Electronic copy available at: https://ssrn.com/abstract=2899834

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 de-

risk 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: https://ssrn.com/abstract=2899834

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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 (https://www.theguardian.com/money/us-money-blog/2014/may/08/hedge-fund-investing-gambling-ira-sohn). 2 See for instance “Hedge Fund Betting on Lawsuits Is Spreading” from Bloomberg on March 18, 2015 (https://www.bloomberg.com/news/articles/2015-03-18/hedge-fund-betting-on-lawsuits-is-spreading). 3 See for instance “Hedge fund derisk by January Month End” from Hedge Fund Insight on February 6, 2014. 4 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.

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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 so-

called “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

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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.

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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 high-

water 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 style-

adjusted 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

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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

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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 high-

water 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

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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 state-

dependent, 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 high-

water 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 high-

water 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.

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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 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 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” (http://richard-wilson.blogspot.com/2012/09/hedge-fund-assets-under-management-aum.html), among others.

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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 2000.

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 2015. 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.

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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,

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖 = 𝑁𝑁𝑁𝑁𝑁𝑁𝑖𝑖𝑖𝑖𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖

− 1, (1)

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,

𝐻𝐻𝑀𝑀𝑀𝑀𝐷𝐷𝑀𝑀𝑀𝑀𝑀𝑀%𝑖𝑖𝑖𝑖 = 𝐻𝐻𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑖𝑖 𝐹𝐹𝑀𝑀𝑀𝑀𝑖𝑖𝑖𝑖𝑇𝑇𝑇𝑇𝑖𝑖𝑀𝑀𝑇𝑇 𝐶𝐶𝑇𝑇𝑀𝑀𝐶𝐶𝑀𝑀𝑀𝑀𝐶𝐶𝑀𝑀𝑖𝑖𝑖𝑖𝑇𝑇𝑀𝑀𝑖𝑖𝑖𝑖

, (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 high-

water 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.

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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,

𝑣𝑣𝑣𝑣𝑣𝑣𝑖𝑖,(𝑖𝑖+1,𝑖𝑖+12) = � 111∑ (𝑟𝑟𝑖𝑖,𝑖𝑖+𝑘𝑘 − 𝜇𝜇𝑖𝑖)212𝑘𝑘=1 , (3)

where 𝜇𝜇𝑖𝑖 is the average return over this one-year period.

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,

𝑟𝑟𝑖𝑖,𝑖𝑖 = 𝛼𝛼𝑖𝑖 + 𝛽𝛽𝑖𝑖 × 𝑆𝑆𝐷𝐷𝑆𝑆𝑣𝑣𝑀𝑀𝑆𝑆𝑆𝑆𝑆𝑆𝑀𝑀𝑒𝑒𝑒𝑒𝑀𝑀𝐷𝐷𝑒𝑒𝑟𝑟𝑆𝑆𝑗𝑗,𝑖𝑖 + 𝜀𝜀𝑖𝑖,𝑖𝑖. (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, 𝛼𝛼𝑖𝑖, 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,

12

and is normally interpreted as the style-adjusted return. Style beta, 𝛽𝛽𝑖𝑖, 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, 𝜀𝜀𝑖𝑖,𝑖𝑖, 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, 𝑟𝑟𝑖𝑖,𝑖𝑖, and the style-

adjusted return, 𝛼𝛼𝑖𝑖, 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,

𝑀𝑀𝑣𝑣𝑣𝑣𝐹𝐹𝑖𝑖,(𝑖𝑖+1,𝑖𝑖+12) = 𝑁𝑁𝐴𝐴𝐻𝐻𝑖𝑖,𝑖𝑖+12−𝑁𝑁𝐴𝐴𝐻𝐻𝑖𝑖,𝑖𝑖×(1+𝐶𝐶𝐶𝐶𝑀𝑀𝐶𝐶𝑇𝑇𝑀𝑀𝑖𝑖𝑖𝑖𝐶𝐶𝑀𝑀 𝑅𝑅𝑀𝑀𝑖𝑖𝐶𝐶𝑅𝑅𝑀𝑀𝑖𝑖,(𝑖𝑖+1,𝑖𝑖+12))𝑁𝑁𝐴𝐴𝐻𝐻𝑖𝑖,𝑖𝑖

, (5)

where 𝐴𝐴𝐴𝐴𝐻𝐻𝑖𝑖,𝑖𝑖 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 (https://secure.hedgeindex.com/hedgeindex/secure/en/documents.aspx?cy=GBP&indexname=HEDG ).

13

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 0.95. 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

14

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 one-

year 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)

15

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,

𝑒𝑒𝐷𝐷𝐷𝐷𝑅𝑅 𝑇𝑇𝑇𝑇𝑅𝑅𝐷𝐷𝑆𝑆𝑀𝑀𝑖𝑖,𝑖𝑖+1,𝑖𝑖+12

= 𝛽𝛽0 + 𝛽𝛽1 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖<0 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖 + 𝛽𝛽2 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖>0 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖

+𝛽𝛽3 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖>0 × 𝐻𝐻𝑀𝑀𝑀𝑀𝐷𝐷𝑀𝑀𝑀𝑀𝑀𝑀%𝑖𝑖𝑖𝑖 + 𝐶𝐶𝑣𝑣𝑆𝑆𝐷𝐷𝑟𝑟𝑣𝑣𝑣𝑣 𝑉𝑉𝑇𝑇𝑟𝑟𝐷𝐷𝑇𝑇𝑉𝑉𝑣𝑣𝑀𝑀𝐷𝐷𝑖𝑖𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑖𝑖. (6)

Here 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖<0 equals one if fund value is below the high-water mark and zero otherwise, and

1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖>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.

16

Table II presents regression results. When funds are below their high-water marks, the

coefficient on Dist2HWM for predicting total volatility is 0.0725 with a t-statistic of -15.19. 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 0.0251 with a t-statistic of 4.84. 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.

