Chapter 20 – Hedge Funds
CHAPTER 20
20-1
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
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
5. b.The S&P 500.The shared goal of all types of hedge funds is seeking absolute
6. a. A market-neutral hedge fund. Using the strategy, the fund tries to achieve a net
7. The incentive fee of a hedge fund is part of the hedge fund compensation structure;
8. 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:
20-2
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
9. No, statistical arbitrage is not true arbitrage because it does not involve
10. Management fee = .02 $1 billion = $20 million
Portfolio Rate
of Return (%)
Incentive Fee
(%)
Incentive Fee
($ million)
Total Fee
($ million)
Total Fee
(%)
a. –5 0 0 20 2
11. 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
12. First, compute the Black-Scholes value of a call option with the following
parameters:
S0= 62
a. Here we use the same parameters used in the Black-Scholes model in part
(a) with the exception that: X = 62
20-3
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
.20 C = .20 $13.253 = $2.651
b. Here we use the same parameters used in the Black-Scholes model in part (a)
with the exception that:
c. Here we use the same parameters used in the Black-Scholes model in part
(a) with the exception that: X = 62 and = .60
Now: C = $15.581
12.
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
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:
20-4
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
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 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:
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:
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:
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:
The rate of return the hedge fund earns on the index is equal to:
The payout of 1.4975 per unit of the index reduces the hedge fund’s
rate of return by:
20-5
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
P
b. For the period October 1982-October 1987:
P
14.
a. Since the hedge fund manager has a long position in the Waterworks
stock, he should sell six contracts, computed as follows:
9
1,000$250
.75$3,000,000
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
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%
.06
Therefore, the probability of a negative return is: N(−.4167) =.3385
15.
a. The residual standard deviation of the portfolio is smaller than each stock’s
b. The expected return of the market-neutral position is still equal to the
20-6
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
16.
a. For the (now improperly) hedged portfolio:
Variance = (.252.052) + .062 = .00375625
Standard deviation =
00375625.
=.06129 = 6.129%
b. Since the manager has misestimated the beta of Waterworks, the manager
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
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
c. The variance for the diversified (but improperly hedged) portfolio is:
(.252.052) + .0062 = 1.9225104
0 － .02625
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.
17. 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%
20-8
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.
Chapter 20 – Hedge Funds
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
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
to each of the component portfolios. If even one of these portfolios does well, there
20-9
© 2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or
distribution in any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a
website, in whole or part.