Are the following statements true or false? Provide a short justification for your answer. (You re evaluated on your justification.) Remember that a statement is false if any part of the statement is false. A single correct counterexample is sufficient to show that a statement is false. a) Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky assets A, B, C, with expected returns and standard deviations: E [FA] = 10%, SD [FA] = 5% E [TB] = 15%, SD [TB] = 7% E [fc] = 12%, SD [fc] =9%
Are the following statements true or false? Provide a short justification for your answer. (You re evaluated on your justification.) Remember that a statement is false if any part of the statement is false. A single correct counterexample is sufficient to show that a statement is false. a) Suppose you are a mean-variance optimizer. The risk-free rate is 3%. There are three risky assets A, B, C, with expected returns and standard deviations: E [FA] = 10%, SD [FA] = 5% E [TB] = 15%, SD [TB] = 7% E [fc] = 12%, SD [fc] =9%
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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Concept explainers
Risk and return
Before understanding the concept of Risk and Return in Financial Management, understanding the two-concept Risk and return individually is necessary.
Capital Asset Pricing Model
Capital asset pricing model, also known as CAPM, shows the relationship between the expected return of the investment and the market at risk. This concept is basically used particularly in the case of stocks or shares. It is also used across finance for pricing assets that have higher risk identity and for evaluating the expected returns for the assets given the risk of those assets and also the cost of capital.
Question
![Question 1
Are the following statements true or false? Provide a short justification for your answer. (You
are evaluated on your justification.) Remember that a statement is false if any part of the statement is false.
A single correct counterexample is sufficient to show that a statement is false.
a)
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 [FA] = 5%
E [řB] = 15%, SD [řB] = 7%
E [řc] = 12%, SD [řc] = 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.
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%2Fa8aefdc9-26fb-4b03-a9d0-8625fb93655a%2F1b08a7f2-3d44-492b-8293-7c1be2921d88%2Fe1spr1r_processed.png&w=3840&q=75)
Transcribed Image Text:Question 1
Are the following statements true or false? Provide a short justification for your answer. (You
are evaluated on your justification.) Remember that a statement is false if any part of the statement is false.
A single correct counterexample is sufficient to show that a statement is false.
a)
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 [FA] = 5%
E [řB] = 15%, SD [řB] = 7%
E [řc] = 12%, SD [řc] = 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.
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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