Hedge fund managers receive a large fraction of their funds' gains, in addition to the small fraction of funds' assets typical of mutual funds. The additional fee is paid only when the fund exceeds its previous maximum - the high-water mark. The most common scheme is 20 percent of the fund profits + 2 percent of assets.
To understand the incentives implied by these fees, we solve the portfolio choice problem of a manager with Constant Relative Risk Aversion and a Long Horizon, who maximizes the utility from future fees.
With constant investment opportunities, and in the absence of fixed fees, the optimal portfolio is constant. It coincides with the portfolio of an investor with a different risk aversion, which depends on the manager's risk aversion and on the size of the fees. This portfolio is also related to that of an investor facing drawdown constraints. The combination of both fees leads to a more complex solution.
The model involves a stochastic differential equation involving the running maximum of the solution, which is related to perturbed Brownian Motions. The solution of the control problem employs a verification theorem which relies on asymptotic properties of positive local martingales.
Joint work with Jan Obloj.