Chapter 07
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Jan 9, 2024
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1.
Award:
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points
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for all students.
Which of the following factors reflect
pure
market risk for a given corporation?
Note: You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a
wrong answer.
Increased short-term interest rates
Fire in the corporate warehouse
Increased insurance costs
Death of the CEO
Increased labor costs
Explanation:
Short-term rates and labor issues are factors that are common to all firms and therefore must be considered as market risk factors. The remaining three factors are unique to this corporation and are not a part of market risk.
Check all that apply
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
2.
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When adding real estate to an asset allocation program that currently includes only stocks, bonds, and cash, which of the properties of real estate returns most affects portfolio risk?
Note: You may select more than one answer. Single click the box with the question mark to produce a check mark for a correct answer and double click the box with the question mark to empty the box for a
wrong answer.
Standard deviation
Expected return
Covariance with returns of the other asset classes
Explanation:
After real estate is added to the portfolio, there are four asset classes in the portfolio: stocks, bonds, cash, and real estate. Portfolio variance now includes a variance term for real estate returns and a covariance term for real
estate returns with returns for each of the other three asset classes. Therefore, portfolio risk is affected by the variance (or standard deviation) of real estate returns and the correlation between real estate returns and returns for
each of the other asset classes. (Note that the correlation between real estate returns and returns for cash is most likely zero.)
Check all that apply
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
3.
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Which of the following statements about the minimum-variance portfolio of all risky securities is valid? (Assume short sales are allowed.)
Valid statement
Its variance must be lower than those of all other securities or portfolios.
Explanation:
Its variance must be lower than those of all other securities or portfolios is valid because it provides the definition of the minimum variance portfolio.
Worksheet
Difficulty: 1 Basic
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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4.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
Required:
a-1.
What are the investment proportions in the minimum-variance portfolio of the two risky funds?
a-2.
What is the expected value and standard deviation of the minimum-variance portfolio rate of return?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
What are the investment proportions in the minimum-variance portfolio of the two risky funds?
Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.
Req A1
Req A2
Portfolio invested in the stock
0.1739
Portfolio invested in the bond
0.8261
Explanation:
a-1.
The parameters of the opportunity set are:
E
(
r
S
) = 20%,
E
(
r
B
) = 12%,
σ
S
= 30%,
B
= 15%,
= 0.10
From the standard deviations and the correlation coefficient we generate the covariance matrix [note that
Cov
(
r
S
,
r
B
) =
ρ
×
σ
S
×
σ
B
]
:
Bonds
Stocks
Bonds
225
45
Stocks
45
900
The minimum-variance portfolio is computed as follows:
w
Min
(S)
=
(σ
B
2
− Cov(r
S
, r
B
)) ÷ (σ
B
2
+ σ
B
2
− 2Cov(r
S
, r
B
)
) = (225 − 45) ÷ (900 + 225 − (2 × 45)) = 0.1739
w
Min
(B)
= 1 − 0.1739 = 0.8261
a-2.
The minimum variance portfolio mean and standard deviation are:
E(r
Min
)
= (0.1739 × 0.20) + (0.8261 × 0.12) = 0.1339
σ
Min
= [
w
S
2
S
2
+
w
B
2
B
2
+ 2
w
S
w
B
Cov(
r
S
,
r
B
)]
1/2
= [(0.1739
2
× 900) + (0.8261
2
× 225) + (2 × 0.1739 × 0.8261 × 45)]
1/2
= 0.1392
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
4.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
Required:
a-1.
What are the investment proportions in the minimum-variance portfolio of the two risky funds?
a-2.
What is the expected value and standard deviation of the minimum-variance portfolio rate of return?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
What is the expected value and standard deviation of the minimum-variance portfolio rate of return?
Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.
Req A1
Req A2
Expected return
0.1339
Standard deviation
0.1392
Explanation:
a-1.
The parameters of the opportunity set are:
E
(
r
S
) = 20%,
E
(
r
B
) = 12%,
σ
S
= 30%,
B
= 15%,
= 0.10
From the standard deviations and the correlation coefficient we generate the covariance matrix [note that
Cov
(
r
S
,
r
B
) =
ρ
×
σ
S
×
σ
B
]
:
Bonds
Stocks
Bonds
225
45
Stocks
45
900
The minimum-variance portfolio is computed as follows:
w
Min
(S)
=
(σ
B
2
− Cov(r
S
, r
B
)) ÷ (σ
B
2
+ σ
B
2
− 2Cov(r
S
, r
B
)
) = (225 − 45) ÷ (900 + 225 − (2 × 45)) = 0.1739
w
Min
(B)
= 1 − 0.1739 = 0.8261
a-2.
The minimum variance portfolio mean and standard deviation are:
E(r
Min
)
= (0.1739 × 0.20) + (0.8261 × 0.12) = 0.1339
σ
Min
= [
w
S
2
S
2
+
w
B
2
B
2
+ 2
w
S
w
B
Cov(
r
S
,
r
B
)]
1/2
= [(0.1739
2
× 900) + (0.8261
2
× 225) + (2 × 0.1739 × 0.8261 × 45)]
1/2
= 0.1392
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
5.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
Tabulate the investment opportunity set of the two risky funds.
Note: Round your answers to 2 decimal places.
Proportion
in Stock Fund
Proportion
in Bond Fund
Expected
Return
Standard
Deviation
0.00 %
100.00 %
12.00
%
15.00
%
20.00
80.00
13.60
13.94
40.00
60.00
15.20
15.70
60.00
40.00
16.80
19.53
80.00
20.00
18.40
24.48
100.00
0.00
20.00
30.00
Explanation:
Graph shown below.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
Your preview ends here
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6.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
Solve numerically for the proportions of each asset and for the expected return and standard deviation of the optimal risky portfolio.
Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.
Portfolio invested in the stock
0.4516
Portfolio invested in the bond
0.5484
Expected return
0.1561
Standard deviation
0.1654
Explanation:
The proportion of the optimal risky portfolio invested in the stock fund is given by:
w
s
= ([
E
(
r
S
) −
r
f
] ×
σ
B
2
− [
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
)) ÷ ([
E
(
r
S
) −
r
f
] ×
σ
B
2
+ [
E
(
r
B
) −
r
f
] ×
σ
S
2
− [
E
(
r
S
) −
r
f
+
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
))
= ([(0.20 − 0.08) × 225] − [(0.12 − 0.08) × 45]) ÷ ([(0.20 − 0.08) × 225] + [(0.12 − 0.08) × 900] − [(0.20 − 0.08 + 0.12 − 0.08) × 45]) = 0.4516
w
B
= 1 − 0.4516 = 0.5484
The mean and standard deviation of the optimal risky portfolio are:
E(r
P
)
= (0.4516 × 0.20) + (0.5484 × 0.12)
= 0.1561
σ
p
= [(0.4516
2
× 900) + (0.5484
2
× 225) + (2 × 0.4516 × 0.5484 × 45)]
1/2
= 0.1654
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
7.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
What is the Sharpe ratio of the best feasible CAL?
Note: Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.
Sharpe ratio
0.4603
Explanation:
The proportion of the optimal risky portfolio invested in the stock fund is given by:
w
s
= ([
E
(
r
S
) −
r
f
] ×
σ
B
2
− [
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
)) ÷ ([
E
(
r
S
) −
r
f
] ×
σ
B
2
+ [
E
(
r
B
) −
r
f
] ×
σ
S
2
− [
E
(
r
S
) −
r
f
+
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
))
= ([(0.20 − 0.08) × 225] − [(0.12 − 0.08) × 45]) ÷ ([(0.20 − 0.08) × 225] + [(0.12 − 0.08) × 900] − [(0.20 − 0.08 + 0.12 − 0.08) × 45]) = 0.4516
w
B
= 1 − 0.4516 = 0.5484
The mean and standard deviation of the optimal risky portfolio are:
E(r
P
)
= (0.4516 × 0.20) + (0.5484 × 0.12) = 0.1561
σ
p
= [(0.4516
2
× 900) + (0.5484
2
× 225) + (2 × 0.4516 × 0.5484 × 45)]
1/2
= 0.1654
The reward-to-volatility ratio of the optimal CAL is:
(E
(
r
p
) −
r
f
) ÷ (
σ
p
) = (0.1561 − 0.08) ÷ (0.1654) = 0.4603
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
You require that your portfolio yield an expected return of 14%, and that it be efficient, that is, on the steepest feasible CAL:
Required:
a.
What is the standard deviation of your portfolio?
b.
What is the proportion invested in the money market fund and each of the two risky funds?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the standard deviation of your portfolio?
Note: Do not round intermediate calculations. Round your answer to 2 decimal places.
Required A
Required B
Standard deviation
13.04
%
Explanation:
The proportion of the optimal risky portfolio invested in the stock fund is given by:
w
s
= ([
E
(
r
S
) −
r
f
] ×
σ
B
2
− [
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
)) ÷ ([
E
(
r
S
) −
r
f
] ×
σ
B
2
+ [
E
(
r
B
) −
r
f
] ×
σ
S
2
− [
E
(
r
S
) −
r
f
+
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
))
= ([(0.20 − 0.08) × 225] − [(0.12 − 0.08) × 45]) ÷ ([(0.20 − 0.08) × 225] + [(0.12 − 0.08) × 900] − [(0.20 − 0.08 + 0.12 − 0.08) × 45]) = 0.4516
w
B
= 1 − 0.4516 = 0.5484
The mean and standard deviation of the optimal risky portfolio are:
E(r
P
)
= (0.4516 × 0.20) + (0.5484 × 0.12) = 0.1561
= 15.61%
σ
p
= [(0.4516
2
× 900) + (0.5484
2
× 225) + (2 × 0.4516 × 0.5484 × 45)]
1/2
= 0.1654
The reward-to-volatility ratio of the optimal CAL is:
(E
(
r
p
) −
r
f
) ÷ (
σ
p
) = (0.1561 − 0.08) ÷ 0.1654 = 0.4603
a.
