Chapter 26
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1.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A hedge fund with $1 billion of assets charges a management fee of 2% and an incentive fee of 20% of returns over a money market rate, which currently is 5%.
Required:
Calculate total fees, both in dollars and as a percent of assets under management, for the portfolio returns in the table below.
Note: Enter your answers for Total Fee ($ millions) in millions not dollars.
$
$
$
$
Portfolio Rate of
Return (%)
Total Fee
($ million)
Total Fee
(%)
a.
-5
20
2
b.
0
20
2
c.
5
20
2
d.
10
30
3
Explanation:
Management fee = 0.02 × $1 billion = $20 million
For a single period (assuming no highwater mark), the incentive fee is $0 or $10,000,000, depending on the returns (above or below the hurdle rate):
Incentive Fee =
r
Incentive
× [
V
0
× (1 +
r
Assets
) −
V
0
× (1 +
r
Hurdle
)] = [
V
0
× (
r
Assets
−
r
Hurdle
)]
For
r
Assets
= 0.10(part d.)
Incentive Fee = 0.20 × [$1,000,000,000 × (0.10 − 0.05)] = $10,000,000
Portfolio Rate of
Return (%)
Management Fee
($ million)
Incentive Fee ($
million)
Total Fee ($
million)
Total Fee (%)
a.
−5
20
0
20
2
b.
0
20
0
20
2
c.
5
20
0
20
2
d.
10
20
10
30
3
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
2.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A hedge fund with net asset value of $62 per share currently has a high-water mark of $66.
Required:
Is the value of its incentive fee more or less than it would be if the high-water mark were $67?
Incentive fee
Less
Explanation:
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 the fund exceeds its previous high-water mark. The incentive fee is less valuable if the high-water mark is $67, rather than $66. With a high-water mark of $67, the net asset value of the fund must reach $67
before the hedge fund can assess the incentive fee. The high-water mark for a hedge fund is equivalent to the exercise price for a call option on an asset with a current market value equal to the net asset value of the fund.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
3.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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% of annual returns, but its current high-water mark is $66, and net asset value is $62.
Required:
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.)
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
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?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
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?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
d.
Recalculate the incentive fee value for part (
b
) if an increase in fund leverage increases volatility to 60%.
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
$
$
$
$
a. Annual incentive fee
2.34
per share
b. Annual incentive fee
2.65
per share
c. Annual incentive fee
2.45
per share
d. Annual incentive fee
3.12
per share
Explanation:
a.
First, compute the Black Scholes value of a call option with the following parameters:
S
0
= $62
X
= $66
r
= 0.04
σ
= 0.50
T
= 1 year
= 0.2050
= 0.2950
N
(
d
1
) =
N
(0.2050) = 0.5812
N
(
d
2
) =
N
(−0.2950) = 0.3840
C
0
=
S
0
N
(
d
1
) −
Xe
−
rT
N
(
d
2
) = $62 × 0.5812 − $66 ×
e
-0.04 × 1
× 0.3840
= $36.0344 − $24.3489 = $11.6853
$11.69
The value of the incentive fee is 0.20 × $11.6853
$2.34
b.
Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that
X
= $62.
= 0.33
= −0.17
N
(
d
1
) =
N
(0.33) = 0.6293
N
(
d
2
) =
N
(−0.17) = 0.4325
C
0
=
S
0
N
(
d
1
) −
Xe
−
rT
N
(
d
2
) = $62 × 0.6293 − $62 ×
e
−0.04 × 1
× 0.4325
= $13.253 ≈ $13.25
The value of the annual incentive fee is
0.20 ×
C
0
= 0.20 × $13.25 ≈ $2.65
c.
Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that:
X
=
S
0
×
e
0.04
= 62 ×
e
0.04
= 64.5303
= 0.25
= −0.25
N
(
d
1
) =
N
(0.25) = 0.5987
N
(
d
2
) =
N
(−0.25) = 0.4013
C
0
=
S
0
N
(
d
1
) −
Xe
−
rT
N
(
d
2
) = $62 × 0.5987 − $64.5303 ×
e
−0.04 × 1
× 0.4013
≈ $12.24
The value of the annual incentive fee is
0.20 ×
C
0
= 0.20 × $12.24 ≈ $2.45
d.
Here we use the same parameters used in the Black-Scholes model in part (a) with the exception that
X
= 62 and σ = 0.60
= 0.3667
= −0.2333
N
(
d
1
) =
N
(0.3667) = 0.6431
N
(
d
2
) =
N
(−0.2333) = 0.4078
C
0
=
S
0
N
(
d
1
) −
Xe
−
rT
N
(
d
2
) = $62 × 0.6431 − $62 ×
e
−0.04 × 1
× 0.4078
= $15.58
The value of the annual incentive fee is
0.20 × C
0
= 0.20 × $15.58 = $3.12
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
4.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A market-neutral fund ($150,000,000) strives for very low market risk (β = 0.15). It believes it can generate α = 0.04 per quarter. The β of the underlying portfolio is 1.35. The risk-free rate is 0.5% per quarter and the S&P 500 is
currently priced at 4,000 (E-mini S&P 500 multiplier = $50).
