Consider the following facts. The standard deviation of the cash flows associated with Business I is 0.8.

The larger this standard deviation, the riskier a business’s future cash flows are likely to be. The standard deviation of the cash flows associated with Business II is 1.3.

That is, Business II is riskier than Business I. Finally, the correlation between the cash flows of these two businesses over time is 0.8.

This means that when Business I is up, Business II tends to be down, and vice versa. Suppose one firm owns both of these businesses.

(a) Assuming that Business I constitutes 40 percent of this firm’s revenues and Business II constitutes 60 percent of its revenues, calculate the riskiness of this firm’s total revenues using the following equation:

sdI,II = 3w2 sdI 2 + 11 - w22 sdII 2 + 2w11 + w21rI,IIsdIsdII2 Where w = 0.40; sdI = 0.8, sdII = 1.3, and rI, II = -8.

(b) Given this result, does it make sense for this firm to own both Business I and Business II? Why or why not?