If you require that your portfolio yield an expected return of 14%, then you can find the corresponding standard deviation from the optimal CAL:
0.14 =
E
(
r
c
) = (
r
f
+
E
(
r
p
) −
r
f
) ÷ (
σ
P
×
C
) = (0.08 + 0.1561 − 0.08) ÷ (0.1654 ×
C
) = 0.08 + (0.4603 ×
C
) = 0.1304 = 13.04%
If
E(r
C
)
14%, then the standard deviation of the portfolio is 13.0403%
.
b.
To find the proportion invested in the Money market fund, remember that the mean of the complete portfolio (here, 14%) is an average of the T-bill rate and the optimal combination of stocks and bonds
(P)
. Let y be the
proportion invested in the portfolio
P
. The mean of any portfolio along the optimal CAL is:
E
(
r
c
) = (1 −
y
) ×
r
f
+
y
×
E
(
r
P
) =
r
f
+
y
× [
E
(
r
p
) −
r
f
] = 0.08 +
y
× (0.1561 − 0.08)
Setting
E
(
r
c
) = 14%
we find:
y
= 0.7881 and (1 −
y
) = 0.2119 (the proportion invested in the Money market fund).
To find the proportions invested in each of the funds, multiply 0.7884 times the respective proportions of stocks and bonds in the optimal risky portfolio:
Proportion of stocks in complete portfolio = 0.7884 × 0.4516 = 0.3559
Proportion of bonds in complete portfolio = 0.7884 × 0.5484 = 0.4322
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
Your preview ends here
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8.
Award:
10.00
points
Problems?
Adjust credit
for all students.
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 8%. The characteristics of the risky
funds are as follows:
Expected
Return
Standard
Deviation
Stock fund (
S
)
20%
30%
Bond fund (B)
12
15
The correlation between the fund returns is 0.10.
You require that your portfolio yield an expected return of 14%, and that it be efficient, that is, on the steepest feasible CAL:
Required:
a.
What is the standard deviation of your portfolio?
b.
What is the proportion invested in the money market fund and each of the two risky funds?
Required A
Required B
Complete this question by entering your answers in the tabs below.
What is the proportion invested in the money market fund and each of the two risky funds?
Note: Do not round intermediate calculations. Round your answers to 2 decimal places.
Required A
Required B
Proportion
Invested
Money market fund
21.19
%
Stocks
35.59
%
Bonds
43.22
%
Explanation:
The proportion of the optimal risky portfolio invested in the stock fund is given by:
w
s
= ([
E
(
r
S
) −
r
f
] ×
σ
B
2
− [
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
)) ÷ ([
E
(
r
S
) −
r
f
] ×
σ
B
2
+ [
E
(
r
B
) −
r
f
] ×
σ
S
2
− [
E
(
r
S
) −
r
f
+
E
(
r
B
) −
r
f
] ×
Cov
(
r
S
,
r
B
))
= ([(0.20 − 0.08) × 225] − [(0.12 − 0.08) × 45]) ÷ ([(0.20 − 0.08) × 225] + [(0.12 − 0.08) × 900] − [(0.20 − 0.08 + 0.12 − 0.08) × 45]) = 0.4516
w
B
= 1 − 0.4516 = 0.5484
The mean and standard deviation of the optimal risky portfolio are:
E(r
P
)
= (0.4516 × 0.20) + (0.5484 × 0.12) = 0.1561
= 15.61%
σ
p
= [(0.4516
2
× 900) + (0.5484
2
× 225) + (2 × 0.4516 × 0.5484 × 45)]
1/2
= 0.1654
The reward-to-volatility ratio of the optimal CAL is:
(E
(
r
p
) −
r
f
) ÷ (
σ
p
) = (0.1561 − 0.08) ÷ 0.1654 = 0.4603
a.
If you require that your portfolio yield an expected return of 14%, then you can find the corresponding standard deviation from the optimal CAL:
0.14 =
E
(
r
c
) = (
r
f
+
E
(
r
p
) −
r
f
) ÷ (
σ
P
×
C
) = (0.08 + 0.1561 − 0.08) ÷ (0.1654 ×
C
) = 0.08 + (0.4603 ×
C
) = 0.1304 = 13.04%
If
E(r
C
)
14%, then the standard deviation of the portfolio is 13.0403%
.
b.
To find the proportion invested in the Money market fund, remember that the mean of the complete portfolio (here, 14%) is an average of the T-bill rate and the optimal combination of stocks and bonds
(P)
. Let y be the
proportion invested in the portfolio
P
. The mean of any portfolio along the optimal CAL is:
E
(
r
c
) = (1 −
y
) ×
r
f
+
y
×
E
(
r
P
) =
r
f
+
y
× [
E
(
r
p
) −
r
f
] = 0.08 +
y
× (0.1561 − 0.08)
Setting
E
(
r
c
) = 14%
we find:
y
= 0.7881 and (1 −
y
) = 0.2119 (the proportion invested in the Money market fund).
To find the proportions invested in each of the funds, multiply 0.7884 times the respective proportions of stocks and bonds in the optimal risky portfolio:
Proportion of stocks in complete portfolio = 0.7884 × 0.4516 = 0.3559
Proportion of bonds in complete portfolio = 0.7884 × 0.5484 = 0.4322
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
9.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Suppose that there are many stocks in the security market and that the characteristics of stocks
A
and
B
are given as follows:
Stock
Expected
Return
Standard
Deviation
A
10%
5%
B
15%
10%
Correlation = –1
Suppose that it is possible to borrow at the risk-free rate,
r
f
. What must be the value of the risk-free rate? (
Hint:
Think about constructing a risk-free portfolio from stocks
A
and
B
.)
Note: Do not round intermediate calculations. Round your answer to 3 decimal places.
Risk-free rate
11.667
%
Explanation:
Since Stock A and Stock B are perfectly negatively correlated, a risk-free portfolio can be created and the rate of return for this portfolio, in equilibrium, will be the risk-free rate. To find the proportions of this portfolio [with the
proportion
w
A
invested in Stock A and
w
B
= (1 −
w
A
)
invested in Stock B], set the standard deviation equal to zero. With perfect negative correlation, the portfolio standard deviation is:
σ
P
= Absolute value [
w
A
σ
A
–
w
B
σ
B
]
0 = 5 ×
w
A
− [10 × (1 −
w
A
)]
w
A
= 0.6667
The expected rate of return for this risk-free portfolio is:
E
(
r
) = (0.6667 × 10) + (0.3333 × 15) = 11.667%
Therefore, the risk-free rate is: 11.667%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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Award:
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Problems?
Adjust credit
for all students.
Assume that expected returns and standard deviations for all securities (including the risk-free rate for borrowing and lending) are known. In this case, all investors will have the same optimal risky portfolio.
Assume that expected returns and standard deviations for all securities (including the risk-free rate for borrowing and
lending) are known. In this case, all investors will have the same optimal risky portfolio.
False
Explanation:
If the borrowing and lending rates are not identical, then, depending on the tastes of the individuals (that is, the shape of their indifference curves), borrowers and lenders could have different optimal risky portfolios.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
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The standard deviation of the portfolio is always equal to the weighted average of the standard deviations of the assets in the portfolio.
The standard deviation of the portfolio is always equal to the weighted average of the standard deviations of the assets in the portfolio.
False
Explanation:
The portfolio standard deviation equals the weighted average of the component-asset standard deviations
only
in the special case that all assets are perfectly positively correlated. Otherwise, as the formula for portfolio standard
deviation shows, the portfolio standard deviation is
less
than the weighted average of the component-asset standard deviations. The portfolio
variance
is a weighted
sum
of the elements in the covariance matrix, with the
products of the portfolio proportions as weights.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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Suppose you have a project that has a 0.7 chance of doubling your investment in a year and a 0.3 chance of halving your investment in a year. What is the standard deviation of the rate of return on this investment?
Note: Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places.
Standard deviation
68.74
%
Explanation:
The probability distribution is:
Probability
Rate of
Return
0.7
100%
0.3
−50
Mean = [0.7 × 100%] + [0.3 × (−50%)] = 55%
Variance = [0.7 ×
(100 − 55)
2
] + [0.3 ×
(−50 − 55)
2
] = 4,725
Standard deviation =
4,725
1/2
= 0.6874 = 68.74%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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Suppose that you have $1 million and the following two opportunities from which to construct a portfolio:
Required:
a.
Risk-free asset earning 12% per year.
b.
Risky asset with expected return of 30% per year and standard deviation of 40%.
If you construct a portfolio with a standard deviation of 30%, what is its expected rate of return?
Note: Do not round your intermediate calculations. Round your answer to 1 decimal place.
Expected return on portfolio
25.5
%
Explanation:
E(r
c
)
=
r
f
+
E(r
p
)
−
r(f) σ
C
÷
σ
P
σ
P
= 30 =
y
×
σ
= 40 ×
y
y
= 0.75
E(r
P
)
= 12 + 0.75(30 − 12) = 25.5%
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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The correlation coefficients between several pairs of stocks are as follows: Corr(
A
,
B
) = 0.85; Corr(
A
,
C
) = 0.60; Corr(
A
,
D
) = 0.45. Each stock has an expected return of 8% and a standard deviation of 20%.
If your entire portfolio is now composed of stock
A
and you can add some of only one stock to your portfolio, would you choose:
If your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio, would you choose:
D
Explanation:
The correct choice is Stock D. Intuitively, we note that since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is the stock that has the lowest
correlation with Stock A.
More formally, we note that when all stocks have the same expected rate of return, the optimal portfolio for any risk-averse investor is the global minimum variance portfolio (G). When the portfolio is restricted to Stock A and one
additional stock, the objective is to find G for any pair that includes Stock A, and then select the combination with the lowest variance. With two stocks, I and J, the formula for the weights in G is:
Since all standard deviations are equal to 20%:
This intuitive result is an implication of a property of any efficient frontier, namely, that the covariances of the global minimum variance portfolio with all other assets on the frontier are identical and equal to its own variance.
(Otherwise, additional diversification would further reduce the variance.) In this case, the standard deviation of G(I, J) reduces to:
This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D. The optimal portfolio is equally invested in Stock A and Stock D, and the standard deviation is
17.03%.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
15.
