Question

Stock S is expected to return 12 percent in a boom and 6 percent in a normal economy. Stock T is expected to return 20 percent in a boom and 4 percent in a normal economy. There is a 40 percent probability that the economy will boom; otherwise, it will be normal. What is the portfolio variance if 30 percent of the portfolio is invested in Stock S and 70 percent is invested in Stock T?

A. .002220 

B. .008080 

C. .006224 

D. .004056 

E. .098000

Answer 1

stock S

expected return = 12 * 0.4 + 6 * 0.6 = 8.4

E(X^2) = 12^2 * 0.4 + 6^2 * 0.6 = 79.2

=> variance = 79.2 - 8.4^2 = 8.64

stock T

expected return = 20 * 0.4 + 4 * 0.6 = 10.4

E(X^2) = 20^2 * 0.4 + 4^2 * 0.6 = 169.6

variance = 169.6 - 10.4^2 = 61.44

variance of portifolio = 0.3 * 8.64 + 61.44 * 0.7 = 0.004056

hence D is the correct choice