Bruno's stock should return 14 percent in a boom,11 percent in a normal economy,and 4 percent in a recession.The probabilities of a boom,normal economy,and recession are 8 percent,90 percent,and 2 percent,respectively.What is the variance of the returns on this stock?
A)011387
B).000169
C)001506
D)001538
E)011561

Question

Quizplus · Accepted Answer

The variance is calculated using the formula: Variance = Σ [P(x) * (x - μ)^2], where P(x) is the probability of each state, x is the return in each state, and μ is the expected return. First, calculate the expected return: μ = (0.08 * 0.14) + (0.90 * 0.11) + (0.02 * 0.04) = 0.1106. Then, calculate the variance: Variance = (0.08 * (0.14 - 0.1106)^2) + (0.90 * (0.11 - 0.1106)^2) + (0.02 * (0.04 - 0.1106)^2) = 0.000169.

Bruno's Stock Should Return 14 Percent in a Boom,11 Percent