Award:
10.00
points
Problems?
Adjust credit
for all students.
The correlation coefficients between several pairs of stocks are as follows: Corr(
A
,
B
) = 0.85; Corr(
A
,
C
) = 0.60; Corr(
A
,
D
) = 0.45. Each stock has an expected return of 8% and a standard deviation of 20%.
a.
If your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio, would you choose (assuming short sales are not allowed):
b.
Would your answer change for more risk-averse or risk-tolerant investors?
Required A
Required B
Complete this question by entering your answers in the tabs below.
If your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio, would you
choose (assuming short sales are not allowed):
Required A
Required B
If your entire portfolio is now composed of stock A and you can add some of only one
stock to your portfolio, would you choose
D
Explanation:
a.
The correct choice is Stock D. Intuitively, we note that since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is the stock that has the lowest
correlation with Stock A.
More formally, we note that when all stocks have the same expected rate of return, the optimal portfolio for any risk-averse investor is the global minimum variance portfolio (G). When the portfolio is restricted to Stock A and
one additional stock, the objective is to find G for any pair that includes Stock A, and then select the combination with the lowest variance. With two stocks, I and J, the formula for the weights in G is:
Since all standard deviations are equal to 20%:
This intuitive result is an implication of a property of any efficient frontier, namely, that the covariances of the global minimum variance portfolio with all other assets on the frontier are identical and equal to its own variance.
(Otherwise, additional diversification would further reduce the variance.) In this case, the standard deviation of G(I, J) reduces to:
This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D. The optimal portfolio is equally invested in Stock A and Stock D, and the standard
deviation is 17.03%.
b.
No, at least if investors are not risk lovers. Risk neutral investors would not care which portfolio they held since all portfolios have an expected return of 8%.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
15.
Award:
10.00
points
Problems?
Adjust credit
for all students.
The correlation coefficients between several pairs of stocks are as follows: Corr(
A
,
B
) = 0.85; Corr(
A
,
C
) = 0.60; Corr(
A
,
D
) = 0.45. Each stock has an expected return of 8% and a standard deviation of 20%.
a.
If your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio, would you choose (assuming short sales are not allowed):
b.
Would your answer change for more risk-averse or risk-tolerant investors?
Required A
Required B
Complete this question by entering your answers in the tabs below.
Would your answer change for more risk-averse or risk-tolerant investors?
Required A
Required B
Would your answer change for more risk-averse or risk-tolerant investors?
No
Explanation:
a.
The correct choice is Stock D. Intuitively, we note that since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in lowest risk. This is the stock that has the lowest
correlation with Stock A.
More formally, we note that when all stocks have the same expected rate of return, the optimal portfolio for any risk-averse investor is the global minimum variance portfolio (G). When the portfolio is restricted to Stock A and
one additional stock, the objective is to find G for any pair that includes Stock A, and then select the combination with the lowest variance. With two stocks, I and J, the formula for the weights in G is:
Since all standard deviations are equal to 20%:
This intuitive result is an implication of a property of any efficient frontier, namely, that the covariances of the global minimum variance portfolio with all other assets on the frontier are identical and equal to its own variance.
(Otherwise, additional diversification would further reduce the variance.) In this case, the standard deviation of G(I, J) reduces to:
This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D. The optimal portfolio is equally invested in Stock A and Stock D, and the standard
deviation is 17.03%.
b.
No, at least if investors are not risk lovers. Risk neutral investors would not care which portfolio they held since all portfolios have an expected return of 8%.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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for all students.
The correlation coefficients between several pairs of stocks are as follows: Corr(A, B) = 0.85; Corr(A, C) = 0.60; Corr(A, D) = 0.45. Each stock has an expected return of 8% and a standard deviation of 20%.
Your entire portfolio is now composed of stock A and you can add some of only one stock to your portfolio. Suppose that in addition to investing in one more stock you can invest in T-bills as well. If the T-bill rate is 8%, would you
choose:
If the T-bill rate is 8%, would you choose:
T-bill
Explanation:
The efficient frontier of risky assets is horizontal at 8%, so the optimal CAL runs from the risk-free rate through G. This implies risk-averse investors will just hold Treasury bills.
Worksheet
Difficulty: 2 Intermediate
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
17.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Compute the estimated annual risk premiums, standard deviations, and Sharpe ratios for the two portfolios.
Note: Do not round your intermediate calculations. Round "Sharpe ratios" to 4 decimal places and other answers to 2 decimal places.
S&P Portfolio
Hedge Fund
Portfolio
Risk premiums
0.05
0.10
Standard deviations
0.20
0.35
Sharpe ratios
0.2500
0.2857
Explanation:
The risk premium for the S&P portfolio is: (1 + 0.05)
1
− 1 = 0.05
The 3-year risk premium for the hedge fund portfolio is (1 + 0.1)
1
− 1 = 0.1
The S&P 3-year standard deviation is:
0.2 ×
= 0.20
The hedge fund 3-year standard deviation is:
0.35 ×
= 0.35
S&P Sharpe ratio : 0.05 ÷ 0.20 = 0.2500
Hedge fund Sharpe ratio : 0.10 ÷ 0.35 = 0.2857
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
18.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Required:
a-1.
Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation?
a-2.
What is the expected risk premium on the portfolio?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset
allocation?
Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.
Req A1
Req A2
S&P
0.6049
Hedge
0.3951
Explanation:
The risk premium for the S&P portfolio is: (1 + 0.5)
1
− 1 = 0.05
The 3-year risk premium for the hedge fund portfolio is (1 + 1)
1
− 1 = 0.1
The S&P 3-year standard deviation is:
0.2 ×
= 0.20.
The hedge fund 3-year standard deviation is:
0.35 ×
= 0.35
S&P Sharpe ratio: 0.05 ÷ 0.20 = 0.2500
Hedge fund Sharpe ratio: 0.10 ÷ 0.35 = 0.2857.
a-1.
With a ρ = 0, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 (0 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0 × 20 × 35)) = 0.6049
W
Hedge
= 1 − 0.6049 = 0.3951
a-2.
With these weights,
E(r
p
)
= 0.6049 × 5% + 0.3951 × 10% = 0.0698 = 6.98%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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18.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Required:
a-1.
Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation?
a-2.
What is the expected risk premium on the portfolio?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
What is the expected risk premium on the portfolio?
Note: Do not round intermediate calculations. Enter your answer as decimals rounded to 4 places.
Req A1
Req A2
Expected risk premium
0.0698
Explanation:
The risk premium for the S&P portfolio is: (1 + 0.5)
1
− 1 = 0.05
The 3-year risk premium for the hedge fund portfolio is (1 + 1)
1
− 1 = 0.1
The S&P 3-year standard deviation is:
0.2 ×
= 0.20.
The hedge fund 3-year standard deviation is:
0.35 ×
= 0.35
S&P Sharpe ratio: 0.05 ÷ 0.20 = 0.2500
Hedge fund Sharpe ratio: 0.10 ÷ 0.35 = 0.2857.
a-1.
With a ρ = 0, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 (0 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0 × 20 × 35)) = 0.6049
W
Hedge
= 1 − 0.6049 = 0.3951
a-2.
With these weights,
E(r
p
)
= 0.6049 × 5% + 0.3951 × 10% = 0.0698 = 6.98%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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19.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
What should be Greta’s capital allocation?
Note: Do not round your intermediate calculations. Round your answers to 2 decimal places.
S&P
41.67
%
Hedge
27.21
%
Risk-free asset
31.12
%
Explanation:
With a ρ = 0, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 × (0 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0 × 20 × 35)) = 0.6049
W
Hedge
= 1 − 0.6049 = 0.3951
With these weights,
E(r
p
)
= 0.6049 × 5 + 0.3951 × 10 = 0.0698 = 6.9753%
Greta has a risk aversion of
A
= 3,
y =
0.06975 ÷ (3 ×
0.1837
2
) = 0.6888 = 68.88%
Therefore, she will invest of her wealth in this risky portfolio. The resulting investment composition will be S&P Fund: 0.6888 × 0.6049 = 41.67% and Hedge Fund: 0.6888 × 0.3951 = 27.21%. The remaining 31.12% will be
invested in the risk-free asset.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
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20.
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Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
If the correlation coefficient between annual portfolio returns is actually 0.3, what is the covariance between the returns?
Note: Round your answer to 3 decimal places.
Annual covariance
0.021
Explanation:
With ρ = 0.3, the annual covariance is 0.3 × 0.2 × 0.35 = 0.021.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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21.
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10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Required:
a-1.
Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation?
a-2.
What is the expected risk premium on the portfolio?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation?
Note: Do not round intermediate calculations. Enter your answers as decimals rounded to 4 places.
Req A1
Req A2
S&P
0.5771
Hedge
0.4229
Explanation:
a-1.
With a ρ = 0.3, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 × (0.3 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0.3 × 20 × 35)) = 0.5771
W
Hedge
= 1 − 0.5771 = 0.4229
a-2.
With these weights,
E(r
p
)
= 0.5771 × 5 + 0.4229 × 10 = 0.0711 = 7.11%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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21.
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10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Required:
a-1.
Assuming the correlation between the annual returns on the two portfolios is 0.3, what would be the optimal asset allocation?
a-2.
What is the expected risk premium on the portfolio?
Req A1
Req A2
Complete this question by entering your answers in the tabs below.
What is the expected risk premium on the portfolio?
Note: Do not round intermediate calculations. Enter your answers as a decimal rounded to 4 places.
Req A1
Req A2
Expected Risk Premium
0.0711
Explanation:
a-1.
With a ρ = 0.3, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 × (0.3 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0.3 × 20 × 35)) = 0.5771
W
Hedge
= 1 − 0.5771 = 0.4229
a-2.
With these weights,
E(r
p
)
= 0.5771 × 5 + 0.4229 × 10 = 0.0711 = 7.11%
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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22.
Award:
10.00
points
Problems?
Adjust credit
for all students.
