Question

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

Probability	A		B
0.1	(6	%)	(21	%)
0.2	6		0
0.5	15		22
0.1	24		29
0.1	35		36

1. Calculate the expected rate of return, , for Stock B ( = 14.00%.) 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 = 16.21%.) 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 lower beta than Stock A, and hence be less risky in a portfolio sense.
   2. 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. 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.
   4. 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.
   5. 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-IIIIIIIVVItem 4

3. 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 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

1.
=0.1*(-21%)+0.2*0%+0.5*22%+0.1*29%+0.1*36%
=15.4000%

2.
=sqrt(0.1*(-6%-14.00%)^2+0.2*(6%-14.00%)^2+0.5*(15%-14.00%)^2+0.1*(24%-14.00%)^2+0.1*(35%-14.00%)^2)
=10.3634%

3.
=16.21%/15.4000%
=1.0526

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.
=(14%-2.5%)/10.3634%
=1.1097

6.
=(15.4000%-2.5%)/16.21%
=0.7958

7.
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.