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 probability of 40 percent that the economy will boom; otherwise, it will be normal. What is the portfolio variance and standard deviation if 30 percent of the portfolio is invested in Stock S and 70 percent is invested in Stock T? Briefly discuss what this means to the stock.

Answer 1

E(r) = [Pi x Ri]

E(rS) = [0.40 x 12%] + [0.60 x 6%] = 4.8% + 3.6% = 8.4%

E(rT) = [0.40 x 20%] + [0.60 x 4%] = 8% + 2.4% = 10.4%

E(rP) = [0.30 x 8.4%] + [0.70 x 10.4%] = 2.52% + 7.28% = 9.8%

² = [Pi x {E(r) - Ri}²]

= [0.30 x (9.8% - 8.4%)²] + [0.70 x (9.8% - 10.4%)²] = 0.588%² + 0.252%² = 0.84%²

= [²]^1/2 = [0.84%²]^1/2 = 0.92%