Gambling or De-risking: Hedge Fund Risk Taking

Transcription

1 Gambling or De-risking: Hedge Fund Risk Taking Chengdong Yin and Xiaoyan Zhang * August 2016 Abstract In this article, we examine the impact of hedge fund fee structure on managers risk taking. We find that fund managers take more risk when fund value both increases above and falls below the high-water mark, and they reduce risk taking when the management fee becomes the more important part of total compensation. Following theoretical predictions, we find that hedge fund risk taking is also influenced by other determinants, such as managerial ownership, termination policy, outside options, strategy scalability, and volatility of fee income. During the financial crisis, managers take less risk to increase survival probability. However, taking more risk does not necessarily generate better future performance and thus does 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. We would like to thank Lu Zheng, and participants of Krannert School Alcoa Workshop for helpful comments and suggestions. All remaining errors are ours.

2 Gambling or De-risking: Hedge Fund Risk Taking August 2016 Abstract In this article, we examine the impact of hedge fund fee structure on managers risk taking. We find that fund managers take more risk when fund value both increases above and falls below the high-water mark, and they reduce risk taking when the management fee becomes the more important part of total compensation. Following theoretical predictions, we find that hedge fund risk taking is also influenced by other determinants, such as managerial ownership, termination policy, outside options, strategy scalability, and volatility of fee income. During the financial crisis, managers take less risk to increase survival probability. However, taking more risk does not necessarily generate better future performance and thus does not benefit investors. Key Words: Hedge Fund, Risk Taking, Incentive Fee, Management Fee, High-water Mark. JEL Classification: G23

3 Hedge funds are an important part of the investment society, and they have many unique features that separate them from conventional investment vehicles, such as pension funds and mutual funds. Two important differences are investment constraints and the incentive structure. In terms of investment constraints, hedge fund managers enjoy more freedom in investment decisions than typical mutual fund managers and pension fund managers do, and they are allowed to short sell and invest in highly leveraged products such as derivatives. In terms of the incentive structure, hedge fund managers compensation depends on both the incentive fee and the management fee, while most managers of pension funds and mutual funds only rely on the latter. The incentive structure of hedge funds can be highly nonlinear, because most funds adopt the high-water mark (HWM) provision, which requires fund managers to make up any losses before they can collect the incentive fee. The combination of the incentive fee and the high-water mark provision makes hedge fund managers compensation look like a call option In this article, we examine the interesting question of hedge fund risk taking behavior. On the one hand, the public worries that hedge funds may take excessive risk because not only hedge funds are less regulated and commonly use short sale, derivatives, and leverage to enhance their performance, 1 but also the call-option-like compensation may induce managers to take more risk when fund value falls below high-water mark. 2 On the other hand, the industry and the academia also worry that hedge funds become less ambitious about their own performance and behave similarly to mutual funds when they grow large. 3 The management fee increases with fund size and provides a more stable source of income for fund managers. Yin (2016) shows that because hedge funds suffer from diseconomies of scale, the management fee becomes the more important part of managers total compensation when funds grow large. In addition, hedge fund investors are sophisticated and withdraw their money when fund performance falls below style average. 1 See The Problem with Hedge Funds ( and SEC Warns Investors of Hedge-Fund Risks ( among others. 2 However, option-like compensation does not necessarily lead to more risk taking. See Carpenter (2000) and Ross (2004), among others, for a discussion. 3 See Hedge Fund AUM: Why Assets Matter to Family Offices and Other Investors ( among others. 1

4 Therefore, fund managers may risk little when the management fee contributes more so that they can retain fund size and keep collecting fees. Conceptually, hedge fund managers choose the optimal level of risk taking based on the incentives and constraints they face. The optimal choice of hedge fund risk taking has been studied extensively in the literature, but there are still many unanswered questions. In terms of theoretical work, most papers have quite different predictions, caused by differences in assumptions and setups. For example, Hodder and Jackwerth (2007) show that hedge fund managers would take more risk when fund value fall below high-water mark. However, Lan, Wang, and Yang (2013) argue that fund managers would reduce risk taking to increase survival probability. We provide a more detailed review of related theoretical work in the next section, and we try to understand which model(s) best explains the data. In terms of empirical studies, most papers mainly focus on risk shifting within a calendar year, that is, the tournament behavior, rather than the overall level of risk taking. 4 Besides, the empirical studies commonly neglect the impact of the management fee. In this article, we first document the general pattern of hedge fund risk taking behaviors. Next, we link the choices of the risk taking level to hedge fund fee structures, as well as various other potential determinants, as indicated by many previous theoretical studies. Furthermore, we examine how the risk taking choices affect fund performance in the future and investors responses. Our results can help investors better manage their portfolio s risk and can shed light on future compensation contract design. To be more specific, we measure hedge fund risk taking using volatility, beta, and residual risk. Volatility is the standard deviation of fund returns over a one-year period. Beta measures the co-movement between a hedge fund and its style index, while residual risk is the standard deviation of the error when we regress fund returns on style index returns. In other words, Beta represents hedge fund risk caused by style strategies, and residual risk represents fund specific risk. Using these measures, we find that fund managers would take more risk when fund value deviates from high-water mark. The increase in risk taking when funds are below their high-water mark is 4 See Aragon and Nanda (2011) and Kolokolova and Mattes (2014), among others. 2

