Chapter 26
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Jan 9, 2024
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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
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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
Your preview ends here
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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 C
Complete this question by entering your answers in the tabs below.
What is the standard deviation of the monthly return of the hedged portfolio?
Required A
Required B
Required C
Required D
Required E
Standard deviation
6 %
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
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 B
Required D
Complete this question by entering your answers in the tabs below.
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.
Note: Do not round intermediate calculations. Enter your answer as percent rounded to 2 decimal places, e.g., enter
"12.53%" and not "0.1253."
Required A
Required B
Required C
Required D
Required E
Show less
Probability
33.85
%
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
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 C
Required E
Complete this question by entering your answers in the tabs below.
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?
Note: Round your answer to 1 decimal place.
Required A
Required B
Required C
Required D
Required E
Show less
Residual standard deviation
0.6
%
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
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
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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 D
Required E
Complete this question by entering your answers in the tabs below.
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.
Note: Do not round intermediate calculations. Enter your answer as percent rounded to 5 decimal places.
Required A
Required B
Required C
Required D
Required E
Probability of a loss
0.00155
%
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
6.
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)
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%. If the fund holds a $4 million position in
Waterworks stock. The S&P 500 currently is at 4,000 and the contract multiplier is $50.
Required:
a.
What is the standard deviation of the (now improperly) hedged portfolio?
b.
What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and a standard deviation of 5%? 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. The S&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.5% per month.
c.
What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50
instead of 0.75? 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. The S&P 500 currently is at 4,000 and
the contract multiplier is $50. 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.
What is the standard deviation of the (now improperly) hedged portfolio?
Note: Round your answer to 3 decimal places. Enter your answer as percentages and not as a numbers. (Eg: Enter "12%" and
not "0.12").
Required A
Required B
Required C
Standard deviation
6.129
%
Explanation:
a.
For the (now improperly) hedged portfolio:
Variance = (
0.25
2
×
5
2
) +
6
2
= 37.5625
Standard deviation = 6.129%
b.
Since the manager has misestimated the beta of Waterworks, the manager will sell ten S&P 500 contracts (rather than the 15 contracts):
($4,000,000 × 0.50) ÷ (4,000 × $50) = 10 contracts
The portfolio is not completely hedged so the expected rate of return is no longer 2.5 percent. We can determine the expected rate of return by first computing the total dollar value of the stock plus futures position.
The dollar value of the stock portfolio is:
$4,000,000 × (1 +
r
portfolio
) = $4,000,000 × [1 + 0.005 + 0.75 × (
r
M
− 0.005) + 0.02 +
e
]
= $4,085,000 + $3,000,000 ×
r
M
+ $4,000,000 ×
e
The dollar proceeds from the futures position equal
10 × $50 × [
F
0
−
S
1
] = $500 × [
S
0
× 1.005 −
S
0
× (1 +
r
M
)]
= $500 × [4,000 × (0.005 −
r
M
)]
= $10,000 − 2,000,000 ×
r
M
Combine the value of the portfolio and the dollar proceeds from the future position:
$4,085,000 + 3,000,000 ×
r
M
+ $4,000,000 ×
e
+ $10,000 − 2,000,000 ×
r
M
= $4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
Using an expected return of the market of 1%, calculate the expected rate of return for the (improperly) hedged portfolio is
(
E
($4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
) − $4,000,000) ÷ $4,000,000
($4,095,000 + 10,000 − $4,000,000) ÷ $4,000,000
= 0.02625
Now the
z
-value for a rate of return of zero is:
0.02625 ÷ 0.06129 = −0.4283
The probability of a negative return is
N
(−0.4283) = 0.33422 or 33.42%
The probability of a negative return is like the probability.
c.
The variance for the diversified (but improperly hedged) portfolio is
(
0.25
2
×
5
2
) +
0.6
2
= 1.9225
Standard deviation = 1.3865%
The
z
-value for a rate of return of zero is: −0.02625 ÷ 0.013865 = −1.8933
The probability of a negative return is
N
(−1.8933) = 0.02916015, or 2.92%
The probability of a negative return is now far greater than the result with proper hedging.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
Your preview ends here
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6.
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)
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%. If the fund holds a $4 million position in
Waterworks stock. The S&P 500 currently is at 4,000 and the contract multiplier is $50.
Required:
a.
What is the standard deviation of the (now improperly) hedged portfolio?
b.
What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and a standard deviation of 5%? 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. The S&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.5% per month.
c.
What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50
instead of 0.75? 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. The S&P 500 currently is at 4,000 and
the contract multiplier is $50. Assume the risk-free rate is 0.5% per month.
Required A
Required C
Complete this question by entering your answers in the tabs below.
What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and
a standard deviation of 5%? 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. The S&P 500 currently is at 4,000 and the contract
multiplier is $50. Assume the risk-free rate is 0.5% per month.
Note: Round your answer to 2 decimal places. Enter your answer as percentages and not as a numbers. (Eg: Enter "12%" and
not "0.12").
Required A
Required B
Required C
Show less
Probability of a loss
33.42
%
Explanation:
a.
For the (now improperly) hedged portfolio:
Variance = (
0.25
2
×
5
2
) +
6
2
= 37.5625
Standard deviation = 6.129%
b.
Since the manager has misestimated the beta of Waterworks, the manager will sell ten S&P 500 contracts (rather than the 15 contracts):
($4,000,000 × 0.50) ÷ (4,000 × $50) = 10 contracts
The portfolio is not completely hedged so the expected rate of return is no longer 2.5 percent. We can determine the expected rate of return by first computing the total dollar value of the stock plus futures position.
The dollar value of the stock portfolio is:
$4,000,000 × (1 +
r
portfolio
) = $4,000,000 × [1 + 0.005 + 0.75 × (
r
M
− 0.005) + 0.02 +
e
]
= $4,085,000 + $3,000,000 ×
r
M
+ $4,000,000 ×
e
The dollar proceeds from the futures position equal
10 × $50 × [
F
0
−
S
1
] = $500 × [
S
0
× 1.005 −
S
0
× (1 +
r
M
)]
= $500 × [4,000 × (0.005 −
r
M
)]
= $10,000 − 2,000,000 ×
r
M
Combine the value of the portfolio and the dollar proceeds from the future position:
$4,085,000 + 3,000,000 ×
r
M
+ $4,000,000 ×
e
+ $10,000 − 2,000,000 ×
r
M
= $4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
Using an expected return of the market of 1%, calculate the expected rate of return for the (improperly) hedged portfolio is
(
E
($4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
) − $4,000,000) ÷ $4,000,000
($4,095,000 + 10,000 − $4,000,000) ÷ $4,000,000
= 0.02625
Now the
z
-value for a rate of return of zero is:
0.02625 ÷ 0.06129 = −0.4283
The probability of a negative return is
N
(−0.4283) = 0.33422 or 33.42%
The probability of a negative return is like the probability.
c.
The variance for the diversified (but improperly hedged) portfolio is
(
0.25
2
×
5
2
) +
0.6
2
= 1.9225
Standard deviation = 1.3865%
The
z
-value for a rate of return of zero is: −0.02625 ÷ 0.013865 = −1.8933
The probability of a negative return is
N
(−1.8933) = 0.02916015, or 2.92%
The probability of a negative return is now far greater than the result with proper hedging.
References
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
6.
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)
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%. If the fund holds a $4 million position in
Waterworks stock. The S&P 500 currently is at 4,000 and the contract multiplier is $50.
Required:
a.
What is the standard deviation of the (now improperly) hedged portfolio?
b.
What is the probability of incurring a loss over the next month if the monthly market return has an expected value of 1% and a standard deviation of 5%? 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. The S&P 500 currently is at 4,000 and the contract multiplier is $50. Assume the risk-free rate is 0.5% per month.
c.
What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks with the same alpha, beta, and residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50
instead of 0.75? 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. The S&P 500 currently is at 4,000 and
the contract multiplier is $50. Assume the risk-free rate is 0.5% per month.
Required B
Required C
Complete this question by entering your answers in the tabs below.
What would be the probability of a loss if you hold an equally weighted portfolio of 100 stocks
with
the same alpha, beta, and
residual standard deviation as Waterworks and the manager similarly misestimated beta as 0.50 instead of 0.75? The
manager 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. The S&P 500 currently is at 2,000 and the contract multiplier is $50. Assume the
risk-free rate is 0.5% per month.
Note: Round your answer to 2 decimal places. Enter your answer as percentages and not as a numbers. (Eg: Enter "12%" and
not "0.12").
Required A
Required B
Required C
Show less
Probability of a loss
2.92
%
Explanation:
a.
For the (now improperly) hedged portfolio:
Variance = (
0.25
2
×
5
2
) +
6
2
= 37.5625
Standard deviation = 6.129%
b.
Since the manager has misestimated the beta of Waterworks, the manager will sell ten S&P 500 contracts (rather than the 15 contracts):
($4,000,000 × 0.50) ÷ (4,000 × $50) = 10 contracts
The portfolio is not completely hedged so the expected rate of return is no longer 2.5 percent. We can determine the expected rate of return by first computing the total dollar value of the stock plus futures position.
The dollar value of the stock portfolio is:
$4,000,000 × (1 +
r
portfolio
) = $4,000,000 × [1 + 0.005 + 0.75 × (
r
M
− 0.005) + 0.02 +
e
]
= $4,085,000 + $3,000,000 ×
r
M
+ $4,000,000 ×
e
The dollar proceeds from the futures position equal
10 × $50 × [
F
0
−
S
1
] = $500 × [
S
0
× 1.005 −
S
0
× (1 +
r
M
)]
= $500 × [4,000 × (0.005 −
r
M
)]
= $10,000 − 2,000,000 ×
r
M
Combine the value of the portfolio and the dollar proceeds from the future position:
$4,085,000 + 3,000,000 ×
r
M
+ $4,000,000 ×
e
+ $10,000 − 2,000,000 ×
r
M
= $4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
Using an expected return of the market of 1%, calculate the expected rate of return for the (improperly) hedged portfolio is
(
E
($4,095,000 + 1,000,000 ×
r
M
+ $4,000,000 ×
e
) − $4,000,000) ÷ $4,000,000
($4,095,000 + 10,000 − $4,000,000) ÷ $4,000,000
= 0.02625
Now the
z
-value for a rate of return of zero is:
0.02625 ÷ 0.06129 = −0.4283
The probability of a negative return is
N
(−0.4283) = 0.33422 or 33.42%
The probability of a negative return is like the probability.
c.
The variance for the diversified (but improperly hedged) portfolio is
(
0.25
2
×
5
2
) +
0.6
2
= 1.9225
Standard deviation = 1.3865%
The
z
-value for a rate of return of zero is: −0.02625 ÷ 0.013865 = −1.8933
The probability of a negative return is
N
(−1.8933) = 0.02916015, or 2.92%
The probability of a negative return is now far greater than the result with proper hedging.
