Risking or Derisking: How Management Fees Affect Hedge Fund Risk-Taking Choices

Abstract

Media articles routinely associate hedge funds with aggressive risk-taking.¹ According to these articles, hedge fund managers speculate on movements of all types of financial assets, which include stocks, currencies, interest rates, commodities, and even exotic ones, such as sporting events and lawsuits.² The characterizations in these articles 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 more weapons in the investment armory, including highly risky ones, such as leverage, derivatives, and short selling. Meanwhile, the compensation structure for hedge fund managers, especially the combination of the incentive fee and the high-water mark, is highly nonlinear and resembles a call option. Because the value of an option is likely to increase with uncertainty, hedge fund managers’ compensation structure may encourage managers to take more risk. Thus, it is reasonable for the public to worry that hedge funds may take on excessive risk.

The landscape of the hedge fund industry clearly changed after the global financial crisis in 2008. With more regulations and less-than-stellar returns in recent years, many hedge funds have become more conservative and take less risk. One possible explanation for this “derisking” behavior is that hedge fund managers became more reliant on the management fee for their compensation. As discussed in Lan, Wang, and Yang (2013, LWY hereafter) and Yin (2016), the management fee might be the dominant component of many hedge fund managers’ total compensation. Because fund managers can always collect the asset-based management fee as long as their funds are alive, fund survival becomes their first priority. Consequently, fund managers have incentives to take less risk to increase survival probabilities so that they can keep collecting the management fee in the future.

Understanding how hedge funds choose between more or less risk-taking is an interesting and important research topic. According to the long literature on fund managers’ risk-taking choices, hedge fund managers choose their optimal levels of risk-taking to maximize their total future compensation. For instance, Merton (1969) suggests that a CRRA-type fund manager should maintain constant leverage over time, and Carpenter (2000) examines the impact of call options embedded in the incentive fee on managers’ risk-taking. Most existing studies, including Goetzmann, Ingersoll, and Ross (2003, GIR hereafter), Hodder and Jackwerth (2007), and Panageas and Westerfield (2009), focus on the incentive fee and the high-water mark provision and neglect the management fee. More recent studies, such as LWY, Drechsler (2014), and Buraschi, Kosowski, and Sritrakul (2014), do consider managers’ total compensation, but do not explicitly examine the impact of each component of managers’ compensation on their risk-taking behavior. In this study, we take a unique perspective to examine how the management fee affects hedge fund managers’ risk-taking choices.

Given that existing theoretical models either neglect the management fee or include the management fee without providing clear guidance on how it affects managers’ risk-taking, we first introduce a simple model to illustrate the intuition and derive testable hypotheses regarding the impact of the management fee on managers’ risk-taking behavior. To keep the model tractable, we simplify the model structure while retaining key assumptions from previous studies, such as GIR and LWY. The model predicts a negative relation between managers’ risk-taking choices and the relative importance of future management fees. That is, hedge fund managers take less risk when their future management fees contribute more to their total compensation, possibly to increase survival probabilities and protect their future income. Meanwhile, we incorporate decreasing returns to scale in our model. When hedge funds suffer from decreasing returns to scale, they are more likely to rely on the management fee for compensation and thus are more sensitive to the relative importance of future management fees. Consistent with this possibility, our model suggests that funds with decreasing returns to scale reduce risk-taking even more than their peers when future management fees become more important.

Using fund-level data from the Lipper TASS database from 1994 to 2015, we empirically test our hypothesis that higher relative importance of future management fees is associated with lower risk-taking. Because managers’ compensation is not directly observable in the data, we compute the present value of future compensation following the procedure outlined in Lim, Sensoy, and Weisbach (2016, LSW hereafter) and Agarwal, Daniel, and Naik (2009, ADN hereafter). We calculate the contribution of future management fees to managers’ total compensation as the ratio of the present value of future management fees to the present value of managers’ total compensation, which includes future management fees, future incentive fees, and managers’ coinvestments.³ Meanwhile, we measure hedge fund risk-taking using total fund return volatility, style beta, and style residual volatility, following Buraschi, Kosowski, and Sritrakul (2014).

Consistent with LWY, we find that future management fees comprise the largest portion of managers’ total compensation. The mean contribution of future management fees to managers’ total compensation is about 40|$\%$| with a standard deviation of 18.30|$\%$|⁠. Meanwhile, about 30|$\%$| of managers’ total compensation comes from future incentive fees and the rest comes from managers’ coinvestments. More importantly, when the contribution of future management fees to managers’ total compensation increases, hedge fund managers take less risk, which supports the theoretical prediction from our simple model. For instance, an interdecile increase in the contribution of future management fees is associated with a decrease in total volatility of 0.2413|$\%$| per month, a decrease in style beta of 0.2315, and a decrease in residual volatility of 0.2955|$\%$| per month. Thus, we are the first to provide evidence of a negative relation between the management fee and managers’ risk-taking behavior.

As mentioned earlier, one possible reason for the reduced risk-taking is to increase fund survival probabilities, so that fund managers can keep collecting the management fee in the future. Our empirical results show that termination probabilities of hedge funds significantly decrease when future management fees become more important, which is consistent with this mechanism. Economically, if all other variables are set at their median values, an increase from the 10th to the 90th percentiles of the contribution of future management fees is associated with a 5|$\%$| decrease in termination probability.

