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Cornell University
Fall 2009
Economics 3330: Problem Set 8 Solutions
1. A hedge fund has a net asset value of $62 per share and a high water mark of $66.
The
standard deviation of the fund’s annual returns is 50% and the riskfree rate is 4%.
The incentive
fee is 20%.
All answers should be given in terms of one year.
a. According to BlackScholes, what is the value of the incentive fee?
First, compute the BlackScholes value of a call option with the following parameters:
S
0
= 62
X = 66
R = 0.04
σ
= 0.50
T = 1 year
Therefore: C = $11.685
The value of the annual incentive fee is:
0.20 × C = 0.20 × $11.685 = $2.337
b. What would the incentive fee be worth if the fund had no high water mark?
Here we use the same parameters used in the BlackScholes model in part (a) with the exception
that: X = 62
Now: C = $13.253
The value of the annual incentive fee is
0.20 × C = 0.20 × $13.253 = $2.651
c. Suppose that the fund is contemplating a change in strategy that would increase the standard
deviation of returns to 100%.
How would your answers to (a) and (b) change under the new
strategy?
The values of the incentive fee become 4.66 and 4.90.
2. Based on current dividend yields and expected capital gains, the expected rates of return on
portfolios A and B are 12% and 16%, respectively.
The beta of A is 0.7, while that of B is 1.4.
The Tbill rate is currently 5%, whereas the expected rate of return of the S&P 500 index is 13%.
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 Fall '08
 MBIEKOP
 Economics

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