References
Your preview ends here
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Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
7.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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, also charging its
investors a 20% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Start of year value (millions)
$ 100
$ 100
$ 100
Gross portfolio rate of return
20%
10%
30%
Required:
a.
Compute the rate of return after incentive fees to an investor in the fund of funds.
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 20% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
d.
Now suppose that the return on the portfolio held by hedge fund 3 were −30% rather than +30%. Recalculate your answers to parts (a) and (b).
Required A
Required B
Complete this question by entering your answers in the tabs below.
Compute the rate of return after incentive fees to an investor in the fund of funds.
Note: Do not round your intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required D
Rate of return
12.80
%
Explanation:
a. & b.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 130.0
$ 360.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 6.0
$ 12.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 124.0
$ 348.0
$ 348.0
Incentive fee (Fund of Funds)
$ 9.6
End of year value (Fund of Funds)
$ 338.4
Rate of return (after fee)
16.0%
8.0%
24.0%
12.80%
16.00%
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 incentive fees. Therefore, the investor’s rate of return
in SA (16.0%) is higher than in FF (12.8%) by an amount equal to the extra layer of fees ($9.6 million, or 3.2%) charged by the Fund of Funds.
d.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 70.0
$ 300.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 0.0
$ 0.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 70.0
$ 294.0
$ 300.0
Incentive fee (Fund of Funds)
$ 0.0
End of year value (Fund of Funds)
$ 294.0
Rate of return (after fee)
16.0%
8.0%
−30.0%
−2.00%
0.00%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
7.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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, also charging its
investors a 20% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Start of year value (millions)
$ 100
$ 100
$ 100
Gross portfolio rate of return
20%
10%
30%
Required:
a.
Compute the rate of return after incentive fees to an investor in the fund of funds.
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 20% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
d.
Now suppose that the return on the portfolio held by hedge fund 3 were −30% rather than +30%. Recalculate your answers to parts (a) and (b).
Required A
Required D
Complete this question by entering your answers in the tabs below.
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 20% incentive fees,
what would be the value of the investor’s portfolio at the end of the year?
Note: Do not round your intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required D
Show less
Percentage return
16.00
%
Explanation:
a. & b.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 130.0
$ 360.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 6.0
$ 12.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 124.0
$ 348.0
$ 348.0
Incentive fee (Fund of Funds)
$ 9.6
End of year value (Fund of Funds)
$ 338.4
Rate of return (after fee)
16.0%
8.0%
24.0%
12.80%
16.00%
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 incentive fees. Therefore, the investor’s rate of return
in SA (16.0%) is higher than in FF (12.8%) by an amount equal to the extra layer of fees ($9.6 million, or 3.2%) charged by the Fund of Funds.
d.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 70.0
$ 300.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 0.0
$ 0.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 70.0
$ 294.0
$ 300.0
Incentive fee (Fund of Funds)
$ 0.0
End of year value (Fund of Funds)
$ 294.0
Rate of return (after fee)
16.0%
8.0%
−30.0%
−2.00%
0.00%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
Your preview ends here
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7.
Award:
10.00
points
Problems?
Adjust credit
for all students.
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, also charging its
investors a 20% incentive fee. For simplicity, assume also that management fees other than incentive fees are zero for all funds.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Start of year value (millions)
$ 100
$ 100
$ 100
Gross portfolio rate of return
20%
10%
30%
Required:
a.
Compute the rate of return after incentive fees to an investor in the fund of funds.
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 20% incentive fees, what would be the value of the investor’s portfolio at the end of the year?
d.
Now suppose that the return on the portfolio held by hedge fund 3 were −30% rather than +30%. Recalculate your answers to parts (a) and (b).
Required B
Required D
Complete this question by entering your answers in the tabs below.
Now suppose that the return on the portfolio held by hedge fund 3 were −30% rather than +30%. Recalculate your answers
to parts (a) and (b).
Note: 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.
Required A
Required B
Required D
Show less
Fund of fund return
(2.00)
%
Stand-alone fund return
0.00
%
Explanation:
a. & b.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 130.0
$ 360.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 6.0
$ 12.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 124.0
$ 348.0
$ 348.0
Incentive fee (Fund of Funds)
$ 9.6
End of year value (Fund of Funds)
$ 338.4
Rate of return (after fee)
16.0%
8.0%
24.0%
12.80%
16.00%
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 incentive fees. Therefore, the investor’s rate of return
in SA (16.0%) is higher than in FF (12.8%) by an amount equal to the extra layer of fees ($9.6 million, or 3.2%) charged by the Fund of Funds.
d.
Hedge Fund 1
Hedge Fund 2
Hedge Fund 3
Fund of Funds
Stand-Alone
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
$ 110.0
$ 70.0
$ 300.0
Incentive fee (Individual funds)
$ 4.0
$ 2.0
$ 0.0
$ 0.0
End of year value (after fee)
$ 116.0
$ 108.0
$ 70.0
$ 294.0
$ 300.0
Incentive fee (Fund of Funds)
$ 0.0
End of year value (Fund of Funds)
$ 294.0
Rate of return (after fee)
16.0%
8.0%
−30.0%
−2.00%
0.00%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You are an early-stage VC conducting due diligence on an IT start-up. You are willing to cotribute $1,500,000 in the A round of financing and require a capital return (i.e., capital multiplier) of 12. You anticipate B and C rounds of
financing in years 3 and 6 that will dilute your position by 30% and 40%, respectively, because your firm will not participate in either additional round. You estimate firm value at $120,000,000 in nine years.
Required:
a.
What initial ownership position should you require for your investment?
b.
What is your initial valuation of the company before your investment?
c.
What is the expected IRR of the investment?
d.
Suppose you stage the distribution of the capital into $500,000 installments disbursed immediately, at the end of the first year, and at the end of the second year. What is the IRR of the investment in this scenario?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What initial ownership position should you require for your investment?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
Initial weight
35.71
%
Explanation:
a.
The initial weight is 35.71%
w
9
= (
v
VC
,0
× Capital Returned) ÷
v
9
= ($1,500,000 × 12) ÷ $120,000,000 = 0.15, or 15%
w
3
= 0.15 ÷ (1 − 0.40) = 0.25, or 25%
w
0
= 0.25 ÷ (1 − 0.30) = 0.3571, or 35.71%
b.
The pre-money valuation is $2,700,000
V
Post
=
v
VC
,0
÷ w
0
= $1,500,000 ÷ 0.3571 = $4,200,000
V
Pre
=
V
Post
−
v
VC
,0
= $4,200,000 − $1,500,000 = $2,700,000
c.
The IRR is 31.80%
CF
0
=
−
$1,500,000
CF
9
= $18,000,000
IRR
= 31.80%
d.
The IRR is 35.90%
CF
0
=
−
$500,000
CF
1
=
−
$500,000
CF
2
=
−
$500,000
CF
9
= $18,000,000
IRR
= 35.90%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You are an early-stage VC conducting due diligence on an IT start-up. You are willing to cotribute $1,500,000 in the A round of financing and require a capital return (i.e., capital multiplier) of 12. You anticipate B and C rounds of
financing in years 3 and 6 that will dilute your position by 30% and 40%, respectively, because your firm will not participate in either additional round. You estimate firm value at $120,000,000 in nine years.
Required:
a.
What initial ownership position should you require for your investment?
b.
What is your initial valuation of the company before your investment?
c.
What is the expected IRR of the investment?
d.
Suppose you stage the distribution of the capital into $500,000 installments disbursed immediately, at the end of the first year, and at the end of the second year. What is the IRR of the investment in this scenario?
Required A
Required C
Complete this question by entering your answers in the tabs below.
What is your initial valuation of the company before your investment?
Note: Do not round intermediate calculations.
Required A
Required B
Required C
Required D
$
Pre-money valuation
2,700,000
Explanation:
a.
The initial weight is 35.71%
w
9
= (
v
VC
,0
× Capital Returned) ÷
v
9
= ($1,500,000 × 12) ÷ $120,000,000 = 0.15, or 15%
w
3
= 0.15 ÷ (1 − 0.40) = 0.25, or 25%
w
0
= 0.25 ÷ (1 − 0.30) = 0.3571, or 35.71%
b.
The pre-money valuation is $2,700,000
V
Post
=
v
VC
,0
÷ w
0
= $1,500,000 ÷ 0.3571 = $4,200,000
V
Pre
=
V
Post
−
v
VC
,0
= $4,200,000 − $1,500,000 = $2,700,000
c.
The IRR is 31.80%
CF
0
=
−
$1,500,000
CF
9
= $18,000,000
IRR
= 31.80%
d.
The IRR is 35.90%
CF
0
=
−
$500,000
CF
1
=
−
$500,000
CF
2
=
−
$500,000
CF
9
= $18,000,000
IRR
= 35.90%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You are an early-stage VC conducting due diligence on an IT start-up. You are willing to cotribute $1,500,000 in the A round of financing and require a capital return (i.e., capital multiplier) of 12. You anticipate B and C rounds of
financing in years 3 and 6 that will dilute your position by 30% and 40%, respectively, because your firm will not participate in either additional round. You estimate firm value at $120,000,000 in nine years.
Required:
a.
What initial ownership position should you require for your investment?
b.
What is your initial valuation of the company before your investment?
c.
What is the expected IRR of the investment?
d.
Suppose you stage the distribution of the capital into $500,000 installments disbursed immediately, at the end of the first year, and at the end of the second year. What is the IRR of the investment in this scenario?
Required B
Required D
Complete this question by entering your answers in the tabs below.
What is the expected IRR of the investment?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
IRR
31.80
%
Explanation:
a.
The initial weight is 35.71%
w
9
= (
v
VC
,0
× Capital Returned) ÷
v
9
= ($1,500,000 × 12) ÷ $120,000,000 = 0.15, or 15%
w
3
= 0.15 ÷ (1 − 0.40) = 0.25, or 25%
w
0
= 0.25 ÷ (1 − 0.30) = 0.3571, or 35.71%
b.
The pre-money valuation is $2,700,000
V
Post
=
v
VC
,0
÷ w
0
= $1,500,000 ÷ 0.3571 = $4,200,000
V
Pre
=
V
Post
−
v
VC
,0
= $4,200,000 − $1,500,000 = $2,700,000
c.
The IRR is 31.80%
CF
0
=
−
$1,500,000
CF
9
= $18,000,000
IRR
= 31.80%
d.