5 consistent with literature, such as Hodder and Jackwerth (2007), Panageas and Westerfield (2009), and Buraschi, Kosowski, and Sritrakul (2014), and suggests that fund managers take more risk to boost performance and make up the losses. The result of taking more risk when fund value is above high-water mark is quite surprising and different from the prediction of constant risk taking in the literature. It implies that fund managers would take more risk to further enhance their compensation, rather than reduce risk taking to lock their gains. We also examine the impact of the management fee on hedge fund risk taking. 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. We find that managers reduce risk taking when the contribution of the management fee to managers total compensation increases and thus provide some supporting evidence for their predictions. In addition, we test whether other determinants documented in the literature would influence hedge fund risk taking. For example, Lan, Wang, and Yang (2013) and Drechsler (2014) show that managerial ownership, termination policy, and outside options may change managers behavior. Consistent with their predictions, we find that hedge funds take less risk when managerial ownership is lower or when funds are near termination. However, our results show that funds with higher outside options take less risk. It seems that fund managers are motivated to protect their outside options by reducing risk. Following Kolokolova and Mattes (2014), we examine the impact of the scalability of hedge fund strategies. We find that hedge funds with scalable strategies are less sensitive to the impact of the contribution of the management fee. Our understanding is that, when strategies are scalable, hedge funds suffer less from diseconomies of scale and thus the management fee becomes less important. We also examine the volatility of managers total compensation, because fund managers may have incentives to smooth their fees over time. The volatility of managers compensation is more likely to increase when fund value falls below high-water mark, because fund managers can only charge the management fee then. Thus, fund managers would take more risk to boost performance so that they can charge the incentive fee and smooth compensation. This hypothesis is supported by our results. During the recent Financial Crisis, many hedge funds suffered huge losses and fell below their high-water 3

6 mark. Managers of these funds face a dilemma, that is, whether increase risk to make up the losses or reduce risk to enhance survival probability. Our results show that hedge funds did have higher volatility during the crisis period. When we look at beta and residual risk, we find that fund managers increased beta but reduced residual risk. In other words, managers would herd with other funds in the same style to increase survival likelihood. This study contributes to the literature in several ways. First, we comprehensively test predictions of theoretical research related to hedge fund risk taking. We find that fund managers take more risk not only when fund value falls below high-water mark, but also when funds grow above their high-water mark. The former result is consistent with most of the literature. The reason that our results are different from the prediction of decreasing risk taking is that, in real practice, hedge funds only survive a few years. This is quite different from the infinite horizon assumption in many models, which predicts decreasing risk taking. The latter result is different from the prediction of constant risk taking in the literature. The difference may also come from the finite life span of hedge funds in practice. When fund value is far enough above high-water mark, fund managers may have incentives to improve their compensation by taking more risk. Second, 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 the literature, such as Lan, Wang, and Yang (2013), we find that hedge funds take less risk when the management fee contributes more to managers total compensation. Because the management fee is a more stable source of income, when the management fee becomes the major part of total compensation, survival becomes more important for fund managers and thus they have incentives to reduce risk to retain fund size and lock their gains. Third, we provide an explicit analysis of hedge fund risk taking during the Financial Crisis. Our results show that the sensitivities of beta to the distance between fund value and high-water mark increased during the crisis, while the sensitivities of residual risk declined. In other words, hedge fund likely herd with their peers in the same style during the crisis period. Our study complements the large body of literature regarding hedge funds behavior during the Financial crisis and thus can help investors better understand hedge fund risk taking. 4

