Are the following statements true or false? Provide a short justification for vour answer. Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky a) assets A, B, C, with expected returns and standard deviations: E [FA) = 10%, SD (řa] = 5% %3D E [řB] = 15%, SD (FB] = 7% E [řc] = 12%, SD [řc] = 9% %3D You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets (A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer the set of assets (A, B) to the set assets (A, C). Suppose the CAPM holds. Consider three stocks A, B, C. Suppose that assets A, B, C have b) the same market B's. The covariance matrix between A, B, C is: 0.05 0.03 0.03 0.05 0.05 Assets A, B, C have the same variance. However, assets A and B are positively correlated with each other, so they have larger systematic risk exposures than asset C: a portfolio with assets A and B will have higher variance than a portfolio with A and C, or B and C. Thus, in market equilibrium, the expected returns on assets A and B should be higher than the expected return on asset C, to compensate for their higher systematic risk. c) market. If you are currently holding the market portfolio and want to reduce your return risk, you could decrease the portfolio weight on gold, and this would decrease the variance of your portfolio Suppose gold has a negative CAPM beta. This implies that gold is a hedge against the returns. d) each other. Then there are always benefits from diversification in holding both stocks in a portfolio: it is possible to construct a portfolio with positive weights in both A and B and a return variance that is lower than the return variances of both A and B. Suppose two stocks, A and B, have returns that are not perfectly correlated with
Are the following statements true or false? Provide a short justification for vour answer. Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky a) assets A, B, C, with expected returns and standard deviations: E [FA) = 10%, SD (řa] = 5% %3D E [řB] = 15%, SD (FB] = 7% E [řc] = 12%, SD [řc] = 9% %3D You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets (A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer the set of assets (A, B) to the set assets (A, C). Suppose the CAPM holds. Consider three stocks A, B, C. Suppose that assets A, B, C have b) the same market B's. The covariance matrix between A, B, C is: 0.05 0.03 0.03 0.05 0.05 Assets A, B, C have the same variance. However, assets A and B are positively correlated with each other, so they have larger systematic risk exposures than asset C: a portfolio with assets A and B will have higher variance than a portfolio with A and C, or B and C. Thus, in market equilibrium, the expected returns on assets A and B should be higher than the expected return on asset C, to compensate for their higher systematic risk. c) market. If you are currently holding the market portfolio and want to reduce your return risk, you could decrease the portfolio weight on gold, and this would decrease the variance of your portfolio Suppose gold has a negative CAPM beta. This implies that gold is a hedge against the returns. d) each other. Then there are always benefits from diversification in holding both stocks in a portfolio: it is possible to construct a portfolio with positive weights in both A and B and a return variance that is lower than the return variances of both A and B. Suppose two stocks, A and B, have returns that are not perfectly correlated with
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
![Are the following statements true or false? Provide a short justification for vour answer.
а)
assets A, B, C, with expected returns and standard deviations:
Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky
E [řA] = 10%, SD [řA] = 5%
E [řB] = 15%, SD [řB] = 7%
E [řc] = 12%, SD [ŕc] = 9%
You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets
(A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and
lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer
the set of assets (A, B) to the set assets (A, C).
b)
the same market B's. The covariance matrix between A, B, C is:
Suppose the CAPM holds. Consider three stocks A, B, C. Suppose that assets A, B, C have
0.05
0.03
0.03
0.05
0.05
Assets A, B, C have the same variance. However, assets A and B are positively correlated with each
other, so they have larger systematic risk exposures than asset C: a portfolio with assets A and B
will have higher variance than a portfolio with A and C, or B and C. Thus, in market equilibrium,
the expected returns on assets A and B should be higher than the expected return on asset C, to
compensate for their higher systematic risk.
c)
Suppose gold has a negative CAPM beta. This implies that gold is a hedge against the
you are currently holding the market portfolio and want to reduce your return risk, you
could decrease the portfolio weight on gold, and this would decrease the variance of your portfolio
market. If
returns.
d)
each other. Then there are always benefits from diversification in holding both stocks in a portfolio: it
is possible to construct a portfolio with positive weights in both A and B and a return variance that is
lower than the return variances of both A and B.
Suppose two stocks, A and B, have returns that are not perfectly correlated with](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe35d795b-3b3a-45a5-a595-ba94ec33b836%2F7b85a6b5-91d6-472a-8f9e-8c7a628628d4%2Fbt9d5qi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Are the following statements true or false? Provide a short justification for vour answer.
а)
assets A, B, C, with expected returns and standard deviations:
Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky
E [řA] = 10%, SD [řA] = 5%
E [řB] = 15%, SD [řB] = 7%
E [řc] = 12%, SD [ŕc] = 9%
You cannot invest in all three risky assets. Instead, you have to choose whether to invest in only assets
(A, B), or only assets (A, C). Asset B mean-variance dominates asset C, since it has higher return and
lower standard deviation than asset C. Thus, as long as you are risk-averse, you would always prefer
the set of assets (A, B) to the set assets (A, C).
b)
the same market B's. The covariance matrix between A, B, C is:
Suppose the CAPM holds. Consider three stocks A, B, C. Suppose that assets A, B, C have
0.05
0.03
0.03
0.05
0.05
Assets A, B, C have the same variance. However, assets A and B are positively correlated with each
other, so they have larger systematic risk exposures than asset C: a portfolio with assets A and B
will have higher variance than a portfolio with A and C, or B and C. Thus, in market equilibrium,
the expected returns on assets A and B should be higher than the expected return on asset C, to
compensate for their higher systematic risk.
c)
Suppose gold has a negative CAPM beta. This implies that gold is a hedge against the
you are currently holding the market portfolio and want to reduce your return risk, you
could decrease the portfolio weight on gold, and this would decrease the variance of your portfolio
market. If
returns.
d)
each other. Then there are always benefits from diversification in holding both stocks in a portfolio: it
is possible to construct a portfolio with positive weights in both A and B and a return variance that is
lower than the return variances of both A and B.
Suppose two stocks, A and B, have returns that are not perfectly correlated with
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