17

The other key independent variable in Table II is MgmtFee%. The coefficient on MgmtFee%

for total volatility is -0.0068 with a t-statistic of -9.06. 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 2009. 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

18

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 0.3192, 5.9159, and 0.7783, 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 -0.3358, -3.9443, and -

0.3245, 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

19

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 -2.4446, -8.1504,

and -1.5107, 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

20

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 -11.97% 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%

21

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,

22

𝑆𝑆𝑆𝑆𝐻𝐻𝑖𝑖𝑖𝑖 = �𝑆𝑆{𝐻𝐻𝐷𝐷𝑆𝑆[(𝑟𝑟𝑖𝑖𝑖𝑖 − 𝜇𝜇𝑖𝑖), 0]2}. (7)

Here, 𝑟𝑟𝑖𝑖𝑖𝑖 is hedge fund i’s after-fee raw return in month t, and 𝜇𝜇𝑖𝑖 is the average return for fund i.

SEM is similar to the standard deviation except that we only consider the deviation from the mean

when it is negative.

The second approach is Value-at-Risk (VaR). In this study, we use both nonparametric VaR

(denoted by VaR_NP) and Cornish-Fisher VaR (denoted by VaR_CF). We compute the

nonparametric VaR, VaR_NP, as the fifth 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 VaR, we define VaR_CF as follows (the subscripts are

omitted for simplicity),

𝑉𝑉𝑇𝑇𝑒𝑒_𝐶𝐶𝑀𝑀 = 𝜇𝜇 + Ω(𝛼𝛼) × 𝜎𝜎, (8)

Ω(𝛼𝛼) = 𝑧𝑧(𝛼𝛼) + 16

(𝑧𝑧(𝛼𝛼)2 − 1)𝑆𝑆 + 124�𝑧𝑧(𝛼𝛼)3 − 3𝑧𝑧(𝛼𝛼)�𝐾𝐾 − 1

36�2𝑧𝑧(𝛼𝛼)3 − 5𝑧𝑧(𝛼𝛼)�𝑆𝑆2. (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 VI Panel B. 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 the high-water mark and take less risk when the management fee becomes more important.

This is consistent with our main findings using volatility, style beta, and residual volatility as the

risk measures.

A.3. Seasonality/Tournament Behavior

Previous papers, such as Aragon and Nanda (2011) and Kolokolova and Mattes (2014),

shows that hedge funds may change their risk taking within a year, or the so-called “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

23

the volatility of fund returns over the next quarter. Table VI Panel C shows that the pattern of the

relation between risk taking and our key variables, Dist2HWM and MgmtFee%, is robust and

significant in all quarters. In other words, our results in Table II are not driven by managers’

behavior in certain quarters.

A.4. Different Size Groups

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 Table VI Panel D, we examine whether the relation between risk

taking and managers’ compensation structure is driven by funds in certain size groups. Every

quarter, we sort funds by their assets under management into three groups. Then we run the

piecewise regression for each size group separately. Consistent with Table II, we find that hedge

fund managers take more risk when fund value grows above and falls below the high-water mark,

and they reduce risk taking when the management fee becomes the more important part of their

compensation. Thus, our results are not driven by funds with certain size.

A.5. Funds without High-water Mark Provisions

In the baseline model, we only include hedge funds that have high-water mark provisions

and charge both the management fee and the incentive fee. Would the same results apply to the

larger sample when we include funds without high-water mark provisions? Notice that, for funds

without high-water mark provisions, managers can charge the incentive fee when the profit is

positive, and they do not need to make up the losses. Thus, we expect fund managers without high-

water mark provisions to be more aggressive. To calculate Dist2HWM for funds without high-

water mark provisions, we use their historical highest NAV as their hypothetical high-water mark.

We compute MgmtFee% based on their real compensation structure. That is, we do not use the

hypothetical high-water mark to calculate their incentive fee, and those fund managers can charge

the incentive fee when fund profits are positive

We then include a HWM indicator, which equals one if a fund has a high-water mark

provision and zero otherwise, in the regression. Table VI Panel E shows two findings. First, all the

24

coefficients on Dist2HWM and MgmtFee% are significant with expected signs and similar

magnitudes as in Table II. Second, coefficients on the interaction terms with the HWM dummy

are insignificant in almost all specification. That is to say, our main results are robust and can be

generalized to funds without high-water mark provisions, and the high-water mark provision itself

does not significantly alter managers’ risk-taking behavior.

A.6. Seven-factor Model

In Equation (4), we only consider one factor, the style index return. An alternative is to use

multi-factor models to capture managers’ preference for risk taking. In this section, we use the

Fung and Hsieh (2004) seven-factor model. We make two modifications when we examine risk

loadings and residual volatility in this model. First, when there are seven factors on the right hand

side, we estimate factor loadings over a two-year period to increase degrees of freedom and to

reduce potential noise. Second, to facilitate interpretation, we focus only on loadings on market

systematic risk, such as the beta on the market factor and the beta on the size factor, rather than

presenting results on all seven factors.

Table VI Panel F presents regression results when we use two-year volatility, beta of the

market factor, beta of the size factor, and residual volatility as dependent variables. When funds

are below their high-water marks, the negative and significant coefficients on Dist2HWM indicate

that fund managers would take more risk. When fund value increases above water, we find that

fund managers increase total return volatility and residual volatility based on the significantly

positive coefficients. In addition, consistent with Table II, we find that fund managers take less

risk when the management fee contributes more to their total compensation.

To summarize, results in this section suggest that our baseline model is robust and captures

the impact of Dist2HWM and MgmtFee% on the risk taking of hedge funds. In the following

analysis, we are going to extend the baseline model and examine various variables that could affect

risk taking as discussed in the literature. We keep volatility, beta, and residual volatility 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.

25

B. Discussion: Other Variables Related to Hedge Fund Risk Taking

Our empirical results show that both the distance to the high-water mark and the

importance of the management fee affect hedge fund risk taking. From Hypothesis H4, we know

that the risk-taking behavior can also be affected by other variables, such as termination policy,

outside options, and managerial ownership. In addition, empirical research also considers variables

such as liquidation probabilities as in Aragon and Nanda (2011) and scalability of hedge funds’

strategies as in Kolokolova and Mattes (2014). Furthermore, we also consider volatility of

managers’ compensation because fund managers may want to smooth their compensation over

time by adjusting their risk taking.

