10. Problem 8.19 Problem 8-19 Evaluating risk and return Stock X has a 10.5% exp
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10. Problem 8.19 Problem 8-19 Evaluating risk and return Stock X has a 10.5% expected return, a beta coefficient of 1.0, and a 40% standard deviation of expected returns. Stock Y has a 13.0% expected return, a beta coefficient of 1.3, and a 25.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. a. Calculate each stock's coefficient of variation. Round your answers to two decimal places. b. Which stock is riskier for a diversified investor? I. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of II. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is more risky. Stock X has the lower beta so it is more III. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of IV. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is less risky. Stock Y has the higher beta so it is less V. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is more risky. Stock Y has the higher beta so it is more expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y risky than Stock Y expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock x risky than Stock X. risky than Stock X. Select. c. Calculate each stock's required rate of return. Round your answers to two decimal places. d. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor? Select. e. Calculate the required return of a portfolio that has $8,500 invested in Stock X and $8,000 invested in Stock Y. Round your answer to two decimal places. f. If the market risk premium increased to 696, which of the two stocks would have the larger increase in its required return? Select.Explanation / Answer
a) Coefficient of variation (CV)= Standard deviatio of stock / expected return of stock
CVx = 40% / 10.5%
= 3.8
CVy = 25% / 13%
= 1.92
b) I. For a diversified investor, the relevant risk is measured by standard deviation of expected returns. Therefore, stock with higher standard deviation is more risky than stock with lower standard deviation. Stock x has higher std dev, hence is more risky.
c) Required rate of return = risk free rate + beta* market risk premium
rx = 0.06+ 1*0.05
= 11%
ry = 0.06+ 1.3*0.05
= 12.5%
d) Stock Y is more attractive to a diversifed investor bacuase it has a higher required rate of return, also the expected returns are higher with a lower standard deviation.
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