Question

Stock X has a 10.5% expected return, a beta coefficient of 1.0, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, 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 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. 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. 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 $4,500 invested in Stock X and $3,000 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

So, CVx = 35/10.5 = 3.33

And CVy = 20/12.5 = 1.60

The risk for a diversified investor is only systematic risk which is measured by beta. Since, beta of Y is greater than beta of X, for a diversified investor Y is more risky.

Now, from CAPM-

Required return of X = 6 + 1*5 =11.00%

Required return if Y = 6 + 1.2*5=12.00%

Since, expected return of Y exceeds it's required return whereas expected return of X is lower than it's required return, Y is more attractive to a diversified investor.

Now,

Where Wi are weights of each stock

So, Portfolio return = (4500/7500)*11 + (3000/7500)*12 = 11.40%

If the market risk premium increases, the stock with greater beta, here Y, will see larger increase in it's required return, as evident from CAPM-.