Chapter 20 – Hedge Funds
CHAPTER 20
HEDGE FUNDS
1. No, a market-neutral hedge fund would not be a good candidate for an investor’s
entire retirement portfolio because such a fund is not a diversified portfolio. The
2. # of contracts = 1,200,000,000/(250 800) .6 = 3,600 contracts
3. At the end of two years, the fund value must reach at least 104% of its base value.
4. a. Survivorship bias and backfill bias both result in upwardly biased hedge fund
index returns. Survivorship bias happens when unsuccessful funds cease
5. b. The S&P 500. The shared goal of all types of hedge funds is seeking absolute
returns— finding positive alpha which is above the required returns of the market
6. c. The extra layer of fees only.
7. a. A market-neutral hedge fund. Using the strategy, the fund tries to achieve a net
8. The incentive fee of a hedge fund is part of the hedge fund compensation structure;
the incentive fee is typically equal to 20% of the hedge fund’s profits beyond a
particular benchmark rate of return. Therefore, the incentive fee resembles the
9. There are a number of factors that make it harder to assess the performance of a
hedge fund portfolio manager than a typical mutual fund manager. Some of these
factors are:
Hedge funds tend to invest in more illiquid assets so that an apparent alpha
10. No, statistical arbitrage is not true arbitrage because it does not involve
establishing risk-free positions based on security mispricing. Statistical arbitrage
11. Management fee = .02 $1 billion = $20 million
Portfolio Rate
Incentive Fee
Incentive Fee
Total Fee
Total Fee
12. The incentive fee is typically equal to 20% of the hedge fund’s profits beyond a
particular benchmark rate of return. However, if a fund has experienced losses
in the past, then the fund may not be able to charge the incentive fee unless the
13.
a. First, compute the Black-Scholes value of a call option with the
following parameters:
S0= 62
X = 66
R = .04
Chapter 20 – Hedge Funds
b. Here we use the same parameters used in the Black-Scholes model in part
with the exception that:
X = S0 e0.04 = 62 e0.04 = 64.5303
Now: C = $12.240
The value of the annual incentive fee is
.20 C = .20 $12.240 = $2.448
14.
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:
.95 96.53 = 91.7035
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.
b. In October 1987, the S&P 500 decreased by more than 21%, from 321.83
305.7385 – 251.79 = 53.9485
The average gross monthly payout for the period October 1977 through
15.
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:
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
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1.4975/160.05 = .00936 = .936%
The rate of return the hedge fund earns is therefore equal to:
– .05936 – .0936 = –6.872%
The end of month value of the fund is:
P
P
16.
a. Since the hedge fund manager has a long position in the Waterworks
stock, he should sell six contracts, computed as follows:
$3,000,000×. 75
$250×1,000 =9
b. The standard deviation of the monthly return of the hedged portfolio is
equal to the standard deviation of the residuals, which is 6%. The standard
deviation 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 deviation.
c. The expected rate of return of the market-neutral position is equal to
the risk-free rate plus the alpha: .005 + .02 = .025 = 2.5%
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Chapter 20 – Hedge Funds
6 contracts $250 (F0 − F1) = $1,500 [(S0 1.005) – S1]
= $1,500 S0 [1.005 – (1 + rM )] = $1,500 [1,000 ( .005 – rM )]
= $7,500 − ($1,500,000 rM)
= $3,078,750 + ($3,000,000 e)
The expected rate of return for the (improperly) hedged portfolio is:
($3,078,750/$3,000,000) – 1 = .02625 = 2.625%
Now the z-value for a rate of return of zero is:
0 － .02625
. 06129
The probability of a negative return is: N( .4283) = .3342
Here, the probability of a negative return is very close to the probability
computed earlier.
c. The variance for the diversified (but improperly hedged) portfolio is:
( .252 .052) + .0062 = 1.9225 104
Standard deviation =
√
1. 9225×10−4
= 1.3865%
The z-value for a rate of return of zero is:
0 － .02625
.013865
The probability of a negative return is: N(1.8933) = .0292
The probability of a negative return is now far greater than the result with
proper hedging.
d. The market exposure from improper hedging is far more important in
contributing to total volatility (and risk of losses) in the case of the 100-
stock portfolio because the idiosyncratic risk of the diversified portfolio is
so small.
19. a., b., c.
Hedge Hedge Hedge Fund Stand-
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website, in whole or part.
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%
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
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 charges an incentive fee.
The reason for the difference is the fact that the Fund of Funds pays an incentive fee
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