Implicit Incentives for Fund Managers with Partial Information

The reward of a fund manager usually increases when the Asset Under Management (AUM) grows, while it decreases when the AUM shrinks. The AUM may grow either because of a higher value of the assets or because of new money flowing into the fund. Good performances of the fund with respect to its relative benchmark are likely to attract new investors. Therefore, contracts based on the AUM create an implicit incentive for the manager to beat the benchmark. We study the problem of a portfolio manager whose compensation depends on the AUM modelled through the relative performances with respect to a benchmark. This framework generalizes the setting of Basak, et al. (2007), by considering a market model with one risk-free and one risky asset whose expected returns depend on an unobservable stochastic process, the market price of risk. We introduce the realistic assumption that the manager has a limited knowledge on the market, she can only observe stock prices and estimates the market price of risk from them. Therefore, the manager is facing an optimization problem under partial information