Bernard Companies stock has an expected return of 9.5 percent. The stock is expected to return 11 percent in a normal economy and 13.4 percent in a boom. The probabilities of a recession, normal economy, and a boom are 10 percent, 84 percent, and 6 percent, respectively. What is the expected return if the economy is in a recession?

Expected rate of return during recession is -5.44%

Explanation:

Firstly , let’s assume the expected return during recession = x

From the question, the expected return = 9.5% = 9.5/100 = 0.095

Mathematically;

Expected return = [ ( probability of recession * return during recession) + (probability of normal economy * return during normal economy) + (probability of boom * return during boom)]

Using the data obtainable from the question;

0.095 = (0.1)(x) + (0.11)(0.84) + (0.134)(0.06)

0.095 = 0.1x + 0.0924 + 0.00804

0.1x = 0.095-0.0924-0.00804

0.1x = -0.00544

x = -0.00544/0.1

x = -0.0544 or simply -5.44%