There is a probability of 25 percent that the economy will boom; otherwise,it will be normal.Stock Q is expected to return 18 percent in a boom and 9 percent otherwise.Stock R is expected to return 9 percent in a boom and 5 percent otherwise.What is the standard deviation of a portfolio that is invested 40 percent in Stock Q and 60 percent in Stock R?
A).7 percent
B)1.4 percent
C)2.6 percent
D)6.8 percent
E)8.1 percent

Question

Quizplus · Accepted Answer

First, we need to find the expected return of the portfolio:

Expected return = (0.25 x 18% x 0.4) + (0.75 x 9% x 0.4) + (0.25 x 9% x 0.6) + (0.75 x 5% x 0.6)
Expected return = 6.3%

Next, we need to find the standard deviation of the portfolio:

σ² = (0.25 x 0.4 x (18% - 6.3%)²) + (0.75 x 0.4 x (9% - 6.3%)²) + (0.25 x 0.6 x (9% - 6.3%)²) + (0.75 x 0.6 x (5% - 6.3%)²)
σ² = 0.01197
σ = 3.46%

Therefore, the standard deviation of the portfolio is 3.46%, which is closest to option C (2.6%).

There Is a Probability of 25 Percent That the Economy