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 variance of the returns on this common stock?
A) .001150
B) .001306
C) .001524
D) .001389
E) .001421

Question

Quizplus · Accepted Answer

To calculate the variance of the returns on the common stock, we need to first calculate the expected return and the expected squared return.

Expected return (E(R)):
E(R) = (0.12 x 0.18) + (0.78 x 0.08) + (0.10 x 0.02)
E(R) = 0.048 + 0.0624 + 0.002
E(R) = 0.1124 or 11.24%

Expected squared return (E(R^2)):
E(R^2) = (0.12 x (0.18^2)) + (0.78 x (0.08^2)) + (0.10 x (0.02^2))
E(R^2) = 0.03888 + 0.0048384 + 0.0004
E(R^2) = 0.0441184

Now we can use the formula for variance:
Variance = E(R^2) - [E(R)]^2
Variance = 0.0441184 - (0.1124^2)
Variance = 0.001524 or 0.1524% (rounded)

Therefore, the correct answer is C.

The Rate of Return on the Common Stock of Lancaster