7 The rest of our article is organized as follows. Section I provides a literature review and develops our hypotheses. Section II defines key variables and describes the data. Section III presents basic empirical relations between fund incentive structure and risk taking. In Section IV, we examine other potential determinants of hedge fund risk taking. Section V provides evidence how risk taking affects future performance. Section VI concludes. I. Literature Review and Hypotheses Development How hedge fund managers incentive structure influences fund managers risk taking has been studied theoretically in the literature. However, the assumptions and focuses of these studies vary, and they reach mixed conclusions. In this section, we review six previous studies in the order of publication time and we compare each study s main assumptions and conclusions. Building on the previous studies, we develop our testable hypotheses. One of the earliest work is Goetzmann, Ingersoll, and Ross (2003), who examine 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 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 probability, and adopt larger volatility at higher asset levels to increase the value of the incentive fee. Hodder and Jackwerth's (2007) assume that fund managers have 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 high-water mark and approaches an endogenous shutdown barrier. When fund value is above high-water mark, fund managers allocate a constant proportion to the risky asset, that is, the Merton s constant. Panageas and Westerfield (2009) develop a model in which fund managers with CRRA risk preference maximize the present value of the incentive fee. The authors argue that managers risk taking depends on the time horizon. With infinite horizon, fund managers allocate a constant 5

8 fraction of capital in the risky asset. But with 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) lean 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 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 settings, the management fee becomes the more important part of managers total compensation, and thus survival is more important for fund managers. Therefore, hedge fund managers would choose to de-risk when they are below high-water mark. Drechsler (2014) examine the optimal risk choice of fund managers who maximize the present value of total fees with infinite horizon. The author argues that hedge fund risk taking depends not only on the ratio of fund assets to high-water mark, but also on other factors. When a manager s outside option value is low, investors termination policy is strict, or management fees are high, then negative returns 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 finite time horizon and maximize 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 relationship between risk taking and fund value relative to high-water mark. Fund managers increase risk taking when fund value falls below high-water mark but decrease risk taking when funds are near termination. 6

9 Based on the extant literature, we first examine the relationship between risk taking and fund value relative to high-water mark. Although the incentive fee contract and the high-water mark provision make hedge fund managers compensation look like a call option, Lan, Wang, and Yang (2013) and Drechsler (2014) show that 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 high-water mark. 5 Therefore, our first hypothesis is: H1: When hedge fund value falls below high-water mark, managers will take less risk. At the same time, hedge fund risk taking when fund value is above high-water mark is either 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 high-water mark in our sample, it is also important to examine managers behavior when their option-like compensation is in the money. To be more specific, our second hypotheses is: H2: When hedge fund value grows above high-water mark, managers will take constant risk. The importance of the management fee has been recognized by both academics and practitioners recently. 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 probability 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 Lan, Wang, and Yang (2013) and Drechsler (2014), funds with different characteristics may behave differently. In this study, we are interested in three determinants in the literature. The first one is managerial ownership. Many hedge fund managers are required to invest in their own funds, and the purpose is to align managers incentives with investors best interests. 5 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 IV.F. 7

10 Thus, it is expected that fund managers will take more risk and boost fund performance when the managerial ownership is high. The second determinant is 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 the survival probability. The last factor is fund managers outside options. Fund managers may take more risk when they have the opportunity to start a new fund. H4: Hedge fund managers take less risk when the managerial ownership is low, the termination policy is strict, or the outside option is low. II. Data The data used in this study are from the Lipper TASS database. Following the literature, we only keep funds that report monthly net-of-fee returns in US dollars (USD). 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. Thus, the risk taking of funds of hedge funds is different from regular hedge funds. The Option Strategy style is also excluded, because only a few funds belong to this style, and there is no matching index from Credit Suisse. To mitigate the survivorship bias, we include defunct funds in our sample. Because TASS began to provide data of defunct funds since 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. Dependent Variables: 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. 8

11 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: vvvvvv ii,(tt+1,tt+12) = 1 12 (rr 11 kk=1 ii,tt+kk μμ ii ) 2. (1) However, hedge funds in certain styles may have higher volatility than funds in other styles because of their strategy design. For example, hedge funds that bet on the direction of assets prices (e.g., Dedicated Short Bias style) would have higher volatility than funds that aim to minimize market exposure (e.g., Convertible Arbitrage style and Fixed Income Arbitrage style). 6 To take this possibility into account, we regress returns of fund i in style j on the corresponding style index returns, rr ii,tt = αα ii + ββ ii SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS jj,tt + εε ii,tt. (2) The above regression is estimated for each fund using a rolling 12-month of data. Beta, ββ ii, is the coefficient on the style index returns, which measures risk taking of a hedge fund caused by the nature of its strategy. We compute the residual risk as the standard deviation of the error term, εε ii,tt, which measures the fund specific risk taking. Beta and residual risk 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. For the style index, we use the indices provided by Credit Suisse, as in Buraschi, Kosowski, and Sritrakul (2014). B. Independent Variables: High-water Mark and the Management Fee We are interested in two key variables that might affect hedge fund risk taking. The first one is the fund value relative to high-water mark, and the second is the contribution of the management 6 During our sample period, the standard deviation of Credit Suisse Convertible Arbitrage index is 1.87% per month, the standard deviation of Credit Suisse Fixed Income Arbitrage index is 1.52%, and the standard deviation of Credit Suisse Dedicated Short Bias index is 4.73%. 9

