Given the returns and probabilities for the three possible s

Given the returns and probabilities for the three possible states listed here, calculate the covariance between the returns of Stock A and Stock B. For convenience, assume that the expected returns of Stock A and Stock B are 0.11 and 0.16, respectively. (Round your answer to 4 decimal places. For example .1244)

Probability

Return(A)

Return(B)

Good

0.35

0.30

0.50

OK

0.50

0.10

0.10

Poor

0.15

-0.25

-0.30

Solution

We have the follwoing table

cov(A,B)=E(AB)-E(A)E(B)

E(AB)= .3*.5*P(Good)+(.5*.1)*P(Ok)+(-.25*-.30)P(poor)

E(AB)=.15*.35+.05*.5+.075*.15

E(AB)=.07125.

Now cov(A,B)=.07125-.11*.16=.07125-.0176=0.05365