If the economy booms, Meyer&Co. stock will have a return of 20.4 percent. If the economy goes into a recession, the stock will have a loss of 12.7 percent. The probability of a boom is 67 percent while the probability of a recession is 33 percent. What is the standard deviation of the returns on the stock?

The standard deviation of the returns on the stock is 15.56% (Approx).

Explanation:

Expected Return=Respective return*Respective probability

= (20.4*0.67) + (-12.7*0.33) = 9.477%

probability Return probability * (Return-Expected Return) ^2

0.67 20.4 0.67 * (20.4-9.477) ^2=79.93899243

0.33 - 12.7 0.33 * (-12.7-9.477) ^2=162.3003786

Total=242.239371%

Standard deviation=[Total probability * (Return-Expected Return) ^2/Total probability]^ (1/2)

=15.56% (Approx).