Question

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

Probability	A		B
0.1	(7	%)	(21	%)
0.1	5		0
0.5	10		23
0.2	18		30
0.1	30		49

1. Calculate the expected rate of return,  , for Stock B (= 11.40%.) 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 = 17.79%.) 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 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.

   -Select-IIIIIIIVVItem 4

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 higher beta than Stock A, and hence be more risky in a portfolio sense.
   2. 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.
   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 lower beta than Stock A, and hence be less 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 higher beta than Stock A, and hence be more 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 lower beta than Stock A, and hence be less risky in a portfolio sense.

Answer 1

a. Expected Return of Stock B =0.1*-21%+0.1*0%+0.5*23%+0.2*30%+0.1*49% =20.30%

b. Standard Deviation of A
=(0.1*(-7%-11.40%)^2+0.1*(5%-11.40%)^2+0.5*(10%-11.40%)^2+0.2*(18%-11.40%)^2+0.1*(30%-11.40%)^2)^0.5 =9.07%

Coefficient of Variation =Standard Deviation of Stock B/Return of Stock B =17.79%/20.30% =0.88

Option V is correct option. Lower the beta lower the risk with respect to market.

c. Sharpe Ratio of A =(Required Rate-Risk Free Rate)/Standard Deviation =(11.40%-1.5%)/9.07% =1.09
Sharpe Ratio of B =(Required Rate-Risk Free Rate)/Standard Deviation =(20.30%-1.5%)/17.79%=1.06

Option III is correct because in standalone case standard deviation or risk of Stock A is less.