| Abstract | Assets under management (AUM) of hedge funds have grown rapidly in the last two decades. One salient feature of this multi-trillion dollar industry is its complicated management incentive structure. Hedge fund management incentive contracts typically feature both management fees and performance-based incentive fees, and incentive fee is a key characteristic that differentiates hedge funds from mutual funds. The management fee is charged as a fraction (e.g., 2%) of AUM, and the incentive fee is calculated as a fraction (e.g., 20%) of high-water mark (HWM). Not that the separation of the ownership and management of the assets would induce asymmetric information including the manager’s unobservable effort, which leads to moral hazard. Thus, for each hedge fund with different agency costs, we wonder if there exists an optimal contract (but not “2-20” type contract) that could incentive the fund manager to exert effort.
A fund manager would choose shirking to obtain the private benefits if she is charged a lower management fee or incentive fee. Meanwhile, the shirking will enhance the probability of the liquidation of the hedge fund. If the fund is liquidated, the manager could not receive the future cash flows consisted by both management fee and incentive fee and the cost of this loss will be much higher than the private benefits for a long period of time. Thus, the higher management fee and incentive fee will incentive the manager to choose to exert effort but not to shirk. On the other hand, for outside investors, to ensure their expected profits are not lost, management fee and incentive fee can not be very large. Therefore, under the fact that the information between the investors and manager are asymmetrical, the optimal incentive contract is the equilibrium result of the game between two parties of the contract.
Under the situation that the hedge fund can be operated in an infinite-time horizon, we study the optimal incentive contract with dynamic moral hazard. In this paper, we propose and develop a continuous-time principal-agent model, and the optimal management fees and incentive fees are provided by the analytically tractable formulae. This is a major contribution of this paper. Specifically, our analytical tractable model contains the following important features: (1) an alpha-generating strategy; (2) management/incentive fees link to HWM; (3) management fees as fraction of AUM; (4) poor performance-triggered drawdown and endogenously liquidation; (5) moral hazard induced by asymmetric information. In our model, we incorporate these five features and focus on the manager’s key tradeoff between private benefits and liquidation risk which are both induced by shirking.
Furthermore, the principal-agent relationship between the manager and outside investor discussed in this paper is actually about the corporate financing contract, which is different with the traditional agency problem that has discussed in the existing literature. As our limited knowledge, the existing continuous-time principal-agent models have not studied the optimal dynamic corporate financing contract directly. However, the continuous-time financing model developed in our paper studies this agency problem. Thus, we develop the dynamic contracting model and this is another contribution of our paper.
Our model can numerically analysis the impacts of the parameters characterizing the hedge fund and the agency frictions on the optimal incentive contract, which verifies the theoretical results of our model. Based on both theoretical results and numerical results obtained from our proposed dynamic model, we obtain some following main conclusions.
First, the optimal incentive contracts can effectively alleviate the moral hazard, and the optimal contracts are affected by several important factors including strategy, probability of fund liquidation and agency costs. For the hedge funds with different degrees of the above factors, the optimal contracts are different, which implies that optimal management fees and incentive fees are not immutable and this result is consistent with the practice in hedge funds industry.
Second, our model parsimoniously captures the key tradeoff between the costs of fund liquidation by sufficiently poor performance and private benefits from shirking. Importantly, the manager’s aversion to fund’s inefficient liquidation leads to be conservative. Thus, in contrast to the standard risk-seeking intuition, we find out that a risk-neutral manager often behaves risk-averse and chooses variant management fees.
Third, optimal management fees are only endogenously determined by the manager’s size-adjusted exerting effort cost and the factors related with moral hazard. Moreover, optimal incentive fees are affected by management fees. Specifically, the incentive fee is positively related with the management fee.
Fourth, the ratio between AUM and HWM measures the manager’s money-ness and is a critical determinant of optimal incentive fee. For instance, under the situation that the alpha is larger (lower) than the size-adjusted exerting effort cost, the optimal incentive fee would decrease (increase) as the ration of AUM/HWM increases.
Finally, the theoretical research results of this paper also have significant policy assignments in developing hedge funds healthy and rapidly, and make a guidance on how to regular hedge funds correctly and efficiently. For example, our studies imply that hedge funds should develop and utilize fintech deeply to enhance their competitiveness.
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