Next, we examine the impact of decreasing returns to scale on the relation between risk-taking choices and the importance of future management fees. Our model suggests that funds with decreasing returns to scale are more sensitive to the relative importance of future management fees. To test this hypothesis, we follow the literature and examine the behavior of large hedge funds and funds using strategies with capacity constraints, because these funds are more subject to decreasing returns to scale. We find that large hedge funds reduce risk-taking more than small funds when future management fees become the dominant component of their compensation package. Meanwhile, funds using capacity constrained strategies reduce risk-taking more than their peers, especially when they have large capital inflows. Thus, consistent with the hypothesis, decreasing returns to scale makes funds more sensitive and these funds reduce risk-taking more than their peers when future management fees contribute more to managers’ compensation.

Finally, we conduct a comprehensive set of robustness tests. For instance, our results are robust when we control for other manager incentive measures, such as the contribution of future incentive fees, realized fee income as in Yin (2016), and direct incentives as in ADN.⁴ Thus, our measure provides new insights into managers’ incentives and their risk-taking behavior.

To the best of our knowledge, we are the first to empirically examine the impact of the management fee on hedge fund risk-taking. Our unique contribution is that we provide evidence that managers take less risk when the management fee contributes more to their total compensation, possibly because the potential downside losses of fund termination outweigh the potential upside gains of higher risk-taking when fund managers rely on the management fee for compensation.

One closely related work is LWY, which examines fund managers’ optimal leverage choices against the cost of fund liquidation. They show theoretically that a risk-neutral manager becomes endogenously risk averse and decreases leverage following poor performance to increase the fund’s survival likelihood. We borrow key ingredients from LWY and establish a simple model to derive a direct relation between the management fee and managers’ risk-taking choices. The biggest difference between our study and LWY is that the LWY model does not provide direct implications for the relation between hedge fund managers’ risk-taking behavior and future management fees. We study this relation empirically and provide significant evidence supporting our main hypothesis.

Another closely related work is LSW, which calculates indirect incentives for fund managers.⁵ They argue that good current performance attracts future inflows of capital and leads to higher future fees, and they show that these indirect incentives are more important than the direct incentives documented in ADN for hedge fund managers. We follow a similar procedure to calculate the present value of managers’ future compensation. However, our paper is significantly different from LSW because we address very different research questions. First, we focus on the relative importance of the management fee in managers’ future total compensation. In contrast, LSW focus on changes in managers’ total compensation and do not examine individual components, such as the management fee. Second, LSW link indirect incentives to fund performance and capital flows, while we focus on how future management fees affect managers’ risk-taking choices. Given the differences between our study and previous studies, we make a significant contribution to the literature and can help investors better understand hedge fund managers’ risk-taking behavior.

1. A Simple Model on Risk-Taking and Management Fees

1.1 Literature review

Starting with Merton (1969) and Carpenter (2000), the manner in which hedge fund managers’ compensation influences fund managers’ risk-taking behavior has been studied both theoretically and empirically in the literature. However, because assumptions vary across theoretical models, they reach mixed conclusions regarding managers’ risk-taking choices. In this section, we review several key papers that are relevant to our study.

One important early work is GIR, which examines the costs and benefits of high-water mark provisions in hedge fund managers’ compensation contracts. The authors show that fund managers should reduce volatility when fund value is near liquidation to increase survival probabilities and increase volatility at higher asset levels to increase the value of the incentive fee. Several later papers, such as Hodder and Jackwerth (2007) and Panageas and Westerfield (2009), follow the path of GIR and examine the impact of the incentive fee contract and the high-water mark provision on managers’ behavior.⁶

More recently, LWY provides a different perspective by quantitatively valuing both management fees and incentive fees in a model with endogenous leverage choice. 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 baseline model, fund managers have an infinite time horizon and try to maximize the present value of total fees (i.e., the incentive fee plus the management fee).⁷ LWY’s calibration results suggest that the management fee is the more important part of managers’ total compensation, which implies that survival is more important for fund managers. Therefore, hedge fund managers choose to take less risk when fund value is below the high-water mark.⁸

The existing literature also has many empirical papers that test the implications of these theoretical models.⁹ For instance, ADN shows that hedge funds have better performance when their managers have higher direct incentives. Most empirical studies in the recent literature adopt the algorithm in ADN to calculate the market value of investors’ investments and track investors’ high-water marks over time.

LSW provides additional empirical insights by designing an algorithm to calculate managers’ indirect incentives (changes in managers’ future compensation), mostly using the GIR model and the LWY model. Their empirical results show that with capital flows from new investors chasing good performance, the indirect incentives from future fees are much larger than direct incentives for hedge fund managers.

As we can see from above, many studies in the literature primarily focus on the incentive fee and the high-water mark provision, while the management fee is commonly neglected. However, both academics and practitioners have slowly begun to recognize the importance of the management fee in recent years.¹⁰ In addition to the calibration results in LWY, Yin (2016) shows empirically that when funds grow large, the realized management fee in absolute dollar amounts becomes more important than the incentive fee.

