# The incentive fee is less valuable if the high water

This preview shows pages 4–7. Sign up to view the full content.

its previous high water mark. The incentive fee is less valuable if the high-water mark is \$67, rather than \$66. With a high-water mark of \$67, the net asset value of the fund must reach \$67 before the hedge fund can assess the incentive fee. The high-water mark for a hedge fund is equivalent to the exercise price for a call option on an asset with a current market value equal to the net asset value of the fund. 10. a.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. 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 26-4

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Chapter 26 - Hedge Funds c.Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that: X = S 0 × e 0.04 = 62 × e 0.04 = 64.5303 Now: C = \$12.240 The value of the annual incentive fee is 0.20 × C = 0.20 × \$12.240 = \$2.448 d. Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that: X = 62 and σ = 0.60 Now: C = \$15.581 The value of the annual incentive fee is 0.20 × C = 0.20 × \$15.581 = \$3.116 11. a.The spreadsheet indicates that the end-of-month value for the S&P 500 in September 1977 was 96.53, so the exercise price of the put written at the beginning of October 1977 would have been: 0.95 × 96.53 = 91.7035 At the end of October, the value of the index was 92.34, so the put would have expired out of the money and the put writer’s payout was zero. Since it is unusual for the S&P 500 to fall by more than 5 percent in one month, all but ten of the 120 months between October 1977 and September 1987 would have a payout of zero. The first month with a positive payout would have been January 1978. The exercise price of the put written at the beginning of January 1978 would have been: 0.95 × 95.10 = 90.3450 At the end of January, the value of the index was 89.25 (more than a 6% decline), so the option writer’s payout would have been: 90.3450 – 89.25 = 1.0950 The average gross monthly payout for the period would have been 0.2437 and the standard deviation would have been 1.0951. 26-5
Chapter 26 - Hedge Funds b. In October 1987, the S&P 500 decreased by more than 21%, from 321.83 to 251.79. The exercise price of the put written at the beginning of October 1987 would have been: 0.95 × 321.83 = 305.7385 At the end of October, the option writer’s payout would have been: 305.7385 – 251.79 = 53.9485 The average gross monthly payout for the period October 1977 through October 1987 would have been 0.6875 and the standard deviation would have been 5.0026. Apparently, tail risk in naked put writing is substantial. 12. a.In order to calculate the Sharpe ratio, we first calculate the rate of return for each month in the period October 1982-September 1987. The end of month value for the S&P 500 in September 1982 was 120.42, so the exercise price for the October put is: 0.95 × 120.42 = 114.3990 Since the October end of month value for the index was 133.72, the put expired out of the money so that there is no payout for the writer of the option. The rate of

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern