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 if 30 percent of the portfolio is invested in Stock S and 70 percent is invested in Stock T?
A).002220
B).004056
C).006224
D).008080
E).098000

Question

Quizplus · Accepted Answer

Firstly, we need to calculate the expected return for the portfolio:
Expected return = (0.4 × 0.12 × 0.3) + (0.4 × 0.20 × 0.7) + (0.6 × 0.06 × 0.3) + (0.6 × 0.04 × 0.7) = 0.132 or 13.2%.

Secondly, we need to calculate the variance of the portfolio using the formula:
Portfolio variance = (0.3^2 × 0.12^2 × 0.4) + (0.3^2 × 0.20^2 × 0.4) + (0.7^2 × 0.06^2 × 0.4) + (0.7^2 × 0.04^2 × 0.4) + 2 × (0.3 × 0.7 × 0.12 × 0.20 × 0.4) - (0.132)^2

Portfolio variance = 0.004056 or 0.4056%
Therefore, the answer is B.

Stock S Is Expected to Return 12 Percent in a Boom