Reconsider the hedge fund in the previous problem. Suppose it is January 1, the standard deviation of the fund’s annual returns is 50%, and the risk-free rate is 4%. The fund has an incentive fee of 20%, but its current high water mark is $66, and net asset value is $62.
a. What is the value of the annual incentive fee according to the Black-Scholes formula?
b. What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its total return?
c. What would the annual incentive fee be worth 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.)
d. Recalculate the incentive fee value for part (b) now assuming that an increase in fund leverage increases volatility to 60%.