1.2 A simple model on risk-taking and the management fee

How hedge fund managers make their risk-taking choices clearly depends on their compensation structure. While the performance-based incentive fee and the high-water mark provision are likely to motivate fund managers to take more risk and improve fund performance, the asset-based management fee provides a stable source of income for fund managers so long as their funds are not liquidated. When fund managers rely more on the management fee for compensation, would they reduce risk-taking to increase survival probabilities so that they can continue to collect the management fee in the future?

The existing theoretical literature does not provide a ready answer to this question. Moreover, managers’ decisions in extant theoretical models often involve many factors, and thus it is difficult to observe a direct relation between managers’ risk-taking and the management fee. Therefore, we establish a simple model in this subsection to illustrate the direct relation between hedge fund managers’ risk-taking and the relative importance of the management fee. This model is highly stylized to ensure tractability. We only keep the key ingredients and the most essential assumptions from the literature (e.g., the GIR model and the LWY model) to derive a testable relation between managers’ risk-taking choices and the relative importance of the management fee.

Consider a hedge fund with a two-period horizon. At initiation (i.e., |$t = 0)$|⁠, the total fund assets are |$W_0 $|⁠, with |$V_0 = (1 - \phi )W_0 $| from outside investors and the rest from the fund manager. That is, the fund manager’s coinvestments in her own fund are |${\it CoInvest}_0 = \phi W_0 $|⁠, where |$\phi $| represents managerial ownership and |$0 \le \phi < 1$|⁠.

Here, |$\alpha_t $| is the levered alpha, and |$\alpha_t = \pi_t \alpha^{\prime}$|⁠. Similarly, |$\varepsilon_t = \pi_t \varepsilon^{\prime}, \ \varepsilon_t \sim N\left( {0,\sigma_t} \right), \ {\rm and} \ \sigma_t = \pi_t \sigma^{\prime}$|⁠.

Here, |${\it MFee}_t $|⁠, |${\it IFee}_t $|⁠, and |${\it Flow}_t $| are the management fee, the incentive fee, and capital flows for period |$t$|⁠, respectively, which we will define below. Consequently, fund assets after fees and flows are |$W_t = V_t + {\it CoInvest}_t $|⁠.

For the first contingency, the fund value is above the high-water mark, so the manager receives the management fee and the incentive fee; for the second contingency, the fund value is below the high-water mark but above the liquidation boundary, so the manager receives the management fee; for the third contingency, the fund value is below the liquidation boundary, so the fund manager loses all the fees but can recoup her coinvestments; for the last contingency, the fund value is nonpositive, so the fund manager receives zero. For the first two contingencies, the fund is not liquidated, and thus the fund manager would keep her coinvestments in the fund.

With our model’s set up, the fund manager first chooses the optimal risk-taking level |$\sigma_1 $| (or the linearly related investment strategy |$\pi_1)$| at the beginning of the first period to maximize her expected total future compensation from both periods, that is, |${\it COMP}_1 $| in Equation (9) and |${\it COMP}_2 $| in Equation (10). At the beginning of the second period, the fund manager chooses the optimal risk-taking level |$\sigma_2 $| (or the linearly related investment strategy |$\pi_2 )$| to maximize her expected compensation for the second period, that is, |${\it COMP}_2 $| in Equation (10).¹²

This variable directly measures the importance of the management fee for a fund in the time series and makes it easy to compare the management fee’s importance across funds.

Our main research question is how managers’ risk-taking choices are related to the importance of future management fees, and we intend to derive testable implications from the optimal solutions to our simple model. However, because of the complexity of the fee structure and the probability of fund liquidation, there are no closed-form solutions for |$\sigma_1 $| and |$\sigma_2 $|⁠. As an alternative, we find numerical solutions by combining Monte Carlo simulations in period 1 with nonlinear optimization in period 2.

For the Monte Carlo simulations in period 1, we follow prior literature and set a subset of parameters to be constants, as presented in Table A.1 in Appendix A. The key varying parameter is the initial fund value, |$W_0 $|⁠, and we need to solve for the optimal |$\sigma_1 $| for each given |$W_0 $|⁠. We normalize |$W_0 $| to be between the liquidation boundary |$b$| and 1. Note that |$W_0 $| is a standardized variable, which mainly reflects the distance to the high-water mark rather than the absolute fund size. For |$\sigma_1 $|⁠, we use the linearly related investment strategy |$\pi_1 $| for the simulation. Following LWY, we assume that |$\pi_1 $| is in the range of (0, 4). Thus, we conduct our simulation on all possible combinations of |$W_0 $| and |$\pi_1 $|⁠. Within each combination, given the value of |$\pi_1 $|⁠, we generate 10,000 values of |$\varepsilon_1 \sim N\left( {0,\sigma_1} \right)$|⁠, where |$\sigma_1 = \pi_1 \sigma^{\prime}$|⁠. For each set of |$\{W_0 $|⁠, |$\pi_1 $|⁠, |$\sigma_1, \varepsilon_1 \}$|⁠, we calculate the manager’s compensation for the first period as in Equations (9). For period 2, we solve for the optimal risk-taking choice, |$\sigma_2^\ast $|⁠, that maximizes expected |${\it COMP}_2 $| in Equation (10) for each set of |$\{W_0 $|⁠, |$\pi_1 $|⁠, |$\sigma_1, \varepsilon_1 \}$|⁠. Finally, for each |$W_0 $|⁠, we find the optimal risk-taking choice in period 1, |$\sigma_1^\ast $|⁠, as the one with the highest mean total compensation from both periods. Appendix A provides more calculation details.¹³

