Suppose that the market risk premium is 5% and the risk-free rate is 4%. Risky assets A and B are perfectly negatively correlated. Asset A has a standard deviation of returns of 40%, while asset B has a standard deviation of returns of 60%. According to the CAPM, what should be the expected return of a zero variance portfolio constructed of assets A and B? O 5% O 3% O Cannot be determined O 4% O 2%

Suppose that the market risk premium is 5% and the risk-free rate is 4%. Risky assets A and B are perfectly negatively correlated. Asset A has a standard deviation of returns of 40%, while asset B has a standard deviation of returns of 60%. According to the CAPM, what should be the expected return of a zero variance portfolio constructed of assets A and B? O 5% O 3% O Cannot be determined O 4% O 2%

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 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…
Assume that the short-term risk-free rate is 6%, the market index S&P500 is expected to pay returns of 30% with the standard deviation equal to 40%. Asset A pays on average 10%, has a standard deviation equal to 40% and is NOT correlated with the S&P500. Asset B pays on average 16%, also has a standard deviation equal to 40% and has a correlation of 1 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Beta of asset i (?i) = ?i ?iM / ?M, where ?i, ?M are standard deviations of asset i and market portfolio, ?iM is the correlation between asset i and the market portfolio)
Which ones of the following statements about portfolio beta are correct? O 1. If portfolio beta is between 0 and 1, then the portfolio expected return is between risk-free rate and the market expected return. O 2. If the return of an asset has zero correlation with the market portfolio returns, the beta of this asset must be zero. O 3. A portfolio that has the same portfolio weights as the market portfolio should have a beta of 1. O 4. Diversification is not a way to reduce portfolio beta. O 5. If two portfolios have the same portfolio weights, but different dollar values, their betas are the same.
Calculate the optimal risky portfolio for the following cases when short-sales are allowed. Compute its expected return and the standard deviation of its returns. 1. Two risky assets: Rp = 3, R' = [6, 9], and 4 5 5 20 2. Three risky assets: Rp = 4, R' = [5,9, 8], and [10 0 0 E=0 40 0 0 20 3. Three risky assets: Rp = 5, R' = [12, 9, 8], and 40 10 -5] E= 10 20 0 5 0 30 4. Five risky assets: Rp = 2, R' = [5, 3, 18, 9, 2], and %3D 2 16 0. -12 5 -12 20 16 10 7 14 27 14 9. -13 8. 7 27 13
4. Suppose there are three uncorrelated assets. Each has a variance of 1.0 and expected rates of return are 1, 2, and 3, respectively. For this example, short sales are allowed. Do the following: a. Find the minimum variance portfolio for the following desired expected portfolio rates of return: 1.0, 1.5, 2.0, 2.5, and 3.0. b. Sketch these on the return versus risk plot (you will need to use the standard deviation of the portfolio, which clearly equals sqrt(w1^2+w2^2+w3^3), where wi are the weights). c. Suppose we have a risk-free asset with a return of 2%. Modify your plot for b.
Calculate the risk (standard deviation) of a 2-asset portfolio, in which asset A has a variance of return = 0.112, asset B a variance of return = 0.045, and the convariance between the return of 2 assets is = 0.102. asset A comprises 60% ans asset B comprises 40% of the total portfolio. Give your answer 0.000.
Consider a risky portfolio, A, with an expected rate of return of 0.16 and a standard deviation of 0.25, that lies on a given indifference curve. Which one of the following portfolios is not likely to lie on the same indifference curve for a risk-averse investor with a mean- variance utility function? a. Expected return = 0.20; Standard deviation = 0.15 b. Expected return = 0.10; Standard deviation = 0.20 Expected return= 0.15; Standard deviation = 0.20 Expected return = 0.12; Standard deviation = 0.10 Expected return = 0.10; Standard deviation = 0.10 C. d. e.
15. (Singular) Suppose there are two stocks that are uncorrelated. Each of these has variance of 1, and there are expected returns are 7₁ and 72, respectively. The risk-free rate is rf. Find the portfolio of weights w₁ and w₂ for the Markowitz (market) portfolio. Show that for some value of rf there is no Markowitz portfolio.
d) Assume that the short-term risk-free rate is 3%, the market index S&P500 is expected to pay returns of 15% with the standard deviation equal to 20%. Asset A pays on average 5%, has standard deviation equal to 20% and is NOT correlated with the S&P500. Asset B pays on average 8%, also has standard deviation equal to 20% and has correlation of 0.5 with the S&P500. Determine whether asset A and B are overvalued or undervalued, and explain why. (Hint: Beta of asset i (B¡) = "PIM , where ơị,ɑm are standard deviations of asset i and market OM portfolio, Pim is the correlation between asset i and the market portfolio)
9. A risk averse, wealth maximising, investor is faced with a choice between four investments (P, Q, R and S) that have profiles as follows:   Mean return (%) Variance (%) P 19 18   Q 16 17  R 22 16   S 20 16   Between which pair of these investments would the investor find it impossible to distinguish on the basis of the above information? A. P and Q   B. R and S   C. P and S   D. Q and R
Asset X has an expected return of 6% and a variance of 0.001. Asset Y has an expected return of 12% and the same variance as X (i.e., 0.001). The returns of assets X and Y are uncorrelated, and the risk-free rate is 3%. Find the variance of the highest Sharpe ratio portfolio that can be formed of the two risky assets X and Y.

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