The common stock of Manchester & Moore is expected to earn 14 percent in a recession, 7 percent in a normal economy, and lose 4 percent in a booming economy. The probability of a boom is 15 percent while the probability of a recession is 5 percent. What is the expected rate of return on this stock?

5.7%

Explanation:

The computation of the expected rate of return is shown below:

= (Expected return of the boom × weightage of boom) + (expected return of the normal economy × weightage of normal economy) + (expected return of the recession × weightage of recession)

= (15% × -4%) + (7% × 80%) + (5% × 14%)  

= -0.6% + 5.6% + 0.7%

= 5.7%

We simply multiply the weightage with each its expected return

The weightage of the normal economy is

= 100% - 15% - 5%

= 80%