Our model delivers two intuitive and testable implications. The first implication is that the fund manager’s optimal risk-taking choice in period 1, |$\sigma_1^\ast $|⁠, is negatively related to the importance of future management fees, |${\it FutureMFee}\% $|⁠. That is, when future management fees contribute more to their total future compensation, hedge fund managers take less risk. Note that we focus on the fund manager’s risk-taking choices in period 1 instead of period 2 because period 2 is the termination period, and thus there is no future compensation to maximize. To illustrate the first implication, panel A of Figure 1 presents the relation between |$\sigma _1^\ast $| and FutureMFee|$\%$|, and we observe a clear negative relation. That is, when the management fee becomes more important, the fund manager takes less risk. One possible reason for the manager’s choice of lower risk-taking is to increase fund survival probabilities. In other words, the fund is more likely to survive when the fund manager takes less risk. Panel B of Figure 1 shows a generally negative relation between the manager’s optimal risk-taking choice in period 1 and the fund’s survival probability at the end of period 1.¹⁴ In other words, the fund is more likely to survive when the fund manager takes less risk. These findings are consistent with LWY, but the LWY model does not provide direct implications for the relation between hedge fund managers’ risk-taking behavior and future management fees.

Figure 1

Calibration results for the two-period model

This figure shows the calibration results for our two-period model explained in Section 1.2. Panel A presents the relation between the optimal risk-taking choice in period 1 (i.e., |$\sigma_1^\ast )$| and the contribution of future management fees (i.e., FutureMFee|$\%$|) to the manager’s total compensation. Panel B reports the relation between the fund’s survival probabilities at the end of period 1 and the manager’s optimal risk-taking choice in period 1. Appendix A summarizes the parameter choices and calculation details.

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The intuition for the first implication is quite simple. When the fund manager takes more risk, she faces a dilemma. On the one hand, taking more risk can boost her expected incentive fee because of increased expected performance. On the other hand, taking more risk increases the probability of fund liquidation, at which point she would lose all future fees. Thus, the fund manager’s decision is associated with the importance of the management fee relative to total compensation. If the expected management fee is more important to the total compensation package, then the fund manager may want to reduce risk-taking because fund liquidation is quite costly to her. However, if the expected management fee is less important, then the fund manager may have stronger incentives to take more risk and boost fund performance. We examine this first implication empirically in Sections 3.1 and 3.2.

The second implication of our model is that funds with higher degrees of decreasing returns to scale (i.e., higher |$\gamma $| in our model) rely more on future management fees and thus take less risk. To clearly illustrate this result, we start by showing FutureMFee|$\%$| for each |$W_0 $| in panel A of Figure 2. Here, we consider two cases for comparison: the solid dots represent the baseline fund from Figure 1 (⁠|$\gamma = 0.003$|⁠), and the circles represent a fund with higher decreasing returns to scale (⁠|$\gamma = 0.006$|⁠). Clearly, the fund with higher |$\gamma $| always has higher FutureMFee|$\%$| for each |$W_0 $|⁠, indicating that funds with higher decreasing returns to scale rely more on future management fees for compensation. Panel B of Figure 2 presents the fund manager’s optimal risk-taking choice in period 1, |$\sigma_1^\ast $|⁠, for the baseline fund (solid dots) and the fund with higher |$\gamma $| (circles). The fund with higher |$\gamma $| clearly always takes less risk. Combining panels A and B, we infer that funds with higher |$\gamma $| rely more on management fees and managers tend to take less risk. Panel C presents the relation between future management fees and the optimal risk-taking choice for the fund with higher |$\gamma $|⁠. The negative relation between FutureMFee|$\%$| and |$\sigma_1^\ast $| is consistent with the model’s first implication. To examine whether the risk-taking choices of the fund with higher |$\gamma $| are more sensitive to the importance of future management fees, we compute the slope of |$\sigma_1^\ast $| with respect to FutureMFee|$\%$| at each |$W_0 $| for both funds. For the benchmark fund with |$\gamma = 0.003$|⁠, the average slope is approximately |$-$|10. For the fund with |$\gamma = 0.006$|⁠, the average slope becomes |$-$|24. This indicates that the fund with higher decreasing returns to scale takes even less risk when FutureMFee|$\%$| becomes higher.