To examine how the variables above might affect the relation between risk taking and

managers’ compensation structure, we modify our baseline model in equation (6) as follows,

𝑒𝑒𝐷𝐷𝐷𝐷𝑅𝑅 𝑇𝑇𝑇𝑇𝑅𝑅𝐷𝐷𝑆𝑆𝑀𝑀𝑖𝑖,(𝑖𝑖+1,𝑖𝑖+12) = 𝛽𝛽0 + 𝛽𝛽1 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖<0 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖

+ 𝛽𝛽2 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖<0 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖 + 𝛽𝛽3 × 1𝐷𝐷𝑖𝑖𝐶𝐶𝑖𝑖2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖>0 × 𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑖𝑖𝑖𝑖

+ 𝛽𝛽4 × 𝑫𝑫𝒊𝒊𝒊𝒊 + 𝐶𝐶𝑣𝑣𝑆𝑆𝐷𝐷𝑟𝑟𝑣𝑣𝑣𝑣 𝑉𝑉𝑇𝑇𝑟𝑟𝐷𝐷𝑇𝑇𝑉𝑉𝑣𝑣𝑀𝑀𝐷𝐷𝑖𝑖𝑖𝑖 + 𝜀𝜀𝑖𝑖𝑖𝑖, (10)

where Dit is an indicator and represents one potential variable.12 Control variables are similarly

defined as before. We define various variables and corresponding Dit in Section IV.B.1, and

present empirical results in Section IV.B.2.

B.1. Relevant Variables

We first consider funds’ termination policy. When fund value is far below the 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. 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 new funds. Thus, fund managers may behave differently when their funds are near

termination.

12 We include interaction terms between Dit and Dist2HWM (MgmtFee%) to examine whether there is any joint impact on hedge fund risk taking in Internet Appendix Table IAII.

26

Unfortunately, neither the endogenous shutdown barrier of fund managers nor the

exogenous termination policy of fund investors is available in the data. As a result, to examine this

question, we follow Aragon and Nanda (2011) and estimate the probability of termination using a

Probit regression. The dependent variable is an indicator, which 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 the 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 Internet Appendix Table IAI suggest that larger, younger, better performing

funds and funds above their high-water marks are less likely to be liquidated. In the second stage,

we calculate the probability of termination based on the Probit regression results. The indicator

variable, Dit, equals one if the probability of termination is above the median and zero otherwise,

in the piecewise regression.

The second variable is managers’ outside options. When fund managers have outside options,

it is likely that they behave more aggressively so that they can reach their high-water marks 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 for

fund managers’ outside options. Every quarter, we rank funds into four portfolios (2-by-2) based

on their returns over the past year and their size at quarter end. The indicator variable, Dit, equals

one if a fund has both performance and fund size above median, that is, has higher outside options.

Funds in the other portfolios are used as a benchmark.

The third variable is 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 use the indicator Personal Capital

27

(i.e., Dit=Personal Capitalit), which equals one if a manager invests in her own fund and zero

otherwise, from TASS in the regression.

The fourth variable is 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

let the indicator, Dit, equal one if a fund uses leverage and has a correlation with MSCI World

Index higher than median.

The last variable is the volatility of managers’ compensation. When managers’ compensation

has been volatile in the past, they may change their behavior to smooth future fees. To test this

possibility, we define the indicator Dit so that it equals one if the standard deviation of managers’

compensation over the past year is above median and zero otherwise.

B.2. Empirical Results

Table VII Panels A through C present the impact of various variables discussed above on

total return volatility, style beta, and residual volatility, respectively.

[Insert Table VII about here]

The first specification examines the impact of termination probabilities. The significant

and negative coefficients of the indicator suggest that fund managers are more conservative and

take less risk when their probabilities of liquidation are high. In other words, hedge fund managers

reduce risk taking when their funds are near termination. The results are consistent with Buraschi,

Kosowski, and Sritrakul (2014), and imply that termination is so costly that fund managers reduce

risk to increase survival likelihood.

The results regarding outside options in regression (2) are different from the predictions in

the literature. The coefficients on the indicator are negative and significant. In other words,

everything else equal, fund managers with higher outside options 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 in their gains by taking

less risk.

28

Specification (3) examines the impact of managerial ownership. In all three panels, the

coefficients of the indicator are not significant at conventional levels. Thus, we do not find strong

evidence that managers who invest in their own funds behave differently from their peers.

The positive and significant coefficients of the indicator in regression (4) suggest that funds

with scalable strategies take more risk on average. One possible explanation is that, because their

strategies are scalable, hedge funds suffer less from diseconomies of scale. As a result, the

importance of the incentive fee increases, and fund managers are motivated to take more risk to

improve fund performance.

In the last column, the positive and significant coefficients of the indicator suggest that

hedge fund managers take more risk when their fees are volatile. Our expectation is that the

volatility of managers’ compensation is higher when fund value falls below the high-water mark,

because managers cannot charge the incentive fee. Thus, fund managers would take more risk to

boost fund performance and smooth their future compensation.

To summarize, Table VII shows that hedge fund managers become more conservative

when probabilities of termination are high and when they have high outside options. They are more

aggressive when their strategies are scalable and when their compensation is more volatile.

Therefore, various variables documented in the literature do have an impact on fund managers’

risk-taking behavior. More importantly, after controlling for these variables, we still find that fund

managers take more risk when fund value falls below and increases above the high-water mark,

and they reduce risk taking when the management fee becomes more important.

V. Conclusions

We examine the impact of hedge fund managers’ compensation contracts on their risk-

taking behavior. We present a few interesting empirical findings. First, as the management fee

becomes more important, fund managers de-risk to lock in gains. Second, fund managers take

more risk when fund value both increases above and falls below the high-water mark, which

challenges previous theoretical predictions. Third, the volatilities of all hedge funds increased

during the global financial crisis, and they were more driven by herding with the style index rather

29

than fund-specific risk taking. Finally, when managers take excessive risk to potentially boost their

performance, they end up improving raw returns rather than style-adjusted returns, and thus do not

necessarily benefit investors.

This study has several important implications for investors and future compensation

contract design. For example, investors should realize that fund managers take more risk not only

when fund value is below the high-water mark, but also when they beat their high-water marks.

For compensation contract design, future design should realize the importance of the management

fee. Most recently, due to mediocre performance, a few hedge funds have started to charge zero

management fee to attract potential investors. Is that a wise choice? Our rational expectation is

that without any management fee, hedge fund managers would surely be hungrier and take more

risks but not necessarily deliver better style-adjusted returns.