The IRR is 35.90%
CF
0
=
−
$500,000
CF
1
=
−
$500,000
CF
2
=
−
$500,000
CF
9
= $18,000,000
IRR
= 35.90%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
Your preview ends here
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- Access to all documents
- Unlimited textbook solutions
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8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You are an early-stage VC conducting due diligence on an IT start-up. You are willing to cotribute $1,500,000 in the A round of financing and require a capital return (i.e., capital multiplier) of 12. You anticipate B and C rounds of
financing in years 3 and 6 that will dilute your position by 30% and 40%, respectively, because your firm will not participate in either additional round. You estimate firm value at $120,000,000 in nine years.
Required:
a.
What initial ownership position should you require for your investment?
b.
What is your initial valuation of the company before your investment?
c.
What is the expected IRR of the investment?
d.
Suppose you stage the distribution of the capital into $500,000 installments disbursed immediately, at the end of the first year, and at the end of the second year. What is the IRR of the investment in this scenario?
Required C
Required D
Complete this question by entering your answers in the tabs below.
Suppose you stage the distribution of the capital into $500,000 installments disbursed immediately, at the end of the first
year, and at the end of the second year. What is the IRR of the investment in this scenario?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
IRR
35.90
%
Explanation:
a.
The initial weight is 35.71%
w
9
= (
v
VC
,0
× Capital Returned) ÷
v
9
= ($1,500,000 × 12) ÷ $120,000,000 = 0.15, or 15%
w
3
= 0.15 ÷ (1 − 0.40) = 0.25, or 25%
w
0
= 0.25 ÷ (1 − 0.30) = 0.3571, or 35.71%
b.
The pre-money valuation is $2,700,000
V
Post
=
v
VC
,0
÷ w
0
= $1,500,000 ÷ 0.3571 = $4,200,000
V
Pre
=
V
Post
−
v
VC
,0
= $4,200,000 − $1,500,000 = $2,700,000
c.
The IRR is 31.80%
CF
0
=
−
$1,500,000
CF
9
= $18,000,000
IRR
= 31.80%
d.
The IRR is 35.90%
CF
0
=
−
$500,000
CF
1
=
−
$500,000
CF
2
=
−
$500,000
CF
9
= $18,000,000
IRR
= 35.90%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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9.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You manage a multi-stage VC fund conducting due diligence on an pharmaceutical start-up. The required rate of return is 33%. You will participate in an A round initially, a B round in four years, and a C round in seven years.
Required:
a.
In the A round, what equity position do you need to justify a $1,000,000 investment if the pre-round valuation of the firm is $2,500,000?
b.
In the B round, an additional $4,500,000 will be raised from a syndication of VCs including your firm. To maintain your equity position, how much must you contribute to the B round of financing? Assume the firm is valued at
cost.
c.
In the C round, an additional $10,000,000 will be raised from the same syndication of VCs. If you wish to continue to maintain the same equity position, how much will you need to invest in this round? Assume the firm
continues to be valued at cost.
d.
If the firm is acquired for $90,000,000 in the 9th year, is your required rate of return satisfied?
Required A
Required B
Complete this question by entering your answers in the tabs below.
In the A round, what equity position do you need to justify a $1,000,000 investment if the pre-round valuation of the firm is
$2,500,000?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
Initial equity position
28.57
%
Explanation:
a.
The initial equity position is 28.57%:
V
Post
=
V
Pre
+
v
VC
,0
= $2,500,000 + $1,000,000 = $3,500,000
w
VC,0
=
v
VC
,0
÷ V
Post
= $1,000,000 ÷ $3,500,000 = 0.2857, or 28.57%
b.
To maintain ownership, the B round of financing is $1,285,714:
0.2857 =
w
VC,A
=
w
VC
,
B
= (
v
B
+ $1,000,000) ÷ ($4,500,000 + $3,500,000)
v
B
= $1,285,714
c.
To maintain ownership, the C round of financing is $2,857,143:
0.2857 =
w
VC,B
=
w
VC
,
C
= (
v
C
+ $2,285,714) ÷ ($10,000,000 + $8,000,000)
v
C
= $2,857,143
d.
The IRR is 34.88%:
CF
0
= −$1,000,000
CF
4
= −$1,285,714
CF
7
= −$2,857,143
CF
9
= $90,000,000 × 0.2857 = $25,714,286
IRR
= 34.88%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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9.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You manage a multi-stage VC fund conducting due diligence on an pharmaceutical start-up. The required rate of return is 33%. You will participate in an A round initially, a B round in four years, and a C round in seven years.
Required:
a.
In the A round, what equity position do you need to justify a $1,000,000 investment if the pre-round valuation of the firm is $2,500,000?
b.
In the B round, an additional $4,500,000 will be raised from a syndication of VCs including your firm. To maintain your equity position, how much must you contribute to the B round of financing? Assume the firm is valued at
cost.
c.
In the C round, an additional $10,000,000 will be raised from the same syndication of VCs. If you wish to continue to maintain the same equity position, how much will you need to invest in this round? Assume the firm
continues to be valued at cost.
d.
If the firm is acquired for $90,000,000 in the 9th year, is your required rate of return satisfied?
Required A
Required C
Complete this question by entering your answers in the tabs below.
In the B round, an additional $4,500,000 will be raised from a syndication of VCs including your firm. To maintain your equity
position, how much must you contribute to the B round of financing? Assume the firm is valued at cost.
Note: Do not round intermediate calculations. Round your final answer to the nearest dollar amount.
Required A
Required B
Required C
Required D
$
Contribute to the B round
1,285,714
Explanation:
a.
The initial equity position is 28.57%:
V
Post
=
V
Pre
+
v
VC
,0
= $2,500,000 + $1,000,000 = $3,500,000
w
VC,0
=
v
VC
,0
÷ V
Post
= $1,000,000 ÷ $3,500,000 = 0.2857, or 28.57%
b.
To maintain ownership, the B round of financing is $1,285,714:
0.2857 =
w
VC,A
=
w
VC
,
B
= (
v
B
+ $1,000,000) ÷ ($4,500,000 + $3,500,000)
v
B
= $1,285,714
c.
To maintain ownership, the C round of financing is $2,857,143:
0.2857 =
w
VC,B
=
w
VC
,
C
= (
v
C
+ $2,285,714) ÷ ($10,000,000 + $8,000,000)
v
C
= $2,857,143
d.
The IRR is 34.88%:
CF
0
= −$1,000,000
CF
4
= −$1,285,714
CF
7
= −$2,857,143
CF
9
= $90,000,000 × 0.2857 = $25,714,286
IRR
= 34.88%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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9.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You manage a multi-stage VC fund conducting due diligence on an pharmaceutical start-up. The required rate of return is 33%. You will participate in an A round initially, a B round in four years, and a C round in seven years.
Required:
a.
In the A round, what equity position do you need to justify a $1,000,000 investment if the pre-round valuation of the firm is $2,500,000?
b.
In the B round, an additional $4,500,000 will be raised from a syndication of VCs including your firm. To maintain your equity position, how much must you contribute to the B round of financing? Assume the firm is valued at
cost.
c.
In the C round, an additional $10,000,000 will be raised from the same syndication of VCs. If you wish to continue to maintain the same equity position, how much will you need to invest in this round? Assume the firm
continues to be valued at cost.
d.
If the firm is acquired for $90,000,000 in the 9th year, is your required rate of return satisfied?
Required B
Required D
Complete this question by entering your answers in the tabs below.
In the C round, an additional $10,000,000 will be raised from the same syndication of VCs. If you wish to continue to
maintain the same equity position, how much will you need to invest in this round? Assume the firm continues to be valued at
cost.
Note: Do not round intermediate calculations. Round your final answer to the nearest dollar amount.
Required A
Required B
Required C
Required D
Show less
$
Investment
2,857,143
Explanation:
a.
The initial equity position is 28.57%:
V
Post
=
V
Pre
+
v
VC
,0
= $2,500,000 + $1,000,000 = $3,500,000
w
VC,0
=
v
VC
,0
÷ V
Post
= $1,000,000 ÷ $3,500,000 = 0.2857, or 28.57%
b.
To maintain ownership, the B round of financing is $1,285,714:
0.2857 =
w
VC,A
=
w
VC
,
B
= (
v
B
+ $1,000,000) ÷ ($4,500,000 + $3,500,000)
v
B
= $1,285,714
c.
To maintain ownership, the C round of financing is $2,857,143:
0.2857 =
w
VC,B
=
w
VC
,
C
= (
v
C
+ $2,285,714) ÷ ($10,000,000 + $8,000,000)
v
C
= $2,857,143
d.
The IRR is 34.88%:
CF
0
= −$1,000,000
CF
4
= −$1,285,714
CF
7
= −$2,857,143
CF
9
= $90,000,000 × 0.2857 = $25,714,286
IRR
= 34.88%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
Your preview ends here
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- Unlimited textbook solutions
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9.
Award:
10.00
points
Problems?
Adjust credit
for all students.
You manage a multi-stage VC fund conducting due diligence on an pharmaceutical start-up. The required rate of return is 33%. You will participate in an A round initially, a B round in four years, and a C round in seven years.
Required:
a.
In the A round, what equity position do you need to justify a $1,000,000 investment if the pre-round valuation of the firm is $2,500,000?
b.
In the B round, an additional $4,500,000 will be raised from a syndication of VCs including your firm. To maintain your equity position, how much must you contribute to the B round of financing? Assume the firm is valued at
cost.
c.
In the C round, an additional $10,000,000 will be raised from the same syndication of VCs. If you wish to continue to maintain the same equity position, how much will you need to invest in this round? Assume the firm
continues to be valued at cost.
d.
If the firm is acquired for $90,000,000 in the 9th year, is your required rate of return satisfied?
Required C
Required D
Complete this question by entering your answers in the tabs below.
If the firm is acquired for $90,000,000 in the 9th year, is your required rate of return satisfied?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Required C
Required D
IRR
34.88
%
Explanation:
a.
The initial equity position is 28.57%:
V
Post
=
V
Pre
+
v
VC
,0
= $2,500,000 + $1,000,000 = $3,500,000
w
VC,0
=
v
VC
,0
÷ V
Post
= $1,000,000 ÷ $3,500,000 = 0.2857, or 28.57%
b.
To maintain ownership, the B round of financing is $1,285,714:
0.2857 =
w
VC,A
=
w
VC
,
B
= (
v
B
+ $1,000,000) ÷ ($4,500,000 + $3,500,000)
v
B
= $1,285,714
c.
To maintain ownership, the C round of financing is $2,857,143:
0.2857 =
w
VC,B
=
w
VC
,
C
= (
v
C
+ $2,285,714) ÷ ($10,000,000 + $8,000,000)
v
C
= $2,857,143
d.
The IRR is 34.88%:
CF
0
= −$1,000,000
CF
4
= −$1,285,714
CF
7
= −$2,857,143
CF
9
= $90,000,000 × 0.2857 = $25,714,286
IRR
= 34.88%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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10.
Award:
10.00
points
Problems?
Adjust credit
for all students.
