If the economy is normal, Charleston Freight stock is expected to return 14.3 percent. If the economy falls into a recession, the stock's return is projected at a negative 8.7 percent. The probability of a normal economy is 80 percent. What is the variance of the returns on this stock?
A) .100346
B) .008464
C) .007420
D) .073927
E) .094315

Question

Quizplus · Accepted Answer

The variance of the returns on this stock can be calculated using the formula for the variance of a discrete random variable, which is the sum of the product of each outcome's probability and the square of its deviation from the mean. First, calculate the expected return (mean):Expected return = (0.8 * 14.3%) + (0.2 * -8.7%) = 11.44% - 1.74% = 9.7%Then, calculate the variance:Variance = (0.8 * (14.3% - 9.7%)^2) + (0.2 * (-8.7% - 9.7%)^2) = (0.8 * (0.046)^2) + (0.2 * (-0.184)^2) = (0.8 * 0.002116) + (0.2 * 0.033856) = 0.001693 + 0.0067712 = 0.008464Therefore, the variance of the returns on this stock is 0.008464.

If the Economy Is Normal, Charleston Freight Stock Is Expected