30

Reference

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Drechsler, Itamar. 2014. “Risk Choice under High-Water Marks.” Review of Financial Studies, January, hht081. doi:10.1093/rfs/hht081.

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32

Table I Summary Statistics Dist2HWM is calculated as NAV/HWM-1, where NAV is the quarter-end net asset value and HWM is the historical highest year-end NAV. We assume that HWM is reset at the end of each year. MgmtFee% is defined as Management Fee/Total Fee, where the management fee and the total fee are in absolute dollar amounts. Volatility is the standard deviation of fund monthly returns over a one-year period. To calculate style beta and residual volatility, we regress fund returns on style index returns as in Equation (4). Style beta is the coefficient on style index returns, residual volatility is the standard deviation of the error term, and style alpha is the intercept of the regression. Cumulative return is calculated over a one-year period. Capital flow is defined as in Equation (5). Fund age is the number of months since the inception date. Management fee is the percentage of fund assets that investors pay to fund managers. Incentive fee is the percentage of fund profits that investors pay to fund managers. Personal capital equals one if a fund manager invests in her own fund and zero otherwise. Leverage equals one when a fund uses leverage, and zero otherwise. Open to public equals one if a fund is open to the public, and zero otherwise. Mean Median Std Dev Inter-quartile Range

Dist2HWM (%) 0.07 2.00 15.94 12.75 MgmtFee% 75.35 82.69 26.48 46.18 Monthly Total Volatility (%) 3.08 2.48 2.25 2.78 Style Beta 0.87 0.74 0.95 1.05 Monthly Residual Volatility (%) 2.38 1.96 1.73 2.01 Cumulative Return (%) 7.90 6.63 17.45 14.95 Annualized Alpha (%) 1.31 1.73 14.63 13.74 Annual Flow (%) 14.57 -1.14 73.92 44.55 Management Fee (%) 1.50 1.5 0.50 1.00 Incentive Fee (%) 19.66 20 2.67 0.00 Fund Size ($million) 245.80 65.72 805.20 174.59 Fund Age (month) 85.05 72 58.26 73.00 Redemption Frequency (days) 74.97 30 85.64 60.00 Subscription Frequency (days) 33.77 30 22.27 0.00 Redemption Notice Period (days) 42.29 30 31.40 30.00 Lockup Period (months) 4.91 0 7.56 12.00 Personal Capital 0.34 0 0.47 1 Leverage 0.66 1 0.47 1 Minimum Investment ($million) 1.18 0.5 3.07 0.75 Open to Public 0.18 0 0.39 0

33

Table II Piecewise Regression: Baseline Model This table shows the regression results of our baseline model. 1𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑡𝑡<0 equals one if fund value is below the high-water mark and zero otherwise. 1𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷2𝐻𝐻𝐻𝐻𝐻𝐻𝑡𝑡>0 is defined similarly. For control variables, we include fund size and fund age at time t, fund performance and capital flows over the past 12 months, and fund characteristics such as fee structure and share restrictions. Style fixed effects and year fixed effects are included. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. Volatility Style Beta Residual Volatility 1Dist2HWMt<0 × Dist2HWMt -0.0725*** -0.0235*** -0.0524*** (0.0048) (0.0024) (0.0046) 1Dist2HWMt>0 × Dist2HWMt 0.0251*** 0.0075*** 0.0208*** (0.0052) (0.0020) (0.0038) 1Dist2HWMt>0 × MgmtFee%t -0.0068*** -0.0021*** -0.0056*** (0.0008) (0.0004) (0.0007) ln(Fund Sizet) -0.0907*** 0.0176* -0.1299*** (0.0235) (0.0105) (0.0200) ln(Fund Aget) 0.0584 0.0532** -0.0310 (0.0614) (0.0262) (0.0582) Fund Returnt−11,t 0.0218*** 0.0087*** 0.0131*** (0.0032) (0.0016) (0.0024) Capital Flowt−11,t -0.0002 -0.0002* -0.0001 (0.0002) (0.0001) (0.0002) Management Fee 0.1140 -0.0772* 0.2820** (0.1248) (0.0398) (0.1164) Incentive Fee 0.0293* -0.0078 0.0316*** (0.0157) (0.0069) (0.0122) Redemption Frequency 0.0001 0.0003* -0.0001 (0.0004) (0.0001) (0.0003) Subscription Frequency 0.0005 0.0000 0.0004 (0.0013) (0.0006) (0.0011) Redemption Notice Period -0.0016 -0.0012* -0.0003 (0.0015) (0.0007) (0.0012) Lockup period 0.0085 0.0022 0.0053 (0.0059) (0.0025) (0.0041) Leverage 0.1370* 0.0168 0.1721*** (0.0712) (0.0329) (0.0587) Open to Public -0.0977 -0.0784** -0.0431 (0.0845) (0.0374) (0.0815) Ln(Minimum Investment) -0.1187*** -0.0132 -0.0775*** (0.0294) (0.0121) (0.0223) Intercept 3.3540*** 0.0901 3.7139*** (0.6181) (0.2944) (0.5774) Style FE Yes Yes Yes Year FE Yes Yes Yes N 30845 30070 30070 adj. R-sq 0.3914 0.1263 0.3336

34

Table III Financial Crisis This table studies hedge fund risk taking during the recent Financial Crisis. Following NBER business cycle reference dates, we define the financial crisis period as January 2008 to June 2009. The Crisis indicator is equal to one if quarter t is in the financial crisis period and zero otherwise. Style fixed effects are included. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. Volatility Style Beta Residual Volatility Crisis 1.1317*** -0.0962* 0.7312*** (0.4160) (0.0554) (0.2674) 1Dist2HWMt<0 × Dist2HWMt -0.0716*** -0.0199*** -0.0536*** (0.0048) (0.0027) (0.0055) Crisis× 1Dist2HWMt<0 × Dist2HWMt 0.0036 -0.0097*** 0.0124* (0.0095) (0.0033) (0.0069) 1Dist2HWMt>0 × Dist2HWMt 0.0201*** 0.0062*** 0.0197*** (0.0065) (0.0021) (0.0044) Crisis× 1Dist2HWMt>0 × Dist2HWMt 0.0062 -0.0041 0.0113 (0.0094) (0.0047) (0.0071) 1Dist2HWMt>0 × MgmtFee%t -0.0066*** -0.0021*** -0.0050*** (0.0008) (0.0004) (0.0007) Crisis× 1Dist2HWMt>0 × MgmtFee%t -0.0009 -0.0004 0.0006 (0.0031) (0.0009) (0.0019) Control Variables Yes Yes Yes Style FE Yes Yes Yes Year FE No No No N 28841 28102 28102 adj. R-sq 0.3696 0.1244 0.3149

