Optimal Investment Under High-Water Mark Contracts with Model Ambiguity

Abstract

This paper incorporates model ambiguity into the traditional hedge fund models to explore how ambiguity influences the manager's investment strategy, risk attitude and compensation structure. We find the manager is ambiguity aversion.  Model ambiguity enhances her level of endogenous risk aversion. The manager holds a conservative attitude on the ambiguity risky asset and reduces the investment to protect herself from the ambiguity. As the ambiguity level increases the investment gets lower. Model uncertainty erodes the manager's value, investors' value and the total fund value, all of them decrease as the ambiguity level increases, and their sensitivities with respect to AUM and HWM also exhibit the same pattern. Model ambiguity increases the proportion of the management fee. The management fee takes about 85% of the manager's total value in our ambiguity model and only takes about 80% in the ambiguity-free model. Such weight exhibits a growing trend as the ambiguity level increases.

Keywords: Hedge Fund, High-water mark (HWM), Portfolio Strategy, Ambiguity