Florida Company (FC)and Minnesota Company (MC)are both service companies. Their stock returns for the past three years were as follows: FC: −5%, 15 percent, 20 percent; MC: 8 percent, 8 percent, 20 percent.
Calculate the covariance between the returns of FC and MC. (Ignore the correction for the loss of a degree of freedom set out in the text.)

Question

Quizplus · Accepted Answer

Covariance can be calculated using the formula:

Cov(FC, MC) = [(R(FC) - E(FC))*(R(MC) - E(MC))] / (n-1)

Where R(FC) and R(MC) are the respective returns for FC and MC, E(FC) and E(MC) are the respective expected returns for FC and MC, and n is the number of years (in this case, 3).

Using the given data, we can calculate:

E(FC) = (−5% + 15% + 20%) / 3 = 10%
E(MC) = (8% + 8% + 20%) / 3 = 12%

Then the covariance is:

Cov(FC, MC) = [(-5% - 10%)*(8% - 12%) + (15% - 10%)*(8% - 12%) + (20% - 10%)*(20% - 12%)] / (3-1)
= [(-15%)*(-4%) + (5%)*(−4%) + (10%)*(8%)] / 2
= [0.6% - 0.2% + 0.8%] / 2
= 0.6%

Therefore, the answer is C (40).

Florida Company (FC)and Minnesota Company (MC)are Both Service Companies