Optimal fees in hedge funds with first-loss compensation

Paper: arXiv 2310.19023

Abstract

Hedge fund managers with the first-loss scheme charge a management fee, a performance fee and guarantee to cover a certain amount of investors’ potential losses. We study how parties can choose a mutually preferred first-loss scheme in a hedge fund with the manager’s first-loss deposit and investors’ assets segregated. For that, we solve the manager’s non-concave utility maximization problem, calculate Pareto optimal first-loss schemes and maximize a decision criterion on this set. The traditional 2% management and 20% performance fees are found to be not Pareto optimal, neither are common first-loss fee arrangements. The preferred first-loss coverage guarantee is increasing as the investor’s risk-aversion or the interest rate increases. It decreases as the manager’s risk-aversion or the market price of risk increases. The more risk averse the investor or the higher the interest rate, the larger is the preferred performance fee. The preferred fee schemes significantly decrease the fund’s volatility.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper is mathematically dense, employing advanced concepts like non-concave utility maximization, concavification techniques, and Pareto optimization, requiring significant theoretical derivation. Empirically, it relies on numerical simulations and theoretical modeling rather than backtesting with real market data or discussing implementation details like slippage or latency.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Find Optimal Fee Schemes<br>in Hedge Funds"] --> B["Methodology<br>Utility Maximization Framework"]
  B --> C["Inputs<br>• Manager/Investor Risk Aversion<br>• Market Price of Risk<br>• Interest Rate"]
  C --> D["Computation<br>1. Solve Non-Concave Utility Problem<br>2. Calculate Pareto Optimal Schemes<br>3. Maximize Decision Criteria"]
  D --> E["Key Findings<br>• Traditional 2%/20% Fees Not Optimal<br>• Preferred Coverage Increases with Investor Risk Aversion/Interest Rate<br>• Preferred Coverage Decreases with Manager Risk Aversion/Market Price of Risk<br>• Preferred Performance Fee Increases with Investor Risk Aversion/Interest Rate<br>• New Schemes Significantly Reduce Fund Volatility"]

Cited References (238)

1. Less is more: Increasing retirement gains by using an upside terminal wealth constraint (2015) — link
2. High-Water Marks and Hedge Fund Management Contracts (2003) — link
3. Robust reinsurance contract with asymmetric information in a stochastic Stackelberg differential game (2022)
4. Optimal excess-of-loss reinsurance contract with ambiguity aversion in the principal-agent model (2020)
5. Optimal reinsurance and investment problem for an insurer and a reinsurer with jump-diffusion risk process under the Heston model (2016)
6. Robust Stochastic Stackelberg Differential Reinsurance and Investment Games for an Insurer and a Reinsurer with Delay (2022)
7. A hybrid stochastic differential reinsurance and investment game with bounded memory (2022) — link
8. A stochastic Stackelberg differential reinsurance and investment game with delay in a defaultable market (2021)

1 of 238 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.