Question

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 30% standard deviation of expected returns. Stock Y has a 13.0% expected return, a beta coefficient of 1.3, and a 30.0% 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. Do not round intermediate calculations.

CVx =

CVy =

B. Which of the following stock is riskier for a diversified investor?

a. 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 risky than Stock X.

b. 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 risky than Stock X.

c. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the higher standard deviation of expected returns is more risky. Stock X has the higher standard deviation so it is more risky than Stock Y.

d. 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 risky than Stock Y.

e. For diversified investors the relevant risk is measured by standard deviation of expected returns. Therefore, the stock with the lower standard deviation of expected returns is more risky. Stock Y has the lower standard deviation so it is more risky than Stock X.

C. Calculate each stock's required rate of return. Round your answers to two decimal places.

rx =

ry =

D. On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor?

E. Calculate the required return of a portfolio that has $3,500 invested in Stock X and $9,000 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.

rp =

F.If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return

Answer 1

a) coefficient of variation (CV) = Expected return (mean) / standard deviation

CV_X = 9.5% / 30% = 0.32

CV_Y = 13% / 30% = 0.43

b) Diversification eliminates the unsystematic risk or the risk associated with an individual company / industry which a stock's standard deviation. Therefore, for well diversified investors the relevant risk is measured by Beta. The stock with the higher beta is more risky. Stock Y has the higher beta so it is more risky than Stock X. (Option b)

c) Required rate of return (r)= rf + beta x market risk premium

rx = 6% + 0.8 x 5% = 10.00%

ry = 6% + 1.3 x 5% = 12.50%

d) The stock with the less required rate would be more attractive, i.e., stock X would be more attractive.

e) Required return of a portfolio = required return of stock X x Weight of stock X + required return of stock Y x weight of stock Y

or, Required return of a portfolio = 10% x [$3500 / ($3500+$9000)] + 12.50% x ($6500 / ($3500+$9000)] = 9.30%

f) If market risk premium is increased to 6%, the stock with the higher beta, i.e., Stock Y, would have the larger increase in required return.