Question

This is only one problem. All parts please.

Problem 8-6
Expected returns

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

Probability	A	B
0.1	-7%	-38%
0.2	6	0
0.4	14	18
0.2	24	25
0.1	28	47

1. Calculate the expected rate of return, r_B, for Stock B (r_A = 13.70%.) 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 = 21.17%.) Do not round intermediate calculations. Round your answer to two decimal places.
   %

3. Now calculate the coefficient of variation for Stock B. Round your answer to two decimal places.

4. 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 the same beta as Stock A, and hence be just as risky in a portfolio sense.
   2. 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. 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. 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.
   5. 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.

Answer 1

Expected returns=Sum(probability*returns)

Standard deviation=Sqrt(Sum(probability*(returns-expected returns)^2))

Coefficient of variation=Standard deviation/expected returns

1.
=0.1*(-38%)+0.2*0%+0.4*18%+0.2*25%+0.1*47%
=13.100%

2.
=sqrt(0.1*(-7%-13.70%)^2+0.2*(6%-13.70%)^2+0.4*(14%-13.70%)^2+0.2*(24%-13.70%)^2+0.1*(28%-13.70%)^2)
=9.82%

3.
=21.17%/13.100%
=1.616030534

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.