An endowment invests $150,000,000 in WeGrow II, an early-stage venture fund with a 20% incentive fee and a 5% preferred return [hurdle rate]. The fund invests in the following companies (for simplicity, ignore staged
financing and management fees; assume instead that all investments occur at the end of their denoted year):
Start-up Name
Investment (Year Invested)
Harvested (Year Harvested)
SPE Incorporated
$ 35,000,000 (2)
$ 62,000,000 (7)
NiteID Corporation
$ 20,000,000 (2)
$ 300,000,000 (9)
D-Ton Incorporated
$ 15,000,000 (2)
$ 0 (8)
IKL Limited
$ 20,000,000 (3)
$ 100,000,000 (7)
H&L Innovations
$ 25,000,000 (3)
$ 125,000,000 (10)
SimLife Technologies
$ 35,000,000 (4)
$ 0 (9)
Required:
a.
Construct a set of yearly cash flows to WeGrow II and to the endowment.
b.
What is the IRR to the endowment, net of fees?
Required A
Required B
Complete this question by entering your answers in the tabs below.
Construct a set of yearly cash flows to WeGrow II and to the endowment.
Note: Negative amounts should be indicated by a minus sign.
Required A
Required B
$
$
$
$
$
$
Year
Net Cash Flows
1
2
(70,000,000)
3
(45,000,000)
4
(35,000,000)
5
6
7
161,100,000
8
9
240,000,000
10
100,000,000
Explanation:
a.
Construct a set of yearly cash flows.
Year
Limited Partner Cash Flow
Net Cash Flows
1
2
−$35,000,000 − $20,000,000 − $15,000,000
−$ 70,000,000
3
−$20,000,000 − $25,000,000
−$ 45,000,000
4
−$35,000,000
−$ 35,000,000
5
6
7
$62,000,000 + $95,500,000 + $4,500,000 × 0.80
$ 161,100,000
8
9
$300,000,000 × 0.80
$ 240,000,000
10
$125,000,000 × 0.80
$ 100,000,000
b.
Using the cash flows and a financial calculator or Excel, the IRR is 23.49%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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10.
Award:
10.00
points
Problems?
Adjust credit
for all students.
An endowment invests $150,000,000 in WeGrow II, an early-stage venture fund with a 20% incentive fee and a 5% preferred return [hurdle rate]. The fund invests in the following companies (for simplicity, ignore staged
financing and management fees; assume instead that all investments occur at the end of their denoted year):
Start-up Name
Investment (Year Invested)
Harvested (Year Harvested)
SPE Incorporated
$ 35,000,000 (2)
$ 62,000,000 (7)
NiteID Corporation
$ 20,000,000 (2)
$ 300,000,000 (9)
D-Ton Incorporated
$ 15,000,000 (2)
$ 0 (8)
IKL Limited
$ 20,000,000 (3)
$ 100,000,000 (7)
H&L Innovations
$ 25,000,000 (3)
$ 125,000,000 (10)
SimLife Technologies
$ 35,000,000 (4)
$ 0 (9)
Required:
a.
Construct a set of yearly cash flows to WeGrow II and to the endowment.
b.
What is the IRR to the endowment, net of fees?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the IRR to the endowment, net of fees?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
IRR
23.49
%
Explanation:
a.
Construct a set of yearly cash flows.
Year
Limited Partner Cash Flow
Net Cash Flows
1
2
−$35,000,000 − $20,000,000 − $15,000,000
−$ 70,000,000
3
−$20,000,000 − $25,000,000
−$ 45,000,000
4
−$35,000,000
−$ 35,000,000
5
6
7
$62,000,000 + $95,500,000 + $4,500,000 × 0.80
$ 161,100,000
8
9
$300,000,000 × 0.80
$ 240,000,000
10
$125,000,000 × 0.80
$ 100,000,000
b.
Using the cash flows and a financial calculator or Excel, the IRR is 23.49%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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11.
Award:
10.00
points
Problems?
Adjust credit
for all students.
An endowment invests $150,000,000 in WeGrow II, an early-stage venture fund with a 20% incentive fee and a 5% preferred return [hurdle rate]. The fund invests in the following companies (for simplicity, ignore staged
financing and management fees; assume instead that all investments occur at the end of their denoted year):
Start-up Name
Investment (Year Invested)
Harvested (Year Harvested)
SPE Incorporated
$ 35,000,000 (2)
$ 62,000,000 (7)
NiteID Corporation
$ 20,000,000 (2)
$ 300,000,000 (9)
D-Ton Incorporated
$ 15,000,000 (2)
$ 0 (8)
IKL Limited
$ 20,000,000 (3)
$ 100,000,000 (7)
H&L Innovations
$ 25,000,000 (3)
$ 125,000,000 (10)
SimLife Technologies
$ 35,000,000 (4)
$ 0 (9)
Instead of a 5% preferred rate, assume there is an 8% preferred rate with a 100% catch-up.
Required:
a.
Recalculate the yearly cash flows.
b.
What is the IRR to the endowment, net of fees?
Required A
Required B
Complete this question by entering your answers in the tabs below.
Recalculate the yearly cash flows.
Note: Negative amounts should be indicated by a minus sign.
Required A
Required B
$
$
$
$
$
$
Year
Net Cash Flows
1
2
(70,000,000)
3
(45,000,000)
4
(35,000,000)
5
6
7
162,000,000
8
9
207,600,000
10
100,000,000
Explanation:
a.
Construct a set of yearly cash flows.
Year
Limited Partner Cash Flow
Net Cash Flows
1
2
−$35,000,000 − $20,000,000 − $15,000,000
−$ 70,000,000
3
−$20,000,000 − $25,000,000
−$ 45,000,000
4
−$ 35,000,000
−$ 35,000,000
5
6
7
$150,000,000
Recovery
+ $1,200,000
Preferred
$ 162,000,000
8
9
($300,000,000 – $40,500,000
Catch-up
) × 0.80
$ 207,600,000
10
$125,000,000 × 0.80
$ 100,000,000
b.
Using the cash flows and a financial calculator or Excel, the IRR is 22.25%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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11.
Award:
10.00
points
Problems?
Adjust credit
for all students.
An endowment invests $150,000,000 in WeGrow II, an early-stage venture fund with a 20% incentive fee and a 5% preferred return [hurdle rate]. The fund invests in the following companies (for simplicity, ignore staged
financing and management fees; assume instead that all investments occur at the end of their denoted year):
Start-up Name
Investment (Year Invested)
Harvested (Year Harvested)
SPE Incorporated
$ 35,000,000 (2)
$ 62,000,000 (7)
NiteID Corporation
$ 20,000,000 (2)
$ 300,000,000 (9)
D-Ton Incorporated
$ 15,000,000 (2)
$ 0 (8)
IKL Limited
$ 20,000,000 (3)
$ 100,000,000 (7)
H&L Innovations
$ 25,000,000 (3)
$ 125,000,000 (10)
SimLife Technologies
$ 35,000,000 (4)
$ 0 (9)
Instead of a 5% preferred rate, assume there is an 8% preferred rate with a 100% catch-up.
Required:
a.
Recalculate the yearly cash flows.
b.
What is the IRR to the endowment, net of fees?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the IRR to the endowment, net of fees?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
IRR
22.25
%
Explanation:
a.
Construct a set of yearly cash flows.
Year
Limited Partner Cash Flow
Net Cash Flows
1
2
−$35,000,000 − $20,000,000 − $15,000,000
−$ 70,000,000
3
−$20,000,000 − $25,000,000
−$ 45,000,000
4
−$ 35,000,000
−$ 35,000,000
5
6
7
$150,000,000
Recovery
+ $1,200,000
Preferred
$ 162,000,000
8
9
($300,000,000 – $40,500,000
Catch-up
) × 0.80
$ 207,600,000
10
$125,000,000 × 0.80
$ 100,000,000
b.
Using the cash flows and a financial calculator or Excel, the IRR is 22.25%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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12.
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points
Problems?
Adjust credit
for all students.
Consider a start-up that is valued at cost throughout the early stages of its life.
Required:
a.
Round A: Cyprus Ventures invests $250,000, bringing the post-round valuation to $800,000. What are the ownership percentages for the founder and Cyprus Ventures, if all voting rights are equal?
b.
Round B: A syndication of Cypress Ventures, Specific Pacific Management, and Mountainhome Capital Group invests $750,000 each. Now determine the ownership for each party assuming the start-up is valued at cost.
c.
What would be the minimum necessary voting rights for the founders to maintain control through both rounds of financing? (Control is defined as greater than 50% ownership, with percentages rounded to whole numbers.)
Required A
Required B
Complete this question by entering your answers in the tabs below.
Round A: Cyprus Ventures invests $250,000, bringing the post-round valuation to $800,000. What are the ownership
percentages for the founder and Cyprus Ventures, if all voting rights are equal?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Required C
Round A
Ownership
Cyprus
31.25
%
Founder
68.75
%
Explanation:
a.
Round A Ownership, Cyprus = 31.25% and Founder = 68.75%:
Cyprus = $250,000 ÷ $800,000 = 0.3125, or 31.25%
Founder = 1 − 0.3125 = 0.6875, or 68.75%
b.
Round B Ownership:
Cyprus = ($250,000 + $750,000) ÷ ($800,000 + 3 × $750,000) = $1,000,000 ÷ $3,050,000 = 0.3279, or 32.79%
Specific Pacific = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Mountainhome = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Founder = 1 − (0.3279 + 0.2459 + 0.2459) = 0.1803, or 18.03%
c.
Five to one voting rights are necessary to maintain control:
1 < (
x
× 0.1803) ÷ 0.8197 →
x
> 4.54 ≈ 5.00
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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12.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Consider a start-up that is valued at cost throughout the early stages of its life.
Required:
a.
Round A: Cyprus Ventures invests $250,000, bringing the post-round valuation to $800,000. What are the ownership percentages for the founder and Cyprus Ventures, if all voting rights are equal?
b.
Round B: A syndication of Cypress Ventures, Specific Pacific Management, and Mountainhome Capital Group invests $750,000 each. Now determine the ownership for each party assuming the start-up is valued at cost.
c.
What would be the minimum necessary voting rights for the founders to maintain control through both rounds of financing? (Control is defined as greater than 50% ownership, with percentages rounded to whole numbers.)
Required A
Required C
Complete this question by entering your answers in the tabs below.
Round B: A syndication of Cypress Ventures, Specific Pacific Management, and Mountainhome Capital Group invests $750,000
each. Now determine the ownership for each party assuming the start-up is valued at cost.
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Required C
Round B
Ownership
Cypress Ventures
32.79
%
Specific Pacific Management
24.59
%
Mountainhome Capital Group
24.59
%
Founder
18.03
%
Explanation:
a.
