The Optimal Dynamic Investment Policy for a Fund Manager Compensated with an Incentive Fee

Abstract

This paper solves the investment problem of a risk averse fund manager compensated with an incentive fee, a call option on the assets he controls. The optimal policy leads to all-or-nothing outcomes: the manager ends up either deep in or deep out of the money. The optimal trading strategy involves dynamically adjusting asset volatility as asset value changes. As assets grow large, the manager moderates portfolio risk. For example, if the manager has constant relative risk aversion, volatility converges to the Merton constant. On the other hand, as asset value goes to zero, portfolio volatility goes to infinity.