Question

Egg Hunter's stock is expected to return 16.5 percent in a normal economy. It is projected at a negative 11.6 percent in case the economy instead falls into a recession. The chance of a normal economy is 80 percent. The chance of a recession is 20 percent. Calculate the variance of the returns on Egg Hunter's stock.

Options:

A. 0.012634
B. 0.013927
C. 0.010346
D. 0.013420
E. 0.014315

Answer 1

The variance of the returns on Egg Hunter's stock, considering the chances of a normal economy and a recession, is calculated to be 0.012634. This corresponds to Option A.

Step-by-step explanation:

To calculate the variance of the returns on Egg Hunter's stock, we will use the expected returns and their associated probabilities. We first find the expected return (mean) and then find the variance by considering the probable outcomes.

• Expected return (mean) = (0.80 * 16.5%) + (0.20 * -11.6%) = 13.2% + (-2.32%) = 10.88%
• Variance = (0.80 * (16.5% - 10.88%)^2) + (0.20 * (-11.6% - 10.88%)^2)
• Variance = (0.80 * (5.62)^2) + (0.20 * (-22.48)^2)
• Variance = (0.80 * 31.5844) + (0.20 * 505.1904)
• Variance = 25.26752 + 101.03808
• Variance = 126.3056
• Since the percentages are represented as whole numbers, the variance should be presented in percentage points squared:
  
  Variance = 0.012634

Hence, the correct answer to the student's question is Option A: 0.012634.