Required:
If the S&P 500 is 3,800 at the end of quarter, what is the expected return on the portfolio?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Expected return
3.68
%
Explanation:
First compute the hedge ratio necessary to keep β low (but not zero).
Hedge Ratio = (Portfolio Value ÷ (Index Price × Contract Multiplier)) × (
β
Portfolio
−
β
Target
)
= ($150,000,000 ÷ (4,000 × $50)) × (1.35 − 0.15) = 900 Contracts (Short)
Next, calculate the portfolio value, the value of the futures proceeds, and the market return:
Value
Portfolio
= Value
0
× (1 +
r
Portfolio
)
= Value
0
× [1 +
r
f
+
β
Portfolio
× (
r
m
−
r
f
) +
α
Portfolio
+
e
]
= $150,000,000 × [1 + 0.005 + 1.35 × (
r
m
− 0.005) + 0.04 +
e
]
= $155,737,500 + $202,500,000 ×
r
m
+ $150,000,000 ×
e
Proceeds
Futures
= Contracts × Multiplier × (
F
0
−
F
1
)
= 900 × $50 × [
S
0
(1 +
r
f
) −
F
1
]
= 900 × $50 × [4000 × 1.005 − 3,800]
= $9,900,000
r
m
= (3,800 − 4,000) ÷ 4,000 = −0.05, or −5.00%
Combining these values generates the hedged proceeds and the expected rate of return:
Value
Hedged
= Value
Portfolio
+ Proceeds
Futures
= $155,737,500 + $202,500,000 × (−0.05) + $150,000,000
e
+ $9,900,000
= $155,512,500 + $150,000,000 ×
e
E(
r
Hedged
) = (
E
(Value
Hedged
) − Value
0
) ÷ Value
0
= ($155,512,500 − $150,000,000) ÷ $150,000,000 = 0.0368, or 3.68%
The expected return on the hedge portfolio is 3.68%.
Note: Here is realized returns if the investor did not hedge:
E(
r
Unhedged
) = ([1 +
r
f
+
α
+
β
× (
r
m
−
r
f
)] × Value
0
− Value
0
) ÷ Value
0
= ($145,612,500 − $150,000,000) ÷ $150,000,000 = −2.93%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
5.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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 believes that Waterworks is underpriced, with an alpha of 2% over the coming
month.
Beta
R
-square
Standard Deviation of Residuals
0.75
0.65
0.06 (i.e., 6% monthly)
Required:
a.
If the fund holds a $4 million position in 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 it enter? Should it buy or sell
contracts? The S&P 500 currently is at 4,000 and the contract multiplier is $50.
b.
What is the standard deviation of the monthly return of the hedged portfolio?
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 0.5% per month.
d.
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?
e.
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 0.5% per month.
Required A
Required B
Complete this question by entering your answers in the tabs below.
If the fund holds a $4 million position in 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 it enter? Should it buy or sell contracts? The S&P 500
currently is at 4,000 and the contract multiplier is $50.
Required A
Required B
Required C
Required D
Required E
Number of contracts
15
Should it buy or sell contracts?
Sell
Explanation:
a.
Since the hedge fund manager has a long position in the Waterworks stock, he should sell 15 contracts, computed as follows:
($4,000,000 × 0.75) ÷ ($50 × 4,000) = 15 contracts
b.
The standard deviation of the monthly return of the hedged portfolio is equal to the standard deviation of the residuals, which is 6 percent. The standard deviation of the residuals for the stock is the volatility that cannot be
hedged away. For a market-neutral (zero-beta) position, this is also the total standard deviation.
c.
The expected rate of return of the market-neutral position is equal to the risk-free rate plus the alpha:
0.5% + 2.0% = 2.5%
We assume that monthly returns are approximately normally distributed. The
z
-value for a rate of return of zero is
−2.5% ÷ 6.0% = −0.4167, or 0.4167 standard deviations below the mean.
Therefore, the probability of a negative return is
N
(−0.4167) = 0.3385 or 33.85%
d.
The residual standard deviation of the portfolio is smaller than each stock’s standard deviation by a factor of
= 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.
e.