12 fee to managers total compensation. Following Buraschi, Kosowski, and Sritrakul (2014), we define the distance to high-water mark at the end of each quarter as follows, DDDDDDDD2HHHHHH tt = NNNNNN tt HHHHHH tt 1. (3) where NAV is the net asset value. Dist2HWM is in percentage and it measures how far the fund value is from its high-water mark. When it is negative, the fund is under the water, and vice versa. One complication is that the high-water mark value is not directly observable. In this study, we assume that hedge funds reset their high-water mark at the end of each year, and high-water mark is the historical highest year-end NAV. We also provide robustness tests with a rolling high-water mark in Section III.C. The contribution of the management fee to manager s overall compensation, MgmtFee%, is calculated as below, where the management fee and managers total compensation are in absolute dollar terms, MMMMMMMMMMMMMM% tt = MMMMMMMMMMMMMMMMMMMM FFFFFF tt TTTTTTTTTT CCCCCCCCCCCCCCCCCCCCCCCC tt. (4) When the management fee becomes the more important part of managers total compensation, liquidation would be very costly to fund managers, and thus they would change their risk taking behavior. We need to be cautious that MgmtFee% is always equal to one when fund value falls below high-water mark, because in this situation fund managers cannot charge the incentive fee. Therefore, we only examine the influence of the management fee when fund value is above HWM in the following analysis. C. Summary Statistics Table I shows the summary statistics of our sample. To eliminate reporting errors and outliers, we winsorize fund returns, capital flows, and Dist2HWM at 1% and 99% level. Both mean (0.02%) and median (1.97%) of Dist2HWM are positive. This suggests that hedge funds, on average, are above their high-water mark during our sample period. However, the large standard deviation and inter-quartile range 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 10

13 median of MgmtFee% are 72.32% and 80.10%, respectively. Because managers can only charge the management fee and thus MgmtFee% always equals 100% when funds are below their highwater mark, the large magnitude of this variable is consistent with the observation that not all funds are above water. [Insert Table I about here] During our sample period, average volatility of hedge fund returns is 3.23% per month, which is below the market volatility of 4.30% per month. This suggests that hedge funds do hedge and provide some protection against market fluctuation. The beta in our sample has a mean of 0.89 and a standard deviation of This result implies that, although hedge funds in the same style category share some commonality, there is a large dispersion in managers behavior. This can also be seen in residual risk. Average residual risk of 2.45%, compared to average volatility of 3.23%, indicates that most of hedge fund volatility are fund specific. At the same time, alpha, which is the intercept of Equation (2), has a mean of 0.09% and a median of 0.13% per month. The positive alphas suggest that smaller funds have better performance, because Credit Suisse indices are calculated using large hedge funds returns. Following Sirri and Tufano (1998), we calculate capital flows over a one-year period as, FFFFFFFF iiii = AAAAAA iiii AAAAAA ii,tt 12 (1+CCCCCCCCCCCCCCCCCCCC RRRRRRRRRRRR ii,(tt 11,tt) ) AAAAAA ii,tt 12, (5) where AUM is assets under management. During our sample period, the average flow is positive (13.75%) and is consistent with the fast growth of total assets under management in the hedge fund industry. In terms of fund characteristics, hedge funds commonly charge a management fee between 1% and 2% and an incentive fee of 20%, and 73% of all funds have high-water mark provisions. Although the average fund size is above $200 million, the median size is only around $60 million. Thus, hedge funds are relative smaller comparing 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 days and 90 days and a notice period of 30 days. However, lockup periods 11