Figure 2

Impact of decreasing returns to scale

This figure examines the impact of decreasing returns to scale. In addition to the baseline fund from Figure 1, we also include a fund with a higher cost parameter (⁠|$\gamma = 0.006)$|⁠. Panel A reports the contribution of future management fees to the manager’s total compensation (i.e., FutureMFee|$\%$|) for both funds. Panel B reports the optimal risk-taking choices in period 1 (i.e., |$\sigma _1^\ast )$| for both funds. Panel C examines the relation between the optimal risk-taking choices in period 1 and the contribution of future management fees to the manager’s total compensation for the fund with higher decreasing returns to scale. Appendix A summarizes the parameter choices and calculation details for the calibration.

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The intuition for the second implication is as follows. For hedge funds suffering from higher decreasing returns to scale, it becomes more difficult to generate good performance when they grow large. Thus, funds with higher decreasing returns to scale are more likely to rely on the management fee for compensation. Meanwhile, funds with higher decreasing returns to scale need to take extra risk to improve performance relative to their peers with lower decreasing returns to scale. Higher risk-taking leads to higher liquidation probabilities, thereby putting future compensation at greater risk. Thus, funds with higher decreasing returns to scale have lower incentives to take risk when future management fees are more important to their total compensation. Taken together, managers of funds with higher decreasing returns to scale tend to rely more on future management fees for compensation and consequently take less risk. We examine the impact of decreasing returns to scale on the relation between risk-taking and future management fees empirically in Section 3.3.

2 Data and Methodology

2.1 Data

Our final sample has 3,062 unique funds, and panel A of Table 1 reports the summary statistics for the fund characteristics. The mean fund size is above $200 million, and the median size is only around $60 million. Given that the median fund age is only 73 months, hedge funds are relatively short lived. The mean cumulative return is 7.91|$\%$| per year. During our sample period, the mean flow is positive at 13.36|$\%$| with a median of |$-$|1.90|$\%$| per year. In terms of fee structure, hedge funds typically charge a management fee between 1|$\%$| and 2|$\%$| and an incentive fee of 20|$\%$|⁠. In our sample, 73|$\%$| of all hedge funds have a high-water mark provision. Share restrictions are common in the hedge fund industry. Most hedge funds have a redemption frequency between 30 and 90 days and a notice period of 30 days. In our sample, lockup periods are not commonly used, as the median lockup period is zero months, while 64|$\%$| of all funds use leverage. The low average of Open to public and the high minimum investment requirements suggest that only qualified investors can invest in hedge funds.

2.2 Risk-taking measures

We estimate the above regression for each fund using a rolling 12-month window of data. For the style index return, |$StyleReturn_{j,m} $|⁠, we use the hedge fund return indexes provided by Credit Suisse, following Buraschi, Kosowski, and Sritrakul (2014).¹⁵ Style beta, |$\beta_i $|⁠, is the coefficient on the style index returns and measures the risk-taking of a hedge fund attributable to the nature of its style strategy. We compute fund-specific volatility, or residual volatility, as the standard deviation of the error term, |$\varepsilon_{i,m}$|⁠, which measures fund-specific risk-taking. Style beta and residual volatilities reflect different aspects of managers’ risk-taking: the fund style or the specific managers’ behavior.

Panel B of Table 1 reports summary statistics for our risk-taking measures. During our sample period, the mean volatility of hedge fund returns is 3.22|$\%$| per month, which is below the stock market volatility of 4.30|$\%$| per month. This suggests that hedge funds provide some protection against stock market fluctuations. The style beta in our sample has a mean of 0.88 and a standard deviation of 0.96. These statistics suggest that hedge funds in the same style category share some commonality with an average style beta close to one, while the dispersion in managers’ style betas is sizeable. This also can be seen in the residual volatility statistics. Compared to the mean total volatility of 3.22|$\%$|⁠, the mean residual volatility of 2.45|$\%$| per month indicates that most hedge fund volatility is fund specific.

2.3 Managers’ compensation

To examine the impact of hedge fund managers’ compensation on their risk-taking behavior, we first need to quantify hedge fund managers’ total compensation, which includes the management fee, the incentive fee, and managers’ coinvestments in their own funds. Our two-period model in Section 1.2 is highly stylized and thus may not be able to fully capture the dynamics of managers’ compensation in practice. Therefore, to better estimate each component of managers’ total compensation and make our calculation comparable with the existing literature, we follow the empirical procedures in ADN and LSW and use the richer and more dynamic setups in LWY. To be specific, we first use the algorithm in ADN to estimate the market value of investors’ investments, their individual high-water marks, and managers’ coinvestments over time. Next, we follow the LSW procedure to calibrate the LWY model with capital flows and coinvestments and calculate present values of future management fees, future incentive fees, and managers’ coinvestments. We provide detailed discussions of the ADN algorithm and the LSW procedure in Appendix B and Appendix C, respectively.