The expected return of the market-neutral position is still equal to the risk-free rate plus the alpha:
0.5% + 2.0% = 2.5%
Now the z-value for a rate of return of zero is:
−2.5% ÷ 0.6% = −4.1667
Therefore, the probability of a negative return is
N
(−4.1667) = 0.0000155 or 0.00155%
A negative return is very unlikely. This is because both sources of risk have been eliminated: market risk has been hedged using the futures, and idiosyncratic risk has been dramatically reduced through diversification.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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- Asaparrow_forwardA company has two investment possibilities, with the following cash inflows: Investment Year 1 Year 2 Year 3 A $1,500 1,900 2,200 B $1,400 1,400 1,400 If the firm can earn 6 percent in other investments, what is the present value of investments A and B? Use Appendix B and Appendix D to answer the question. Round your answers to the nearest dollar.PV(Investment A): $ PV(Investment B): $ If each investment costs $4,000, is the present value of each investment greater than the cost of the investment?The present value of investment A is -Select-less than greater than Item 3 the cost.The present value of investment B is -Select-less than greater than Item 4 the cost.arrow_forwardA company has two investment possibilities, with the following cash inflows: Investment Year 1 Year 2 Year 3 A $1,000 1,400 1,800 B $1,700 1,700 1,700 If the firm can earn 6 percent in other investments, what is the present value of investments A and B? Use Appendix B and Appendix D to answer the question. Round your answers to the nearest dollar.PV(Investment A): $ __________PV(Investment B): $ __________ If each investment costs $4,000, is the present value of each investment greater than the cost of the investment? The present value of investment A is __less than___ / __greater than__ the cost. The present value of investment B is __less than___ / __greater than__ cost.arrow_forward
- 8. You are evaluating five different investments, all of which involve an upfront outlay of cash. Each investment will provide a single cash payment back to you in the future. Details of each investment appears here: 2. Calculate the IRR of each investment. State your answer to the nearest basis point (i.e., the nearest 1/100th of 1%, such as 3.76%). Review Only Click the icon to see the Worked Solution (Calculator Use). Click the icon to see the Worked Solution (Spreadsheet Use). The yield for investment A is %. (Round to two decimal places.) The yield for investment B is %. (Round to two decimal places.) The yield for investment C is %. (Round to two decimal places.) The yield for investment D is %. (Round to two decimal places.) The yield for investment E is %. (Round to two decimal places.) 2: Data Table Initial Future End of Investment Investment Value Year A $1,800 $6,387 14 B $9,500 $14,353 11 $600 $3,091 17 D $3,500 $4,505 3 E $5,800 $12,092 12 (Click on the icon located on the…arrow_forwardAbm (business math questions) can you help me?arrow_forwardHi can you help with this question please? An investment has the following cash flow profile. For each value of MARR below, what is the minimum value of X such that the investment is attractive based on an internal rate of return measure of merit? EOY 0 1 2 3 4 Cash Flow $(30,000.00) $ 6,000.00 $ 13,500.00 $X $ 13,500.00 MARR is 12 percent/yeararrow_forward
- Can you tell me how to get the 0% to 25% rate numbers? I have to plot the NPV profiles. Year Project A Discounted cashflow Discounted cashflow 0 -50,000 -$50,000.00 -$50,000.00 1 25,000 $22,727.27 $23,584.91 2 20,000 $16,528.93 $17,799.93 3 10,000 $7,513.15 $8,396.19 4 5,000 $3,415.07 $3,960.47 5 5,000 $3,104.61 $3,736.29 NPV $3,289.02 $7,477.79 IRR 14% 14% 10% 6% Year Project B Discounted cashflow Discounted cashflow 0 -50,000 -$50,000.00 -$50,000.00 1 15,000 $13,636.36 $14,150.94 2 15,000 $12,396.69 $13,349.95 3 15,000 $11,269.72 $12,594.29 4 15,000 $10,245.20 $11,881.40 5 15,000 $9,313.82 $11,208.87 NPV $6,861.80 $13,185.46 IRR 15% 15% Rate Project A Project B 0% 1% 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25%arrow_forwardPlease help filling out the rest of the tablearrow_forwardAnswer the given problems. Use 360 days in a year. Problem A: Baumol ModelABC Corporation would like to know what is its optimal cash balance for a disbursement account. The daily averagedisbursement is P40,000. Cost to transfer money into the account average P500 each time. If the money is not in this account,it could have been kept in a mutual fund account that would let ABC earn 3% per year.Required:1. Optimum cash balance2. Total cost of holding and maintaining the optimal cash balancearrow_forward
- need asap. thank youarrow_forwarduestion 1: Solve the following TVM problems using Excel formulas. You MUST use Excel formulas (FV or PV) to receive credit. ou can assume that all payments are made at the beginning of the period and use "1" for the "type" argument in the formula. A. Suppose you invest 11,400 today. What is the future value of the investment in 29 years, if interest at 7% is compounded annually? B. Suppose you invest $ 11,400 today. What is the future value of the investment in 29 years, if interest at 7% is compounded quarterly? C. Suppose you invest $ 570 monthly. What is the future value of the investment in 29 29 years, if interest at + 5% is compounded monthly? 5 6 7 8 19 20 21 22 23 24 25 26 27 28 29 Question 1 Question 2 + Ready Accessibility: Investigate MAR 17 A 国 W Xarrow_forward7. Impacts of Costs on Returns. A mutual fund has a 1.6% expense ratio and begins with a $124.655 NAV. It experiences the annual returns shown below. What are the end-of-year NAVS after fees for each year? What are the after-fee returns each year? (LO 4-4) Money to Invest NAV Expense ratio Year 1 return Year 2 return Year 3 return Year 4 return Year 5 return $ 10,000.00 $ 124.655 1.6% 5% -12% 18% 4% 23%arrow_forward
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