Greta has risk aversion of A = 3 and a 1-year investment horizon. She is pondering two portfolios, the S&P 500 and a hedge fund, as well as a number of 1-year strategies. (All rates are annual and continuously compounded.)
The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The returns on both of these portfolios in any
particular year are uncorrelated with its own returns in other years. They are also uncorrelated with the returns of the other portfolio in other years. The hedge fund claims the correlation coefficient between the annual return on
the S&P 500 and the hedge fund return in the same year is zero, but Greta is not fully convinced by this claim.
Calculate Greta’s capital allocation using an annual correlation of 0.3.
Note: Do not round your intermediate calculations.
Round your answers to 2 decimal places.
S&P
30.09
%
Hedge
22.05
%
Risk-free asset
47.86
%
Explanation:
With a ρ = 0.3, the optimal asset allocation is
W
S&P
= (5 × 35
2
− 10 × (0.3 × 20 × 35)) ÷ (5 × 35
2
+ 10 × 20
2
− (5 + 10) × (0.3 × 20 × 35)) = 0.5771
W
Hedge
= 1 − 0.5771 = 0.4229
With these weights,
E(r
p
)
= 0.5771 × 5 + 0.4229 × 10 = 0.0711 = 7.1147%
Greta has a risk aversion of A = 3, Therefore, she will invest
y =
0.07115 ÷ (3 ×
0.2133
2
) = 0.5214 = 52.14%
of her wealth in this risky portfolio. The resulting investment composition will be S&P: 0.5214 × 0.5771 = 30.09% and Hedge: 0.5214 × 0.4229 = 22.05%. The remaining 47.86% will be invested in the risk-free asset.
Worksheet
Difficulty: 3 Challenge
Source: Investments (Bodie, 13e, ISBN 1266836322) > Chapter 07: Efficient Diversification > Chapter 07 Problems - Algorithmic & Static
References
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1.
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10.00 points
2.
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3.
Award:
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4.
Award:
10.00 points
Market risk is also referred to as:
systematic risk or diversifiable risk.
systematic risk or nondiversifiable risk.
unique risk or nondiversifiable risk.
unique risk or diversifiable risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
Systematic risk is also referred to as:
market risk or nondiversifiable risk.
market risk or diversifiable risk.
unique risk or nondiversifiable risk.
unique risk or diversifiable risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
Nondiversifiable risk is also referred to as:
systematic risk or unique risk.
systematic risk or market risk.
unique risk or market risk.
unique risk or firm-specific risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
Diversifiable risk is also referred to as:
systematic risk or unique risk.
systematic risk or market risk.
unique risk or market risk.
unique risk or firm-specific risk.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
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5.
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7.
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8.
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Unique risk is also referred to as:
systematic risk or diversifiable risk.
systematic risk or market risk.
diversifiable risk or market risk.
diversifiable risk or firm-specific risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
Firm-specific risk is also referred to as:
systematic risk or diversifiable risk.
systematic risk or market risk.
diversifiable risk or market risk.
diversifiable risk or unique risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
Nonsystematic risk is also referred to as:
market risk or diversifiable risk.
firm-specific risk or market risk.
diversifiable risk or market risk.
diversifiable risk or unique risk.
None of the options are correct.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
The risk that can be diversified away is:
firm-specific risk.
beta.
systematic risk.
market risk.
No risk can be diversified away.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
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The risk that cannot be diversified away is:
firm-specific risk.
unique.
nonsystematic risk.
market risk.
All risk can be diversified away.
Market, systematic, and nondiversifiable risk are synonyms referring to the risk that cannot be eliminated from the portfolio. Diversifiable, unique, nonsystematic, and firm-specific risks are synonyms referring to the risk that can be
eliminated from the portfolio by diversification.
References
Multiple Choice
Difficulty: 1 Basic
The variance of a portfolio of risky securities:
is a weighted sum of the securities' variances.
is the sum of the securities' variances.
is the weighted sum of the securities' variances and covariances.
is the sum of the securities' covariances.
None of the options are correct.
The variance of a portfolio of risky securities is a weighted sum taking into account both the variance of the individual securities and the covariances between securities.
References
Multiple Choice
Difficulty: 2 Intermediate
The standard deviation of a portfolio of risky securities is:
the square root of the weighted sum of the securities' variances.
the square root of the sum of the securities' variances.
the square root of the weighted sum of the securities' variances and covariances.
the square root of the sum of the securities' covariances.
None of the options are correct.
The standard deviation is the square root of the variance which is a weighted sum of the variance of the individual securities and the covariances between securities.
References
Multiple Choice
Difficulty: 2 Intermediate
The expected return of a portfolio of risky securities:
is a weighted average of the securities' returns.
is the sum of the securities' returns.
is the weighted sum of the securities' variances and covariances.
is a weighted average of the securities' returns and the weighted sum of the securities' variances and covariances.
None of the options are correct.
The expected return of a portfolio of risky securities is a weighted average of the securities' returns.
References
Multiple Choice
Difficulty: 1 Basic
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Other things equal, diversification is most effective when:
securities' returns are uncorrelated.
securities' returns are positively correlated.
securities' returns are high.
securities' returns are negatively correlated.
securities' returns are positively correlated and high.
Negative correlation among securities results in the greatest reduction of portfolio risk, which is the goal of diversification.
References
Multiple Choice
Difficulty: 2 Intermediate
The efficient frontier of risky assets is:
the portion of the minimum-variance portfolio that lies above the global minimum variance portfolio.
the portion of the minimum-variance portfolio that represents the highest standard deviations.
the portion of the minimum-variance portfolio that includes the portfolios with the lowest standard deviation.
the set of portfolios that have zero standard deviation.
Indeterminable
Portfolios on the efficient frontier are those providing the greatest expected return for a given amount of risk. Only those portfolios above the global minimum variance portfolio meet this criterion.
References
Multiple Choice
Difficulty: 2 Intermediate
The capital allocation line provided by a risk-free security and
N
risky securities is:
the line that connects the risk-free rate and the global minimum-variance portfolio of the risky securities.
the line that connects the risk-free rate and the portfolio of the risky securities that has the highest expected return on the efficient frontier.
the line tangent to the efficient frontier of risky securities drawn from the risk-free rate.
the horizontal line drawn from the risk-free rate.
the vertical line drawn from the risk-free rate.
The capital allocation line represents the most efficient combinations of the risk-free asset and risky securities. Only "the line tangent to the efficient frontier of risky securities drawn from the risk-free rate." meets that definition.
References
Multiple Choice
Difficulty: 2 Intermediate
Consider an investment opportunity set formed with two securities that are perfectly negatively correlated. The global-minimum variance portfolio has a standard deviation that is always:
greater than zero.
equal to zero.
equal to the sum of the securities' standard deviations.
equal to 1.
equal to
−
1.
If two securities were perfectly negatively correlated, the weights for the minimum variance portfolio for those securities could be calculated, and the standard deviation of the resulting portfolio would be zero.
References
Multiple Choice
Difficulty: 3 Challenge
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Which of the following statement(s) is(are)
true
regarding the variance of a portfolio of two risky securities?
I. The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II. There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
III. The degree to which the portfolio variance is reduced depends on the degree of correlation between securities.
I only
II only
III only
I and II
I and III
The lower the correlation between the returns of the securities, the more portfolio risk is reduced.
References
Multiple Choice
Difficulty: 2 Intermediate
Which of the following statement(s) is(are)
false
regarding the variance of a portfolio of two risky securities?
I. The higher the coefficient of correlation between securities, the greater the reduction in the portfolio variance.
II. There is a linear relationship between the securities' coefficient of correlation and the portfolio variance.
III. The degree to which the portfolio variance is reduced inversely depends on the degree of correlation between securities.
I only
II only
III only
I and II
I and III
The lower the correlation between the returns of the securities, the more portfolio risk is reduced.
References
Multiple Choice
Difficulty: 2 Intermediate
Efficient portfolios of
N
risky securities are portfolios that:
are formed with the securities that have the highest rates of return regardless of their standard deviations.
have the highest rates of return for a given level of risk.
are selected from those securities with the lowest standard deviations regardless of their returns.
have the highest risk and rates of return and the highest standard deviations.
have the lowest standard deviations and the lowest rates of return.
Portfolios that are efficient are those that provide the highest expected return for a given level of risk.
References
Multiple Choice
Difficulty: 2 Intermediate
Which of the following statement(s) is(are)
true
regarding the selection of a portfolio from those that lie on the capital allocation line?
I. Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.
II. More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.
III. Investors choose the portfolio that maximizes their expected utility.
I only
II only
III only
I and III
II and III
All rational investors select the portfolio that maximizes their expected utility; for investors who are relatively more risk-averse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset.
References
Multiple Choice
Difficulty: 2 Intermediate
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22.
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23.
Award:
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Which of the following statement(s) is(are)
false
regarding the selection of a portfolio from those that lie on the capital allocation line?
I. Less risk-averse investors will invest more in the risk-free security and less in the optimal risky portfolio than more risk-averse investors.
II. More risk-averse investors will invest less in the optimal risky portfolio and more in the risk-free security than less risk-averse investors.
III. Investors choose the portfolio that maximizes their expected utility.
I only
II only
III only
I and II
I and III
All rational investors select the portfolio that maximizes their expected utility; for investors who are relatively more risk-averse, doing so means investing less in the optimal risky portfolio and more in the risk-free asset.
References
Multiple Choice
Difficulty: 2 Intermediate
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The expected rates of return of stocks A and B are ______ and ______, respectively.
13.2%; 9.8%
14.0%; 10.7%
13.2%; 7.7%
7.7%; 13.2%
None of the options are correct.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
References
Multiple Choice
Difficulty: 1 Basic
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The standard deviations of stocks A and B are _____ and _____, respectively.
Note:Do not round intermediate calculations.
1.5%; 1.9%
2.5%; 1.1%
3.2%; 2.0%
1.5%; 1.1%
None of the options are correct.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
References
Multiple Choice
Difficulty: 2 Intermediate
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Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The variances of stocks A and B are _____ and ______, respectively.
