In: Finance
A hedge fund with net asset value of $66 per share currently has
a high water mark of $68. Suppose it is January 1, the standard
deviation of the fund’s annual returns is 55%, and the risk-free
rate is 3%. The fund has an incentive fee of 20%, but its current
high water mark is $68, and net asset value is $66.
a. What is the value of the annual incentive fee
according to the Black-Scholes formula? (Do not round
intermediate calculations. Round your answer to 2 decimal
places.)
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? (Do not round intermediate calculations.
Round your answer to 2 decimal places.)
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.) (Do not round intermediate
calculations. Round your answer to 2 decimal
places.)
d. Recalculate the incentive fee value for part
(b) now assuming that an increase in fund leverage
increases volatility to 65%. (Do not round intermediate
calculations. Round your answer to 2 decimal
places.)