35

Table IV Future Performance and Expected Risk Taking This table examines how hedge fund managers’ risk taking influences their future performance. Style alpha is the intercept from Equation (4). Cumulative return, annualized style alpha, and annual flows are calculated over a one-year period after quarter t. We calculate predicted risk taking based on our baseline model as in Table II. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. (1) (2) (3)

Cumulative Return Annualized Style Alpha Annual Flow

Panel A. Volatility Predicted Volatility 0.3192 -0.3358* -2.4446*** (0.6787) (0.1751) (0.8304) N 30852 30070 30852 adj. R-sq 0.0006 0.0010 0.0029 Panel B. Style Beta Predicted Style beta 5.9159*** -3.9443*** -8.1504*** (2.1045) (0.8261) (2.5381) N 30852 30070 30852 adj. R-sq 0.0120 0.0082 0.0019 Panel C. Residual Volatility Predicted Residual volatility 0.7783 -0.3245 -1.5107 (0.8425) (0.2455) (1.1705) N 30852 30070 30852 adj. R-sq 0.0019 0.0005 0.0006

36

Table V Future Performance and Managers’ Compensation This table examines the relation between fund future performance and managers’ compensation. Style alpha is the intercept from Equation (4). Cumulative return, annualized style alpha, and annual capital flows are calculated over a one-year period after quarter t. In Panel A, 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 performance and average flow of the next 12 months. In Table V Panel B, we rank funds that are above their high-water marks into five groups every quarter based on their MgmtFee% and then calculate their average performance and average flow over the next 12 months. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. Panel A. Portfolios: Dist2HWM vs. future performance Dist2HWM

Rank Average

Dist2HWM Cumulative

Return Annualized Style Alpha Annual Flow

Below HWM

1 (Lowest) -35.35 11.09 -1.56 -11.97 2 -15.61 11.30 0.17 -9.99 3 -8.31 9.90 1.23 -6.57 4 -4.22 8.82 1.68 -10.40

5 (Highest) -1.34 6.74 1.05 -3.87 High-Low -4.34* 2.61** 8.10***

Above HWM

1 (Lowest) 2.18 7.47 1.84 7.48 2 5.13 7.79 3.05 18.47 3 7.95 9.86 4.00 26.08 4 12.44 9.77 2.88 35.53

5 (Highest) 23.51 13.70 3.35 52.49 High-Low 6.23*** 1.51 45.01***

Panel B. Portfolios: MgmtFee% vs. future performance

MgmtFee% Rank Average MgmtFee%

Cumulative Return

Annualized Style Alpha Annual Flow

1 (Lowest) 29.88 13.22 3.36 39.66 2 44.80 10.45 3.62 30.55 3 55.83 9.74 3.07 28.20 4 67.36 7.52 2.87 25.03

5 (Highest) 83.62 7.65 2.35 16.83 High-Low -5.57*** -1.01 -22.83***

37

Table VI Robustness Tests In Panel A, we use the highest year-end NAV over the past three years as the high-water mark to calculate Dist2HWM. Panel B presents regression results using downside risk measures as dependent variables. SEM is semi-deviation of returns as in Equation (7) and measures deviations of returns that are below the mean. VaR_NP is the non-parametric value-at-risk. It is the fifth percentile of the actual distribution of returns. VaR_CF is the Cornish-Fisher value-at-risk and is calculated as in Equations (8) and (9). Panel C examines risk taking by quarter. The dependent variable is volatility of fund returns over the next quarter. Panel D examines whether the relation between risk taking and managers’ compensation structure is driven by funds in certain size groups. Every quarter, we sort funds by their assets under management into three groups. Then we run the piecewise regression for each size group separately. Panel E shows the regression results with a HWM dummy, which equals one if a fund has a high-water mark provision and zero otherwise. Panel F shows regression results using several alternative risk taking measures based on the Fung and Hsieh (2004) seven-factor model. Volatility is the standard deviation of fund returns over a two-year period. BetaMarket and BetaSize are the coefficients of the market factor and the size factor, respectively. Style fixed effects and year fixed effects are included. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively.

Panel B. Alternative Risk Taking Measures SEM -VaR_NP -VaR_CF 1Dist2HWMt<0 × Dist2HWMt -0.0501*** -0.0923*** -0.1010*** (0.0033) (0.0107) (0.0124) 1Dist2HWMt>0 × Dist2HWMt 0.0179*** 0.0247** 0.0290** (0.0035) (0.0111) (0.0122) 1Dist2HWMt>0 × MgmtFee%t -0.0049*** -0.0142*** -0.0138***

(0.0005) (0.0017) (0.0017) Control Variables Yes Yes Yes

Style FE Yes Yes Yes Year FE Yes Yes Yes

Panel A. Rolling High-water Mark Volatility Style Beta Residual

Volatility 1Dist2HWMt<0 × Dist2HWMt -0.0805*** -0.0259*** -0.0572*** (0.0061) (0.0025) (0.0054) 1Dist2HWMt>0 × Dist2HWMt 0.0255*** 0.0069*** 0.0212*** (0.0054) (0.0020) (0.0039) 1Dist2HWMt>0 × MgmtFee%t -0.0066*** -0.0021*** -0.0056*** (0.0008) (0.0004) (0.0006) Control Variables Yes Yes Yes Style FE Yes Yes Yes Year FE Yes Yes Yes

38

Panel C. Seasonality Q1 Q2 Q3 Q4 1Dist2HWMt<0 × Dist2HWMt -0.0689*** -0.0669*** -0.0592*** -0.0708*** (0.0044) (0.0041) (0.0038) (0.0044) 1Dist2HWMt>0 × Dist2HWMt 0.0408*** 0.1225*** 0.0627*** 0.0460*** (0.0031) (0.0105) (0.0054) (0.0038) 1Dist2HWMt>0 × MgmtFee%t -0.0036*** -0.0072*** -0.0066*** -0.0060***

