Question

Southern Wear stock has an expected return of 15.1 percent. The stock is expected to lose 8 percent in a recession and earn 18 percent in a boom. The probabilities of a recession, a normal economy, and a boom are 2 percent, 87 percent, and 11 percent, respectively. What is the expected return on this stock if the economy is normal?

Answer 1

Answer:

15.26%

Explanation:

Let the expected return if economy is normal be X

Expected return ; E(R) = SUM(probability. *return)

E(R) =15.1% OR 0.151 as a decimal

RECESSION: (probability. *return) = -0.08 * 0.02 = -0.0016

NORMAL: (probability. *return) = 0.87 *X = 0.87X

BOOM: (probability. *return) = 0.11 *0.18 = 0.0198

Next, sum the three returns and equate them to 0.151;

-0.0016 + 0.87X + 0.0198 = 0.151

0.87X + 0.0182 = 0.151

Subtract 0.0182 from both sides;

0.87X = 0.151 - 0.0182

0.87X = 0.1328

Divide both sides by 0.87 to solve for X;

X = 0.1526 as a decimal or 15.26%

Therefore, expected return if economy is normal is 15.26%