A hedge fund with net asset value of $71 per share currently has a high water mark of $78. Suppose it is January 1, the standard deviation of the fund's annual returns is 42%, and the risk-free rate is 4%. The fund has an incentive fee of 16%. a. What is the value of the annual incentive fee according to the Black-Scholes formula? (Treat the risk-free rate as a continuously compounded value to maintain consistency with the Black-Scholes formula.)

Answer : The annual incentive fees according to Black Scholes Formular = 2.5

Explanation:

a) Find the value of call option using below parameter

current price (st) = $71

Strike price (X) = $78

Rf=4%

std=42%

time=1

value of call option=15.555

Annual incentive=16% x 15.555=2.5

The annual incentive fees according to Black Scholes Formular = 2.5

(b) The value of annual incentive fee if the fund had no high water mark and it earned its incentive fee on its return in excess of the risk-free rate? (Treat the risk-free rate as a continuously compounded value to maintain consistency with the Black-Scholes formula.)

current price (st) = 71

Strike price (X) = 78

Rf = (e^4%) - 1 = 4.08%

std=42%

time=1

value of call option=17.319

Annual incentive=16% x 17.319=2.77