(0.0010) (0.0007) (0.0008) (0.0008) Control Variables Yes Yes Yes Yes

Style FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes

Panel D. Different Size Groups Small Medium Large Volatility 1Dist2HWMt<0 × Dist2HWMt -0.0699*** -0.0753*** -0.0699*** (0.0057) (0.0067) (0.0079) 1Dist2HWMt>0 × Dist2HWMt 0.0275*** 0.0217*** 0.0214*** (0.0060) (0.0062) (0.0061) 1Dist2HWMt>0 × MgmtFee%t -0.0070*** -0.0066*** -0.0065*** (0.0011) (0.0010) (0.0010) Style Beta 1Dist2HWMt<0 × Dist2HWMt -0.0192*** -0.0283*** -0.0271*** (0.0030) (0.0032) (0.0036) 1Dist2HWMt>0 × Dist2HWMt 0.0047* 0.0061** 0.0099*** (0.0025) (0.0025) (0.0023) 1Dist2HWMt>0 × MgmtFee%t -0.0017*** -0.0013*** -0.0026*** (0.0006) (0.0005) (0.0005) Residual Volatility 1Dist2HWMt<0 × Dist2HWMt -0.0549*** -0.0490*** -0.0463*** (0.0057) (0.0056) (0.0072) 1Dist2HWMt>0 × Dist2HWMt 0.0226*** 0.0198*** 0.0157*** (0.0051) (0.0042) (0.0044) 1Dist2HWMt>0 × MgmtFee%t -0.0061*** -0.0055*** -0.0051*** (0.0010) (0.0008) (0.0008) Control Variables Yes Yes Yes Style FE Yes Yes Yes Year FE Yes Yes Yes

39

Panel E. High-water Mark Provision Volatility Style beta Residual volatility HWM 0.0751 -0.0091 0.0525 (0.1099) (0.0481) (0.0917) 1Dist2HWMt<0 × Dist2HWMt -0.0752*** -0.0254*** -0.0560*** (0.0061) (0.0030) (0.0058) HWM × 1Dist2HWMt<0 × Dist2HWMt 0.0026 0.0016 0.0031 (0.0066) (0.0033) (0.0062) 1Dist2HWMt>0 × Dist2HWMt 0.0382*** 0.0088*** 0.0247*** (0.0070) (0.0028) (0.0048) HWM × 1Dist2HWMt>0 × Dist2HWMt -0.0122** -0.0007 -0.0022 (0.0056) (0.0027) (0.0045) 1Dist2HWMt>0 × MgmtFee%t -0.0058*** -0.0025*** -0.0048*** (0.0013) (0.0007) (0.0011) HWM × 1Dist2HWMt>0 × MgmtFee%t -0.0007 0.0005 -0.0004 (0.0015) (0.0007) (0.0013) Control Variables Yes Yes Yes Style FE Yes Yes Yes Year FE Yes Yes Yes

Panel F. Fung and Hsieh Seven-factor Model Volatility BetaMarket BetaSize Residual volatility 1Dist2HWMt<0 × Dist2HWMt -0.0750*** -0.0091*** -0.0037*** -0.0488*** (0.0049) (0.0012) (0.0013) (0.0047) 1Dist2HWMt>0 × Dist2HWMt 0.0205*** -0.0003 -0.0011 0.0197*** (0.0041) (0.0009) (0.0010) (0.0030) 1Dist2HWMt>0 × MgmtFee%t -0.0060*** -0.0006*** -0.0003 -0.0045*** (0.0008) (0.0002) (0.0002) (0.0007) Control Variables Yes Yes Yes Yes Style FE Yes Yes Yes Yes Year FE Yes Yes Yes Yes

40

Table VII Other Variables on Hedge Fund Risk Taking This table examines the impact of other variables on hedge fund risk taking as in Equation (10). Panels A through C present regression results when we use volatility, style beta, and residual volatility as the dependent variable, respectively. For independent variables, we include a dummy variable, D, to represent five variables documented in the literature. The first variable is termination policy. Following Aragon and Nanda (2011), we estimate the probability of termination using a Probit regression. A fund is near termination if its estimated probability of termination is above median. The second variable is managers’ outside options. We use fund past returns and fund size to proxy for fund managers’ outside options. Every quarter, we rank funds into four portfolios (2-by-2) based on their returns over the past year and their size at quarter end. Funds with both past performance and fund size above median have higher outside options. The third variable is managerial ownership. It indicates whether fund managers invest in their own funds. This information is obtained from TASS. The fourth variable is scalability. We consider a fund’s strategy scalable if a fund uses leverage and has correlation with MSCI world index higher than median. The last variable is the volatility of managers’ compensation. A fund has high volatility of fees if the standard deviation of its manager’s total compensation over the past year is above the median. In all regressions, style fixed effects and year fixed effects are included. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. Panel A. Dependent Variable: Volatility (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option

Managerial Ownership Scalability Std of Fee

1Dist2HWMt<0 × Dist2HWMt -0.0707*** -0.0729*** -0.0726*** -0.0668*** -0.0730*** (0.0047) (0.0048) (0.0048) (0.0047) (0.0048) 1Dist2HWMt>0 × Dist2HWMt 0.0180*** 0.0259*** 0.0251*** 0.0239*** 0.0218*** (0.0049) (0.0052) (0.0052) (0.0049) (0.0052) 1Dist2HWMt>0 × MgmtFee%t -0.0102*** -0.0066*** -0.0068*** -0.0059*** -0.0069*** (0.0008) (0.0007) (0.0008) (0.0008) (0.0008) D -0.6146*** -0.1961*** 0.0735 1.0306*** 0.3070***

(0.0796) (0.0599) (0.0716) (0.1102) (0.0568) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes

41

Panel B. Dependent Variable: Style Beta (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option

Managerial Ownership Scalability Std of Fee

1Dist2HWMt<0 × Dist2HWMt -0.0229*** -0.0236*** -0.0236*** -0.0202*** -0.0233*** (0.0024) (0.0024) (0.0024) (0.0022) (0.0023) 1Dist2HWMt>0 × Dist2HWMt 0.0048** 0.0075*** 0.0074*** 0.0068*** 0.0065*** (0.0020) (0.0020) (0.0020) (0.0017) (0.0020) 1Dist2HWMt>0 × MgmtFee%t -0.0034*** -0.0020*** -0.0020*** -0.0015*** -0.0021*** (0.0004) (0.0004) (0.0004) (0.0003) (0.0004) D -0.2359*** -0.0187 0.0631* 0.5883*** 0.0875***

