Question

Stock X has a 10% expected return, a beta coefficient of 0.9, and a 35% standard deviation of expected returns. Stock Y has a 12.5% expected return, a beta coefficient of 1.2, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

a. Calculate each stock’s coefficient of variation.

b. Which stock is riskier for a diversified investor?

c. Calculate each stock’s required rate of return.

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 $7,500 invested in Stock X and $2,500 invested in Stock Y.

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

(Please make work neat and understandable)

Answer 1

1.
Coefficient of variation=Standard deviation/Expected return
Stock X=35%/10%=3.50000

Stock Y=25%/12.5%=2.00000

2.
The relevant measure of risk for a well diversified investor is beta. Higher beta means higher risk. Hence, Stock Y is riskier.

3.
required return=risk free rate+beta*market risk premium

Stock X=6%+0.9*5%=10.50%
Stock Y=6%+1.2*5%=12.00%

4.
Stock Y as expected return is more than required return

5.
=(7500*10.50%+2500*12.00%)/(7500+2500)
=10.8750%

6.
Stock Y as it has higher beta