Note: Do not round intermediate calculations.
0.015%; 0.019%
0.022%; 0.012%
0.032%; 0.02%
0.015%; 0.011%
None of the options are correct.
E
(
R
A
) = 0.1 × 10% + 0.2 × 13% + 0.2 × 12% + 0.3 × 14% + 0.2 × 15% = 0.132
E
(
R
B
) = 0.1 × 8% + 0.2 × 7% + 0.2 × 6% + 0.3 × 9% + 0.2 × 8% = 0.077
σ
2
A
= 0.1 × (10% − 0.132)
2
+ 0.2 × (13% − 0.132)
2
+ 0.2 × (12% − 0.132)
2
+ 0.3 × (14% − 0.132)
2
+ 0.2 × (15% − 0.132)
2
= 0.000216 = 0.0216%
σ
2
B
= 0.1 × (8% − 0.077)
2
+ 0.2 × (7% − 0.077)
2
+ 0.2 × (6% − 0.077)
2
+ 0.3 × (9% − 0.077)
2
+ 0.2 × (8% − 0.077)
2
= 0.000121 = 0.0121%
References
Multiple Choice
Difficulty: 2 Intermediate
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The coefficient of correlation between A and B is:
Note: Do not round intermediate calculations.
0.47.
0.60.
0.58.
1.20.
None of the options are correct.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
Cov(A,B
) = 0.1 × (10%
− 13.2%) × (8% − 7.7%) + 0.2 × (13% − 13.2%) × (7% − 7.7%) + 0.2 × (12% − 13.2%) × (6% − 7.7%) + 0.3 × (14% − 13.2%) × (9% − 7.7%) + 0.2 × (15% −
13.2%) × (8% − 7.7%)
= 0.0076%
ρ
A
,
B
=
0.0076%
1.1%
×
1.5%
= 0. 47.
References
Multiple Choice
Difficulty: 3 Challenge
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Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
If you invest 40% of your money in A and 60% in B, what would be your portfolio's expected rate of return and standard deviation?
Note: Do not round intermediate calculations.
9.9%; 3%
9.9%; 1.1%
11%; 1.1%
11%; 3%
None of the options are correct.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
cov(A,B)
= 0.1 × (10%
− 13.2%) × (8% − 7.7%) + 0.2 × (13% − 13.2%) × (7% − 7.7%) + 0.2 × (12% − 13.2%) × (6% − 7.7%) + 0.3 × (14% − 13.2%) × (9% − 7.7%) + 0.2 × (15% −
13.2%) × (8% − 7.7%)
= 0.0076%
ρ
A
,
B
=
0.0076%
1.1%
×
1.5%
= 0. 47
E
(
r
P
) =
w
A
E
(
R
A
) +
w
B
E(
R
B
) = 40% × (13.2%) + 60% × (7.7%) = 9.9%
P
= [0.4
2
(1.5%)
2
+ 0.6
2
(1.1%)
2
+ 2 × 0.4 × 0.6 × 0.0076%)]
0.5
= 1.1%.
References
Multiple Choice
Difficulty: 3 Challenge
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
Let G be the global minimum variance portfolio. The weights of A and B in G are __________ and __________, respectively.
Note: Do not round intermediate calculations.
0.40; 0.60
0.66; 0.34
0.34; 0.66
0.77; 0.23
0.24; 0.76
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
Cov(A,B)
= 0.1 × (10%
− 13.2%) × (8% − 7.7%) + 0.2 × (13% − 13.2%) × (7% − 7.7%) + 0.2 × (12% − 13.2%) × (6% − 7.7%) + 0.3 × (14% − 13.2%) × (9% − 7.7%) + 0.2 × (15% −
13.2%) × (8% − 7.7%)
= 0.0076%
w
A
=
σ
2
B
-
Cov
(
A
,
B
)
σ
2
A
+
σ
2
B
+
2
Cov
(
A
,
B
)
=
1.1%
2
-
0.0076%
1.5%
2
+
1.1%
2
-
2
×
0.0076%
= 0. 24
w
B
= 1 −
w
A
= 0.76
References
Multiple Choice
Difficulty: 3 Challenge
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Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
The expected rate of return and standard deviation of the global minimum variance portfolio, G, are __________ and __________, respectively.
Note: Do not round intermediate calculations.
10.07%; 1.05%
8.97%; 2.03%
10.07%; 3.01%
9.04%; 1.05%
None of the options are correct.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
cov(A,B)
= 0.1 × (10%
− 13.2%) × (8% − 7.7%) + 0.2 × (13% − 13.2%) × (7% − 7.7%) + 0.2 × (12% − 13.2%) × (6% − 7.7%) + 0.3 × (14% − 13.2%) × (9% − 7.7%) + 0.2 × (15% −
13.2%) × (8% − 7.7%)
= 0.0076%
w
A
=
α
2
B
-
Cov
(
A
,
B
)
σ
2
A
+
σ
2
B
+
2
Cov
(
A
,
B
)
=
1.1%
-
0.0076%
1.5%
+
1.1%
-2
×
0.0076
0. 24
w
B
= 1 −
w
A
= 0.76
E
(
r
G
) =
w
A
E
(R
A
) +
w
B
E
(
R
B
) = 0.24 × (0.132) + 0.76 × (0.077) = 9.038%
G
= [0.24
2
(1.5%)
2
+ 0.76
2
(1.1%)
2
+ 2 × 0.24 × 0.76 × 0.0076%]
0.5
= 1.05%.
References
Multiple Choice
Difficulty: 3 Challenge
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Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.10
10%
8%
2
0.20
13%
7%
3
0.20
12%
6%
4
0.30
14%
9%
5
0.20
15%
8%
Which of the following portfolio(s) is(are) on the efficient frontier?
Note: Do not round intermediate calculations.
The portfolio with 20 percent in A and 80 percent in B.
The portfolio with 15 percent in A and 85 percent in B.
The portfolio with 26 percent in A and 74 percent in B.
The portfolio with 10 percent in A and 90 percent in B.
A and B are both on the efficient frontier.
E
(
R
A
) = 0.1 × 0.10 + 0.2 × 0.13 + 0.2 × 0.12 + 0.3 × 0.14 + 0.2 × 0.15 = 0.132
E
(
R
B
) = 0.1 × 0.08 + 0.2 × 0.07 + 0.2 × 0.06 + 0.3 × 0.09 + 0.2 × 0.08 = 0.077
σ
A
= [0.1 × (10% − 13.2%)
2
+ 0.2 × (13% − 13.2%)
2
+ 0.2 × (12% − 13.2%)
2
+ 0.3 × (14% − 13.2%)
2
+ 0.2 × (15% − 13.2%)
2
]
0.5
= 1.5%
σ
B
= [0.1 × (8% − 7.7%)
2
+ 0.2 × (7% − 7.7%)
2
+ 0.2 × (6% − 7.7%)
2
+ 0.3 × (9% − 7.7%)
2
+ 0.2 × (8% − 7.7%)
2
]
0.5
= 1.1%.
Cov(A,B
) = 0.1 × (10%
− 13.2%) × (8% − 7.7%) + 0.2 × (13% − 13.2%) × (7% − 7.7%) + 0.2 × (12% − 13.2%) × (6% − 7.7%) + 0.3 × (14% − 13.2%) × (9% − 7.7%) + 0.2 × (15% −
13.2%) × (8% − 7.7%)
= 0.0076%
E
(
r
p
) =
w
A
E
(
R
A
) +
w
B
E
(
R
B
) =
w
A
× (13.2%) +
w
B
× (7.7%)
σ
p
=
w
2
A
(1. 5 % )
2
+
w
2
B
(1. 1 % )
2
+ 2 ×
w
A
×
w
B
× 0. 0076 %
0.5
The Portfolio's Reward/volatility ratios are:
20A ÷ 80B: 8.80% ÷ 1.05% = 8.38;
15A ÷ 85B: 8.53% ÷ 1.06% = 8.07;
26A ÷ 74B: 9.13% ÷ 1.05% = 8.70;
10A ÷ 90B: 8.25% ÷ 1.07% = 7.73.
The portfolio with 26% in A and 74% in B dominates all the other portfolios by the mean-variance criterion.
References
Multiple Choice
Difficulty: 3 Challenge
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
The weights of A and B in the global minimum variance portfolio are _____ and _____, respectively.
0.24; 0.76
0.50; 0.50
0.57; 0.43
0.43; 0.57
0.76; 0.24
w
A
=
σ
B
σ
A
+
σ
B
=
0.12
0.16
+
0.12
= 0. 43
w
B
= 1 −
w
A
= 0.57.
References
Multiple Choice
Difficulty: 2 Intermediate
[
]
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Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 10% and a standard deviation of 16%. B has an expected rate of return of 8% and a standard deviation of 12%.
The risk-free portfolio that can be formed with the two securities will earn a(n) _____ rate of return.
8.5%
9.0%
8.9%
9.9%
None of the options are correct.
w
A
=
σ
B
σ
A
+
σ
B
=
0.12
0.16
+
0.12
= 0. 4286
w
B
= 1
−
w
A
= 0.5714
E
(
r
P
) = 0.4286 × 10 + 0.5714 × 0.08 = 0.0886 or 8.9%.
References
Multiple Choice
Difficulty: 3 Challenge
Given an optimal risky portfolio with expected return of 6%, standard deviation of 23%, and a risk-free rate of 3%, what is the slope of the best feasible CAL?
0.64
0.39
0.08
0.13
0.36
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.06
-
0.03
0.23
= 0. 13
References
Multiple Choice
Difficulty: 2 Intermediate
An investor who wishes to form a portfolio that lies to the right of the optimal risky portfolio on the capital allocation line must:
lend some of the money at the risk-free rate.
borrow some money at the risk-free rate and invest in the optimal riskless portfolio.
invest only in risk-free securities.
borrow some money at the risk-free rate, invest in the optimal risky portfolio, and invest only in risky securities
Such a portfolio cannot be formed.
The only way that an investor can create a portfolio that lies to the right of the capital allocation line is to create a borrowing portfolio (buy stocks on margin). In this case, the investor will not hold any of the risk-free security, but will
hold only risky securities.