14 are not commonly used, given the median of zero month. In our sample, 36% of all funds have investment from their own managers and 64% 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 Fee Structure and Risk Taking In this section, we examine the overall pattern between hedge fund risk taking behavior and the fee structure. We start in section III.A with preliminary analysis. In section III.B, we provide some more rigorous analysis using piecewise regressions. Robustness checks are presented in section III.C. A. Preliminary Analysis To get a heuristic understanding of the relationship between hedge fund risk taking and fund value relative to high-water mark, we rank funds into ten and five groups based on their Dist2HWM and MgmtFee% every quarter, respectively. Then we calculate their average risk taking of the next 12 months over time. That is, we would like to observe how the previous period Dist2HWM and MgmtFee% affect a hedge fund s risk taking over the next one-year period. The results are presented in Figure 1. In Panel A, the relationship between hedge fund risk taking and funds distance to their high-water mark seems to be convex. When fund value falls below 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). When fund value increases above high-water mark, it seems that hedge funds reduce their risk slightly at first but then increase their risk taking with distance. This pattern is somewhat similar to the predictions of Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2014), that is, fund managers would take more risk when fund value is considerably higher than the high-water mark. 7 7 The risk taking increases slowly and is bounded by Merton s constant in Hodder and Jackwerth (2007) and Buraschi, Kosowski, and Sritrakul (2014). 12

15 [Insert Figure 1 about here] Panel B of Figure 1 presents results based on the MgmtFee%. When the MgmtFee% increases from 20% to 80%, we find that beta monotonically decreases from 0.8 to 0.6. The total volatility first decreases from 3.99% to 2.17% but then slightly reverse back to 2.80%. The residual risk follows a similar pattern as the volatility. Overall, it seems that hedge fund managers slowly take less risk when the management fee becomes more important. B. Baseline Piecewise Regression To capture the nonlinear relationship and control for fund characteristics more precisely, we estimate the following piecewise regression, where 1 DDDDDDDD2HHHHHHiiii <0 equals one if fund value is below high-water mark and zero otherwise, and 1 DDDDDDDD2HHHHHHiiii >0 is defined similarly. 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) As discussed above, because MgmtFee% equals one when fund value is below 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 Dist2HWMi,t>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 by fund. Table II present regression results. In Panel A, we do not include additional control variables, and we find that when funds are below their high-water mark, the coefficients of Dist2HWM are all negative and significant at 1% significance level using three different measures of risk taking. This indicates that fund managers increase risk taking when their options to charge the incentive fee fall further out of the money. In terms of magnitude, if fund value falls by one inter-quartile range, volatility increases by 1.03% per month, beta increases by 0.28, and residual risk increases 13

16 by 0.73% per month. Those increases are economically large, given that the overall volatility per year is only 12%, and the betas are mostly around [Insert Table II about here] Consistent with Figure 1, the coefficients of Dist2HWM are all positive and significant when funds are above their high-water mark. Thus, fund managers also take more risk when their funds are above water. Now, one inter-quartile increase in Dist2HWM leads to 0.83% increase in volatility, 0.20 increase in beta, and 0.57% increase in residual risk. Comparing with the corresponding coefficients when funds are below their high-water mark, the additional risk taking is less steep but is still economically large. The coefficient on MgmtFee% is negative and significant at 1% significance level for all three risk taking measures, which is consistent with our prior that fund managers take less risk when the management fee becomes dominant in the compensation package. One standard deviation increase in MgmtFee% would cause volatility to decrease by 0.30% per month, beta to decrease by 0.07, and residual risk to decrease by 0.22% per month. Table II Panel B reports the regression results with many additional fund characteristics controls. The coefficients are almost the same as those in Panel A, except for the Dist2HWM when fund value is above water. The coefficients magnitudes become half of those in Panel A, indicating that when the call option of the incentive fee is in the money, fund managers still take more risk but in a more moderately way after controlling for fund characteristics. Looking into the control variables, we find that hedge funds with smaller size and better past performance take more risk, and it is likely these two characteristics reduce the magnitude of risk-taking when funds are above their high-water mark. Fund age has mixed impact. When funds become older, they have higher beta but lower residual risk. In other words, they behave more like the index. C. Robustness Tests of Baseline Model C.1. High-water Mark Provision 14

