short lived. Thus, fund managers may be motivated to take more risk to further enhance fund performance and improve their incentive fees, especially when fund value is far enough above the high-water mark. 16

18 The other key independent variable in Table II is MgmtFee%. The coefficient on MgmtFee% for total volatility is with a t-statistic of That is, a one inter-quartile increase in MgmtFee% would cause volatility to decrease by 0.31% per month (1.09% per year). Similarly, the coefficients on MgmtFee% for both style beta and residual volatility are negative and significant. A one inter-quartile increase in MgmtFee% would cause style beta to decrease by 0.10 and residual volatility to decrease by 0.26% per month (0.90% per year). In other words, fund managers choose to take less risk when the management fee becomes dominant in the compensation package. The intuition here is that, when the management fee becomes more important, survival may become the priority so that fund managers can keep collecting the fees in the future. Thus, fund managers reduce risk taking to increase survival probabilities. We also present all the coefficients on the control variables for completeness. We find that hedge funds with smaller size and better past performance take more risk. As funds become older, they tend to have higher style betas. In other words, they behave more like the index. Other characteristics are mostly insignificant. C. Financial Crisis The recent Financial Crisis provides a unique opportunity to examine hedge fund risk taking. During the crisis, many hedge funds suffered huge losses. On the one hand, fund managers had incentives to increase risk to improve performance and make up the losses. On the other hand, fund managers might also be cautious and take less risk to increase survival probabilities. Thus, it is interesting to examine hedge fund managers behavior during this period. Following NBER business cycle reference dates, we define the financial crisis period as January 2008 to June In Table III, we add a dummy variable to the baseline model. The indicator, Crisis, is equal to one when time t is in the crisis period and zero otherwise. The significant coefficients of the Crisis indicator suggest that, during the crisis period, the volatility of hedge fund returns was 1.13% per month higher, the residual volatility was 0.73% per month higher, but the style beta was 0.10 lower. In addition, the sensitivities of style beta and residual volatility to Dist2HWM were different during the crisis. It seems that fund managers would 17

19 increase style beta but reduce residual volatility when fund value fell further below the high-water mark. One possible explanation is that hedge fund managers tried to herd with other funds in the same style and increase survival probabilities during the crisis. [Insert Table III about here] D. Future Performance Our empirical results so far show that hedge fund managers compensation structure would affect their subsequent risk taking. For a typical investor, she cares about not only the risk-taking behavior, but also fund performance in the future. In other words, investors would be interested in how the peculiar risk-taking behavior affects funds future performance and whether they can benefit from the increased/decreased risk taking. To examine how managers compensation structure and thus their risk-taking behavior influences future fund performance, we first estimate the expected risk taking using our baseline model in equation (6) and the corresponding coefficients in Table II. Then we regress fund performance over the next year on predicted risk taking, and the results are summarized in Table IV. In the first column, the coefficients of cumulative returns on the expected total volatility, expected style beta, and expected residual volatility are , , and , respectively. All coefficients are positive, indicating that taking more risk actually boosts future performance in terms of cumulative returns. However, the coefficient is statistically significant only when we use predicted style beta. A one inter-quartile increase in the style beta leads to a 6.21% increase in cumulative returns over the next year. However, the pattern changes when we use style-adjusted returns, or style alphas defined in equation (4), in the second column. The coefficients of annualized style alphas on the expected total volatility, expected style beta, and expected residual volatility are , , and , respectively, and the first two coefficients are statistically significant. The negative coefficients imply that taking more risk actually leads to lower style alphas. In other words, investors do not benefit from managers risk-taking behavior in terms of style-adjusted returns. If 18