References
Multiple Choice
Difficulty: 2 Intermediate
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Which one of the following portfolios
cannot lie
on the efficient frontier as described by Markowitz?
Portfolio
Expected Return
Standard Deviation
W
9%
21%
X
5%
7%
Y
15%
36%
Z
12%
15%
Only portfolio W cannot lie on the efficient frontier.
Only portfolio X cannot lie on the efficient frontier.
Only portfolio Y cannot lie on the efficient frontier.
Only portfolio Z cannot lie on the efficient frontier.
Cannot be determined from the information given.
When plotting the above portfolios, only W lies below the efficient frontier as described by Markowitz. It has a higher standard deviation than Z with a lower expected return.
References
Multiple Choice
Difficulty: 2 Intermediate
Which of the following portfolios
can lie
on the efficient frontier as described by Markowitz?
Portfolio
Expected Return
Standard Deviation
W
9%
21%
X
5%
7%
Y
15%
36%
Z
12%
15%
Only portfolio W, X, and Y can lie on the efficient frontier.
Only portfolio W, X, and Z can lie on the efficient frontier.
Only portfolio W, Y, and Z can lie on the efficient frontier.
Only portfolio X, Y, and Z can lie on the efficient frontier.
Cannot be determined from the information given.
When plotting the above portfolios, only W lies below the efficient frontier as described by Markowitz. It has a higher standard deviation than Z with a lower expected return.
References
Multiple Choice
Difficulty: 2 Intermediate
Portfolio theory as described by Markowitz is most concerned with:
the elimination of systematic risk.
the effect of diversification on portfolio risk.
the identification of unsystematic risk.
active portfolio management to enhance returns.
None of the options are correct.
Markowitz was concerned with reducing portfolio risk by combining risky securities with differing return patterns.
References
Multiple Choice
Difficulty: 2 Intermediate
The measure of risk in a Markowitz efficient frontier is:
specific risk.
standard deviation of returns.
reinvestment risk.
beta.
None of the options are correct.
Markowitz was interested in eliminating diversifiable risk (and thus lessening total risk) and thus was interested in decreasing the standard deviation of the returns of the portfolio.
References
Multiple Choice
Difficulty: 2 Intermediate
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A statistic that measures how the returns of two risky assets move together is:
variance.
standard deviation.
covariance.
correlation.
Both covariance and correlation measure this.
Covariance measures whether security returns move together or in opposition; however, only the sign, not the magnitude, of covariance may be interpreted. Correlation, which is covariance standardized by the product of the
standard deviations of the two securities, may assume values only between +1 and
−
1; thus, both the sign and the magnitude may be interpreted regarding the movement of one security's return relative to that of another security.
References
Multiple Choice
Difficulty: 2 Intermediate
The unsystematic risk of a specific security:
is likely to be higher in an increasing market.
results from factors unique to the firm.
depends on market volatility.
cannot be diversified away.
All of the options are correct.
Unsystematic (or diversifiable or firm-specific) risk refers to factors unique to the firm. Such risk may be diversified away; however, market risk will remain.
References
Multiple Choice
Difficulty: 2 Intermediate
Which statement about portfolio diversification is correct?
Proper diversification can eliminate systematic risk.
The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities have been purchased.
Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.
Typically, as more securities are added to a portfolio, total risk would be expected to decrease at a decreasing rate.
None of the statements are correct.
Diversification can eliminate only nonsystematic risk; relatively few securities are required to reduce this risk, thus diminishing returns result quickly.
References
Multiple Choice
Difficulty: 2 Intermediate
The individual investor's optimal portfolio is designated by:
the point of tangency with the indifference curve and the capital allocation line.
the point of highest reward to variability ratio in the opportunity set.
the point of tangency with the opportunity set and the capital allocation line.
the point of the highest reward to variability ratio in the indifference curve.
None of the options are correct.
The indifference curve represents what is acceptable to the investor; the capital allocation line represents what is available in the market. The point of tangency represents where the investor can obtain the greatest utility from
what is available.
References
Multiple Choice
Difficulty: 2 Intermediate
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For a two-stock portfolio, what would be the preferred correlation coefficient between the two stocks?
+1.00
+0.50
0.00
−
1.00
None of the options are correct.
The correlation coefficient of
−
1.00 provides the greatest diversification benefits.
References
Multiple Choice
Difficulty: 2 Intermediate
In a two-security minimum variance portfolio where the correlation between securities is greater than
−
1.0,
the security with the higher standard deviation will be weighted more heavily.
the security with the higher standard deviation will be weighted less heavily.
the two securities will be equally weighted.
the risk will be zero.
the return will be zero.
The security with the higher standard deviation will be weighted less heavily to produce minimum variance. The return will not be zero; the risk will not be zero unless the correlation coefficient is
−
1.
References
Multiple Choice
Difficulty: 3 Challenge
Which of the following is
not
a source of systematic risk?
The business cycle
Interest rates
Personnel changes
The inflation rate
Exchange rates
Personnel changes are a firm-specific event that is a component of nonsystematic risk. The others are all sources of systematic risk.
References
Multiple Choice
Difficulty: 1 Basic
The global minimum variance portfolio formed from two risky securities will be riskless when the correlation coefficient between the two securities is:
0.0.
1.0.
0.5.
−
1.0.
any negative number.
The global minimum variance portfolio will have a standard deviation of zero whenever the two securities are perfectly negatively correlated.
References
Multiple Choice
Difficulty: 2 Intermediate
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Security X has expected return of 12% and standard deviation of 18%. Security Y has expected return of 15% and standard deviation of 26%. If the two securities have a correlation coefficient of 0.7, what is their covariance?
0.038
0.070
0.018
0.033
0.054
Cov(
r
X
,
r
Y
) = 0.7 × 0.18 × 0.26 = 0.033
References
Multiple Choice
Difficulty: 2 Intermediate
When two risky securities that are positively correlated but not perfectly correlated are held in a portfolio,
Note: Do not round intermediate calculations.
the portfolio standard deviation will be greater than the weighted average of the individual security standard deviations.
the portfolio standard deviation will be less than the weighted average of the individual security standard deviations.
the portfolio standard deviation will be equal to the weighted average of the individual security standard deviations.
the portfolio standard deviation will always be equal to the securities' covariance.
None of the options are correct.
Whenever two securities are less than perfectly positively correlated, the standard deviation of the portfolio of the two assets will be less than the weighted average of the two securities' standard deviations. There is some benefit
to diversification in this case.
References
Multiple Choice
Difficulty: 2 Intermediate
The line representing all combinations of portfolio expected returns and standard deviations that can be constructed from two available assets is called the:
risk/reward tradeoff line.
capital allocation line.
efficient frontier.
portfolio opportunity set.
Security Market Line.
The portfolio opportunity set is the line describing all combinations of expected returns and standard deviations that can be achieved by a portfolio of risky assets.
References
Multiple Choice
Difficulty: 1 Basic
Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk-free rate of 5%, what is the slope of the best feasible CAL?
0.64
0.27
0.08
0.33
0.36
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.12
-
0.05
0.26
= 0. 27
References
Multiple Choice
Difficulty: 2 Intermediate
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Given an optimal risky portfolio with expected return of 20%, standard deviation of 24%, and a risk-free rate of 7%, what is the slope of the best feasible CAL?
0.64
0.14
0.62
0.33
0.54
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.20
-
0.07
0.24
= 0. 54
References
Multiple Choice
Difficulty: 2 Intermediate
The risk that can be diversified away in a portfolio is referred to as ___________.
I. diversifiable risk
II. unique risk
III. systematic risk
IV. firm-specific risk
I, III, and IV
II, III, and IV
III and IV
I, II, and IV
I, II, III, and IV
Diversifiable risk, unique risk, and firm-specific risk are terms used interchangeably to refer to the risk that can be removed from a portfolio through diversification.
References
Multiple Choice
Difficulty: 2 Intermediate
As the number of securities in a portfolio is increased, what happens to the average portfolio standard deviation?
It increases at an increasing rate.
It increases at a decreasing rate.
It decreases at an increasing rate.
It decreases at a decreasing rate.
It first decreases, then starts to increase as more securities are added.
Statman's study showed that the risk of the portfolio would decrease as random stocks were added. At first the risk decreases quickly, but then the rate of decrease slows substantially. The minimum portfolio risk in the updated
(through 2017) study was 17.4%.
References
Multiple Choice
Difficulty: 2 Intermediate
In words, the covariance considers the probability of each scenario happening and the interaction between:
securities' returns relative to their variances.
securities' returns relative to their mean returns.
securities' returns relative to other securities' returns.
the level of return a security has in that scenario and the overall portfolio return.
the variance of the security's return in that scenario and the overall portfolio variance.
The covariance of the returns between two securities is the sum over all scenarios of the product of three things. The first item is the probability that the scenario will happen. The second and third terms represent the deviations of
the securities' returns in that scenario from their own expected returns.
References
Multiple Choice
Difficulty: 3 Challenge
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The standard deviation of a two-asset portfolio is a linear function of the assets' weights when:
the assets have a correlation coefficient less than zero.
the assets have a correlation coefficient equal to zero.
the assets have a correlation coefficient greater than zero.
the assets have a correlation coefficient equal to one.
the assets have a correlation coefficient less than one.
When there is a perfect positive correlation (or a perfect negative correlation), the equation for the portfolio variance simplifies to a perfect square. The result is that the portfolio's standard deviation is linear relative to the assets'
weights in the portfolio.
References
Multiple Choice
Difficulty: 2 Intermediate
A two-asset portfolio with a standard deviation of zero can be formed when:
the assets have a correlation coefficient less than zero.
the assets have a correlation coefficient equal to zero.
the assets have a correlation coefficient greater than zero.
the assets have a correlation coefficient equal to one.
the assets have a correlation coefficient equal to negative one.
When there is a perfect negative correlation, the equation for the portfolio variance simplifies to a perfect square. The solution
w
A
=
B
÷ (
A
+
B
)
and
w
B
= (1 −
w
A
)
will yield a zero-standard deviation portfolio.
