Question

Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 35% standard deviation of expected returns. Stock Y has a 12.0% expected return, a beta coefficient of 1.1, and a 20.0% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations. CVx = CVy = Which stock is riskier for a diversified investor? 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. 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. 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. 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. 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. Calculate each stock's required rate of return. Round your answers to two decimal places. rx = % ry = % On the basis of the two stocks' expected and required returns, which stock would be more attractive to a diversified investor? Calculate the required return of a portfolio that has $7,000 invested in Stock X and $8,500 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places. rp = % If the market risk premium increased to 6%, which of the two stocks would have the larger increase in its required return?

Answer 1

Answer 1:

Coefficient of variation =  Standard deviation / Expected Return

CVx = 35% /9.5% = 3.68

CVy = 20% / 12% = 1.67

Hence:

CVx = 3.68

CVy = 1.67

Answer 2:

Correct statement is:

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

Explanation:

For diversified investors, if  CVx = CVy, relevant risk is measured by beta. A stock with higher beta is more risky.

Hence statement 1 is correct and other statements 2,3, 4 and 5 are incorrect.

Answer 3:

Rate of return = Risk free rate + Beta * Market premium

Stock X's required rate of return = 6% + 0.8 * 5% = 10.00%

Stock Y's required rate of return = 6% + 1.1 * 5% = 11.50%

Hence:

Stock X's required rate of return = 10.00%

Stock Y's required rate of return = 11.50%

Answer 4:

On the basis of the two stocks' expected and required returns, Stock Y is more attractive to a diversified investor.

Stock Y's expected return is 12% which is greater than required rate of return of 11.50%

Answer 5:

Total investment = 7000 + 8500 = 15500

Hence:

Portfolio beta = 7000 / 15500 * 0.8 + 8500 /15500 * 1.1

=  0.964516

Required return of a portfolio = 6% + 0.964516 * 5%

= 10.82%

Required return of a portfolio = rp = 10.82%

Answer 6:

If the market risk premium increased to 6%, the stock with higher beta would have the larger increase in its required return.

Stock Y has higher beta.

Hence:

If the market risk premium increased to 6%, the stock Y with higher beta would have the larger increase in its required return.