Question

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

Probability	A	B
0.1	(7%)	(35%)
0.2	3	0
0.3	12	19
0.2	20	30
0.2	32	46

Calculate the expected rate of return, rB, for Stock B (rA = 13.90%.) Do not round intermediate calculations. Round your answer to two decimal places.
%

Calculate the standard deviation of expected returns, σA, for Stock A (σB = 23.05%.) 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 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.

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.

Answer 1

Expected rate of return for Stock B=0.1*(-35%)+0.2*0%+0.3*19%+0.2*30%+0.2*46%=17.400%

Standard Deviation of expected returns for Stock A=sqrt(0.1*(-7%-13.90%)^2+0.2*(3%-13.90%)^2+0.3*(12%-13.90%)^2+0.2*(20%-13.90%)^2+0.2*(32%-13.90%)^2)=11.895%

Now calculate the coefficient of variation for Stock B.
=23.05%/17.40%
=1.324712644

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.