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Mathematical Analysis of Peformance Fees with High-Water Mark
KTH, School of Industrial Engineering and Management (ITM), Industrial Economics and Management (Dept.).
2013 (English)Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesisAlternative title
Matematisk analys av fonder medresultatbaserade avgifterVIKTOR (Swedish)
Abstract [en]


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.


– 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.


– 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.



Place, publisher, year, edition, pages
2013. , 66 p.
Keyword [en]
High-water mark, Performance fee, Management fee, Hedge fund
National Category
Mathematical Analysis
URN: urn:nbn:se:kth:diva-124075OAI: diva2:632590
Educational program
Master of Science in Engineering - Industrial Engineering and Management
Available from: 2013-12-20 Created: 2013-06-25 Last updated: 2013-12-20Bibliographically approved

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