17 In the baseline model, we treat every hedge fund the same as if they all have high-water mark provision. 8 However, about 28% of the hedge funds in our sample do not have high-water mark. These fund managers can charge the incentive fee when the profit is positive, and they do not need to make up the loss. Thus, we expect that fund managers without high-water mark provision might be more aggressive. To test this possibility, we include a HWM indicator, which equals one if a fund has a highwater mark provision and zero otherwise, in the regression. Table III Panel A shows that the coefficients of HWM are not significant. Thus, on average, there is no significant difference in risk taking between funds with and without high-water mark. When fund value is below high-water mark, the coefficients of the interaction term between HWM and Dist2HWM are not significant. This suggests that the sensitivity to Dist2HWM of fund managers with a high-water mark provision is not significantly different from that of their peers. However, when fund value grows above high-water mark, the significantly negative coefficients of the interaction term between HWM and Dist2HWM indicate that fund managers with high-water mark are less aggressive. To be more specific, for hedge funds with high-water mark, one inter-quartile increase in Dist2HWM leads to 0.37% per month increase in volatility and 0.35% increase in residual risk. One possible explanation is that fund managers with high-water mark are more likely to lock their gains by taking less risk. [Insert Table III about here] C.2. Rolling High-water Mark As mentioned earlier, the high-water mark is not directly observable. For our first robustness check, instead of using historical highest NAV, we use the highest NAV over the past three years as the high-water mark. The benefits of using rolling high-water mark is that it controls for the possibility that different investors may have different high-water mark, and the possibility 8 For funds without high-water mark, we use their historical highest NAV as their hypothetical high-water mark to calculate Dist2HWM. However, managers compensation is based on the actual fee structure. In other words, we do not use the hypothetical high-water mark when we calculate the incentive fee, and fund managers can charge the incentive fee when the fund profit is positive. 15

18 that some funds may reset their high-water mark when fund value is deep under water. Table III Panel B shows that fund managers increase their risk taking when fund values are above or below their rolling high-water marks. The results are consistent with our main findings in Table II. C.3. Control for Past Risk Taking Risk taking behavior might be persistent. In Table III Panel C, we include past risk taking in the regression to control for this potential persistence. The significantly positive coefficients of past risk taking indicate that there is some persistence in managers risk taking behavior. After controlling for past risk taking, the coefficients of Dist2HWM and MgmtFee% are still significant and have the sign as in the baseline model. Thus, our results are robust and not driven by the past risk taking. C.4. With Fund Fixed Effects It is possible that risk taking behavior is fund specific and is related to some unobservable characteristics of each fund. To control for this possibility, we include fund fixed effects to take into account the different risk preference of fund managers. Table III Panel D reports regression results with fund fixed effects. We find similar results as in Table II, that is, fund managers take more risk when fund value deviates from high-water mark and take less risk when the management fee becomes more important. Thus, our results are not driven by managers who prefer more risk taking. C.5. Downside Risk The literature 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, SSSSSS iiii = EE{MMMMMM[(rr iiii μμ ii ), 0]}. (7) Here, rr iiii is hedge fund returns and μμ ii is the average return. SEM is similar to the standard deviation except that we only consider the deviation from the mean when it is negative. 16

19 The second approach is Value-at-Risk (VaR). In this study, we use both nonparametric VaR (VaR_NP) and Cornish-Fisher VaR (VaR_CF). We compute the nonparametric VaR, variable VaR_NP, as the five percentile of all observations in a time window. Clearly, this measure does not rely on any assumption on the distribution of returns, by using the left tail of observed returns. For the Cornish-Fisher expansion, we define VaR_CF as follows (the subscripts are omitted for simplicity), VVVVVV_CCCC = μμ + Ω(αα) σσ, (8) Ω(αα) = zz(αα) (zz(αα)2 1)SS zz(αα)3 3zz(αα) KK zz(αα)3 5zz(αα) SS 2. (9) Here, μ is the average return, σ is the standard deviation, S is the skewness, and K is the excess kurtosis. As shown in equation (9), VaR_CF takes the skewness and the kurtosis of the empirical distribution into consideration. The regression results are summarized in Table III Panel E. Notice that, when we use VaR measures as the dependent variable, we add a negative sign because they are always negative. The results suggest that hedge fund managers take more risk when fund value increases above or falls below high-water mark and take less risk when the management fee becomes more important. This is consistent with our main findings using volatility, beta, and residual risk as the risk measures. C.6. Seasonality/Tournament Behavior The literature, such as Aragon and Nanda (2011) and Kolokolova and Mattes (2014), shows that hedge funds may change their risk taking within a year, that is, the tournament behavior in which fund managers increase risk taking in the second half of a year after poor performance in the first half. To examine whether our results are driven by seasonality or tournament behavior, we estimate the piecewise regression by quarter. The dependent variable is the volatility of fund returns over the next quarter. Table III Panel F shows that the relationship between risk taking and Dist2HWM/MgmtFee% is robust in all quarters. In other words, our results in Table II are not driven by managers behavior in certain quarters. C.7. Different Size Groups 17

