EBK INVESTMENTS
11th Edition
ISBN: 9781259357480
Author: Bodie
Publisher: MCGRAW HILL BOOK COMPANY
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Chapter 10, Problem 17PS
Summary Introduction
To define: Various weighting schemes which will generate well-diversified portfolios.
Introduction:
Well-diversified portfolios: Well-diversified portfolios are portfolios that are constructed with a combination of various securities such as stocks, fixed income, and commodities. When the weight of any of such securities is calculated, it will always be small. Systematic risk is the type of risk found in well-diversified portfolios.
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Assume that security returns are generated by the single-index model,
Ri = αi + βiRM + ei
where Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 3%. Suppose also that there are three securities A, B, and C, characterized by the following data:
Security
βi
E(Ri)
σ(ei)
A
1.4
14
%
23
%
B
1.6
16
14
C
1.8
18
17
a. If σM = 22%, calculate the variance of returns of securities A, B, and C.
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Assume that security returns are generated by the single-index model,
Ri = alphai + BetaiRM + ei
where Ri is the excess return for security i and RM is the market's excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data.
Security
Betai
E(Ri)
sigma(ei)
A
1.4
15%
28%
B
1.6
17%
14%
C
1.8
19%
23%
a. If simaM = 24%, calculate the variance of returns of securities A, B, and C (round to whole number).
Variance
Security A
Security B
Security C
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C (enter the variance answers as a whole number decimal and the mean as a whole number percentage)?
Mean
Variance
Security A
?%
Security B
?%
Security C
?%
Assume that security returns are generated by the single-index model,Ri = αi + βiRM + eiwhere Ri is the excess return for security i and RM is the market’s excess return. The risk-free rate is 2%. Suppose also that there are three securities A, B, and C, characterized by the following data:
Security
βi
E(Ri)
σ(ei)
A
0.7
7
%
20
%
B
0.9
9
6
C
1.1
11
15
a. If σM = 16%, calculate the variance of returns of securities A, B, and C.
b. Now assume that there are an infinite number of assets with return characteristics identical to those of A, B, and C, respectively. What will be the mean and variance of excess returns for securities A, B, and C? (Enter the variance answers as a percent squared and mean as a percentage. Do not round intermediate calculations. Round your answers to the nearest whole number.)
Chapter 10 Solutions
EBK INVESTMENTS
Ch. 10 - Prob. 1PSCh. 10 - Prob. 2PSCh. 10 - Prob. 3PSCh. 10 - Prob. 4PSCh. 10 - Prob. 5PSCh. 10 - Prob. 6PSCh. 10 - Prob. 7PSCh. 10 - Prob. 8PSCh. 10 - Prob. 9PSCh. 10 - Prob. 10PS
Ch. 10 - Prob. 11PSCh. 10 - Prob. 12PSCh. 10 - Prob. 13PSCh. 10 - Prob. 14PSCh. 10 - Prob. 15PSCh. 10 - Prob. 16PSCh. 10 - Prob. 17PSCh. 10 - Prob. 18PSCh. 10 - Prob. 19PSCh. 10 - Prob. 1CPCh. 10 - Prob. 2CPCh. 10 - Prob. 3CPCh. 10 - Prob. 4CPCh. 10 - Prob. 5CPCh. 10 - Prob. 6CPCh. 10 - Prob. 7CPCh. 10 - Prob. 8CP
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- For the data in Table below, suppose an investor desires an expected variance less than 8. What is the minimum number of securities for such a portfolio?arrow_forwardSuppose that optimal risky portfolio has an expected return of 16% and a varianceof 0.04. The risk-free rate is 4%.a) Find the slope of Capital Market Line (Optimal Capital Allocation Line)?b) What is the expected return of a portfolio C, which is on Capital Market Line and has astandard deviation of 0.08?arrow_forwardSuppose that the index model for stocks A and B is estimated from excess returns with the following results:RA = 3% + .7RM + eARB = −2% + 1.2RM + eBσM = 20%; R-squareA = .20; R-squareB = .12Break down the variance of each stock into its systematic and firm-specific components.arrow_forward
- Suppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively. Answer the following questions. (a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?arrow_forwardConsider Microsoft Corporation (MSFT) and Meta Platforms, Inc. (META) that have returns variances of 6.25% and 3.24%, respectively. Calculate the standard deviation of portfolio returns for an equal-weighted portfolio of the two assets when their correlation of returns is 0. A. 24.71% B. 19.20% C. 15.40% D. 10.28%arrow_forwardSuppose the index model for stocks A and B is estimated with the following results:rA = 2% + 0.8RM + eA, rB = 2% + 1.2RM + eB , σM = 20%, and RM = rM − rf . The regressionR2 of stocks A and B is 0.40 and 0.30, respectively.(a) What is the variance of each stock? (b) What is the firm-specific risk of each stock? (c) What is the covariance between the two stocks?arrow_forward
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