Round A Ownership, Cyprus = 31.25% and Founder = 68.75%:
Cyprus = $250,000 ÷ $800,000 = 0.3125, or 31.25%
Founder = 1 − 0.3125 = 0.6875, or 68.75%
b.
Round B Ownership:
Cyprus = ($250,000 + $750,000) ÷ ($800,000 + 3 × $750,000) = $1,000,000 ÷ $3,050,000 = 0.3279, or 32.79%
Specific Pacific = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Mountainhome = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Founder = 1 − (0.3279 + 0.2459 + 0.2459) = 0.1803, or 18.03%
c.
Five to one voting rights are necessary to maintain control:
1 < (
x
× 0.1803) ÷ 0.8197 →
x
> 4.54 ≈ 5.00
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
References
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12.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Consider a start-up that is valued at cost throughout the early stages of its life.
Required:
a.
Round A: Cyprus Ventures invests $250,000, bringing the post-round valuation to $800,000. What are the ownership percentages for the founder and Cyprus Ventures, if all voting rights are equal?
b.
Round B: A syndication of Cypress Ventures, Specific Pacific Management, and Mountainhome Capital Group invests $750,000 each. Now determine the ownership for each party assuming the start-up is valued at cost.
c.
What would be the minimum necessary voting rights for the founders to maintain control through both rounds of financing? (Control is defined as greater than 50% ownership, with percentages rounded to whole numbers.)
Required B
Required C
Complete this question by entering your answers in the tabs below.
What would be the minimum necessary voting rights for the founders to maintain control through both rounds of financing?
(Control is defined as greater than 50% ownership, with percentages rounded to whole numbers.)
Note: Do not round intermediate calculations. Round your answer to the nearest whole number.
Required A
Required B
Required C
5
to one voting rights are necessary to maintain control
Explanation:
a.
Round A Ownership, Cyprus = 31.25% and Founder = 68.75%:
Cyprus = $250,000 ÷ $800,000 = 0.3125, or 31.25%
Founder = 1 − 0.3125 = 0.6875, or 68.75%
b.
Round B Ownership:
Cyprus = ($250,000 + $750,000) ÷ ($800,000 + 3 × $750,000) = $1,000,000 ÷ $3,050,000 = 0.3279, or 32.79%
Specific Pacific = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Mountainhome = $750,000 ÷ $3,050,000 = 0.2459, or 24.59%
Founder = 1 − (0.3279 + 0.2459 + 0.2459) = 0.1803, or 18.03%
c.
Five to one voting rights are necessary to maintain control:
1 < (
x
× 0.1803) ÷ 0.8197 →
x
> 4.54 ≈ 5.00
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
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13.
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points
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for all students.
The RRK buyout fund is considering an investment in a fertilizer distribution center. The stock currently trades at $20 per share with 150,000,000 shares outstanding. RRK offers $25 per share, 80% of which is funded by high-
yield debt securities. The fund believes it can work with management to grow the firm at a rate of about 4% while also retiring half of the high-yield debt by an expected exit in year 6, reinvesting any profit in growth and debt
reduction.
What is the expected IRR of this investment?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
IRR
24.90
%
Explanation:
First calculate the changing capital structure and firm value:
Year 0
Year 6
Capital Structure: Debt
0.80
0.5 × 0.80 = 0.40
Capital Structure: Equity
1 – 0.80 = 0.20
1 – 0.40 = 0.60
Firm Value
$3,750,000,000
$3,750,000,000 × (1.04)
6
= $4,744,946,319
Equity Value
$750,000,000
$2,846,967,792
CF
0
= −$25 × 150,000,000 × 0.20 = −$750,000,000
CF
6
= $2,846,967,792
IRR
= 24.90%
The estimated IRR is 24.90%.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 26: Alternative Assets > Chapter 26 Problems - Algorithmic & Static
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1.
Award:
10.00 points
2.
Award:
10.00 points
3.
Award:
10.00 points
4.
Award:
10.00 points
_________ are the dominant form of investing in securities markets for most individuals, but _________ have enjoyed a far greater growth rate in the last decade.
Hedge Funds; hedge funds
Mutual funds; hedge funds
Hedge Funds; mutual funds
Mutual funds; mutual funds
None of the options are correct.
Mutual funds are the dominant form of investing in securities markets for most individuals, and hedge funds have enjoyed a far greater growth rate in the last decade.
References
Multiple Choice
Difficulty: 1 Basic
Like mutual funds, hedge funds and private equity:
allow private investors to pool assets to be managed by a fund manager.
are commonly organized as private partnerships.
are subject to extensive SEC regulations.
are typically only open to wealthy or institutional investors.
are commonly organized as private partnerships and are typically only open to wealthy or institutional investors.
Like mutual funds, hedge funds allow private investors to pool assets to be managed by a fund manager.
References
Multiple Choice
Difficulty: 1 Basic
Unlike mutual funds, hedge funds and private equity:
allow private investors to pool assets to be managed by a fund manager.
are commonly organized as private partnerships.
are subject to extensive SEC regulations.
are typically only open to wealthy or institutional investors.
are commonly organized as private partnerships and are typically only open to wealthy or institutional investors.
Unlike mutual funds, hedge funds are commonly organized as private partnerships and are typically only open to wealthy or institutional investors.
References
Multiple Choice
Difficulty: 1 Basic
Alpha-seeking hedge funds typically _________ relative mispricing of specific securities and _________ broad market exposure.
bet on; bet on
hedge; hedge
hedge; bet on
bet on; hedge
None of the options are correct.
Alpha seeking hedge funds typically bet on relative mispricing of specific securities and hedge broad market exposure.
References
Multiple Choice
Difficulty: 2 Intermediate
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5.
Award:
10.00 points
6.
Award:
10.00 points
7.
Award:
10.00 points
8.
Award:
10.00 points
Hedge funds _________ engage in market timing _________ take extensive derivative positions.
cannot; and cannot
cannot; but can
can; and can
can; but cannot
None of the options are correct.
Hedge funds can engage in market timing and can take extensive derivative positions.
References
Multiple Choice
Difficulty: 2 Intermediate
The risk profile of hedge funds _________, making performance evaluation _________.
can shift rapidly and substantially; challenging
can shift rapidly and substantially; straightforward
is stable; challenging
is stable; straightforward
None of the options are correct.
The risk profile of hedge funds can shift rapidly and substantially, making performance evaluation challenging.
References
Multiple Choice
Difficulty: 2 Intermediate
Shares in hedge funds are priced:
at NAV.
a significant premium to NAV.
a significant discount from NAV.
a significant premium to NAV or a significant discount from NAV.
None of the options are correct.
Shares in hedge funds are priced at NAV.
References
Multiple Choice
Difficulty: 1 Basic
Hedge funds and private equity are typically set up as _________ and provide _________ information about portfolio composition and strategy to their investors.
limited liability partnerships; minimal
limited liability partnerships; extensive
investment trusts; minimal
investment trusts; extensive
None of the options are correct.
Hedge funds are typically set up as limited liability partnerships and provide minimal information about portfolio composition and strategy to their investors.
References
Multiple Choice
Difficulty: 2 Intermediate
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9.
Award:
10.00 points
10.
Award:
10.00 points
11.
Award:
10.00 points
12.
Award:
10.00 points
Hedge funds and private equity are _________ transparent than mutual funds because of _________ strict SEC regulation on hedge funds.
more; more
more; less
less; less
less; more
None of the options are correct.
Hedge funds are less transparent than mutual funds because of less strict SEC regulation on hedge funds.
References
Multiple Choice
Difficulty: 2 Intermediate
_________ must periodically provide the public with information on portfolio composition.
Hedge funds
Mutual funds
ADRs
Hedge funds and ADRs
Hedge funds and mutual funds
Mutual funds must periodically provide the public with information on portfolio composition.
References
Multiple Choice
Difficulty: 2 Intermediate
_________ are subject to the Securities Act of 1933 and the Investment Company Act of 1940 to protect unsophisticated investors.
Hedge funds
Mutual funds
ADRs
Hedge funds and ADRs
Mutual funds and ADRs
Mutual funds are subject to the Securities Act of 1933 and the Investment Company Act of 1940 to protect unsophisticated investors.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge funds and private equity traditionally have _________ than 100 investors and _________ to the general public.
more; advertise
more; do not advertise
less; advertise
less; do not advertise
None of the options are correct.
Hedge funds traditionally have less than 100 investors and do not advertise to the general public.
References
Multiple Choice
Difficulty: 2 Intermediate
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13.
Award:
10.00 points
14.
Award:
10.00 points
15.
Award:
10.00 points
16.
Award:
10.00 points
Alternative assets differ from traditional assets in terms of:
transparency.
investors.
investment strategy.
liquidity.
All of the options are correct.
Funds differ from mutual funds in terms of transparency, investors, investment strategy, and liquidity.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge funds may invest or engage in:
distressed firms.
convertible bonds.
currency speculation.
merger arbitrage.
All of the options are correct.
Hedge funds may invest or engage in distressed firms, convertible bonds, currency speculation, and merger arbitrage.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge funds are prohibited from investing or engaging in:
distressed firms.
convertible bonds.
currency speculation.
merger arbitrage.
None of the options are correct.
Hedge funds may invest or engage in distressed firms, convertible bonds, currency speculation, and merger arbitrage.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge funds and private equity often have _________ provisions as long as _________, which preclude redemption.
crackdown; 2 months
lock-up; 2 months
crackdown; several years
lock-up; several years
None of the options are correct.
Hedge funds often have lock-up provisions as long as several years, which preclude redemption.
References
Multiple Choice
Difficulty: 2 Intermediate
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17.
Award:
10.00 points
18.
Award:
10.00 points
19.
Award:
10.00 points
20.
Award:
10.00 points
Hedge fund strategies can be classified as:
directional or nondirectional.
stock or bond.
arbitrage or speculation.
stock or bond and arbitrage or speculation.
directional or nondirectional and stock or bond.
Hedge fund strategies can be classified as directional and nondirectional.
References
Multiple Choice
Difficulty: 2 Intermediate
A hedge fund pursuing a _________ strategy is betting one sector of the economy will outperform other sectors.
directional
nondirectional
stock or bond
arbitrage or speculation
None of the options are correct.
A hedge fund pursuing a directional strategy is betting one sector of the economy will outperform other sectors.
References
Multiple Choice
Difficulty: 2 Intermediate
A hedge fund pursuing a _________ strategy is attempting to exploit temporary misalignments in relative pricing.
directional
nondirectional
stock or bond
arbitrage or speculation
None of the options are correct.
A hedge fund pursuing a nondirectional strategy is attempting to exploit temporary misalignments in relative pricing.
