Question

Stocks A and B have the following probability distributions of expected future returns: Probability A B 0.2 (5%) (23%), 0.3 6 0, 0.2 11 24, 0.2 20 27, 0.1 35 50

A. Calculate the expected rate of return, , for Stock B ( = 10.50%.) Do not round intermediate calculations. Round your answer to two decimal places. %

B. Calculate the standard deviation of expected returns, σA, for Stock A (σB = 22.46%.) Do not round intermediate calculations. Round your answer to two decimal places. %

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

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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
2. 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.
3. 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.
4. 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.
5. 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.

C. Assume the risk-free rate is 3.0%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to two decimal places.

Stock A:

Stock B:

Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b?

1. In a stand-alone risk sense A is less risky than B. 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.
2. In a stand-alone risk sense A is less risky than B. 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.
3. In a stand-alone risk sense A is less risky than B. 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.
4. In a stand-alone risk sense A is more risky than B. 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. In a stand-alone risk sense A is more risky than B. 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

Expected Return of Stock B =0.2*-23%+0.3*0%+0.2*24%+0.2*27%+0.1*50% =10.60%

B. Standard Deviation of Stock A =(0.2*(-5%-10.50%)^2+0.3*(6%-10.50%)^2+0.2*(11%-10.50%)^2+0.2*(20%-10.50%)+0.1*(35%-10.50%)^2)^0.5 =17.44%

C. Coefficient of Variation of B =Standard Deviation/Expected return =22.46%/10.60% =2.12

d. Option III is correct option 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.

e.Option II is correct option In a stand-alone risk sense A is less risky than B. 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.