20 we take style beta for example, a one inter-quartile increase in style beta leads to a 4.14% decrease in annualized style-adjusted returns. In the third column, we examine the impact on fund annual flows. Fund flows reflect investors reaction to fund performance and managers risk taking. The coefficients on the expected total volatility, expected style beta, and expected residual volatility are , , and , respectively. Again, the first two coefficients are statistically significant. The negative coefficients suggest that the future fund flows are actually negatively related to expected risk taking. This interesting result implies that investors are smart and withdraw their money from managers with higher expected risk taking. [Insert Table IV about here] Now is it possible to use our two key variables, Dist2HWM and MgmtFee%, as useful signals for fund selection purposes? To link the two key variables to next year fund performance, we use a portfolio approach. In Panel A of Table V, we first rank funds into ten groups every quarter based on their Dist2HWM (five groups below the high-water mark and five groups above). Then we calculate their average cumulative return, average annualized style alpha, and average flow of the next 12 months. For all funds below the high-water mark, portfolio 1 includes funds with the largest distance from the high-water mark, or funds that are deeply under water, while portfolio 5 include funds with the smallest distance from the high-water mark, or funds that are slightly under water. From our earlier results, funds in portfolio 1 would take more risk on average. The cumulative 1- year raw returns for portfolio 1 and 5 are 11.09% and 6.74%, respectively, and the return difference is significant. That is to say, funds deep under water outperform funds slightly under water. However, the style alphas have a different pattern. The style alphas for portfolio 1 and 5 are -1.56% and 1.05%, respectively, and the high minus low difference is positive and significant. That is to say, style-adjusted returns are actually higher for funds that are slightly under water. For funds above the high-water mark, portfolio 1 includes funds closest to the high-water mark, and portfolio 5 includes funds furthest from their high-water marks. The cumulative returns for portfolio 1 and 5 are 7.47% and 13.70%, respectively. The difference is highly significant and 19

21 suggests that funds substantially above the high-water mark deliver better returns than funds close to the high-water mark. When we move to the style-adjusted returns, funds in portfolio 5 provide higher style alphas than portfolio 1, although the difference is not statistically significant. Thus, it seems that funds that are well above their high-water marks have better returns and alphas in the next period. [Insert Table V about here] In Table V Panel B, we rank funds that are above their high-water marks into five groups every quarter based on their MgmtFee%. Portfolio 1 contains funds with the lowest proportion of compensation from the management fee, and funds in this portfolio generate a one-year cumulative return of 13.22% on average. Portfolio 5 contains funds with the highest proportion of compensation from the management fee, and funds in this portfolio provide a one-year cumulative return of 7.65% on average. The return difference is -5.57% and statistically significant. This suggests that higher MgmtFee% indicates lower future raw returns. The style-adjusted alphas have a similar but weaker pattern. Funds in portfolio 1 provide style alphas at 3.36%, which is 1.01% higher than funds in portfolio 5. However, the difference in alphas between portfolio 1 and portfolio 5 is not statistically significant. That is to say, lower MgmtFee% is associated with higher future returns, and vice versa. What about future capital flows? Do investors recognize the pattern between fund performance and compensation structure, and thus invest accordingly? In the last column of Table V Panel A, we observe a positive relation between future capital flows and Dist2HWM. For funds deep below water in portfolio 1, they suffer capital outflows of % per year. For funds slightly below water in portfolio 5, they have outflows of -3.87% per year. Because funds under water do not generate higher style alphas when they take more risk, investors are smart not to put more money in those funds. When funds are above their high-water marks, we observe that funds slightly above water in portfolio 1 attract inflows of 7.48% per year, while funds in portfolio 5 have inflows of 52.49% per year. This pattern suggests that investors chase after-fee raw returns and style alphas when funds are above water. We find similar return-chasing results along the MgmtFee% 20

22 dimension. For funds with the lowest MgmtFee% in portfolio 1, the capital flow rate is 39.66%, and for funds with the highest MgmtFee% in portfolio 5, the capital flow rate is 16.83%. IV. Robustness Tests and Further Discussions As discussed in Lan, Wang, and Yang (2013) and Drechsler (2014), many other variables can potentially affect manager s risk-taking decisions. In this section, we offer a comprehensive set of robustness checks and further discussions. A. Robustness Tests: Baseline Model In this section, we examine the robustness of our baseline model in equation (6) by varying ways of computing the high-water mark and risk taking, accounting for fund size and seasonality, etc. [Insert Table VI about here] A.1. Rolling High-water Mark As mentioned earlier, the high-water mark is not directly observable. In this subsection, instead of using historical highest NAV, we use the highest year-end NAV over the past three years as the high-water mark, as in Li, Holland, and Kazemi (2014). The benefit of using a rolling high-water mark is that it controls for the possibility that different investors may have different high-water marks because they invest in the fund at different points in time, and the possibility that some funds may reset their high-water marks when fund value is deep under water. Table VI Panel A shows that fund managers increase their risk taking when fund value increases above or falls below their rolling high-water marks, and managers de-risk when MgmtFee% increases. The magnitude and significance of all coefficients are similar to those in Table II. A.2. Alternative Risk Taking Measures Previous literature, such as Liang and Park (2007), finds that hedge fund returns have a long left tail and volatility may not fully capture the risk. In case our risk-taking measures cannot fully capture the real risk-taking behavior, we compute three additional downside risk measures following Liang and Park (2007). The first one is semi-deviation (SEM), defined as below, 21