References
Multiple Choice
Difficulty: 2 Intermediate
A hedge fund pursuing a _________ strategy is trying to exploit relative mispricing within a market but is hedged to avoid taking a stance on the direction of the broad market.
directional, only
nondirectional, only
market neutral, only
arbitrage or speculation
nondirectional and market neutral
A hedge fund pursuing a nondirectional and market neutral strategy is trying to exploit relative mispricing within a market, but is hedged to avoid taking a stance on the direction of the broad market.
References
Multiple Choice
Difficulty: 2 Intermediate
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21.
Award:
10.00 points
22.
Award:
10.00 points
23.
Award:
10.00 points
24.
Award:
10.00 points
An example of a _________ strategy is the mispricing of a futures contract that must be corrected by contract expiration.
market neutral
directional
relative value
divergence
convergence
An example of a convergence strategy is the mispricing of a futures contract that must be corrected by contract expiration.
References
Multiple Choice
Difficulty: 2 Intermediate
A hedge fund attempting to profit from a change in the spread between mortgages and Treasuries is using a _________ strategy.
market neutral
directional
relative value
divergence
convergence
A hedge fund attempting to profit from a change in the spread between mortgages and Treasuries is using a relative value strategy.
References
Multiple Choice
Difficulty: 2 Intermediate
If the yield on mortgage-backed securities was abnormally high compared to Treasury bonds, a hedge fund pursuing a relative value strategy would:
short sell the Treasury bonds and short sell the mortgage-backed securities.
short sell the Treasury bonds and buy the mortgage-backed securities.
buy the Treasury bonds and buy the mortgage-backed securities.
buy the Treasury bonds and short sell the mortgage-backed securities.
None of the options are correct.
If the yield on mortgage-backed securities was abnormally high compared to Treasury bonds, a hedge fund pursuing a nondirectional strategy would short sell the Treasury bonds and buy the mortgage-backed securities.
References
Multiple Choice
Difficulty: 2 Intermediate
Assume newly-issued 30-year on-the-run bonds sell at higher yields (lower prices) than 29½-year bonds with a nearly identical duration. A hedge fund that sells 29½-year bonds and buys 30-year bonds is taking a:
market neutral position.
conservative position.
bullish position.
bearish position.
None of the options are correct.
A hedge fund that sells 29½-year bonds and buys 30-year bonds is taking a market neutral position.
References
Multiple Choice
Difficulty: 2 Intermediate
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25.
Award:
10.00 points
26.
Award:
10.00 points
27.
Award:
10.00 points
28.
Award:
10.00 points
A bet on particular mispricing across two or more securities with extraneous sources of risk, such as general market exposure hedged away, is a:
pure play, only.
relative play, only.
long shot, only.
sure thing, only.
relative play and sure thing.
A bet on particular mispricing across two or more securities, with extraneous sources of risk such as general market exposure hedged away, is a pure play.
References
Multiple Choice
Difficulty: 2 Intermediate
Assume newly-issued 30-year on-the-run bonds sell at higher yields (lower prices) than 29½-year bonds with a nearly identical duration. A hedge fund that sells 29½-year bonds and buys 30-year bonds is taking a:
market neutral position.
conservative position.
bullish position.
bearish position.
None of the options are correct.
A hedge fund that sells 29½-year bonds and buys 30-year bonds is taking a market neutral position.
References
Multiple Choice
Difficulty: 2 Intermediate
If the yield on mortgage-backed securities was abnormally low compared to Treasury bonds, a hedge fund pursuing a relative value strategy would:
short sell the Treasury bonds and short sell the mortgage-backed securities.
short sell the Treasury bonds and buy the mortgage-backed securities.
buy the Treasury bonds and buy the mortgage-backed securities.
buy the Treasury bonds and short sell the mortgage-backed securities.
None of the options are correct.
If the yield on mortgage-backed securities was abnormally low compared to Treasury bonds, a hedge fund pursuing a non-directional strategy would buy the Treasury and short sell the mortgage-backed securities.
References
Multiple Choice
Difficulty: 2 Intermediate
Statistical arbitrage is a version of a _________ strategy.
market neutral
directional
relative value
divergence
convergence
Statistical arbitrage is a version of a market neutral strategy.
References
Multiple Choice
Difficulty: 2 Intermediate
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29.
Award:
10.00 points
30.
Award:
10.00 points
31.
Award:
10.00 points
32.
Award:
10.00 points
_________ uses quantitative techniques, and often automated trading systems, to seek out many temporary misalignments among securities.
Covered interest arbitrage
Locational arbitrage
Triangular arbitrage
Statistical arbitrage
All arbitrage
Statistical arbitrage uses quantitative techniques and often automated trading systems to seek out many temporary misalignments among securities.
References
Multiple Choice
Difficulty: 2 Intermediate
Assume that you manage a $3 million portfolio that pays no dividends and has a beta of 1.45 and an alpha of 1.5% per month. Also, assume that the risk-free rate is 0.025% (per month) and the S&P 500 is at 1,220. If you expect the
market to fall within the next 30 days, you can hedge your portfolio by _________ S&P 500 futures contracts (the futures contract has a multiplier of $250).
selling 1
selling 14
buying 1
buying 14
selling 6
The hedge ratio is $3,000,000 ÷ (1,220 × $250) × 1.45 = 14.26 Thus, you would need to sell 14 contracts.
References
Multiple Choice
Difficulty: 3 Challenge
Assume that you manage a $1.3 million portfolio that pays no dividends and has a beta of 1.45 and an alpha of 1.5% per month. Also, assume that the risk-free rate is 0.025% (per month) and the S&P 500 is at 1,220. If you expect the
market to fall within the next 30 days, you can hedge your portfolio by _________ S&P 500 futures contracts (the futures contract has a multiplier of $250).
selling 1
selling 6
buying 1
buying 6
selling 4
The hedge ratio is $1,300,000 ÷ (1,220 × $250) × 1.45 = 6.18. Thus, you would need to sell 6 contracts.
References
Multiple Choice
Difficulty: 3 Challenge
Assume that you manage a $2 million portfolio that pays no dividends and has a beta of 1.25 and an alpha of 2% per month. Also, assume that the risk-free rate is 0.05% (per month) and the S&P 500 is at 1,300. If you expect the
market to fall within the next 30 days, you can hedge your portfolio by _________ S&P 500 futures contracts (the futures contract has a multiplier of $250).
selling 1
selling 8
buying 1
buying 8
selling 6
The hedge ratio is $2,000,000 ÷ (1,300 × $250) × 1.25 = 7.69. Thus, you would need to sell 8 contracts.
References
Multiple Choice
Difficulty: 3 Challenge
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33.
Award:
10.00 points
34.
Award:
10.00 points
35.
Award:
10.00 points
36.
Award:
10.00 points
Assume that you manage a $2 million portfolio that pays no dividends and has a beta of 1.3 and an alpha of 2% per month. Also, assume that the risk-free rate is 0.05% (per month) and the S&P 500 is at 1,500. If you expect the
market to fall within the next 30 days, you can hedge your portfolio by _________ S&P 500 futures contracts (the futures contract has a multiplier of $250).
selling 1
selling 7
buying 1
buying 7
selling 11
The hedge ratio is $2,000,000 ÷ (1,500 × $250) × 1.30 = 6.93. Thus, you would need to sell 7 contracts.
References
Multiple Choice
Difficulty: 3 Challenge
Market neutral bets can result in _________ volatility because hedge funds use _________.
very low; hedging techniques to eliminate risk
low; risk management techniques to reduce risk
considerable; risk management techniques to reduce risk
considerable; considerable leverage
None of the options are correct.
Market neutral bets can result in considerable volatility because hedge funds use considerable leverage.
References
Multiple Choice
Difficulty: 2 Intermediate
_________ bias arises because hedge funds only report returns to database publishers if they want to.
Survivorship
Backfill
Omission
Incubation
None of the options are correct.
Backfill bias arises because hedge funds only report returns to database publishers if they want to.
References
Multiple Choice
Difficulty: 2 Intermediate
_________ bias arises when the returns of unsuccessful funds are left out of the sample.
Survivorship
Backfill
Omission
Incubation
None of the options are correct.
Survivorship bias arises when the returns of unsuccessful funds are left out of the sample.
References
Multiple Choice
Difficulty: 2 Intermediate
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37.
Award:
10.00 points
38.
Award:
10.00 points
39.
Award:
10.00 points
40.
Award:
10.00 points
Performance evaluation of hedge funds is complicated by:
liquidity premiums, only.
survivorship bias, only.
unreliable market valuations of infrequently-traded assets, only.
merger arbitrage, only.
All of the options are correct.
Performance evaluation of hedge funds is complicated by liquidity premiums, survivorship bias, unreliable market valuations of infrequently traded assets, and unstable risk attributes.
References
Multiple Choice
Difficulty: 2 Intermediate
The previous value of a portfolio that must be reattained before a hedge fund can charge incentive fees is known as a:
benchmark.
water stain.
water mark.
high water mark.
low water mark.
The previous value of a portfolio that must be reattained before a hedge fund can charge incentive fees is known as a high water mark.
References
Multiple Choice
Difficulty: 2 Intermediate
The typical hedge fund fee structure is:
an annual management fee of 1% to 3%.
an annual incentive fee equal to 20% of investment profits beyond a stipulated benchmark performance.
a 12-b1 fee of 1%.
an annual management fee of 1% to 3% plus an incentive fee equal to 20% of investment profits beyond a stipulated benchmark performance.
an annual management fee of 1% to 3% and a 12-b1 fee of 1%.
The typical hedge fund fee structure is an annual management fee of 1% to 3% plus an incentive fee equal to 20% of investment profits beyond a stipulated benchmark performance.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge fund incentive fees are essentially:
put options on the portfolio with a strike price equal to the current portfolio value.
put options on the portfolio with a strike price equal to the expected future portfolio value.
call options on the portfolio with a strike price equal to the expected future portfolio value.
call options on the portfolio with a strike price equal to the current portfolio value times one plus the benchmark return.
straddles.
Hedge fund incentive fees are essentially call options on the portfolio with a strike price equal to the current portfolio value times one plus the benchmark return.
References
Multiple Choice
Difficulty: 2 Intermediate
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41.
Award:
10.00 points
42.
Award:
10.00 points
43.
Award:
10.00 points
44.
Award:
10.00 points
Regarding hedge fund incentive fees, hedge fund managers _________ if the portfolio return is very large and _________ if the portfolio return is negative.
get nothing; get nothing
refund the fee; get the fee
get the fee; lose nothing except the incentive fee
get the fee; lose the management fee
None of the options are correct.
Regarding hedge fund incentive fees, hedge fund managers get the fee if the portfolio return is very large and lose nothing except the incentive fee if the portfolio return is negative.