20 Fund size may influence managers risk preference. For example, managers of smaller funds may want to take more risk to boost fund performance and thus attract capital inflows. Managers of larger funds might be more cautious and reduce risk taking to protect their compensation and reputation. In Figure 2, we examine whether the relationship between risk taking and Dist2HWM is driven by funds in certain size groups. Every quarter, we first double sort funds by their assets under management and their Dist2HWM, and then calculate average risk taking of each portfolio over time. Figure 2 is consistent with Figure 1 Panel A and shows a convex relationship for different size groups, that is, hedge fund managers take more risk when fund value deviates from high-water mark. [Insert Figure 2 about here] Figure 3 presents average risk taking of portfolios double sorted by fund size and MgmtFee%. The results in Figure 3 are similar to Figure 1 Panel B and indicate that fund managers would reduce risk taking when the management fee becomes the more important part of their compensation. Figure 2 and Figure 3 provide some evidence that our results are not driven by funds with certain size. [Insert Figure 3 about here] In summary, results in this section suggest that our baseline model is robust and captures the impact of Dist2HWM and MgmtFee% on hedge funds risk taking. In the following analysis, we are going to extend the baseline model and examine other determinants discussed in the literature. We keep volatility, beta, and residual risk as dependent variables because they have been used in the literature, and they can be easily calculated and thus can be observed by all investors. IV. Other Determinants of Hedge Fund Risk Taking As discussed in Section I, there are determinants, other than Dist2HWM and MgmtFee%, which may influence hedge fund managers risk taking. Hypothesis H4 lists several determinants discussed in the theoretical literature, such as managerial ownership, termination policy, and outside options. In addition to those factors, empirical research also considers determinants such 18

21 as liquidation probability and scalability of hedge funds strategies. 9 Furthermore, volatility of managers compensation might also affect hedge fund manager s risk taking behavior, because fund managers may want to smooth their compensation over time by changing their risk taking. To examine the potential impact of above determinants, we modify our baseline model of Equation (6) by adding interactions as follows, RRRRRRRR TTTTTTTTTTTT ii,(tt+1,tt+12) = ββ 0 + DD iiii + ββ 1 1 DDDDDDDD2HHHHHHiiii <0 DDDDDDDD2HHHHHH iiii +ββ 2 1 DDDDDDDD2HHHHHHiiii <0 DDDDDDDD2HHHHHH iiii DD iiii + ββ 3 1 DDDDDDDD2HHHHHHiiii >0 DDDDDDtt2HHHHHH iiii +ββ 4 1 DDDDDDDD2HHHHHHiiii >0 DDDDDDDD2HHHHHH iiii DD iiii + ββ 5 1 DDDDDDDD2HHHHHHiiii >0 MMMMMMMMMMMMMM% iiii + ββ 6 1 DDDDDDDD2HHHHHHiiii >0 MMMMMMMMMMMMMM% iiii DD iiii + CCCCCCCCCCCCCC VVVVVVVVVVVVVVVVVV iiii + εε iiii, (10) where Dit is an indicator and represents one potential determinant. We include interaction terms between Dit and Dist2HWM (MgmtFee%) to examine whether there is any joint impact on hedge fund risk taking. Control variables are similarly defined as before. A. Managerial ownership Many hedge fund managers are required to invest in their own funds. The purpose is to align managers incentives with investors best interests. The impact of managerial ownership on risk taking is mixed in the literature. Lan, Wang, and Yang (2013) show that fund managers with higher ownership in their own funds take more risk, while Aragon and Nanda (2011) argue that managerial ownership makes a hedge fund manager more conservative with regard to risk shifting. To study this issue, we include Personal Capital, which is an indicator provided by TASS and equals one if a manager invests in her own fund and zero otherwise, in the regression. In Table IV Panel A, coefficients on the Dist2HWM and MgmtFee% have consistent signs and significances as in earlier tables. The coefficients of Personal Capital are positive and marginal significant. This provides some evidence that fund managers who invest in their own funds take more risk on average. However, coefficients of the interaction terms between Personal Capital and 9 For liquidation probability, see Aragon and Nanda (2011), among others. See Kolokolova and Mattes (2014), among others, for a discussion about strategy scalability. 19

