Estimating fees for managed futures: a continuous-time model with a knockout feature

Past research regarding incentive fees based on high-water marks has developed models for the specific characteristics of hedge funds. These theoretical models have used either discrete time or a Black-Scholes type differential equation. However, for managed futures, high-water marks are measured more frequently than for hedge funds, so a continuous-time model for managed futures may be appropriate. A knockout feature is added to a continuous model, which is something unique to managed futures although it could also have some relevance to hedge funds. The procedures allow one to derive the distribution function for the fund's survival time, which has not been derived in past research. The distribution of the maximum until ruin is derived as well, and used to provide an estimate of expected incentive fees. An estimate of the expected fixed fee is also obtained. The model shows that the expected incentive fee would be maximized if all funds were invested in margins, but for total fees to be maximized in the presence of a knockout feature, less than half of the funds should be invested. This is precisely what fund managers do. This result suggests that designing a fund with incentive fees only may cause fund managers to adopt the highest leverage, and thus, highest risk possible.