For the calibration exercise, we need to set three key parameters: managers’ skills, represented by levered alpha |$\alpha $|⁠, the total withdrawal rate, represented by investor redemption probability |$\delta $| plus exogenous liquidation probability |$\lambda $|⁠, and the liquidation boundary as a fraction of the high-water mark, represented by |$b$|⁠.¹⁶ For our benchmark case, we follow LWY and use their parameter values: managers’ skills |$\alpha = 3\% $|⁠, total withdrawal rate |$\delta + \lambda = 10\% $|⁠, and liquidation boundary as a faction of the high-water mark |$b = 0.685$|⁠. Other combinations of parameter values are discussed later in our empirical results. We follow LSW and assume that fund managers reset their high-water marks every quarter, and thus we calculate the present value of their future compensation at the end of each quarter. For each fund, we first obtain the present value of future management fees and future incentive fees per investor in the fund, and the present value of managers’ total future coinvestments for the fund. Then, we sum across all of the fund’s investors to compute the present value of total future management fees and total future incentive fees for the fund. Fund managers’ total compensation is the sum of the fund’s total future management fees, total future incentive fees, and managers’ total coinvestments.

Table 1, panel C, presents summary statistics for our key compensation variables using the benchmark parameter choices (i.e., |$\alpha = 3\% $|⁠, |$\delta + \lambda = 10\% $|⁠, and |$b = 0.685)$|⁠. We find that the mean and median of FutureMFee|$\%$| are 39.23|$\%$| and 41.61|$\%$|⁠, respectively. Thus, on average, about 40|$\%$| of managers’ total future compensation comes from future management fees. At the same time, the average contributions of future incentive fees (FutureIFee|$\%$|) and managers’ coinvestments (CoInvest|$\%$|) are 29.09|$\%$| and 31.68|$\%$|⁠, respectively.¹⁷ These numbers indicate that future management fees are the most important part of managers’ total compensation, consistent with the prediction in LWY. Prior literature has shown that managerial ownership (i.e., the percentage of fund assets contributed by fund managers) significantly affects managers’ risk-taking.¹⁸ Therefore, we calculate managerial ownership in their own funds as managers’ coinvestments divided by fund assets. On average, close to 10|$\%$| of fund assets come from managers’ coinvestments in our sample.

One important feature of our two-period model is decreasing returns to scale. The original LWY model does not directly consider decreasing returns to scale, but LWY (p. 321) state that “|$\ldots$| the key results that we emphasize in this paper tend to remain valid even with decreasing returns to scale.” The LSW procedure also does not include decreasing returns to scale, possibly because including this additional feature requires solving complicated partial differential equations (PDEs) for each fund in each period, and thus significantly increases the difficulty of estimating managers’ compensation. To employ decreasing returns to scale in our empirical analysis, we take three steps. First, we make sure that our theoretical predictions from the two-period model remain intact with the LWY model setup with decreasing returns to scale. Hence, we calibrate the LWY model with the feature of decreasing returns to scale and present the results in Internet Appendix Section B. The calibration results support both predictions from our simpler two-period model.¹⁹ Second, given the complication of directly estimating the LWY model with decreasing returns to scale for each fund in each period, we follow LSW’s choice and mainly use the original LWY model for our empirical analysis. Third, we carefully examine the impact of decreasing returns to scale on the relation between managers’ risk-taking and future management fees in Section 3.3, by focusing on fund-level properties, which are directly connected to decreasing returns to scale.

3. Empirical Results

In this section, we examine the general relation between hedge fund risk-taking behavior and the contribution of future management fees to managers’ total compensation. We start in Section 3.1 with a baseline regression analysis of the impact of future management fees on managers’ risk-taking behavior. In Section 3.2, we will examine whether this relation is connected to survival probability. In Section 3.3, we will study how decreasing returns to scale affect the relation between managers’ risk-taking behavior and future management fees.

3.1 Baseline regression

The dependent variable is one of the following risk-taking measures for fund |$i$|⁠: total volatility, style beta, or residual volatility over the next year. The independent variable, FutureMFee|$\%$|, is the contribution of future management fees to managers’ total compensation for fund |$i$| at the end of quarter |$q$|⁠. If our hypothesis is correct, then we expect the coefficient |$b_1 $| to be significantly negative. As discussed in Section 2, we assume that fund managers reset their high-water marks every quarter and thus we compute FutureMFee|$\%$| at the end of each quarter. Therefore, we use quarterly frequencies for our regressions, and all time-variant variables are calculated at the end of each calendar quarter.

Regarding control variables, given that a manager might prefer a certain level of volatility and that her risk-taking might be persistent over time, we include a lagged measure of risk-taking. To capture other relevant fund characteristics, we include fund size and fund age at the end of quarter |$q$|⁠, fund performance and capital flows over the past year, fee structure, share restrictions, and managerial ownership at the end of quarter |$q$|⁠. We also include style-quarter fixed effects in all regressions. We estimate Equation (16) using a pooled regression over funds and quarters. Following Petersen (2009), we cluster standard errors at both the fund and the quarter level.

Table 2 reports the regression results when we estimate FutureMFee|$\%$| using the benchmark parameter choices (i.e., |$\alpha = 3\% $|⁠, |$\delta + \lambda = 10\% $|⁠, and |$b = 0.685)$|⁠. In the first column of Table 2, when we use total volatility as the risk-taking measure, the coefficient on FutureMFee|$\%$| is |$-$|0.0049 with a |$t$|-statistic of |$-$|2.99. The significant negative coefficient supports our theoretical hypothesis. In terms of magnitude, an interdecile increase in FutureMFee|$\%$| at the end of quarter |$q$| is associated with a decrease in total volatility of 0.2413|$\%$| per month over the next year, while the average monthly volatility is 3.22|$\%$|⁠. The magnitude of our finding is comparable to the literature. For instance, Aragon and Nanda (2011) show that a drop in relative performance rank from 100|$\%$| to 0|$\%$| is associated with a 0.12|$\%$| per month increase in volatility for funds without incentive pay, and a 0.76|$\%$| per month increase for funds with incentive pay. Thus, the decrease in total volatility that we document is economically significant.

