A stock is expected to earn 15 percent in a boom economy and 7 percent in a normal economy. There is a 35 percent chance the economy will boom and a 65.0 percent chance the economy will be normal. What is the standard deviation of these returns?

A. 3.82 PercentB. 4.85 PercentC. 4.97 PercentD. 5.63 Percent.

A. 3.82

Explanation:

First, find the expected return of the stock;

E (r) = SUM (prob * return)

E (r) = (0.35 * 0.15) + (0.65 * 0.07)

= 0.0525 + 0.0455

=0.098 or 9.8%

Next, use the variance formula to find the stock's standard deviation;

σ² = 0.35 (0.15 - 0.098) ² + 0.65 (0.07 - 0.098) ²

σ² = 0.0009464 + 0.0005096

σ² = 0.001456

As a percentage, it becomes; 0.001456 * 100 = 0.1456%

The variance is therefore 0.1456%

Find standard deviation;

Standard deviation = SQRT (0.001456)

STDEV = 0.03816 or 3.82%