22 Dist2HWM (or MgmtFee%) are not significant. Thus, sensitivities to Dist2HWM (or MgmtFee%) of managers who invest in their own funds are not different from those of their peers. [Insert Table IV about here] B. Near Termination When fund value is far below high-water mark, on the one hand, investors may lose their confidence in fund managers and choose to leave the fund. On the other hand, fund managers may also shut down their funds voluntarily when their options to charge the incentive fee are deep out of the money. Unfortunately, neither the endogenous shutdown barrier of fund managers nor the exogenous termination policy of fund investors is available in the data. In this subsection, we examine fund managers behavior when their funds are near termination, that is, fund value is far below high-water mark, in general. As discussed earlier, termination could be costly for fund managers. They lose all their future fees and many of them are not able to start a new fund. Thus, fund managers may behave differently when their funds are near termination. To examine this question, we use two approaches. In the first approach, we define a dummy variable, Near Termination, which is equal to 1 when fund value is 20% below high-water mark or further. We pick this cutoff point (i.e., Dist2HWM = -20%) because it is suggested by Goetzmann, Ingersoll, and Ross (2003) and Buraschi, Kosowski, and Sritrakul (2014), and it is around the tenth percentile of Dist2HWM in our sample. 10 Table IV Panel B shows that the coefficients of the interaction term between Near Termination and Dist2HWM are all positive and significant. The results suggest that fund managers increase risk taking much slower when fund value falls further below. One possible explanation is that fund managers become more conservative and want to increase the survival probability. 10 Goetzmann, Ingersoll, and Ross (2003) argue that many investors would liquidate if fund value falls by 15% to 25% from their high-water mark. Buraschi, Kosowski, and Sritrakul (2014) find that hedge funds on average have 20% drawdown tolerance before suffering from large outflows or forced deleveraging. 20

23 In the second approach, we follow Aragon and Nanda (2011) and estimate the probability of termination using a Probit regression. The dependent variable is an indicator and equals one if a fund is alive in current quarter and is liquidated over the next 12 months. The independent variables include fund size, fund age, and cumulative return and the standard deviation of fund returns over the past 12 months. We also include a dummy variable to indicate whether a fund is under its high-water mark. The results in Table IV Panel C suggest that funds with larger size, older age, better performance, and fund value above high-water mark are less likely to be liquidated. In the second stage, we calculate the probability of termination based on the Probit regression results. Then we include High ProbTerm, which equals one if the probability of termination is above median and zero otherwise, in the piecewise regression. The significant and negative coefficients of the indicator suggest that fund managers would take less risk when their probabilities of liquidation increase. However, fund managers sensitivities to Dist2HWM are not significantly different except when we use volatility as the dependent variable. The positive coefficient of the interaction term indicates that fund managers would be more conservative when the probabilities of liquidation are high. In summary, although the results of the two approaches are somewhat different, one thing in common is that hedge fund managers would take less risk when their funds are near termination. This result is consistent with Buraschi, Kosowski, and Sritrakul (2014), and implies that termination is so costly that fund managers would reduce risk to increase survival likelihood. C. Outside options When fund managers have outside options, it is likely that they would behave more aggressively so that they can reach their high-water mark or exercise their outside options faster. Lan, Wang, and Yang (2013) argue that fund mangers outside options are related to past performance, while Drechsler (2014) assume that outside options are related to fund size. Therefore, in this study, we use fund past returns and fund size to proxy fund managers outside options. Every quarter, we rank funds into four portfolios (2-by-2) based on their returns over the 21

24 past year and their size at the quarter end. Funds with both performance and fund size above median have higher outside options, represented by High Outside Option dummy. Funds in the other portfolios are used as benchmark. The results in Table IV Panel D are different from the predictions in the literature. The coefficients of the interaction terms between outside options and Dist2HWM suggest that fund managers with higher outside options are less sensitive to Dist2HWM. In other words, everything else equal, fund managers with higher outside options would take less risk. One possible explanation is that, even with outside options, it is still costly for a fund manager to shut down the current fund and start a new one. Thus, fund managers with better performance, larger fund size, and thus higher compensation, may want to protect their options and lock their gains by taking less risk. D. Scalability Kolokolova and Mattes (2014) argue that hedge funds that can easily scale their strategy are more likely to increase risk taking. Following their approach, we add an indicator Scalability, which equals one if a fund uses leverage and has a correlation with MSCI World Index higher than median, in the piecewise regression. The positive and significant coefficients of the indicator in Table IV Panel E suggest that funds with scalable strategies take more risk on average. But their sensitivities to Dist2HWM are not significantly different from their peers. At the same time, funds with scalable strategies are less sensitive to MgmtFee%. In other words, they are likely to take more risk even when the management fee becomes the more important part of managers total compensation. One possible explanation is that, because their strategies are scalable, hedge funds suffer less from diseconomies of scale, and thus the management fee becomes less important. E. Volatility of Managers Compensation When managers compensation is volatile in the past, they may change their behavior to smooth future fees. To test this possibility, we include an indicator High Fee Std, which equals to one if the standard deviation of managers compensation over the past year is above median, in 22