(0.0322) (0.0238) (0.0323) (0.0433) (0.0282) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes

Panel C. Dependent Variable: Residual Volatility (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option

Managerial Ownership Scalability Std of Fee

1Dist2HWMt<0 × Dist2HWMt -0.0511*** -0.0527*** -0.0525*** -0.0489*** -0.0529*** (0.0045) (0.0046) (0.0046) (0.0045) (0.0046) 1Dist2HWMt>0 × Dist2HWMt 0.0147*** 0.0214*** 0.0208*** 0.0201*** 0.0179*** (0.0036) (0.0038) (0.0038) (0.0038) (0.0038) 1Dist2HWMt>0 × MgmtFee%t -0.0085*** -0.0054*** -0.0056*** -0.0050*** -0.0056*** (0.0007) (0.0006) (0.0007) (0.0007) (0.0007) D -0.5348*** -0.1404*** 0.0559 0.6095*** 0.2776***

(0.0562) (0.0452) (0.0636) (0.0918) (0.0483) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes

42

Panel A. Dist2HWM vs. Risk Taking

Panel B. MgmtFee% vs. Risk Taking

Figure 1 Hedge Fund Risk Taking. In Panel A, we rank funds into ten groups (five groups below the high-water mark and five groups above) based on their Dist2HWM at the end of every quarter. Then we calculate their average risk taking of the next 12 months over time. In Panel B, we rank funds above their high-water mark into five groups based on their MgmtFee%, and then calculate their average risk taking of the next 12 months over time.

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1

Internet Appendix for “Gambling or De-risking: Hedge Fund Risk Taking vs. Managers’ Compensation”

Chengdong Yin and Xiaoyan Zhang1

December 2016

This document provides supplementary results for the paper “Gambling or De-risking:

Hedge Fund Risk Taking vs. Managers’ Compensation.” The first section presents the Probit

regression results for termination probabilities discussed in Section IV.B. The second section

presents additional tests of the joint impact between managers’ compensation structure and various

variables on managers’ risk-taking behavior.

A. Probit Regression for Termination Probabilities

Following Aragon and Nanda (2011), we estimate hedge funds’ termination probabilities

using a Probit regression. The dependent variable is an indicator, which equals one if a fund is

alive in the current quarter and is liquidated over the next 12 months. The independent variables

include fund size, fund age, and the 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 Internet Appendix Table IAI suggest that larger, younger, better

performing funds and funds above their high-water marks are less likely to be liquidated.

B. Other Variables Related to Hedge Fund Risk Taking: Joint Impact

In Section IV.B, we examine the impact of various variables documented in the literature

on hedge fund managers’ risk taking. However, we only include those variables as control

1 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.

2

variables in the piecewise regressions. In this section, we examine whether those variable would

also affect managers’ sensitivities to Dist2HWM and MgmtFee% by including interaction terms

in our baseline model. The results are summarized in Table IAII.

The first specification examines the impact of termination probability. The significant and

negative coefficients of the indicator suggest that when their probabilities of liquidation are high,

fund managers would reduce volatility by 0.55% per month (or 1.91% per year), style beta by 0.20,

and residual volatility by 0.53% (or 1.84% per year). At the same time, the coefficients of the

interaction terms are positive and significant except for the residual volatility. The results indicate

that fund managers are more conservative when the probabilities of liquidation are high. The

results are consistent with Buraschi, Kosowski, and Sritrakul (2014), and imply that termination

is so costly that fund managers reduce risk to increase survival likelihood.

Regression (2) examines the impact of outside options. After we include the interaction

terms, the coefficients on the indicator are not significant in all three panels. The coefficients of

the interaction terms between outside options and Dist2HWM are positive when funds are below

their high-water marks and negative when they are above water, although they are only significant

for the residual volatility. The sign of the coefficients suggests that fund managers with higher

outside options are less sensitive to Dist2HWM. The results are consistent with Table VII, and

suggest that, everything else equal, fund managers with higher outside options take less risk. Our

interpretation is that, because it is so costly for a fund manager to shut down the current fund and

start a new one, fund managers may want to protect their outside options and lock in their gains

by taking less risk.

Regression (3) examines managerial ownership. The coefficients of the indicator and the

coefficients of the interaction terms between the indicator and Dist2HWM (or MgmtFee%) are not

significant in almost all cases. Thus, we do not find strong evidence that managers who invest in

their own funds behave differently from their peers.

The positive and significant coefficients of the indicator in regression (4) suggest that funds

with scalable strategies take more risk on average. However, their sensitivities to Dist2HWM are

not significantly different from their peers. At the same time, funds with scalable strategies are

3

less sensitive to MgmtFee%, given the positive and significant coefficients of the interaction term

between the indicator and 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.

In the last column, the positive and significant coefficients of the indicator suggest that

hedge fund managers take more risk when their fees are volatile. To be more specific, fund

managers would increase volatility by 0.23% per month (0.80% per year) and residual volatility

by 0.28% per month (or 0.97% per year). However, the coefficients of the interaction terms are

insignificant in almost all cases. The results are similar to Table VII and indicate that fund

managers would take more risk to boost fund performance and smooth their future compensation.

To summarize, the results in Table IAII are consistent with Table VII and show that hedge

fund managers become more conservative when the termination probability is high and when they

have high outside options. They are more aggressive when their strategy is scalable and when their

compensation is more volatile. There are two interesting results regarding the joint impact. First,

when funds are near termination, fund managers become less sensitive to Dist2HMW. This is

consistent with Buraschi, Kosowski, and Sritrakul (2014) and suggests that fund managers are

more conservative. Second, when fund strategies are scalable, the impact of the management fee

decreases. Funds suffer less from diseconomies of scale when they can easily scale up their

investment. In this case, the incentive fee would be the more important part of managers’ total

compensation even when funds grow large, and thus motivate managers to take more risk to boost

fund performance.