References
Multiple Choice
Difficulty: 2 Intermediate
When borrowing and lending at a risk-free rate are allowed, which capital allocation line (CAL) should the investor choose to combine with the efficient frontier?
I. The one with the highest reward-to-variability ratio.
II. The one that will maximize his utility.
III. The one with the steepest slope.
IV. The one with the lowest slope.
I and III
I and IV
II and IV
I only
I, II, and III
The optimal CAL is the one that is tangent to the efficient frontier. This CAL offers the highest reward-to-variability ratio, which is the slope of the CAL. It will also allow the investor to reach his highest feasible level of utility.
References
Multiple Choice
Difficulty: 3 Challenge
Given an optimal risky portfolio with expected return of 13%, standard deviation of 26%, and a risk free rate of 5%, what is the slope of the best feasible CAL?
0.60
0.14
0.08
0.36
0.31
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.13
-
0.05
0.26
= 0. 31
References
Multiple Choice
Difficulty: 2 Intermediate
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The separation property refers to the conclusion that:
the determination of the best risky portfolio is objective, and the choice of the best complete portfolio is subjective.
the choice of the best complete portfolio is objective, and the determination of the best risky portfolio is objective.
the choice of inputs to be used to determine the efficient frontier is objective, and the choice of the best CAL is subjective.
the determination of the best CAL is objective, and the choice of the inputs to be used to determine the efficient frontier is subjective.
investors are separate beings and will, therefore, have different preferences regarding the risk-return tradeoff.
The determination of the optimal risky portfolio is purely technical and can be done by a manager. The complete portfolio, which consists of the optimal risky portfolio and the risk-free asset, must be chosen by each investor based
on preferences.
References
Multiple Choice
Difficulty: 3 Challenge
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.15
8%
8%
2
0.20
13%
7%
3
0.15
12%
6%
4
0.30
14%
9%
5
0.20
16%
11%
The expected rates of return of stocks A and B are _____ and _____, respectively.
13.2%; 9%
13.0%; 8.4%
13.2%; 7.7%
7.7%; 13.2%
None of the options are correct.
E
(
R
A
) = 0.15 × 0.08 + 0.2 × 0.13 + 0.15 × 0.12 + 0.3 × 0.14 + 0.2 × 0.16 = 0.130
E
(
R
B
) = 0.15 × 0.08 + 0.2 × 0.07 + 0.15 × 0.06 + 0.3 × 0.09 + 0.2 × 0.11 = 0.084
References
Multiple Choice
Difficulty: 1 Basic
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.15
8%
8%
2
0.20
13%
7%
3
0.15
12%
6%
4
0.30
14%
9%
5
0.20
16%
11%
The standard deviations of stocks A and B are _____ and _____, respectively.
Note: Do not round intermediate calculations.
1.56%; 1.99%
2.45%; 1.66%
3.22%; 2.01%
1.54%; 1.11%
E
(
R
A
) = 0.15 × 0.08 + 0.2 × 0.13 + 0.15 × 0.12 + 0.3 × 0.14 + 0.2 × 0.16 = 0.130
E
(
R
B
) = 0.15 × 0.08 + 0.2 × 0.07 + 0.15 × 0.06 + 0.3 × 0.09 + 0.2 × 0.11 = 0.084
σ
A
= [0.15 × (8% − 13%)
2
+ 0.2 × (13% − 13%)
2
+ 0.15 × (12% − 13%)
2
+ 0.3 × (14% − 13%)
2
+ 0.2 × (16% − 13%)
2
]
0.5
= 2.45%
σ
B
= [0.15 × (8% − 8.4%)
2
+ 0.2 × (7% − 8.4%)
2
+ 0.15 × (6% − 8.4%)
2
+ 0.3 × (9% − 8.4%)
2
+ 0.2 × (11% − 8.4%)
2
]
0.5
= 1.66%.
References
Multiple Choice
Difficulty: 2 Intermediate
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Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.15
8%
8%
2
0.20
13%
7%
3
0.15
12%
6%
4
0.30
14%
9%
5
0.20
16%
11%
The coefficient of correlation between
A
and
B
is:
Note: Do not round intermediate calculations.
0.47.
0.61.
0.59.
1.21.
None of the options are correct.
E
(
R
A
) = 0.15 × 0.08 + 0.2 × 0.13 + 0.15 × 0.12 + 0.3 × 0.14 + 0.2 × 0.16 = 0.130
E
(
R
B
) = 0.15 × 0.08 + 0.2 × 0.07 + 0.15 × 0.06 + 0.3 × 0.09 + 0.2 × 0.11 = 0.084
σ
A
= [0.15 × (8% − 13%)
2
+ 0.2 × (13% − 13%)
2
+ 0.15 × (12% − 13%)
2
+ 0.3 × (14% − 13%)
2
+ 0.2 × (16% − 13%)
2
]
0.5
= 2.45%
σ
B
= [0.15 × (8% − 8.4%)
2
+ 0.2 × (7% − 8.4%)
2
+ 0.15 × (6% − 8.4%)
2
+ 0.3 × (9% − 8.4%)
2
+ 0.2 × (11% − 8.4%)
2
]
0.5
= 1.66%.
cov(A,B)
= 0.15 × (8% − 13%) × (8% − 8.4%) + 0.2 × (13% − 13%) × (7% − 8.4%) + 0.15 × (12% − 13%) × (6% − 8.4%) + 0.3 × (14% − 13%) × (9% − 8.4%) + 0.2 × (16% − 13%) ×
(11% − 8.4%)
= 0.024%
ρ
A
,
B
=
0.024%
2.45%
×
1.66%
= 0. 59.
References
Multiple Choice
Difficulty: 3 Challenge
Consider the following probability distribution for stocks A and B:
State
Probability
Return on Stock A
Return on Stock B
1
0.15
8%
8%
2
0.20
13%
7%
3
0.15
12%
6%
4
0.30
14%
9%
5
0.20
16%
11%
If you invest 35% of your money in A and 65% in B, what would be your portfolio's expected rate of return and standard deviation?
Note: Do not round intermediate calculations.
9.9%; 3%
9.9%; 1.1%
10%; 1.7%
10%; 3%
None of the options are correct.
E
(
R
A
) = 0.15 × 0.08 + 0.2 × 0.13 + 0.15 × 0.12 + 0.3 × 0.14 + 0.2 × 0.16 = 0.130
E
(
R
B
) = 0.15 × 0.08 + 0.2 × 0.07 + 0.15 × 0.06 + 0.3 × 0.09 + 0.2 × 0.11 = 0.084
σ
A
= [0.15 × (8% − 13%)
2
+ 0.2 × (13% − 13%)
2
+ 0.15 × (12% − 13%)
2
+ 0.3 × (14% − 13%)
2
+ 0.2 × (16% − 13%)
2
]
0.5
= 2.45%
σ
B
= [0.15 × (8% − 8.4%)
2
+ 0.2 × (7% − 8.4%)
2
+ 0.15 × (6% − 8.4%)
2
+ 0.3 × (9% − 8.4%)
2
+ 0.2 × (11% − 8.4%)
2
]
0.5
= 1.66%.
cov(A,B)
= 0.15 × (8% − 13%) × (8% − 8.4%) + 0.2 × (13% − 13%) × (7% − 8.4%) + 0.15 × (12% − 13%) × (6% − 8.4%) + 0.3 × (14% − 13%) × (9% − 8.4%) + 0.2 × (16% − 13%) ×
(11% − 8.4%)
= 0.024%
A,B
= 0.024% ÷ (2.45% × 1.66%) = 0.59
E
(
r
P
) =
w
A
E
(
R
A
) +
w
B
E
(
R
B
) = 0.35 × (13%) + 0.65 × (8.4%) = 10.0%
σ
P
= [(0.35)
2
(2.45%)
2
+ (0.65)
2
(1.66%)
2
+ 2 × 0.35 × 0.65 × 2.45% × 1.66% × 0.59]
0.5
= 1.7%.
References
Multiple Choice
Difficulty: 3 Challenge
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64.
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65.
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Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The weights of A and B in the global minimum variance portfolio are _____ and _____, respectively.
0.24; 0.76
0.50; 0.50
0.57; 0.43
0.45; 0.55
0.76; 0.24
w
A
=
σ
B
σ
A
+
σ
B
=
0.14
0.17
+
0.14
= 0. 45
w
B
= 1 −
w
A
= 0.55.
References
Multiple Choice
Difficulty: 2 Intermediate
Consider two perfectly negatively correlated risky securities A and B. A has an expected rate of return of 12% and a standard deviation of 17%. B has an expected rate of return of 9% and a standard deviation of 14%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
Note: Do not round intermediate calculations.
9.55%
10.35%
10.95%
9.90%
None of the options are correct.
w
A
=
σ
B
σ
A
+
σ
B
=
0.14
0.17
+
0.14
= 0. 4516
w
B
= 1 −
w
A
= 0.5484.
E
(
r
P
) = 0.4516 × 12% + 0.5484 × 9% = 10.35%.
References
Multiple Choice
Difficulty: 3 Challenge
Security X has expected return of 14% and standard deviation of 22%. Security Y has expected return of 16% and standard deviation of 28%. If the two securities have a correlation coefficient of 0.8, what is their covariance?
0.038
0.049
0.018
0.013
0.054
Cov
(
X,Y
) = 0.8 × 22% × 28% = 0.049.
References
Multiple Choice
Difficulty: 2 Intermediate
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67.
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68.
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Given an optimal risky portfolio with expected return of 16%, standard deviation of 20%, and a risk-free rate of 4%, what is the slope of the best feasible CAL?
0.60
0.14
0.08
0.36
0.31
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.16
-
0.04
0.20
= 0. 60
References
Multiple Choice
Difficulty: 2 Intermediate
Given an optimal risky portfolio with expected return of 12%, standard deviation of 26%, and a risk-free rate of 3%, what is the slope of the best feasible CAL?
