If the economy is normal, Charleston Freight stock is expected to return 16.5 percent. If the economy falls into a recession, the stock's return is projected at a negative 11.6 percent. The probability of a normal economy is 80 percent while the probability of a recession is 20 percent. What is the variance of the returns on this stock?

A. 0.010346

B. 0.012634

C. 0.013420

D. 0.013927

E. 0.014315

option (B) 0.012634

Explanation:

Data provided in the question:

Expected return Probability

16.5% 80%

-11.6% 20%

Now,

Mean return = ∑ (Probability * Expected return)

= (0.8 * 16.5%) + (0.2 * (-11.6%))

= 13.2% - 2.32%

= 10.88%

Thus,

Variance = ∑ (Probability * [ Expected return - Mean return ]²)

= 0.8 * (16.5% - 10.88%) ² + 0.2 * (-11.6% - 10.88%) ²

= 0.8 * (5.62%) ² + 0.2 * (-22.48%) ²

= 0.8 * 0.0562² + 0.2 * 0.2248²

= 0.002526752 + 0.010107008

= 0.01263376 ≈ 0.012634

Hence,

The correct answer is option (B) 0.012634