Profit Sharing in Hedge Funds

Abstract

In a new scheme for hedge fund managerial compensation known as the first‐loss scheme, a fund manager uses her investment in the fund to cover any fund losses first; by contrast, in the traditional scheme currently used in most US funds, the manager does not cover investors' losses in the fund. We propose a framework based on cumulative prospect theory to compute and compare the trading strategies, fund risk, and managers' and investors' utilities in these two schemes analytically. The model is calibrated to the historical attrition rates of US hedge funds. We find that with reasonable parameter values, both fund managers' and investors' utilities can be improved and fund risk can be reduced simultaneously by replacing the traditional scheme (with 10% internal capital and 20% performance fee) with a first‐loss scheme (with 10% first‐loss capital and 30% performance fee). When the performance fee in the first‐loss scheme is 40% (a current market practice), however, such substitution renders investors worse off.

Optimal investment with S-shaped utility and trading and Value at Risk constraints: An application to defined contribution pension plan

“…For example, Berkelaar et al (2004) derive the optimal investment strategies with two utility functions under loss aversion in a continuous-time case. He and Kou (2018) investigate the S-shaped utility maximization under a minimum guarantee. Dong and Zheng (2019) include both short-selling and portfolio insurance (PI) constraints in the model and apply the dual control method to solve the corresponding constrained optimization problem.…”

A Unified Formula of the Optimal Portfolio for Piecewise Hyperbolic Absolute Risk Aversion Utilities

“…Context RA RS LA First-order RA Merton (1969) CRRA and CARA Carpenter (2000) Option payoff with HARA utilities Berkelaar, Kouwenberg and Post (2004) Loss aversion case Berkelaar, Kouwenberg and Post (2004) Kinked power utility case Lin, Saunders and Weng (2017) Participating insurance contracts He and Kou (2018) First-Loss schemes in hedge funds He, Liang, Liu and Ma (2019) Incentive schemes in pension funds Liang and Liu (2019) Central-planned portfolio selection Liang and Liu (2020) Principal's constraint…”

“…On its whole domain, the utility may not be concave, differentiable or continuous. The family comes from the following practical aspects: (1) the basic HARA utility (e.g., Merton (1969Merton ( , 1971)); (2) in many decision-based areas (e.g., hedge fund management), the actual utility/objective function is the composition of the HARA preference and piecewise linear payoff (e.g., Carpenter (2000); Berkelaar, Kouwenberg and Post (2004); He, Liang, Liu and Ma (2019)); (3) some non-concave utilities in behavioral settings (e.g., Kouwenberg and Ziemba (2007); Lin, Saunders and Weng (2017); He and Kou (2018); Liang and Liu (2019)). Nevertheless, the extensive literature solve the optimization problem and express the optimal portfolio in different closed forms.…”

Pricing Shared-Loss Hedge Fund Fee Structures

“…While for some parameter values, the first-loss structure improves the utility of both the investor and the hedge fund manager, they find that for typical values, the manager is better off, while the investor is worse off. In this paper, we investigate the shared-loss fee structures from the perspective of risk-neutral valuation, with no further assumptions about investor preferences, while He and Kou [5] solve the stochastic control problem (under the real-world measure) corresponding to the manager maximizing the utility function from cumulative prospect theory, and also evaluate the investor's payoff using the same type of criterion.…”

“…Recent work on the analysis of hedge fund fee structures includes that of Goetzmann et al [3], who value a fee structure with a highwater mark provision, using a PDE approach with a fixed investment portfolio, Panageas and Westerfield [8], who consider the portfolio selection decision of maximizing the present value of fees for a risk-neutral manager over an infinite horizon, and Guasoni and Obłój [4], who extend this work to managers with risk-averse power utility. Closest to the current work is He and Kou [5], who analyze shared-loss fee structures for hedge funds by looking at the portfolio selection decision of a hedge fund manager whose preferences are modeled using cumulative prospect theory. The problem is considered in the presence of a manager investing in the fund, and with a predetermined liquidation barrier.…”