References
Multiple Choice
Difficulty: 2 Intermediate
Hedge funds often employ _________ that require investors to provide _________ notice of their desire to redeem funds.
redemption notices; several weeks to several months
redemption notices; several hours to several days
redemption notices; several days to several weeks
lock-up; several years
lock-up; several hours
Hedge funds often employ redemption notices that require investors to provide several weeks to several months notice of their desire to redeem funds.
References
Multiple Choice
Difficulty: 2 Intermediate
Pairs trading is associated with:
triangular arbitrage, only.
statistical arbitrage, only.
data mining, only.
triangular arbitrage and data mining.
statistical arbitrage and data mining.
Pairs trading is associated with statistical arbitrage and is based on data mining.
References
Multiple Choice
Difficulty: 2 Intermediate
_________ refers to sorting through huge amounts of historical data to uncover systematic patterns in returns that can be exploited by traders.
Data mining
Pairs trading
Alpha transfer
Beta shifting
None of the options are correct.
Data mining refers to sorting through huge amounts of historical data to uncover systematic patterns in returns that can be exploited by traders.
References
Multiple Choice
Difficulty: 2 Intermediate
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45.
Award:
10.00 points
46.
Award:
10.00 points
47.
Award:
10.00 points
48.
Award:
10.00 points
Hedge fund performance may reflect significant compensation for _________ risk.
liquidity
systematic
unsystematic
default
unsystematic and default
Hedge fund performance may reflect significant compensation for liquidity risk.
References
Multiple Choice
Difficulty: 2 Intermediate
A _________ is an investment fraud in which a manager collects funds from clients, claims to invest those funds on their behalf, and reports extremely favorable investment returns, but in fact uses the funds for his or her own use.
Ponzi scheme
bonsai scheme
statistical arbitrage scheme
pairs trading scheme
None of the options are correct.
A Ponzi scheme is an investment fraud in which a manager collects funds from clients, claims to invest those funds on their behalf, reports extremely favorable investment returns, but in fact uses the funds for his or her own use.
References
Multiple Choice
Difficulty: 2 Intermediate
Sadka (2010) shows that exposure to unexpected declines in _________ is an important determinant of average hedge fund returns, and that the spreads in average returns across funds with the highest and lowest _________
may be as much as 6% annually.
market risk; systematic risk
market liquidity; liquidity risk
unsystematic risk; unique risk
default risk; default risk
Sadka (2010) shows that exposure to unexpected declines in market liquidity is an important determinant of average hedge fund returns and that the spreads in average returns across funds with the highest and lowest liquidity risk
may be as much as 6% annually.
References
Multiple Choice
Difficulty: 2 Intermediate
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. How much money will a hedge fund make in fees over the course of a year if AUM started at $1,000,000 and ended the year at $1,120,000?
$8,000
$22,400
$30,400
$38,000
None of the options are correct.
($1,120,000 × 0.02) + [$1,120,000
−
($1,000,000 × 1.08)] × 0.2 = $30,400
References
Multiple Choice
Difficulty: 3 Challenge
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49.
Award:
10.00 points
50.
Award:
10.00 points
51.
Award:
10.00 points
52.
Award:
10.00 points
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. What is the Net IRR to the investors if over the course of a year if AUM started at $1,000,000 and ended the year at $1,120,000?
8.96%
10.96%
11.30%
12.00%
None of the options are correct.
($1,120,000 × 0.02) + [$1,120,000
−
($1,000,000 × 1.08)] × 0.2 = $30,400
IRR
= ($1,120,000
−
$30,400
−
$1,000,000) ÷ $1,000,000 = 0.0896 = 8.96%
References
Multiple Choice
Difficulty: 3 Challenge
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. How much money will a hedge fund make in fees over the course of a year if AUM started at $2,000,000 and ended the year at $2,300,000?
$68,300
$74,000
$80,400
$92,040
None of the options are correct.
($2,300,000 × 0.02) + [$2,300,000
−
($2,000,000 × 1.08)] × 0.2 = $74,000
References
Multiple Choice
Difficulty: 3 Challenge
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. What is the Net IRR to the investors if over the course of a year if AUM started at $2,000,000 and ended the year at $2,300,000?
8.96%
10.96%
11.30%
12.00%
None of the options are correct.
($2,300,000 × 0.02) + [$2,300,000
−
($2,000,000 × 1.08)] × 0.2 = $74,000
IRR
= ($2,300,000
−
$74,000
−
$2,000,000) ÷ $2,000,000 = 0.113 = 11.30%
References
Multiple Choice
Difficulty: 3 Challenge
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. How much money will a hedge fund make in fees over the course of a year if AUM started at $4,000,000 and ended the year at $5,300,000?
$68,300
$74,000
$80,400
$92,040
None of the options are correct.
($5,300,000 × 0.02) + [$5,300,000
−
($4,000,000 × 1.08)] × 0.2 = $302,000
References
Multiple Choice
Difficulty: 3 Challenge
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53.
Award:
10.00 points
54.
Award:
10.00 points
55.
Award:
10.00 points
56.
Award:
10.00 points
A hedge fund sets its fee at 2% and a 20% carry with an 8% benchmark. What is the Net IRR to the investors if over the course of a year if AUM started at $4,000,000 and ended the year at $5,300,000?
28.65%
26.87%
24.95%
22.00%
None of the options are correct.
($5,300,000 × 0.02) + [$5,300,000
−
($4,000,000 × 1.08)] × 0.2 = $302,000
IRR
= ($5,300,000
−
$302,000
−
$4,000,000) ÷ $4,000,000 = 0.2495 = 24.95%
References
Multiple Choice
Difficulty: 3 Challenge
Which of the following are typically organized as limited partnerships?
1. Angel Investors
2. Venture Capital Funds
3. LBO funds
4. Publicly traded corporations
1 and 2
2 and 3
1, 2, and 3
2, 3, and 4
None of the options are correct.
Like VC funds, LBO funds are typically organized as limited partnerships with a typical fund life of 10 years.
References
Multiple Choice
Difficulty: 1 Basic
In an LBO, which group controls how committed capital is invested (subject to some protective covenants)?
Limited Partners
General Partners
Board of Directors
Board of Advisors
All of the groups listed in options control how capital is committed
GPs control how committed capital is invested subject to some protective covenants. For example, the maximum percent of the total fund that can be invested in any one company may be limited.
References
Multiple Choice
Difficulty: 1 Basic
Most LBO fund last how many years?
5 years
8 years
10 years
21 years
None of the options are correct.
Like VC funds, LBO funds are typically organized as limited partnerships with a typical fund life of 10 years.
References
Multiple Choice
Difficulty: 1 Basic
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57.
Award:
10.00 points
58.
Award:
10.00 points
59.
Award:
10.00 points
Typically LBO offers are funded by _________ equity and _________ debt.
60 – 90%; 10 – 40%
10 – 40%; 60 – 90%
50%; 50%
1 – 5%; 95 – 99%
95 – 99%; 1 – 5%
The offer is funded by about 10–40% equity drawn down from the fund and 60–90% debt (the leverage).
References
Multiple Choice
Difficulty: 1 Basic
An LBO purchases a business for $150,000,000, 75% of which is debt. In 5 years, the LBO sells it for $300,000,000. If the debt principal remains the same, what is the internal rate of return (IRR) of this investment?
14.86%
20.00%
25.00%
37.97%
42.85%
V
0
=
E
0
+
D
0
$150,000,000 = 0.25 × $150,000,000 + 0.75 × $150,000,000
E
0
= $37,500,000 &
D
0
= $112,500,000
E
5
= $300,000,000 − $112,500,000 = $187,500,000
E
0
=
E
5
÷ (1 +
IRR
)
5
$37,500,000 = $187,500,000 ÷ (1 +
IRR
)
5
IRR
= 37.97%
References
Multiple Choice
Difficulty: 2 Intermediate
An LBO purchases a business for $250,000,000, 80% of which is debt. In 7 years, the LBO sells it for $350,000,000. If the debt principal remains the same, what is the internal rate of return (IRR) of this investment?
5.71%
12.50%
16.99%
20.00%
40.00%
V
0
=
E
0
+
D
0
$250,000,000 = 0.20 × $250,000,000 + 0.80 × $250,000,000
E
0
= $50,000,000 &
D
0
= $200,000,000
E
7
= $350,000,000 − $200,000,000 = $150,000,000
E
0
=
E
7
÷ (1 +
IRR
)
7
$50,000,000 = $150,000,000 ÷ (1 +
IRR
)
7
IRR
= 16.99%
References
Multiple Choice
Difficulty: 2 Intermediate
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60.
Award:
10.00 points
61.
Award:
10.00 points
62.
Award:
10.00 points
An LBO purchases a business for $160,000,000, 70% of which is debt. In 6 years, the LBO sells it for $325,000,000. If the debt principal remains the same, what is the internal rate of return (IRR) of this investment?
15.75%
20.00%
25.00%
28.19%
103.13%
V
0
=
E
0
+
D
0
$160,000,000 = 0.30 × $160,000,000 + 0.70 × $160,000,000
E
0
= $48,000,000 &
D
0
= $112,000,000
E
6
= $325,000,000 − $112,000,000 = $213,000,000
E
0
=
E
6
÷ (1 +
IRR
)
6
$48,000,000 = $213,000,000 ÷ (1 +
IRR
)
6
IRR
= 28.19%
References
Multiple Choice
Difficulty: 2 Intermediate
An LBO purchases a business for $150,000,000, 75% of which is debt. In 5 years, the LBO sells it for $250,000,000. If the debt principal is reduced to 50% of the original principal, what is the internal rate of return (IRR) of this
investment?
14.86%
20.00%
25.24%
38.88%
75.00%
V
0
=
E
0
+
D
0
$150,000,000 = 0.25 × $150,000,000 + 0.75 × $150,000,000
E
0
= $37,500,000 &
D
0
= $112,500,000
D
5
= 0.50 × $112,500,000 = $56,250,000
E
5
= $250,000,000 − $56,250,000 = $193,750,000
E
0
=
E
5
÷ (1 +
IRR
)
5
$37,500,000 = $193,750,000 ÷ (1 +
IRR
)
5
IRR
= 38.88%
References
Multiple Choice
Difficulty: 3 Challenge
An LBO purchases a business for $250,000,000, 80% of which is debt. In 7 years, the LBO sells it for $350,000,000. If the debt principal is reduced to 50% of the original principal, what is the internal rate of return (IRR) of this
investment?
5.71%
12.50%
16.99%
25.85%
40.00%
V
0
=
E
0
+
D
0
$250,000,000 = 0.20 × $250,000,000 + 0.80 × $250,000,000
E
0
= $50,000,000 &
D
0
= $200,000,000
D
7
= 0.50 ×
D
0
= 0.50 × $200,000,000 = $100,000,000
E
7
= $350,000,000 − $100,000,000 = $250,000,000
E
0
=
E
7
÷ (1 +
IRR
)
7
$50,000,000 = $250,000,000 ÷ (1 +
IRR
)
7
IRR
= 25.85%
References
Multiple Choice
Difficulty: 3 Challenge
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63.
