EVALUATING RISK AND RETURN
Stock X has a 9.5% expected return, a beta coefficient of 0.8, and a 40% 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%.
a. Calculate each stock's coefficient of variation. Round your answers to two decimal places. Do not round intermediate calculations.
CVx = ________
CVy = ________
b. Which stock is riskier for a diversified investor?
I. 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. II. 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.
III. 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.
IV. 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.
V. 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. _________________
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 $6,500 invested in Stock X and $7,500 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-A: Coefficient of Variation
CV = Standard Deviation of Stock / Expected Return on Stock
CV(X) = 40% / 9.5% = 4.21
CV(Y) = 20% / 12.5% = 1.6
Answer-B: Which stock is riskier for a diversified investor?
A diversified investor means the investor holds a portfolio consisting different stocks. Therefore, for a diversified investor the relevant risk measure is beta of the stock. Higher the beta more the stock is risky. As the stock Y has beta 1.2, stock Y is the riskier stock.
So, the statement IV is correct.
Answer-C: Required Rate of Return:
Required Rate of return is calculated as follow:
R = Rf + (Rm – Rf) B
(Here; Rf is risk free rate, Rm is market return and B is beta of the stock)
R(X) = 6% + (5%) 0.8 = 10%
R(Y) = 6% + (5%) 1.2 = 12%
Answer-D:
Stock |
Required Return |
Expected Return |
X |
10% |
9.5% |
Y |
12% |
12.5% |
Stock Y would be better option for a diversified investor as its expected return (12.5%) is more than the required return (12%).
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