Question

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

Probability	A		B
0.1	(13%)		(31%)
0.2	5		0
0.5	14		24
0.1	20		26
0.1	32		44

1. Calculate the expected rate of return,  , for Stock B ( = 11.90%.) 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 = 19.81%.) 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.

   %

2.Is it possible that most investors might regard Stock B as being less risky than Stock A? (Select one)

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.

2.C. 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:

3. Are these calculations consistent with the information obtained from the coefficient of variation calculations in Part b? (select one)

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

1.
=0.1*(-31%)+0.2*0%+0.5*24%+0.1*26%+0.1*44%
=15.9000%

2.
=sqrt(0.1*(-13%-11.90%)^2+0.2*(5%-11.90%)^2+0.5*(14%-11.90%)^2+0.1*(20%-11.90%)^2+0.1*(32%-11.90%)^2)
=10.9859%

3.
=19.81%/15.9000%
=1.2459119

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.
=(11.90%-1.5%)/10.9859%=0.9466680

6.
=(15.9000%-1.5%)/19.81%=0.7269056

7.
Yes

8.
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