# Return the hedge fund earns on the index is therefore

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return the hedge fund earns on the index is therefore equal to: (133.72/120.42) – 1 = 0.11045 = 11.045% Assuming that the hedge fund invests the \$0.25 million premium along with the \$100 million beginning of month value, then the end of month value of the fund is: \$100.25 million × 1.11045 = \$111.322 million The rate of return for the month is: (\$111.322/\$100.00) – 1 = 0.11322 = 11.322% The first month that the put expires in the money is May 1984. The end of month value for the S&P 500 in April 1984 was 160.05, so the exercise price for the May put is: 0.95 × 160.05 = 152.0475 The May end of month value for the index was 150.55, and therefore the payout for the writer of a put option on one unit of the index is: 152.0475 – 150.55 = 1.4975 The rate of return the hedge fund earns on the index is equal to: (150.55/160.05) – 1 = -0.05936 = –5.936% 26-6

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Chapter 26 - Hedge Funds The payout of 1.4975 per unit of the index reduces the hedge fund’s rate of return by: 1.4975/160.05 = 0.00936 = 0.936% The rate of return the hedge fund earns is therefore equal to: –5.936% – 0.936% = –6.872% The end of month value of the fund is: \$100.25 million × 0.93128 = \$93.361 million The rate of return for the month is: (\$93.361/\$100.00) – 1 = –0.06639 = –6.639% For the period October 1982-September 1987: Mean monthly return = 1.898% Standard deviation = 4.353% Sharpe ratio = (1.898% – 0.7%)/4.353% = 0.275 b. For the period October 1982-October 1987: Mean monthly return = 1.238% Standard deviation = 6.724% Sharpe ratio = (1.238% – 0.7%)/6.724% = 0.080 13. a., b., c. Hedge Fund 1 Hedge Fund 2 Hedge Fund 3 Fund of Funds Stand- Alone Fund Start of year value (millions) \$100.0 \$100.0 \$100.0 \$300.0 \$300.0 Gross portfolio rate of return 20% 10% 30% End of year value (before fee) \$120.0 \$110.0 \$130.0 \$360.0 Incentive fee (Individual funds) \$4.0 \$2.0 \$6.0 \$12.0 End of year value (after fee) \$116.0 \$108.0 \$124.0 \$348.0 \$348.0 Incentive fee (Fund of Funds) \$9.6 End of year value (Fund of Funds) \$338.4 Rate of return (after fee) 16.0% 8.0% 24.0% 12.8% 16.0% Note that the end of year value (after-fee) for the Stand-Alone (SA) Fund is the same as the end of year value for the Fund of Funds (FF) before FF charges its extra layer of incentive fees. Therefore, the investor’s rate of return in SA (16.0%) is higher than in FF (12.8%) by an amount equal to the extra layer of fees (\$9.6 million, or 3.2%) charged by the Fund of Funds. 26-7
Chapter 26 - Hedge Funds d. Hedge Fund 1 Hedge Fund 2 Hedge Fund 3 Fund of Funds Stand- Alone Fund Start of year value (millions) \$100.0 \$100.0 \$100.0 \$300.0 \$300.0 Gross portfolio rate of return 20% 10% -30% End of year value (before fee) \$120.0 \$110.0 \$70.0 \$300.0 Incentive fee (Individual funds) \$4.0 \$2.0 \$0.0 \$0.0 End of year value (after fee) \$116.0 \$108.0 \$70.0 \$294.0 \$300.0 Incentive fee (Fund of Funds) \$0.0 End of year value (Fund of Funds) \$294.0 Rate of return (after fee) 16.0% 8.0% -30.0% -2.0% 0.0% Now, the end of year value (after fee) for SA is \$300, while the end of year value for FF is only \$294, despite the fact that neither SA nor FF charge an incentive fee. The reason for the difference is the fact that the Fund of Funds pays an incentive fee to each of the component portfolios. If even one of these portfolios does well, there will be an incentive fee charged. In contrast, SA charges an incentive fee only if the aggregate portfolio does well (at least better than a 0% return). The fund of funds structure therefore results in total fees at least as great as (and usually greater than) the stand- alone structure. 26-8
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