投資學10版習題答案26

1、Chapter 26 - Hedge FundsCHAPTER 26: HEDGE FUNDSPROBLEM SETS1. No, a market-neutral hedge fund would not be a good can didate for an in vestor sen tire retireme nt portfolio because such a fund is not a diversified portfolio. The term market -n eutral refers to a portfolio positi on with respect to a

2、 specified marketinefficiency. However, there could be a role for a market-neutral hedge fund in the investor s overall portfolio; the ma-neutral hedge fund can be thought of as an approach for the inv estor to add alpha to a more passive in vestme nt positi on such as an in dex mutual fund.2. The i

3、ncen tive fee of a hedge fund is part of the hedge fund compe nsati on structure;the incentive fee is typically equal to 20% of the hedge fund s profits beyond aparticular ben chmark rate of return. Therefore, the incen tive fee resembles the payoff to a call option, which is more valuable when vola

4、tility is higher. Consequently, the hedge fund portfolio man ager is motivated to take on high-risk assets in the portfolio, thereby in creas ing volatility and the value of the incen tive fee.3. There are a nu mber of factors that make it harder to assess the performa nee of a hedge fund portfolio

5、man ager tha n a typical mutual fund man ager. Some of these factors are* Hedge funds tend to in vest in more illiquid assets so that an appare nt alpha may be in fact simply compensation for illiquidity.* Hedge funds valuati on of less liquid assets is questi on able.* Survivorship bias and backfil

6、l bias result in hedge fund databases that report performa nee only for more successful hedge fun ds.* Hedge funds typically have unstable risk characteristics making performanee evaluation that depends on a consistent risk profile problematic.* Tail events skew the distribution of hedge fund outcom

7、es, making it difficult to obta in a represe ntative sample of retur ns over relatively short periods of time.4. The problem of survivorship bias is that on ly the returns for survivors will be reported and the index return will be biased upwards. Backfill bias results when anew hedge fund is added

8、to an index and the fund s historical performanee is addedto the index s historical performTihceproblem is that only funds that survived will have their performa nee added to the in dex, result ing in upward bias in in dex returns.26-15. The Merrill Lynch High Yield in dex may be the best in dividua

9、l market in dex for fixed in come hedge funds and the Russell 3000 may be the in dividual market in dex for equity hedge fun ds. However, a comb in ati on of in dexes may be the best market index, as it has been found that multifactor model do the best in explaining hedge fund returns. Of equity hed

10、ge fun ds, market n eutral strategies should have a return that is closest to risk-free, but they are not risk free.6. Funds of funds are usually con sidered good choices for in dividual in vestors because they offer diversification and usually more liquidity. One problem with funds of funds is that

11、 they usually have lower retur ns. This is a result from both theadditi on al layer of fees and cash drag (result ing from the desire for liquidity).7. Of the equity hedge fun ds, market n eutral strategies should have a return that is closest to risk-free; however, they are not completely risk-free

12、 and typically have exposure to both systematic and un systematic risks.8. No, statistical arbitrage is not true arbitrage because it does not involve establishing risk-free positions based on security mispricing. Statistical arbitrage is essentially a portfolio of risky bets. The hedge fund takes a

13、 large nu mber of small positi ons based on apparent small, temporary market inefficiencies, relying on the probability that the expected return for the totality of these bets is positive.9.Management fee = 0.02 $1 為illion = $20 millionTotal Fee ($ millio n)Total Fee(%)Portfolio Rate of Retur n (%)I

14、ncen tive Fee Incen tive Fee(%)($ millio n)a.-500202b.000202c.500202d.10201030310. The incentive fee is typically equal to 20 percentf the hedge fund s profits bey ond a particular ben chmark rate of retur n. However, if a fund has experie need losses in the past, the n the fund may not be able to c

15、harge the incen tive fee uni ess the fund exceeds 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 incen tive fee. The hi

16、gh-water mark for a hedge fund is equivale nt 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.26-2Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent of

