Question

Stocks A and B have the following probability distributions of expected future returns: Probability A B 0.2 (7%) (37%) 0.2 4 0 0.2 13 19 0.3 18 27 0.1 38 48 Calculate the expected rate of return, , for Stock B ( = 11.20%.) Do not round intermediate calculations. Round your answer to two decimal places.   % Calculate the standard deviation of expected returns, σA, for Stock A (σB = 26.62%.) 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? 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. 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. 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. 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. 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. -Select- Assume the risk-free rate is 2.5%. 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? 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. 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. 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. 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. 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. -Select-

Answer 1

a. Expected Return of Stock B =0.2*-37%+0.2*0%+0.2*19%+0.3*27%+0.1*48% =9.30%

b. Standard Deviation of Stock A =(0.2*(-7%-11.20%)^2+0.2*(4%-11.20%)^2+0.2*(13%-11.20%)^2+0.3*(18%-11.20%)^2+0.1*(38%-11.200%)^2)^0.5 =12.77%

Coefficient of Variation =Standard Deviation of B/Expected Return of B =12.77%/9.30% =1.37

Option II is correct option 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.

c. Sharpe Ratio of A =(Expected Return -Risk free rate)/Standard Deviation =(11.20%-2.5%)/12.77% =0.68
Sharpe Ratio of B =(Expected Return -Risk free rate)/Standard Deviation =(9.30%-2.5%)/26.62% =0.26
Option I 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.