Question

The rate of return on the common stock of Lancaster Woolens is expected to be 18 percent in a boom economy, 8 percent in a normal economy, and only 2 percent in a recessionary economy. The probabilities of these economic states are 12 percent for a boom and 10 percent for a recession. What is the expected risk on this common stock? [3 points] a. 0.01150 b. 0.01306 c. 0.12345 d. 0.001389 e. 0.001421

Answer 1

Return during Boom = 18%
Return during Normal = 8%
Return during Recession = 2%

Probability of Boom = 12%
Probability of Normal = 78%
Probability of Recession = 10%

Expected Return = 0.12 * 0.18 + 0.78 * 0.08 + 0.10 * 0.02
Expected Return = 0.0860 or 8.60%

Variance = 0.12 * (0.18 - 0.086)^2 + 0.78 * (0.08 - 0.086)^2 + 0.10 * (0.02 - 0.086)^2
Variance = 0.001524

Standard Deviation = (0.001524)^(1/2)
Standard Deviation = 0.0390 or 3.90%

Therefore, expected risk on this common stock is 0.001524