HW7 - FIN 655
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Grand Canyon University *
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Course
655
Subject
Finance
Date
Feb 20, 2024
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3
Uploaded by CorporalWillpowerWaterBuffalo22
A hedge fund with $1.2 billion of assets charges a management fee of 2% and an incentive fee of 15% of returns over a money market rate, which currently is 7.4%.
1.
Calculate total fees, both in dollars and as a percent of assets under management, for the portfolio returns in the table below.
(Enter your answers for Total Fee ($ millions) in millions not dollars. Round your answers to 1 decimal place.)
Portfolio Rate of Return (%)
Total Fee ($ million)
Total Fee (%)
a.
-5%
24.0 2.0%
b.
0%
24.0 2.0%
c.
5%
24.0 2.0%
d.
10%
28.7 2.4%
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 2.2% over the coming month.
2.
Beta
R
-square
Standard Deviation
of Residuals
1.45
0.65
0.11 (i.e., 11% 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.)
Residual Standard Deviation
1.1%
b.
Calculate the probability of a loss on a market-neutral strategy involving equally weighted, market-
hedged positions in the 100 stocks over the next month. Assume the risk-free rate is 0.2% per month.
(Do not round intermediate calculations. Enter your answer as percent rounded to 5 decimal places.)
Probability of a loss
1.45615%
A hedge fund with net asset value of $110 per share currently has a high water mark of $119. Suppose it is January 1, the standard deviation of the fund’s annual returns is 39%, and the risk-free rate is 5%. The fund has an incentive fee of 10%.
3.
a.
What is the value of the annual incentive fee according to the Black-Scholes formula? (Treat the risk-free rate as a continuously compounded value to maintain consistency with the Black-Scholes formula.)
(Do not round intermediate calculations. Round your answer to 3 decimal places.)
Annual incentive fee
$ 1.570
per share
b.
What would the annual incentive fee be worth if the fund had no high water mark and it earned its HOMEWORK #7 - FIN 655
Wednesday, November 8, 2023
2:17 PM
incentive fee on its total return?
(Do not round intermediate calculations. Round your answer to 3 decimal places.)
Annual incentive fee
$ 1.941 per share
c.
What would the annual incentive fee be worth if the fund had no high water mark and it earned its incentive fee on its return in excess of the risk-free rate?
(Do not round intermediate calculations. Round your answer to 3 decimal places.)
Annual incentive fee
$ 1.701 per share
d.
Recalculate the incentive fee value for part (b) assuming that an increase in fund leverage increases volatility to 49%.
(Do not round intermediate calculations. Round your answer to 3 decimal places.)
Annual incentive fee
$ 2.356 per share
Calculate the forecast for next year’s sales using regression.
4.
Suppose a firm has had the following historic sales figures.
Year
Sales
2009
1,410,000 2010
1,670,000 2011
1,580,000 2012
2,170,000 2013
1,810,000 What would be the forecast for next year's sales using regression to estimate a trend?
Complete the following analysis. Do not hard code values in your calculations, and do not round intermediate calculations
Next year's sales
2,118,000 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.
5.
Beta
R
-square
Standard Deviation
of Residuals
2
0.65
0.15 (i.e., 15% 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 maturity S&P 500 futures contracts, how many contracts should he enter? The S&P 500 currently is at 1,000 and thecontract multiplier is $250.
Number of contracts
16
a-2.
Should he buy or sell contracts?
Buy
○
Sell
○
b.
What is the standard deviation of the monthly return of the hedged portfolio?
Standard Deviation %
15.00%
c.
Assuming that monthly returns are approximately normally distributed, what is the probability that this market-neutral strategy will lose money over the next month? Assume the risk-free rate is 0.6% per month.
(Enter your answer as percent rounded to 2 decimal places, e.g., enter "12.53%" and not "0.1253.")
Probability 43.38%
Here are data on three hedge funds. Each fund charges its investors an incentive fee of 10% 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 10% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
6.
Hedge
Fund 1
Hedge
Fund 2
Hedge
Fund 3
Start of year value (millions)
$120
$120
$120
Gross portfolio rate of return
15%
30%
45%
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.)
Rate of return
24.30%
b.
Suppose that instead of buying shares in each of the three hedge funds, a stand-alone (SA) hedge fund purchases the same
portfolio
as the three underlying funds. The total value and composition of the SA fund is therefore identical to the one that would result from aggregating the three hedge funds. Consider an investor in the SA fund. After paying 10% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
(Do not round your intermediate calculations. Round your answer to 2 decimal places.)
Percentage of return
27.00%
d.
Now suppose that the return on the portfolio held by hedge fund 3 were −45% rather than +45%. Recalculate your answers to parts (
a
) and (
b
).
(Do not round your intermediate calculations. Negative amount should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 2 decimal places.)
Fund of fund return
-1.50%
Stand-alone fund return
0.00%
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