Risk-Taking in Contests: The Impact of Fund-Manager Compensation on Investor Welfare

Abstract

We provide a tractable model of competition in rank-order contests with general prize structures. A leading example of such a situation is the competition between fund managers whose compensation depends on how well they performed relative to their peers. We analyze their trading behavior In a dynamic financial market model a la Black Scholes. In the unique symmetric equilibrium, fund managers use randomized trading strategies which endogenously create risk. This risk is unrelated to the uncertainty generated by the assets traded in the underlying financial market. Furthermore, this risk is excessive as there exists a trading strategy that dominates the equilibrium return distribution in the sense of second-order stochastic dominance. This trading strategy takes the form of a simple index strategy. Excessive risk-taking of fund managers leads to welfare losses if investors are risk-averse. Numerical examples indicate that welfare losses are substantial. Finally, we show that fund managers use more risky strategies, in the sense of second-order stochastic dominance, when competition between the agents increases.