Chapter 26 – Hedge Funds
CHAPTER 26: HEDGE FUNDS
PROBLEM SETS
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. 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
3. 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 may
be in fact simply compensation for illiquidity.
4. The problem of survivorship bias is that only the returns for survivors will be
reported and the index return will be biased upwards. Backfill bias results when a
Chapter 26 – Hedge Funds
26-2
5. The Merrill Lynch High Yield index may be the best individual market index for
fixed income hedge funds and the Russell 3000 may be the individual market index
6. Funds of funds are usually considered good choices for individual investors because
7. Of the equity hedge funds, market neutral strategies should have a return that is
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
9. Management fee = 0.02 × $1 billion = $20 million
Portfolio Rate
of Return (%)
Incentive Fee
(%)
Incentive Fee
($ million)
Total Fee
($ million)
Total Fee
(%)
a.
-5
0
0
20
2
0
0
20
2
c.
0
0
20
2
10
10
30
3
10. The incentive fee is typically equal to 20 percent 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
11. a. First, compute the Black Scholes value of a call option with the
following parameters:
Chapter 26 – Hedge Funds
26-3
S0 = 62
b. Here we use the same parameters used in the Black-Scholes model in part (a)
with the exception that X = 62
c. Here we use the same parameters used in the Black-Scholes model in part (a) with
the exception that:
d. Here we use the same parameters used in the Black-Scholes model in part (a)
with the exception that X = 62 and = 0.60
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
Chapter 26 – Hedge Funds
26-4
b. In October 1987, the S&P 500 decreased by more than 21 percent, from
321.83 to 251.79. The exercise price of the put written at the beginning of
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
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
Chapter 26 – Hedge Funds
26-5
The rate of return the hedge fund earns on the index is equal to
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
b. For the period October 1982—October 1987
Mean monthly return = 1.238%
14. a. Since the hedge fund manager has a long position in the Waterworks stock,
he should sell six contracts, computed as follows:
c. The expected rate of return of the market-neutral position is equal to the
risk-free rate plus the alpha:
Chapter 26 – Hedge Funds
26-6
15. a. The residual standard deviation of the portfolio is smaller than each stock’s
standard deviation by a factor of 100 = 10 or, equivalently, the residual
variance of the portfolio is smaller by a factor of 100. So, instead of a residual
standard deviation of 6 percent, residual standard deviation is now 0.6 percent.
b. The expected return of the market-neutral position is still equal to the
risk-free rate plus the alpha:
16. a. For the (now improperly) hedged portfolio:
b. Since the manager has misestimated the beta of Waterworks, the manager
will sell four S&P 500 contracts (rather than the six contracts in Problem 6):
$2,000,000 0.50 4
$250 1,000
=
contracts
The portfolio is not completely hedged so the expected rate of return is
Chapter 26 – Hedge Funds
26-7
$2,047,500 ($1,500,000 $1,000,000) $2,000,000
M
re
+ − +
c. The variance for the diversified (but improperly hedged) portfolio is
(0.252 × 52) + 0.62 = 1.9225
Standard deviation = 1.3865%
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.
Chapter 26 – Hedge Funds
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%
End of year value (before fee)
$120.0
$130.0
$360.0
Incentive fee (Individual funds)
End of year value (after fee)
$116.0
$124.0
$348.0
$348.0
Incentive fee (Fund of Funds)
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
Gross portfolio rate of return
20%
10%
-30%
End-of-year value (before fee)
$120.0
$300.0
Incentive fee (Individual funds)
End-of-year value (after fee)
$116.0
$294.0
$300.0
Incentive fee (Fund of Funds)
End-of-year value (Fund of Funds)
$294.0
Rate of return (after fee)
16.0%
8.0%
-30.0%
0.0%