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
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CHAPTER 26: HEDGE FUNDS
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
they offer diversification and usually more liquidity. One problem with funds of
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
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
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CHAPTER 26: HEDGE FUNDS
11. a. First, compute the Black Scholes value of a call option with the
following parameters:
S0= 62
The value of the annual incentive fee is:
b. Here we use the same parameters used in the Black-Scholes model in part (a)
The value of the annual incentive fee is
c. Here we use the same parameters used in the Black-Scholes model in part (a) with
the exception that:
The value of the annual incentive fee is
d. Here we use the same parameters used in the Black-Scholes model in part (a)
The value of the annual incentive fee is
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
At the end of October, the value of the index was 92.34, so the put would
have expired out of the money and the put writer’s payout was zero. Since it
is unusual for the S&P 500 to fall by more than 5 percent in one month, all
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CHAPTER 26: HEDGE FUNDS
At the end of January, the value of the index was 89.25 (more than a
6% decline), so the option writer’s payout would have been:
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 percent, from
At the end of October, the option writer’s payout would have been:
The average gross monthly payout for the period October 1977 through
13. a. In order to calculate the Sharpe ratio, we first calculate the rate of return for
Since 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 rate of return the hedge fund earns on the index is therefore equal to
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 rate of return for the month 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
The rate of return the hedge fund earns is therefore equal to
The end of month value of the fund is
The rate of return for the month is
For the period October 1982—September 1987
Mean monthly return = 1.898%
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:
$2,000,000 0.75 15
$50 2,000
´=
´
contracts
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c. The expected rate of return of the market-neutral position is equal to the
risk-free rate plus the alpha:
We assume that monthly returns are approximately normally distributed.
The z-value for a rate of return of zero is
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
risk-free rate plus the alpha:
Now the z-value for a rate of return of zero is
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
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CHAPTER 26: HEDGE FUNDS
d. The market exposure from improper hedging is far more important in
17. a.-f..
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CHAPTER 26: HEDGE FUNDS
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
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
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
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
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