Award:
10.00 points
64.
Award:
10.00 points
65.
Award:
10.00 points
66.
Award:
10.00 points
An LBO purchases a business for $160,000,000, 70% of which is debt. In 6 years, the LBO sells it for $300,000,000. If the debt principal is reduced to 50% of the original principal, what is the internal rate of return (IRR) of this
investment?
15.25%
20.00%
22.96%
31.13%
87.50%
V
0
=
E
0
+
D
0
$160,000,000 = 0.30 × $160,000,000 + 0.70 × $160,000,000
E
0
= $48,000,000 &
D
0
= $112,000,000
D
6
=0.50 ×
D
0
= 0.50 × $112,000,000 = $56,000,000
E
6
= $300,000,000 − $56,000,000 = $244,000,000
E
0
=
E
6
÷ (1 +
IRR
)
6
$48,000,000 = $244,000,000 ÷ (1 +
IRR
)
6
IRR
= 31.13%
References
Multiple Choice
Difficulty: 3 Challenge
According to Kaplan and Strömberg, approximately what percent of LBO-acquired firms are sold to a strategic buyer (traditional acquisition)?
1%
5%
6%
24%
38%
Kaplan and Strömberg calculate about 38% of LBO portfolio companies are sold to a strategic buyer (a more traditional acquisition), while 24% are acquired in a second buyout. Around 1% are sold to their management (in a so-
called management buyout) and 5% to another LBO-backed firm. About 6% declare bankruptcy and the rest have unknown fates because data collection is inherently challenging in this arena.
References
Multiple Choice
Difficulty: 1 Basic
According to Kaplan and Strömberg, approximately what percent of LBO-acquired firms are acquired in a second buyout?
1%
5%
6%
24%
38%
Kaplan and Strömberg calculate about 38% of LBO portfolio companies are sold to a strategic buyer (a more traditional acquisition), while 24% are acquired in a second buyout. Around 1% are sold to their management (in a so-
called management buyout) and 5% to another LBO-backed firm. About 6% declare bankruptcy and the rest have unknown fates because data collection is inherently challenging in this arena.
References
Multiple Choice
Difficulty: 1 Basic
According to Kaplan and Strömberg, approximately what percent of LBO-acquired firms are sold to their management (management buyout)?
1%
5%
6%
24%
38%
Kaplan and Strömberg calculate about 38% of LBO portfolio companies are sold to a strategic buyer (a more traditional acquisition), while 24% are acquired in a second buyout. Around 1% are sold to their management (in a so-
called management buyout) and 5% to another LBO-backed firm. About 6% declare bankruptcy and the rest have unknown fates because data collection is inherently challenging in this arena.
References
Multiple Choice
Difficulty: 1 Basic
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67.
Award:
10.00 points
68.
Award:
10.00 points
69.
Award:
10.00 points
70.
Award:
10.00 points
The name of the first year of the venture fund is called its _________.
vintage year
sovereign year
entry year
venture year
initial year
The vintage year is the first year of the venture fund, typically when raised capital is first deployed.
References
Multiple Choice
Difficulty: 1 Basic
Which of the following is typically not organized as a limited partnership?
Angel investors
Early-stage venture capital
Late-stage venture capital
Leveraged buyouts
None are organized as limited partnerships
Angel investors are wealthy individuals or families.
References
Multiple Choice
Difficulty: 1 Basic
Which of the following are not considered private equity?
Angel investors
Early-stage venture capital
Growth Capital
Leveraged buyouts
All are considered private equity
Private equity includes angel investors, early-stage venture capital, growth capital, and leveraged buyouts.
References
Multiple Choice
Difficulty: 1 Basic
A _________ is the written agreement specifying the deal structure between the VC and an entrepreneur.
indenture
debenture
term sheet
vintage agreement
red herring
At the conclusion of successful due diligence, the VC and the entrepreneur draw up a term sheet, or written agreement specifying the deal structure.
References
Multiple Choice
Difficulty: 1 Basic
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71.
Award:
10.00 points
72.
Award:
10.00 points
73.
Award:
10.00 points
74.
Award:
10.00 points
The _________ is the rate of venture cash consumption.
incentive rate
draw-down rate
burn rate
partnership rate
All of the options are correct.
Venture capital cash consumption is known as the burn rate.
References
Multiple Choice
Difficulty: 1 Basic
Which of the following are examples of venture capital exits (from portfolio companies)?
Initial public offerings, only
Acquisitions, only
Write-offs and acquisitions, only
Acquisitions and initial public offerings, only
Initial public offerings, acquisitions, and write-offs
Successful exits from portfolio companies generate returns for venture capitalists and their limited partners and represent the end of the fund’s life. There are three types of exits: initial public offerings (IPOs), acquisitions, and write-
offs.
References
Multiple Choice
Difficulty: 1 Basic
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $2,000,000 in the first round of financing, and you target a final exit multiple of 10× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $90,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 50%.
What final equity position (weight) must you require for your investment?
10.00%
15.55%
19.00%
22.22%
26.79%
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($2,000,000 × 10) ÷ $90,000,000 = 0.2222 = 22.22%
References
Multiple Choice
Difficulty: 1 Basic
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $1,500,000 in the first round of financing, and you target a final exit multiple of 12× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $80,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 50%.
What final equity position (weight) must you require for your investment?
1.80%
15.40%
19.00%
22.50%
26.79%
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($1,500,000 × 12) ÷ $80,000,000 = 0.2250 = 22.50%
References
Multiple Choice
Difficulty: 1 Basic
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75.
Award:
10.00 points
76.
Award:
10.00 points
77.
Award:
10.00 points
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $2,000,000 in the first round of financing, and you target a final exit multiple of 10× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $90,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 50%.
What initial equity position must you require for your investment? What must be your initial valuation of the company excluding the amount of your investment? What is the internal rate of return for this investment?
11.11%
15.55%
19.00%
22.22%
44.44%
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($2,000,000 × 10) ÷ $90,000,000 = 0.2222
w
Initial
=
w
Terminal
÷ (1
−
Dilution) = 0.2222 ÷ (1
−
0.50) = 0.4444 = 44.44%
References
Multiple Choice
Difficulty: 2 Intermediate
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $1,500,000 in the first round of financing, and you target a final exit multiple of 12× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $80,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 40%.
What final equity position (weight) must you require for your investment?
1.80%
15.40%
37.50%
50.00%
76.79%
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($1,500,000 × 12) ÷ $80,000,000 = 0.2250
w
Initial
=
w
Terminal
÷ (1 − Dilution) = 0.2250 ÷ (1 − 0.40) = 0.3750 = 37.50%
References
Multiple Choice
Difficulty: 1 Basic
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $2,000,000 in the first round of financing, and you target a final exit multiple of 10× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $90,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 50%.
What must be your initial valuation of the company excluding the amount of your investment?
$2,000,000
$2,500,000
$4,500,000
$90,000,000
None of the options are correct.
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($2,000,000 × 10) ÷ $90,000,000 = 0.2222
w
Initial
=
w
Terminal
÷ (1 − Dilution) = 0.2222 ÷ (1 − 0.50) = 0.4444
w
Initial
×
V
Initial
= 0.4444 ×
V
Initial
= $2,000,000
V
Initial
= $4,500,000
V
pre-venture
= $4,500,000 − $2,000,000 = $2,500,000
References
Multiple Choice
Difficulty: 3 Challenge
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78.
Award:
10.00 points
79.
Award:
10.00 points
80.
Award:
10.00 points
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $1,500,000 in the first round of financing, and you target a final exit multiple of 12× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $80,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 40%.
What must be your initial valuation of the company excluding the amount of your investment?
$2,000,000
$2,500,000
$4,500,000
$90,000,000
None of the options are correct.
w
Terminal
= (
V
Initial
× Capital Multiplier) ÷
V
Terminal
= ($1,500,000 × 12) ÷ $80,000,000 = 0.2250
w
Initial
=
w
Terminal
÷ (1 − Dilution) = 0.2250 ÷ (1 − 0.40) = 0.3750
w
Initial
×
V
Initial
= 0.3750 ×
V
Initial
= $1,500,000
V
Initial
= $4,000,000
V
pre-venture
= $4,000,000 − $1,500,000 = $2,500,000
References
Multiple Choice
Difficulty: 3 Challenge
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $2,000,000 in the first round of financing, and you target a final exit multiple of 10× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $90,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 50%.
What is the expected internal rate of return for this investment?
10.00%
18.40%
19.00%
25.89%
26.79%
V
Initial
× Capital Multiplier = $2,000,000 × 10 = $20,000,000
$2,000,000 = $20,000,000 ÷ (1 +
IRR
)
10
IRR
= 25.89%
References
Multiple Choice
Difficulty: 2 Intermediate
You are an early-stage venture capitalist conducting due diligence on a biotech start-up. You are willing to contribute $1,500,000 in the first round of financing, and you target a final exit multiple of 12× invested capital, which
estimate will happen in ten years. At that time, you estimate the firm will sell for $80,000,000. You expect an additional round of financing in four years in which you will not participate that will dilute your ownership share by 40%.
What is the expected internal rate of return for this investment?
10.00%
12.00%
18.40%
28.21%
34.70%
V
Initial
× Capital Multiplier = $1,500,000 × 12 = $18,000,000
$1,500,000 = $18,000,000 ÷ (1 +
IRR
)
10
IRR
= 28.21%
References
Multiple Choice
Difficulty: 2 Intermediate
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Related Questions
A company has two investment possibilities, with the following cash inflows:
Investment
Year 1
Year 2
Year 3
A
$1,500
1,900
2,200
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1,400
1,400
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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
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Year
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$1,800
$6,387
14
B
$9,500
$14,353
11
$600
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Hi 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/year
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Solve this early and correctly. But not explain in excel works.
Typed or handwriting image onlys.
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Can someone please help me to solve the following question showing all work and formulas neatly. And please show the cash flow diagram as well. PLEASE ANS THANK YOU!!!!!
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- $920.33 at time 1 = 0 (negative since this is your initial investment)
S407 at time
= 1 in years
$222 at time
= 2 in years
$426 at time = 3 in years
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Excel Functon
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A hedge fund with $1.8 billion of assets charges a management fee of 3% and an incentive fee of 20% of returns over a money market
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(Enter your answers in millions rounded to 1 decimal place.)
Portfolio Rate
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a. -1
b. 0
c. 6
d. 12
Total Fee
($ million)
Total Fee
(%)
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1 55,000
2 43,000
3 45,000
Suppose that the discount rate (interest rate) is 12%. The NPV is
Group of answer choices
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$15,416.59
$10,206.14
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