In the second and third columns, where we use style beta and residual volatility, respectively, as risk-taking measures, we find similar patterns: the coefficients for FutureMFee|$\%$| are both negative and highly significant. An interdecile increase in FutureMFee|$\%$| at the end of quarter |$q$| is associated with a decrease in style beta of 0.2315 and a decrease in residual volatility of 0.2955|$\%$| per month over the next year. The results show that fund managers take less risk when the management fee becomes the dominant component of their compensation package. This supports our hypothesis that when the management fee becomes more important in the overall compensation package, fund managers reduce risk-taking to increase survival probabilities.

For completeness, we also present the coefficients for all control variables in Table 2. The positive and significant coefficients for lagged risk-taking confirm the persistence in managers’ risk-taking behavior. Hedge funds with larger size, lower past performance, lower management fee percentages, and higher minimum investment requirements take less risk. The signs on the incentive fee percentage coefficients are mixed but mostly positive. It is possible that funds with higher incentive fee percentages rely less on the management fee and thus are likely to take more risk. The coefficients for managerial ownership are all negative, and they are significant for style beta and residual volatility. Our results are consistent with Aragon and Nanda (2011) and Gupta and Sachdeva (2019) and suggest that managerial ownership makes a hedge fund manager more conservative with regard to risk-taking. Other characteristics are mostly insignificant.

To investigate whether our findings are sensitive to our calibration parameter choices, we follow LSW and estimate FutureMFee|$\%$| using different parameter combinations, with the managers’ skills parameter (⁠|$\alpha $|⁠) being 3|$\%$| or 0|$\%$|⁠, the total withdrawal rate (⁠|$\delta +\lambda $|⁠) being 10|$\%$| or 5|$\%$|⁠, and the liquidation boundary of fund value as a fraction of the high-water mark (⁠|$b$|⁠) being 0.685 or 0.8. In panels A through C of Table 3, we present results using the eight possible combinations of the three parameters, and each panel reports results using total volatility, beta, and residual volatility as the risk-taking measure, respectively.

For example, the first column of each panel in Table 3 repeats the analysis reported in Table 2. In the last column of each panel, we use the parameter choices in GIR, that is, |$\alpha \ = \ 0$|⁠, |$\delta + \lambda \ = \ 5\% $|⁠, and |$b \ = \ 0.8$|⁠. Zero alpha indicates that managers’ compensation mainly depends on future management fees and their coinvestments; the lower |$\delta + \lambda $| suggests that funds are expected to survive longer; and the higher |$b$| means that investors are less tolerant when a fund has poor performance. In this case, an interdecile increase in FutureMFee|$\%$| at the end of quarter |$q$| is associated with a decrease of 0.2315|$\%$| per month in total volatility, a decrease of 0.1724 in style beta, and a decrease of 0.2660|$\%$| per month in residual volatility over the next year, respectively. Across all panels and for all combinations of the parameters in Table 3, the coefficient on FutureMFee|$\%$| ranges between |$-$|0.0061 and |$-$|0.0009 and is significant in 22 of 24 cases.²⁰

One potential concern with our test design is that we apply the same parameter values to all funds in our sample, when in reality, parameter values can vary significantly across funds. To ease this concern, we conduct two experiments. In the first experiment, to allow for cross-fund variation in parameter values, we assign funds randomly to groups with different parameter value combinations. With two choices of the managers’ skill parameter value (⁠|$\alpha $|⁠), two choices of the withdrawal rate (⁠|$\delta +\lambda $|⁠), and two choices of the liquidation boundary (⁠|$b$|⁠), we have eight groups as in Table 3. After each fund is randomly assigned to a group, we calculate FutureMFee|$\%$| for each fund and conduct our baseline regression using this new sample. Table 4, panel A, reports the results. The coefficients for FutureMFee|$\%$| are negative and significant in all regressions. An interdecile increase in FutureMFee|$\%$| at the end of quarter |$q$| is associated with a decrease of 0.1034|$\%$| per month in total volatility, a decrease of 0.0936 in style beta, and a decrease of 0.1182|$\%$| per month in residual volatility over the next year, respectively.

