3330%20PS8%20solution - Cornell University Fall 2009...

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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 risk-free rate is 4%. The incentive fee is 20%. All answers should be given in terms of one year. a. According to Black-Scholes, what is the value of the incentive fee? First, compute the Black-Scholes 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 Black-Scholes 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 T-bill rate is currently 5%, whereas the expected rate of return of the S&P 500 index is 13%.
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3330%20PS8%20solution - Cornell University Fall 2009...

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