Risk Choice under High-Water Marks

Abstract

I solve in closed form for the optimal dynamic risk choice of a fund manager who is compensated with a high-water mark contract. The optimal risk choice depends on the ratio of the fund's assets under management to its high-water mark. If the manager's outside option value is low, investors' termination policy is strict, or management fees are high, then negative returns induce the manager into “derisking.” Otherwise, he engages in “gambling.” Having the option to walk away increases risk taking, though in many cases exercise is never optimal. In particular, leaving to restart at a proportionally smaller fund is always suboptimal.