For the second experiment, we conduct three additional calibrations based on the LWY model, but with parameter values that differ from those used in prior literature. In the first group, we set managers’ skills at |$\alpha = 1.5\% $|⁠. This value is between the values used in the LWY model and GIR model, and we keep the other parameters at the same values as in LWY (i.e., |$\delta + \lambda = 10\% \ \mbox{and} \ b = 0.685)$|⁠. Because |$\alpha $| reflects managers’ skills, this allows us to examine whether managers with different skills have similar risk-taking behavior. In the second group, we set investors’ withdrawal rate at |$\delta + \lambda = 20\% $| and keep the other parameters at the same values as in LWY (i.e., |$\alpha = 1.5\% \ \mbox{and} \ b = 0.685)$|⁠. Higher withdrawal rates indicate shorter average life spans for hedge funds. This allows us to examine whether managers still care about their future management fees when their funds are expected to be liquidated sooner. In the third group, we lower the liquidation boundary to |$b = 0.5$| and keep the other parameters at the same values as in LWY (i.e., |$\alpha = 1.5\% \ \mbox{and} \ \delta + \lambda = 10\% )$|⁠. A lower boundary means that a fund can suffer a higher loss before liquidation. In other words, a lower liquidation boundary may motivate fund managers to take more risk, and we want to examine whether managers still reduce risk-taking when future management fees become more important. Panels B to D of Table 4 summarize the results. The coefficients for FutureMFee|$\%$| are negative in all regressions, and they are statistically significant in 8 of 9 regressions. Thus, the negative relation between managers’ risk-taking and future management fees is robust when we use parameter values different from those used in prior literature.

In summary, the results from our two experiments are consistent with those reported in Tables 2 and 3 and suggest that regardless of parameter value choices, hedge fund managers take less risk when future management fees become more important to their total compensation.

3.2 Future management fees and fund survival

In this subsection, we examine a potential mechanism behind the negative relation between hedge fund risk-taking and future management fees. LWY argue that when the management fee becomes the dominant part of managers’ total compensation, fund managers might take less risk to increase survival probabilities, because fund liquidation becomes so costly, and survival becomes the priority. Our model in Section 1.2 generates similar results. As shown in panel B of Figure 1, when the fund manager takes more risk, the survival probability of her fund decreases.

The dependent variable, Termination, is an indicator variable that is equal to one if a fund is alive at the end of quarter |$q$| but becomes liquidated over the next year, and zero otherwise. The key independent variable is FutureMFee|$\%$|. If fund managers reduce risk-taking to increase survival probabilities when future management fees become more important, then we expect the coefficient on FutureMFee|$\%$| to be negative.²¹ Following Aragon and Nanda (2011), we also include the following control variables: fund assets and fund age at the end of quarter |$q$|⁠, fund performance over the past year, volatility of fund returns over the past year, a high-water mark indicator, and style fixed effects. Following Petersen (2009), we cluster the standard errors at both the fund and the quarter level.

Table 5 presents the estimation results. The coefficient on FutureMFee|$\%$| is |$-$|0.0041 with a statistically significant |$t$|-statistic of |$-$|9.96. Economically, if all other variables are set at their median values, then an increase in FutureMFee|$\%$| from the 10th to the 90th percentiles is associated with a 5|$\%$| decrease in termination probability. As for the other variables, similar to Aragon and Nanda (2011), funds with larger size, older age, better past performance, and a high-water mark provision are less likely to be liquidated.

Our earlier results in Table 2 indicate that hedge fund managers take less risk when future management fees contribute more to their total compensation. Thus, consistent with LWY and our model, the results in Tables 2 and 5 suggest that when future management fees become more important, fund managers take less risk and their expected survival probabilities increase.

3.3 Risk-taking and decreasing returns to scale

In this subsection, we examine how decreasing returns to scale is related to managers’ risk-taking behavior and test the second implication of our simple model. Previous studies have suggested that hedge funds are likely to suffer from decreasing returns to scale. Funds with higher decreasing returns to scale are more likely to rely on the management fee for compensation when they grow large, as in Figure 2, panel A. Moreover, as shown in panel B of Figure 2, funds with higher decreasing returns to scale tend to take less risk for the same starting fund size. Therefore, funds with higher decreasing returns to scale are likely to reduce risk-taking more when future management fees become more important.

However, decreasing returns to scale are not observable in the data. Thus, we follow the literature and examine the impact of decreasing returns to scale using two approaches. In the first approach, we examine the behavior of managers of large hedge funds.²² As documented in Teo (2009), Getmansky (2012), and Yin (2016), large funds are more likely to suffer from decreasing returns to scale. Meanwhile, large hedge funds collect more management fees in absolute dollars than small funds because the management fee mainly depends on fund size. Thus, large hedge funds might be more sensitive to future management fees and have more incentive to reduce risk-taking to increase survival probabilities.

If large funds are more sensitive to future management fees, then we expect the coefficient on the interaction term, |$d_2 $|⁠, to be negative.

Table 6, panel A, presents the estimation results. As in Table 2, the coefficients for FutureMFee|$\%$| are all negative and significant. More importantly, the coefficients for the interaction term are negative, and they are significant when we use style beta and residual volatility as the risk-taking measure. The results suggest that, relative to small funds, for an interdecile increase in FutureMFee|$\%$|, large funds reduce volatility by an additional 0.1084|$\%$| per month, reduce beta by an additional 0.1034, and reduce residual volatility by an additional 0.1379|$\%$| per month. In summary, risk-taking by large funds is more sensitive to FutureMFee|$\%$| than it is for small funds. When future management fees contribute more to managers’ total compensation, large funds reduce risk-taking more than do small funds.