Question

Stock X has a 10.0% expected return, a beta coefficient of 0.9, and a 30% standard deviation of expected returns. Stock Y has a 13.0% expected return, a beta coefficient of 1.3, and a 25% standard deviation. The risk-free rate is 6%, and the market risk premium is 5%.

1. Calculate each stock's coefficient of variation. Do not round intermediate calculations. Round your answers to two decimal places.

   CV_x =

   CV_y =

2. Which stock is riskier for a diversified investor?
   1. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is riskier. Stock Y has the higher beta so it is riskier than Stock X.
   2. 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 riskier. Stock X has the higher standard deviation so it is riskier than Stock Y.
   3. For diversified investors the relevant risk is measured by beta. Therefore, the stock with the lower beta is riskier. Stock X has the lower beta so it is riskier than Stock Y.
   4. 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 riskier. Stock Y has the lower standard deviation so it is riskier than Stock X.
   5. 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.

   -Select-

3. Calculate each stock's required rate of return. Round your answers to one decimal place.

   r_x =   %

   r_y =   %

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

   -Select-Stock X or Stock Y?

5. Calculate the required return of a portfolio that has $7,500 invested in Stock X and $2,500 invested in Stock Y. Do not round intermediate calculations. Round your answer to two decimal places.

   r_p =   %

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

   -Select-Stock X or Stock Y

Answer 1

1) Coefficient of Variation (CV) = Volatility / Expected Return * 100

CV_X = 30%/10% * 100%
CV_X = 300% or 3.0

CV_Y = 25%/13% * 100%
CV_Y = 192.30769% or 1.92

2) A) For diversified investors the relevant risk is measured by beta. Therefore, the stock with the higher beta is riskier. Stock Y has the higher beta so it is riskier than Stock X.

Beta is used to measure the riskiness of any diversified investor. The higher the beta, the riskier the stock will be
Since Beta of Stock Y (1.3) is higher than Beta of Stock X (0.9). Therefore, Stock Y is riskier than Stock X.

3) Required Rate of Return = Risk-Free Rate + (Beta * Market Risk Premium)

Required Rate of Return_X = 6% + (0.9 * 5%)
= 6% + 4.5%
Required Rate of Return_X = 10.5%

Required Rate of Return_Y = 6% + (1.3 * 5%)
= 6% + 6.5%
Required Rate of Return_Y = 12.5%

4) Stock Y is more attractive because the expected return (13%) is higher than the required rate of return (12.5%).
For Stock X, the Required Rate of return (10.5%) is higher than the expected rate of return (10%) and hence it is NOT ATTRACTIVE.

5)

Stocks	Amount Invested	Weightage	Beta	Weighted Avg. Beta
A	7,500	0.75	0.9	0.675
B	2,500	0.25	1.3	0.325
Total	10,000	1		1

Weightage = Amount Invested in Stock / Total Amount Invested
Weighatage of A = 7,500 / 10,000 = 0.75

Weighted Avg Beta = Weightage * Beta
Weighted Avg Beta of A = 0.75 * 0.9 = 0.675

Beta of Portfolio = 1

Required Rate of Return of Portfolio = 6% + (1 * 5%)
= 6% + 5%
Required Rate of Return of Portfolio = 11%