Astock 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%

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