Answer:
Answer:
Survivorsh
Problem 26-4
Which of the following is most
accurate in describing the problems of survivorship bias and backfill bias in the performance
evaluation of hedge funds?
Survivorship bias and backfill bias both result in upwardly biased hedge fund index returns.
Survivorship bias and backfill bias both result in downwardly biased hedge fund index returns.
Survivorship bias results in upwardly biased hedge fund index returns, but backfill bias results in downwardly biased hedge
fund index returns.
Answer:
Problem 26-5
Which of the following would be the most appropriate benchmark to use for hedge fund evaluation?
A multifactor model.
The S&P 500.
The risk-free rate.
Answer:
Both the
Problem 26-6
With respect to hedge fund investing, the net return to an investor in a fund of funds would be lower than that
earned from an individual hedge fund because of:
Both the extra layer of fees and the higher liquidity offered.
No reason; fund of funds earn returns that are equal to those of individual hedge funds.
The extra layer of fees only.
Answer:
Problem 26-7
Which of the following hedge fund types is most likely to have a return that is closest to risk-free?
A market-neutral hedge fund.
An event-driven hedge fund.
A long/short hedge fund.
Inputs:
Assets
under
mgmt
1300000000 1300
Mgmt fee
%
0.015
Incentive
fee %
0.15
Answers:
Portfolio
ROR
Total Fee
($ million)
Total fee
%
a. -0.05 19.5 1.50%
Problem 26-9
A hedge fund with $1 billion of assets charges a management fee of 2% and an incentive fee of 20% of returns
over a money market rate, which currently is 5%.
Calculate total fees, both in dollars and as a percent of assets under management, for portfolio returns of: (Enter
your answers in millions. Omit the “$” & “%” signs in your response.)
Portfolio rate of return (%) Total fee($ million) Total fee (%)
a. −5
Money
mkt rate
%
Answer:
Problem 26-10
A hedge fund with net asset value of $62 per share currently has a high water mark of $66.
Is the value of its incentive fee more or less than it would be if the high water mark were $67?
Less
More
Inputs:
Part d.
NAV 50
High
Water
Mark
53
Std Dev of
Fund
0.47 0.57
rf 0.03
Incentive
fee
0.12
b. C 9.908439
c. C 9.288537
d. C 11.79919
c. X 51.52273
d. X 50
ơ57.00%
Answers:
a.
Incentive
fee based
upon
Black-
Scholes
$1.047
fisk-free
rate total
return
mark
b.
Incentive
fee on
total
Problem 26-11
A hedge fund with net asset value of $62 per share currently has a high water mark of $66. Suppose it is January 1, the
standard deviation of the fund’s annual returns is 50%, and the risk-free rate is 4%. The fund has an incentive fee of 20%.
a.What is the value of the annual incentive fee according to the Black-Scholes formula? (Do not round intermediate
calculations. Round your answer to 3 decimal places. Omit the “$” sign in your response.)
Annual incentive fee $
b.What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its
total return?
(Do not round intermediate calculations. Round your answer to 3 decimal places. Omit the “$” sign in your
response.)
Output
Data
Output
Data for
Output
Data for
Output
Data for
Inputs:
Portfolio
Value
2000000
S&P 500
Index
1000
Contract
multiplier
250
R-square
of
residuals
0.06
Alpha 0.02
rf 0.005
Answers:
a.1. 6 contracts
Problem 26-14
The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 index.
A hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.
Standard Deviation Beta R-square of Residuals
0.65 0.75 0.06 (i.e., 6% monthly)
a-1.If he holds a $2 million portfolio of Waterworks stock, and wishes to hedge market exposure for the next month using 1 -month
Number of contracts
a-2.Should he buy or sell contracts? BuySell
b.What is the standard deviation of the monthly return of the hedged portfolio? (Omit the “%” sign in your response.)
Standard
Deviation
Inputs:
# of stocks
in
portfolio
100
Standard
deviation
0.65
Beta 0.75
R-square
of
Answers:
a.
Residual
Problem 26-15
The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 index. A
hedge fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.
Standard Deviation Beta R-square of Residuals
0.65 0.75 0.06 (i.e., 6% monthly)
a.Suppose you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as
Waterworks. Assume the residual returns on each of these stocks are independent of each other. What is the residual standard
deviation of the portfolio? (Round your answer to 1 decimal place. Omit the “%” sign in your response.)
residuals
a market
neutral
position
Inputs:
Standard
deviation
0.65
Beta 0.75
R-square
of
residuals
6.00% 0.6
Alpha 0.02
Standard
deviation
of
monthly
market
rate of
return
5.00%
Portfolio
value
2000000
Beta 0.5
Variance 0.003756
market
return
Standard
deviation
Portfolio
value
S&P 500
Index
Contract
multiplier
Risk-free
rate
0.50%
# of
contracts
for hedge
4 sell
Expected
ROR
w/hedge
2042488
Proceeds
from
futures
position:
10000
Expected
ROR from
improperl
y hedged
portfolio
0.26244
z-value of
ROR of
properly
hedged
portfolio
-4.2820
c.
# of
stocks 100
Beta 0.75
Answers: rf 0.50%
for
improperl
y hedged
portfolio
Standard
deviation
z-value
for a ROR
of zero
Variance
Problem 26-16
The following is part of the computer output from a regression of monthly returns on Waterworks stock against the S&P 500 ind ex. A hedge
fund manager believes that Waterworks is underpriced, with an alpha of 2% over the coming month.
Standard Deviation Beta R-squareof Residuals
0.65 0.75 0.06 (i.e., 6% monthly)
Now suppose that the manager misestimates the beta of Waterworks stock, believing it to be 0.50 instead of 0.75. The standard deviation of
the monthly market rate of return is 5%.
a.What is the standard deviation of the (now improperly) hedged portfolio? (Round your answer to 3 decimal places. Omit the “%” sign in
your response.)
Standard deviation %
b.What is the probability of incurring a loss on improperly hedged portfolioover the next month if the monthly market return has an
Probability of a negative return %
c.What would be the probability of a loss you if hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual
R-square
of
residuals
Inputs:
a. & b.
Hedge
Fund 1
Hedge
Fund 2
Hedge
Fund 3
Fund of
Funds
Stand-
alone
Fund
c.
Hedge
Fund 1
Hedge
Fund 2
Hedge
Fund 3
Fund of
Funds
Stand-
alone
Fund
Start of yr
value
100 100 100 300 300
Start of yr
value
100 100 100 300 300
Gross
portfolio
ROR
0.2 0.1 0.3
Gross
portfolio
ROR
0.2 0.1 -0.3
EOY value
(before
EOY value
(before
Incentive
fee
0.2
Answers:
a. 12.80%
b. 16.00%
c.
Problem 26-17
Here are data on three hedge funds. Each fund charges its investors an incentive fee of 20% of total returns. Suppose initially
that a fund of funds (FF) manager buys equal amounts of each of these funds, and also charges its investors a 20% incentive
fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
HedgeFund 1 HedgeFund 2 HedgeFund 3
Start of year value (millions) $100 $100 $100
Gross portfolio rate of return 20% 10% 30%
a.Compute the rate of return after incentive fees to an investor in the fund of funds. (Do not round your intermediate
calculations. Round your answer to 2 decimal places. Omit the “%” sign in your response.)
fee)
fee)
Incentive
fee
Incentive
fee
EOY value
(after fee)
EOY value
(after fee)
Incentive
fee Fund
of Funds
Incentive
fee Fund
of Funds
EOY value
(Fund of
Funds)
EOY value
(Fund of
Funds)
(after fee)
(after fee)