17、McGraw-Hill Education.Chapter 26 - Hedge Fun ds11. a. First, compute the Black Scholes value of a call option with thefollow ing parameters:S0 = 62X = 66R = 0.04二=0.50T = 1 yearTherefore: C = $11.685The value of the annual incen tive fee is:0.20 懇=0.20 $*1.685 = $2.337b. Here we use the same paramet

18、ers used in the Black-Scholes model in part (a) with the exception that X = 62Now: C = $13.253The value of the annual incen tive fee is0.20 * = 0.20 $*3.253 = $2.651c. Here we use the same parameters used in the Black-Scholes model in part (a) with the excepti on that:X = S0 *e0.04 = 62 e0.04 = 64.5

19、303Now: C = $12.240The value of the annual incen tive fee is0.20 C = 0.20 $12.240 = $2.448d. Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that X = 62 and 二=0.60Now: C = $15.581The value of the annual incen tive fee is0.20 C = 0.20 $15.581 = $3.11612.

20、 a. The spreadsheet in dicates that the en d-of- month value for the S&P 500 inSeptember 1977 was 96.53, so the exercise price of the put writte n at the begi nning of October 1977 would have bee n0.95 96.53 = 91.7035At the end of October, the value of the in dex was 92.34, so the put would have exp

21、ired out of the money and the put wrer s payout was zeSinee it is unusual for the S&P 500 to fall by more than 5 percent in one month, all but 10 of the 120 mon ths between October 1977 and September 1987 would26-3Copyright ? 2014 McGraw-Hill Education. All rights reserved. No reproduction or distri

22、bution without the prior written consent ofMcGraw-Hill Education.Chapter 26 - Hedge Fundshave 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 been0.95 05.10 = 90.3450At the end of

23、 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 = 1.0950The average gross monthly payout for the period would have been 0.2437 and the standard deviation would have been 1.0951.b. In October 1987, the S&P 500 decreased

24、 by more than 21 percent, from 321.83 to 251.79. The exercise price of the put written at the beginning of October 1987 would have been0.95 321.83 = 305.7385At the end of October, the option writer s payout would have been:305.7385 -251.79 = 53.9485The average gross monthly payout for the period Oct

25、ober 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.13. a. In order to calculate the Sharpe ratio, we first calculate the rate of return for each month in the period October 1982 September

26、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 is0.95 120.42 = 114.3990Since 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 ra

27、te of 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

28、millionThe 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 is26-40.95 160.05 = 152.0475The May end of month val

29、ue for the index was 150.55, and therefore the payout for the writer of a put option on one unit of the index is152.0475 -150.55 = 1.4975The rate of retur n the hedge fund earns on the in dex is equal tos rate(150.55/160.05) -1 = -0.05936 = 5936%The payout of 1.4975 per unit of the in dex reduces th

30、e hedge fund of retur n by1.4975/160.05 = 0.00936 = 0.936%The rate of return the hedge fund earns is therefore equal to5936% -0.936% = -.872%The end of month value of the fund is$100.25 millio n 0.93128 = $93.361 millio nThe rate of return for the month is($93.361/$100.00) -1 = -0.06639 = -.639%For

31、the period October 198September 1987Mean monthly return = 1.898%Sta ndard deviation = 4.353%Sharpe ratio = (1.898% -0.7%)/4.353% = 0.275b.For the period October 198October 1987Mean monthly return = 1.238%Sta ndard deviation = 6.724%Sharpe ratio = (1.238% -0.7%)/6.724% = 0.08014. a. Si nee the hedge

32、fund man ager has a long positi on in the Waterworks stock, he should sell six con tracts, computed as follows:二 6 con tracts$2,000,000 0.75$250 1,000b. The sta ndard deviati on of the mon thly return of the hedged portfolio is equal to the sta ndard deviati on of the residuals, which is 6 perce nt.