0.64
0.14
0.08
0.35
0.36
Slope
=
SR
=
r
risky
-
r
f
σ
risky
=
0.12
-
0.03
0.26
= 0. 35
References
Multiple Choice
Difficulty: 2 Intermediate
Consider the following probability distribution for stocks C and D:
State
Probability
Return on Stock C
Return on Stock D
1
0.30
7%
−
9%
2
0.50
11%
14%
3
0.20
−
16%
26%
The expected rates of return of stocks C and D are _____ and _____, respectively.
4.4%; 9.5%
9.5%; 4.4%
6.3%; 8.7%
8.7%; 6.2%
None of the options are correct.
E
(
r
C
) = 0.3 × 7% + 0.5 × 11% + 0.2 × (−16%) = 4.4%
E
(
r
D
) = 0.30 × (−9%) + 0.5 × 14% + 0.2 × (26%) = 9.5%.
References
Multiple Choice
Difficulty: 1 Basic
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70.
Award:
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Consider the following probability distribution for stocks C and D:
State
Probability
Return on Stock C
Return on Stock D
1
0.30
7%
−
9%
2
0.50
11%
14%
3
0.20
−
16%
26%
The standard deviations of stocks C and D are _____ and _____, respectively.
Note: Do not round intermediate calculations.
7.62%; 11.24%
11.24%; 7.62%
10.35%; 12.93%
12.93%; 10.35%
None of the options are correct.
E
(
r
C
) = 0.3 × 7% + 0.5 × 11% + 0.2 × (−16%) = 4.4%
E
(
r
D
) = 0.30 × (−9%) + 0.5 × 14% + 0.2 × (26%) = 9.5%.
σ
C
= [0.3 × (7% − 4.4%)
2
+ 0.5 × (11% − 4.4%)
2
+ 0.2 × (−16% − 4.4%)
2
]
0.5
= 10.35%
σ
D
= [0.3 × (−9% − 9.5%)
2
+ 0.5 × (14% − 9.5%)
2
+ 0.2
× (26% − 9.5%)
2
]
0.5
= 12.93%.
References
Multiple Choice
Difficulty: 2 Intermediate
Consider the following probability distribution for stocks C and D:
State
Probability
Return on Stock C
Return on Stock D
1
0.30
7%
−
9%
2
0.50
11%
14%
3
0.20
−
16%
26%
The coefficient of correlation between C and D is:
Note: Do not round intermediate calculations.
0.67.
0.50.
−
0.50.
−
0.67.
None of the options are correct.
E
(
r
C
) = 0.3 × 7% + 0.5 × 11% + 0.2 × (−16%) = 4.4%
E
(
r
D
) = 0.30 × (−9%) + 0.5 × 14% + 0.2 × (26%) = 9.5%.
σ
C
= [0.3 × (7% − 4.4%)
2
+ 0.5 × (11% − 4.4%)
2
+ 0.2 × (−16% − 4.4%)
2
]
0.5
= 10.35%
σ
D
= [0.3 × (−9% − 9.5%)
2
+ 0.5 × (14% − 9.5%)
2
+ 0.2(26% − 9.5%)
2
]
0.5
= 12.93%.
Cov
(
C,D
) = 0.3 × (7% − 4.4%) × (−9% − 9.5%) + 0.5 × (11% − 4.4%) × (14% − 9.5%) + 0.2 × (−16% − 4.4%) × (26% − 9.5%)
= −0.6690%
ρ
A
,
B
=
-0.6690%
10.35%
×
12.93%
=
- 0. 50
References
Multiple Choice
Difficulty: 3 Challenge
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72.
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73.
Award:
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Consider the following probability distribution for stocks C and D:
State
Probability
Return on Stock C
Return on Stock D
1
0.30
7%
−
9%
2
0.50
11%
14%
3
0.20
−
16%
26%
If you invest 25% of your money in C and 75% in D, what would be your portfolio's expected rate of return and standard deviation?
Note: Do not round intermediate calculations.
9.89%; 8.70%
9.94%; 11.12%
8.23%; 8.70%
10.28%; 11.12%
None of the options are correct.
E
(
r
C
) = 0.3 × 7% + 0.5 × 11% + 0.2 × (−16%) = 4.4%
E
(
r
D
) = 0.30 × (−9%) + 0.5 × 14% + 0.2 × 26% = 9.5%.
σ
C
= [0.3 × (7% − 4.4%)
2
+ 0.5 × (11% − 4.4%)
2
+ 0.2 × (−16% − 4.4%)
2
]
0.5
= 10.35%
σ
D
= [0.3 × (−9% − 9.5%)
2
+ 0.5 × (14% − 9.5%)
2
+ 0.2 × (26% − 9.5%)
2
]
0.5
= 12.93%.
Cov
(
C,D
) = 0.3 × (7% − 4.4%) × (−9% − 9.5%) + 0.5 × (11% − 4.4%) × (14% − 9.5%) + 0.2 × (−16% − 4.4%) × (26% − 9.5%)
= −0.6690%
E
(
r
P
) = 0.25 × 4.4% + 0.75 × 9.5% = 8.23%
A,B
= −0.6690% ÷ (10.35% × 12.93%) = −0.50
σ
P
= [0.25
2
× 10.35%
2
+ 0.75
2
× 12.93%
2
+ 2 × 0.25 × 0.75 × 10.35% × 12.93% × (−0.50)]
2
= 8.70%.
References
Multiple Choice
Difficulty: 3 Challenge
Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 13% and a standard deviation of 21%. L has an expected rate of return of 10% and a standard deviation of 15%.
The weights of K and L in the global minimum variance portfolio are _____ and _____, respectively.
0.2411; 0.7261
0.5000; 0.5000
0.4167; 0.5833
0.4532; 0.5511
0.7665; 0.2488
w
k
=
σ
L
σ
k
+
σ
L
=
0.15
0.21
+
0.15
= 0. 4167
w
L
= 1 −
w
K
= 0.5833.
References
Multiple Choice
Difficulty: 2 Intermediate
Consider two perfectly negatively correlated risky securities, K and L. K has an expected rate of return of 12% and a standard deviation of 17%. L has an expected rate of return of 9% and a standard deviation of 11%.
The risk-free portfolio that can be formed with the two securities will earn _____ rate of return.
9.52%
11.39%
10.18%
9.90%
None of the options are correct.
w
k
=
σ
L
σ
k
+
σ
L
=
0.11
0.17
+
0.11
= 0. 3929
w
L
= 1
−
w
K
= 0.6071
E
(
r
P
) = 0.3929 × 12% + 0.6071 × 9% = 10.18%.
References
Multiple Choice
Difficulty: 3 Challenge
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75.
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76.
Award:
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77.
Award:
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Security M has expected return of 17% and standard deviation of 28%. Security S has expected return of 13% and standard deviation of 15%. If the two securities have a correlation coefficient of 0.78, what is their covariance?
0.0185
0.0291
0.0328
0.0453
0.0544
Cov
(
M,S
) =
M,S
M
S
= 0.78 × 0.28% × 15% = 0.0328.
References
Multiple Choice
Difficulty: 2 Intermediate
Security X has expected return of 7% and standard deviation of 14%. Security Y has expected return of 11% and standard deviation of 22%. If the two securities have a correlation coefficient of 0.45, what is their covariance?
0.0388
0.0108
0.0184
0.0139
0.1512
Cov
(
X,Y
) =
ρ
X
,
Y
σ
X
σ
Y
= 0.45 × 14% × 22% = 0.0139.
References
Multiple Choice
Difficulty: 2 Intermediate
Security X has expected return of 9% and standard deviation of 18%. Security Y has expected return of 12% and standard deviation of 21%. If the two securities have a correlation coefficient of 0.4, what is their covariance?
0.0388
0.0706
0.0184
0.0133
0.0151
Cov
(
X,Y
) =
ρ
X
,
Y
σ
X
σ
Y
= 0.4 × 18% × 21% = 0.0151.
References
Multiple Choice
Difficulty: 2 Intermediate
Two securities have a covariance of 0.056. If their respective standard deviations are 23% and 31%, what is their correlation coefficient?
0.32
0.45
0.79
0.82
0.95
ρ
A
,
B
=
Cov
(
A
,
B
)
σ
A
σ
B
=
0.056
0.31×0.23
= 0. 79
References
Multiple Choice
Difficulty: 2 Intermediate
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79.
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80.
Award:
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81.
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Two securities have a covariance of 0.016. If their respective standard deviations are 13% and 22%, what is their correlation coefficient?
0.22
0.56
0.59
0.72
1.79
ρ
A
,
B
=
Cov
(
A
,
B
)
σ
A
σ
B
=
0.016
0.13×0.22
= 0. 56
References
Multiple Choice
Difficulty: 2 Intermediate
Two securities have a covariance of 0.022. If their correlation coefficient is 0.52 and one has a standard deviation of 15%, what must be the standard deviation of the other security?
12%
19%
22%
28%
32%
ρ
A
,
B
=
Cov
(
A
,
B
)
σ
A
σ
B
→
σ
B
=
Cov
(
A
,
B
)
σ
A
ρ
A
,
B
=
0.022
0.15×0.52
= 0. 2821 or 28 % .
References
Multiple Choice
Difficulty: 2 Intermediate
A portfolio contains 3 stocks with expected returns of 15%, 18%, and 12%, with corresponding weights of 25%, 45%, and 30%, respectively. What is the expected return of the portfolio?
13.2%
14.4%
15.5%
17.7%
None of the options are correct.
E
(
R
p
) = 0.25
× 0.15 + 0.45
× 0.18 + 0.30
× 0.12 = 0.1545 or 15.5%.
References
Multiple Choice
Difficulty: 1 Basic
A portfolio contains 3 stocks with expected returns of 12%, 15%, and 9%, with corresponding weights of 30%, 35%, and 35%, respectively. What is the expected return of the portfolio?
12%
13%
14%
15%
None of the options are correct.
E
(
R
p
) = 0.3 × 0.12 + 0.35
× 0.15 + 0.35 × 0.09 = 0.12
References
Multiple Choice
Difficulty: 1 Basic
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