Question

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

Probability	A		B
0.1	(15	%)	(37	%)
0.1	4		0
0.5	14		23
0.2	19		27
0.1	39		37

1. Calculate the expected rate of return, , for Stock B ( = 13.60%.) 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 = 19.96%.) Do not round intermediate calculations. Round your answer to two decimal places.

     %

   Now calculate the coefficient of variation for Stock B. Do not round intermediate calculations. 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 a lower 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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
   3. 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.
   4. 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.
   5. 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. Assume the risk-free rate is 1.5%. What are the Sharpe ratios for Stocks A and B? Do not round intermediate calculations. Round your answers to four 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 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.
   2. 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.
   3. 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.
   4. 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.
   5. 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.

Answer 1

a. Expected return of B =0.1*-37%+0.1*0%+0.5*23%+0.2*27%+0.1*37% =16.90%

b. Standard Deviation of A
=(0.1*(-15%-13.60%)^2+0.1*(4%-13.60%)^2+0.5*(14%-13.60%)^2+0.2*(19%-13.60%)^2+0.1*(39%-13.60%)^2)^0.5=12.71%

Coefficient of Variation =Standard Deviation/Expected Return of B =19.96%/16.90% =1.18

Option III is correct option because lower the beta lower is the risk.

c. Sharpe Ratio of A =(Return of A-Risk free rate)/Standard Deviation=(13.60%-1.5%)/12.71% =0.9523
Sharpe Ratio of B =(Return of A-Risk free rate)/Standard Deviation=(16.90%-1.5%)/19.96% =0.7715

Option IV is correct option