Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Which stock is riskier for a diversified investor? b. Calculate 50/50 portfolio's required rate of return and market rate. c. Calculate the required return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y.
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- You have observed the following returns over time: Assume that the risk-free rate is 6% and the market risk premium is 5%. What are the betas of Stocks X and Y? What are the required rates of return on Stocks X and Y? What is the required rate of return on a portfolio consisting of 80% of Stock X and 20% of Stock Y?Suppose Stock A has B = 1 and an expected return of 11%. Stock B has a B = 1.5. The risk- free rate is 5%. Also consider that the covariance between B and the market is 0.135. Assume the CAPM is true. Answer the following questions: a) Calculate the expected return on share B. b) Find the equation of the Capital Market Line (CML). c) Build a portfolio Q with B = 0 using actions A and B. Indicate weights (interpret your result) and expected return of portfolio Q.Suppose that the risk-free rate r, = 0.03, the expected market return uM = 0.11, and the market volatility oM = 0.16. Stock A has beta = 1.2 and diversifiable risk o̟ = 0.08. Stock B has beta = 0.8 and 0, = 0.03. Stock C has beta = 1.5 and o̟ = 0.1. Consider a portfolio P which is 45% in Stock A, 25% in Stock B, and 30% in Stock C. (a) Find the value of beta for this portfolio. (b) Assuming CAPM, find the portfolio's expected return µp. (c) Find the standard deviation of the portfolio's systematic (or mar- ket) risk. (d) Find the standard deviation o, of the diversifiable risk of P. (You may assume that the diversifiable risks of A,B, and C are uncorrelated.)
- 1. Stock Y has a beta of 1.2 and an expected return of 11.1 percent. Stock Z has a beta of .8 and an expected return of 7.85 percent. If the risk-free rate is 2.4 percent and the market risk premium is 7.2 percent, the reward-to-risk ratios for stocks Y and Z are ____ and ____ percent, respectively. Since the SML reward-to-risk is ____ percent, Stock Y is ____(undervalued/ overvalued) and Stock Z is ____(undervalued/ overvalued).Consider an investment portfolio that consists of three different stocks, with the amount invested in each asset shownbelow. Assume the risk-free rate is 2.5% and the market risk premium is 6%. Use this information to answer thefollowing questions.Stock Weights BetasChesapeake Energy 25% 0.8Sodastream 50% 1.3Pentair 25% 1.0a) Compute the expected return for each stock using the CAPM and assuming that the stocks are all fairly priced.b) Compute the portfolio beta and the expected return on the portfolio.c) Now assume that the portfolio only includes 50% invested in Pentair and 50% invested in Sodastream (i.e., a twoassetportfolio). The yearly-return standard deviation of Pentair is 48% and the yearly-return standard deviation ofSodastream is 60%. The correlation coefficent between Pentair’s returns and Sodastream’s returns is 0.3 What is theexpected yearly-return standard deviation for this portfolio?Assume an economy in which there are three securities: Stock A with rA = 10% and σA = 10%; Stock B with rB = 15% and σB = 20%; and a riskless asset with rRF = 7%. Stocks A and B are uncorrelated (rAB = 0). Which of the following statements is most CORRECT? 1. b. The expected return on the investor’s portfolio will probably have an expected return that is somewhat below 10% and a standard deviation (SD) of approximately 10%. 2. d. The investor’s risk/return indifference curve will be tangent to the CML at a point where the expected return is in the range of 7% to 10%. 3. e. Since the two stocks have a zero correlation coefficient, the investor can form a riskless portfolio whose expected return is in the range of 10% to 15%. 4. a. The expected return on the investor’s portfolio will probably have an expected return that is somewhat above 15% and a standard deviation (SD) of approximately 20%. 5.…
- b) You are given the following information about Stock X and the market: The annual effective risk-frec rate is 5%. The expected return and volatility for Stock X and the market are shown in the table below: Expected Return Volatility Stock X 5% 40% Market 8% 25% The correlation between the returns of stock X and the market is -0.25. Assume the Capital Asset Pricing Model holds. Calculate the required return for Stock X and determine if the investor should invest in Stock X.Stock M has a relevant risk equals 1.75, and unsystematic risk equals 2. If the real risk-free rate of interest equals 3 percent, inflation premium equals 2 percent, expected market return equals 11 percent, and the required rate of return on a portfolio consisting of all stocks, which is the market portfolio equals 11 percent, what is Stock M's required rate of return? Interpret your answer.(c) Explain why, in general, the portfolio risk is lower than the weighted average of individual stocks’ risk. (d) Suppose the risk-free rate is 4%, the market risk premium is 15% and the betas for stocks X and Y are 1.2 and 0.2 respectively. Using the CAPM model, estimate the required rates ofreturn of Stock X and Stock Y. (e) Given the results above, are Stocks X and Y overpriced or underpriced? Explain.
- The expected return and standard deviation of Stock A are 12% and 24%, respectively. The expected return and standard deviation of Stock B are 5% and 19%, respectively. The correlation between the two stocks is 0.4. The risk-free rate in the economy is 1%. A. What is the Sharpe ratio for Stock A and Stock B? Show your calculation steps briefly and clearly. B. Calculate the optimal risky portfolio P*. You do not need to show your calculation steps for this subquestion. C. Now suppose that the correlation between the two stocks is -0.2 (instead of 0.4). Re-calculate the optimal risky portfolio P* and compare it to your answer in Part B. What do you observe? You do not need to show your calculation steps for this subquestion. D. Using the results above, briefly explain why investors might still consider investing in stocks with a (relatively) low Sharpe ratio as a part of their portfolio.(d) Suppose the risk-free rate is 4%, the market risk premium is 15% and the betas for stocks X and Y are 1.2 and 0.2 respectively. Using the CAPM model, estimate the required rates ofreturn of Stock X and Stock Y. (e) Given the results above, are Stocks X and Y overpriced or underpriced? Explain.Suppose the total risk of Portfolios A, B and C are 49% ², 64%² and 100% ² respectively. The market price of risk is 8%. The Market Portfolio (M) has an expected return and a total risk of 11% and 100% respectively. (a) You want to form another Portfolio H by investing $7,000 in Portfolio A and $3,000 in Portfolio B. Compute the standard deviation of Portfolio H if the correlation coefficient between Portfolio A and Portfolio B is: i) perfectly positively correlated ii) uncorrelated iii) perfectly negatively correlated (b) If the expected return of Portfolio C is 9.4% and it is lying on the Securities Market Line, what is the beta of Portfolio C? State the answer in %². (c) Is Portfolio C a Market Portfolio as it has same level of total risk (i.e. 100% 2) as the Market Portfolio? Why or Why not?