Mathematical Analysis of Peformance Fees with High-Water Mark

Abstract: Abstract Purpose – The purpose of this thesis is to give the investors a better understanding on how to interpret the costs of funds with performance fee with high-water mark and give some guidelines when comparing funds with different fee structures, i.e. mutual funds and hedge funds. Mathematical approaches – Two mathematical approaches are used in the study. The first approach is to describe the high-water mark contract as a partial differential equation, which has the characteristics of Black-Scholes equation. The second approach is to numerically simulate the evolution of a fund’s value. During the development of the fund’s value the cost of the fees are calculated and discounted. Findings – It is found that the expected cost of the performance fee with high-water mark, vary a lot. An example is when the volatility increases the expected cost of performance fee drastically raises while the management fee is unchanged. Another interesting finding is that the order of when the fees’ are charged affects the expected cost of the performance fee. Conclusion – The guidelines for the investor is to invest in a fund with a performance fee in low volatile markets and a fund with just the management fee in high volatile markets. Another impact is the time step which the high-water mark level is controlled. The investor wants these controls as infrequently as possible. If the controls are done at a daily basis the expected cost of the performance fee is higher than in a monthly control. It is also concluded that the Normanbelopp of a fund with a performance fee should not be trusted. Key-words: