Consider a world with only two risky assets, A and B, and a risk-free asset. Stock A has 200 shares outstanding, a price per share of $3.00, an expected return of 16%, and a stdev of 30%. Stock B has 300 shares outstanding, a price per share of $4.00, an expected return of 10%, and a stdev of 15%. The correlation coefficient ρAB = 0.4. a) What is the (market) beta of each stock? b) Assume that the risk-free interest rate on margins (i.e., borrowing cost) is 0. I have $100. I decide to invest $200 in Stock A, and borrow the rest. What is the beta of my portfolio?

Consider a world with only two risky assets, A and B, and a risk-free asset. Stock A has 200 shares outstanding, a price per share of $3.00, an expected return of 16%, and a stdev of 30%. Stock B has 300 shares outstanding, a price per share of $4.00, an expected return of 10%, and a stdev of 15%. The correlation coefficient ρAB = 0.4. a) What is the (market) beta of each stock? b) Assume that the risk-free interest rate on margins (i.e., borrowing cost) is 0. I have $100. I decide to invest $200 in Stock A, and borrow the rest. What is the beta of my portfolio?

Intermediate Financial Management (MindTap Course List)

13th Edition

ISBN:9781337395083

Author:Eugene F. Brigham, Phillip R. Daves

Publisher:Eugene F. Brigham, Phillip R. Daves

Chapter2: Risk And Return: Part I

Section: Chapter Questions

Problem 3Q: Security A has an expected return of 7%, a standard deviation of returns of 35%, a correlation...

