Question

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

Probability	A	B
0.1	(8%)	(24%)
0.2	5	0
0.3	13	23
0.3	24	30
0.1	30	44

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 14.30%.) 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 = 18.96%.) 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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Answer 1

Answer a.

Stock B:

Expected Rate of Return = 0.10 * (-0.24) + 0.20 * 0.00 + 0.30 * 0.23 + 0.30 * 0.30 + 0.10 * 0.44
Expected Rate of Return = 0.1790 or 17.90%

Answer b.

Stock A:

Variance = 0.10 * (-0.08 - 0.1430)^2 + 0.20 * (0.05 - 0.1430)^2 + 0.30 * (0.13 - 0.1430)^2 + 0.30 * (0.24 - 0.1430)^2 + 0.10 * (0.30 - 0.1430)^2
Variance = 0.012041

Standard Deviation = (0.012041)^(1/2)
Standard Deviation = 0.1097 or 10.97%

Answer c.

Stock B:

Coefficient of Variation = Standard Deviation / Expected Return
Coefficient of Variation = 0.1896 / 0.1790
Coefficient of Variation = 1.06

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.