33、 The sta ndard deviati on of the residuals for the stock is the volatility that cannot be hedged away. For a market-neutral (zero-beta) position, this is also the total standard deviati on.26-5c. The expected rate of return of the market -n eutral positi on is equal to the risk-free rate plus the al

34、pha:0.5% + 2.0% = 2.5%We assume that mon thly returns are approximately n ormally distributed. The z-value for a rate of retur n of zero is-2.5%/6.0% = -0.4167Therefore, the probability of a negative return isN(-0.4167) = 0.338515. a. The residual standard deviation of the portfoliois smaller than e

35、ach stock s standard deviation by a factor o”100 = 10 or, equivalently, the residual varia nee of the portfolio is smaller by a factor of 100. So, in stead of a residual sta ndard deviati on of 6 perce nt, residual sta ndard deviatio n is now 0.6 perce nt.b. The expected retur n of the market -n eut

36、ral positi on is still equal to the risk-free rate plus the alpha:0.5% + 2.0% = 2.5%Now the z-value for a rate of retur n of zero is-2.5%/0.6% = -4.1667Therefore, the probability of a negative return isN(-4.1667) = 0.0000155 A n egative return is very un likely.16. a. For the (now improperly) hedged

37、 portfolio:Variance = (0.252 対)+ 62 = 37.5625Sta ndard deviation = 6.129%b.Si nee the man ager has misestimated the beta of Waterworks, the man agerwill sell four S&P 500 con tracts (rather tha n the six con tracts in Problem 6):$2,000,000 0.504 con tracts$250 1,000The portfolio is not completely he

38、dged so the expected rate of return is no Ion ger 2.5 perce nt. We can determ ine the expected rate of return by first computing the total dollar value of the stock plus futures position.The dollar value of the stock portfolio is$2,000,000 (1 rp0rtfoH0 ) = $2,000,000 1 0.005 0.75 (皿-0.005) 0.02 e二 $

39、2,042,500 $1,500,000 g $2,000,000 eThe dollar proceeds from the futures positi on equal26-64 $250 (F0 - FJ =$1,000 (S0 1.005)-S,二 $1,000 S0 1.005 -(1 rM)= $1,000 1,000 0.005 rM=$5,000 - $1,000,000 rMThe total value of the stock plus futures positi on at the end of the month is$2,047,500 ($1,500,000

40、- $1,000,000) rM$2,000,000 e=$2,047,500 $500,000 (0.01) $2,000,000 e二 $2,052,500 $2,000,000 eThe expected rate of return for the (improperly) hedged portfolio is($,2052,500 / $2,000,000) -1 = .02625 = 2.625%Now the z-value for a rate of retur n of zero is:-2.625%/6.129% = -0.4283The probability of a

41、 negative return isN(-0.4283) = 0.3342Here, the probability of a n egative return is similar to the probability computed in Problem 14.c. The varia nee for the diversified (but improperly hedged) portfolio is2 2 2(0.25 5 ) + 0.6 = 1.9225Sta ndard deviation = 1.3865%The z-value for a rate of retur n

42、of zero is:-2.625%/1.3865% = -1.8933The probability of a negative return isN(-1.8933) = 0.0292The probability of a negative return is now far greater than the result with proper hedg ing in Problem 15.d. The market exposure from improper hedg ing is far more importa nt incon tribut ing to total vola

43、tility (and risk of losses) in the case of the 100-stock portfolio because the idios yn cratic risk of the diversified portfolio is so small.26-717. a., b., c.Stand-HedgeHedgeHedgeFundAloneFund 1Fund 2Fund 3of FundsFundStart of year value (millions)$100.0$100.0$100.0$300.0$300.0Gross portfolio rate

44、of return20%10%30%End of year value (before fee)$120.0$110.0$130.0$360.0Incentive fee (Individual funds)$4.0$2.0$6.0$12.0End of year value (after fee)$116.0$108.0$124.0$348.0$348.0Incentive fee (Fund of Funds)$9.6End of year value (Fund of Funds)$338.4Rate 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