A hedge fund with net asset value of $108 per share currently has a high-water mark of $115. Suppose it is January 1, the standard deviation of the fund's annual returns is 45%, and the risk-free rate is 4%. The fund has an incentive fee of 16% of annual returns, but its current high-water mark is $115, and net asset value is $108. Required: 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.) Note: 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? Note: 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? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. d. Recalculate the incentive fee value for part (b) if an increase in fund leverage increases volatility to 55%. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Answer is complete but not entirely correct. a. Annual incentive fee $ 2.92 per share b. Annual incentive fee $ 16.37 per share c. Annual incentive fee $ 1.91 per share d. Annual incentive fee $ 3.68 per share
A hedge fund with net asset value of $108 per share currently has a high-water mark of $115. Suppose it is January 1, the standard deviation of the fund's annual returns is 45%, and the risk-free rate is 4%. The fund has an incentive fee of 16% of annual returns, but its current high-water mark is $115, and net asset value is $108. Required: 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.) Note: 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? Note: 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? Note: Do not round intermediate calculations. Round your answer to 2 decimal places. d. Recalculate the incentive fee value for part (b) if an increase in fund leverage increases volatility to 55%. Note: Do not round intermediate calculations. Round your answer to 2 decimal places. Answer is complete but not entirely correct. a. Annual incentive fee $ 2.92 per share b. Annual incentive fee $ 16.37 per share c. Annual incentive fee $ 1.91 per share d. Annual incentive fee $ 3.68 per share
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
Related questions
Question
Transcribed Image Text:A hedge fund with net asset value of $108 per share currently has a high-water mark of $115. Suppose it is January 1, the standard
deviation of the fund's annual returns is 45%, and the risk-free rate is 4%. The fund has an incentive fee of 16% of annual returns, but its
current high-water mark is $115, and net asset value is $108.
Required:
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.)
Note: 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?
Note: 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?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
d. Recalculate the incentive fee value for part (b) if an increase in fund leverage increases volatility to 55%.
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Answer is complete but not entirely correct.
a. Annual incentive fee
$
2.92
per share
b. Annual incentive fee
$
16.37 per share
c. Annual incentive fee
$
1.91
per share
d. Annual incentive fee
$
3.68 per share
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