4

Table IAI Probit Regression: Probability of Termination This table shows the results of the Probit regression. The dependent variable is an indicator and equals one if a fund is alive in the current quarter and will be liquidated over the next 12 months. Past performance is the cumulative return over the past year. We also calculate the standard deviation of fund returns over the past year. Underwater is an indicator and equals one if a fund’s value is below its high-water mark at time t. Style fixed effects and year fixed effects are included. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively. Intercept 0.2985** (0.1268) Log Fund Assets -0.1201*** (0.0057) Log Fund Age 0.0475*** (0.0129) Past Performance -0.0039*** (0.0005) Std of Past Performance -0.0399*** (0.0042) Underwater 0.3364*** (0.0194) Style FE Yes Year FE Yes N 45732 Pseudo R-sq 0.0577

5

Table IAII Other Variables This table examines the impact of various variables on hedge fund risk taking and their joint impact with Dist2HWM and MgmtFee%. Panels A through C present regression results when we use volatility, beta, and residual volatility as the dependent variable, respectively. For independent variables, we include a dummy variable, D, to represent five variables documented in the literature. The first variable is termination policy. Following Aragon and Nanda (2011), we estimate the probability of termination using a Probit regression. A fund is near termination if its estimated probability of termination is above median. The second variable is managers’ outside options. We use fund past returns and fund size to proxy for fund managers’ outside options. Every quarter, we rank funds into four portfolios (2-by-2) based on their returns over the past year and their size at quarter end. Funds with both past performance and fund size above median have higher outside options. The third variable is managerial ownership. It indicates whether fund managers invest in their own funds. This information is provided by TASS. The fourth variable is scalability. We consider a fund’s strategy scalable if a fund uses leverage and has correlation with MSCI world index higher than the median. The last variable is the volatility of managers’ compensation. A fund has high volatility of fees if the standard deviation of managers’ total compensation over the past year is above the median. In all regressions, style fixed effects and year fixed effects are included. Standard errors are clustered at both fund and quarter level and are reported in parentheses. ***, **, and * represent significance at the 1%, 5%, and 10% level, respectively.

6

Panel A. Volatility (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option Managerial Ownership Scalability Std of Fee

D -0.5527*** -0.1518 0.1158 0.8724*** 0.2317*** (0.0798) (0.1319) (0.1112) (0.1289) (0.0844) 1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 -0.0777*** -0.0739*** -0.0740*** -0.0624*** -0.0701*** (0.0061) (0.0049) (0.0055) (0.0055) (0.0050) D×1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 0.0102* 0.0130 0.0042 -0.0100 -0.0110 (0.0058) (0.0096) (0.0074) (0.0067) (0.0072) 1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 0.0191*** 0.0273*** 0.0249*** 0.0237*** 0.0171*** (0.0050) (0.0060) (0.0054) (0.0049) (0.0061) D×1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 -0.0051 0.0003 0.0006 0.0067 (0.0050) (0.0055) (0.0056) (0.0047) 1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 -0.0099*** -0.0069*** -0.0066*** -0.0068*** -0.0065*** (0.0008) (0.0008) (0.0009) (0.0009) (0.0009) D×1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 0.0003 -0.0006 0.0030** -0.0003 (0.0014) (0.0013) (0.0013) (0.0011) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes N 30841 30845 30845 30845 30561 adj. R-sq 0.4001 0.3927 0.3917 0.4220 0.3938

7

Panel B. Style Beta (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option Managerial Ownership Scalability Std of Fee

D -0.1955*** -0.0663 0.0989** 0.5344*** 0.0495 (0.0331) (0.0488) (0.0491) (0.0534) (0.0444) 1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 -0.0277*** -0.0234*** -0.0246*** -0.0181*** -0.0217*** (0.0025) (0.0025) (0.0027) (0.0024) (0.0024) D×1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 0.0068** 0.0006 0.0028 -0.0044 -0.0060** (0.0027) (0.0048) (0.0037) (0.0032) (0.0027) 1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 0.0055*** 0.0068*** 0.0080*** 0.0078*** 0.0053** (0.0020) (0.0022) (0.0021) (0.0021) (0.0024) D×1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 0.0017 -0.0014 -0.0024 0.0019 (0.0022) (0.0026) (0.0026) (0.0022) 1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 -0.0031*** -0.0022*** -0.0019*** -0.0020*** -0.0020*** (0.0004) (0.0004) (0.0004) (0.0004) (0.0004) D×1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 0.0008 -0.0004 0.0013** -0.0000 (0.0006) (0.0007) (0.0006) (0.0005) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes N 30059 30070 30070 30070 29793 adj. R-sq 0.1342 0.1264 0.1274 0.1815 0.1272

8

Panel C. Residual Volatility (1) (2) (3) (4) (5)

Near termination:

Based on Termination Probability

Outside Option Managerial Ownership Scalability Std of Fee

D -0.5265*** 0.0101 0.0250 0.4413*** 0.2752*** (0.0621) (0.1041) (0.1013) (0.1107) (0.0779) 1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 -0.0521*** -0.0544*** -0.0512*** -0.0422*** -0.0523*** (0.0062) (0.0046) (0.0052) (0.0045) (0.0052) D×1Dist2HWM𝑡𝑡<0 × Dist2HWM𝑡𝑡 0.0014 0.0195** -0.0036 -0.0144* -0.0024 (0.0059) (0.0087) (0.0080) (0.0074) (0.0064) 1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 0.0149*** 0.0239*** 0.0200*** 0.0206*** 0.0134*** (0.0036) (0.0046) (0.0045) (0.0040) (0.0046) D×1Dist2HWM𝑡𝑡>0 × Dist2HWM𝑡𝑡 -0.0087** 0.0018 -0.0012 0.0058 (0.0041) (0.0052) (0.0050) (0.0039) 1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 -0.0084*** -0.0054*** -0.0056*** -0.0061*** -0.0050*** (0.0007) (0.0007) (0.0008) (0.0007) (0.0008) D×1Dist2HWM𝑡𝑡>0 × MgmtFee%𝑡𝑡 -0.0013 0.0001 0.0030** -0.0010 (0.0012) (0.0012) (0.0012) (0.0009) Control Variables Yes Yes Yes Yes Yes Style FE Yes Yes Yes Yes Yes Year FE Yes Yes Yes Yes Yes N 30059 30070 30070 30070 29793 adj. R-sq 0.3433 0.3351 0.3338 0.3518 0.3366