See similar textbooks

Similar questions

Consider a world with only two risky assets, A and B, and a risk-free asset. Stock A has 200 shares outstanding, a price per share of $3.00, an expected return of 16%, and a stdev of 30%. Stock B has 300 shares outstanding, a price per share of $4.00, an expected return of 10%, and a stdev of 15%. The correlation coefficient PAB = 0.4. a) What is the (market) beta of each stock? b) Assume that the risk-free interest rate on margins (i.e., borrowing cost) is 0. I have $100. I decide to invest $200 in Stock A, and borrow the rest. What is the beta of my portfolio?
Give typing answer with explanation and conclusion Consider a world with only two risky assets, A and B, and a risk-free asset. Stock A is held at 1/3 at a price per share of $3.00, an expected return of 16% and a σ of 30%. Stock B is held at 2/3 at a price per share of $4.00, an expected return of 10% and a σ of 15%. The correlation between A and B is 0.4 , the covariance of stock A with the market Cov(RA,RM) is 0.042. (a) What is the expected return of the market portfolio? Answer % (b) What is the variance of the market portfolio? Answer (c) What is the beta of each stock? β_Α=Answer β_Β=Answer
Suppose the risk-free rate is 5%. The expected return and standard deviation of a risky asset are 10% and 20%, respectively. a. What is the slope of the capital allocation line (CAL) constructed using the risk-free asset and the risky asset? A. 0.30 B. 0.15 C. 0.25 D. 0.20 b. If an investor has a risk aversion coefficient of A=2, what is the optimal fraction of the money that she invests in the risky asset? A. 62.5% B. 42.5% C. 30% D. 20% c. If an investor invest 25% of her money in the risky asset, which is the investor’s risk aversion coefficient? a. 5 b. 1 c. 3 d. 4
An investor has an opportunity to invest in two risky assets and a risk-free asset. Theexpected return of the two risky assets are μ1 = 0.12, μ2 = 0.15. Their standarddeviations are σ1 = 0.05 and σ2 = 0.1, and the correlation coefficient between theirreturn is 0.2. The risk-free rate is 0.05. Suppose the investor has $1000 and he wantsto hold a portfolio with expected return of 0.1. If the investor is risk averse, how muchshould he invest in the two risky assets and the risk-free asset?
Consider a world with only two risky assets, A and B, and a risk-free asset. The two riskyassets are in equal supply in the market, i.e., the market portfolio M = 0.5A + 0.5B. Itis known that R¯M = 11%, σA = 20%, σB = 40% and ρAB = 0.75. The risk-free rate is2%. Assume CAPM holds.(a) What is the beta for each stock?(b) What are the values for R¯A and R¯B?
2C) Assume that the CAPM holds in the economy. The following data is available about the market portfolio, the riskless rate, and two risky assets, W and X: The market portfolio has a standard deviation equals to 10%, stock W has an expected return equals to 16%, standard deviation equals to 12%, and beta equals to one, stock X has a standard deviation equals to 6% and beta equals to 0.7. The risk-free rate is 3%. What is the expected return and the beta of the market portfolio? What is the expected return on asset X? Does asset W lie on the Capital Market Line? Explain why or why not. Suppose you invested $100,000 in these two stocks. The beta of your portfolio is 1.25. How much did you invest in each stock? What is the expected return of this portfolio?
We believe that the single factor model can predict any individual asset’s realized rate of return well. Both Portfolio A and Portfolio B are well-diversified: ri = E(ri) + βiF + Ei, where E(ei) = 0 and Cov(F, i) = 0 A B β 1.2 0.8 E(r) 0.1 0.08 (1) What is the rate of return of the risk-free asset? (2) What is the expected rate of return of the well-diversified portfolio C with βC = 1.6, which also exists in the market? (3) A fund constructs a well-diversified portfolio D. Studies show that βD = 0.6. The expected rate of return of D is 0.06. Is there an arbitrage opportunity? If so, construct a trading strategy to earn profits with no risk. If not, why?
Assume that you are considering investing in two risky assets, namely PKX and XIY, with the following probability distribution. Assume that short selling is allowed. Stock РКХ XIY State of the world Probability Return (%) Return (%) 1 0.25 18 2 0.30 5 -3 3 0.20 12 15 4 0.10 4 12 0.15 6 1 1. Calculate the expected return and risk for each of these assets. Interpret. 2. Consider a portfolio that contains PKX and XIY. Note that XIY comprises 30% of the portfolio. What is the expected return and risk of this portfolio? 3. How will your answer in (2) change if XIY comprises 20% of the portfolio only? Comment on your findings.
Suppose that there are two assets: A and B. Asset A has expected return of 20%. B has expected return of 12% and standard deviation of σ* σ* = standard Deviation (σ) (a) “As B is strictly dominated by A in terms of total risk (standard deviation), there is no value in having B in portfolio formation.” (Without doing any calculation) (b) “If the correlation coefficient ρ between A and B = 1, it is always optimal to invest in A only.” (Show your proof) (c) “If the correlation coefficient ρ between A and B = -1, it is always optimal to invest in 50% in A and 50% in B when forming a minimum variance portfolio of the two.” (Show your proof) [ (d) “Given that σA= σB=σ*, it is always optimal to combine half of A and half of B when forming a minimum variance portfolio of the two when ρ ε (-1,1).” (Show your proof)
Consider the following securities: state Probability A B A B H M L 0.2 0.5 0.3 с 6 10 6 3 7 12 2 5 14 1. The expected payoff of A is: 2. The standard deviation of A is: 3. If the price of A is 3, its expected return is: 4. The covariance between A and B is: 5. The correlation coefficient between A and B is: 6. Is it possible to build a portfolio that has zero variance using A and C? YES/ NO
Suppose the CAPM is true. Consider two assets, X and Y, and the market M. Suppose cov(X,M) = .3, cov(Y,M) = .5. %3D (a) Is the expected return higher on X or Y? (b) Suppose var(M) = 1.5, what are the betas of X and Y? (c) Suppose the expected market return is 20% and the risk free rate is 5%, what is the expected returns of X and Y?. (d) Given your analysis in (a)-(c), what type of investor would prefer asset X to asset Y?
Consider an economy with a (net) risk-free return r1 = 0:1 and a market portfolio with normally distributed return, with ErM = 0:2 and 2M = 0:02. Suppose investor A has CARA preferences, with risk aversion coe¢ cient equal to 1 and an endowment of 10. a) Write down the maximization problem for the investor. b) Determine the amount invested in the risky portfolio and in the risk-free asset. c) Suppose another investor (B) has a coe¢ cient of absolute risk aversion equal to 2 (and the same endowment 10). Compute his optimal portfolio and compare it to that of investor A. Explain the di§erent results for investors A and B. d) Finally, consider Investor C with mean-variance preferences Ec V ar(c) (and endowment 10). Compute his optimal portfolio and compare it to that of investors A and B (as obtained in questions b and c). Compare your result with those obtained for investors A and B.