Question

EXPECTED RETURNS

Stocks A and B have the following probability distributions of expected future returns:

Probability	A	B
0.1	(13%)	(35%)
0.2	5	0
0.3	12	20
0.3	18	29
0.1	38	38

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 12.50%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

2. Calculate the standard deviation of expected returns, σ_A, for Stock A (σ_B = 20.35%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. Is it possible that most investors might regard Stock B as being less risky than Stock A?

   1. If Stock B is less highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be more risky in a portfolio sense.
   2. If Stock B is more highly correlated with the market than A, then it might have a higher beta than Stock A, and hence be less risky in a portfolio sense.
   3. If Stock B is more highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.
   4. If Stock B is more highly correlated with the market than A, then it might have the same beta as Stock A, and hence be just as risky in a portfolio sense.
   5. If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense.

Answer 1

Answer a.

Stock B:

Expected Return = 0.10 * (-0.35) + 0.20 * 0.00 + 0.30 * 0.20 + 0.30 * 0.29 + 0.10 * 0.38
Expected Return = 0.15 or 15.00%

Answer b.

Stock A:

Variance = 0.10 * (-0.13 - 0.1250)^2 + 0.20 * (0.05 - 0.1250)^2 + 0.30 * (0.12 - 0.1250)^2 + 0.30 * (0.18 - 0.1250)^2 + 0.10 * (0.38 - 0.1250)^2
Variance = 0.015045

Standard Deviation = (0.015045)^(1/2)
Standard Deviation = 0.1227 or 12.27%

Answer c.

Stock B:

Coefficient of Variance = Standard Deviation / Expected Return
Coefficient of Variance = 0.2035 / 0.1500
Coefficient of Variance = 1.36

Answer d.

If Stock B is less highly correlated with the market than A, then it might have a lower beta than Stock A, and hence be less risky in a portfolio sense