Kurt's Adventures, Inc. stock is quite cyclical. In a boom economy, the stock is expected to return 30% in comparison to 12% in a normal economy and a negative 20% in a recessionary period. The
Probability of a recession is 15%. There is a 30% chance of a boom economy. The remainder of the
Time the economy will be at normal levels. What is the standard deviation of the returns on Kurt's
Adventures, Inc. stock?
A) 10.05%
B) 12.60%
C) 15.83%
D) 17.46%
E) 25.04%

Question

Quizplus · Accepted Answer

To find the standard deviation, first calculate the expected return: E(R) = 0.30*0.30 + 0.12*0.55 + (-0.20)*0.15 = 0.099 or 9.9%. Then, calculate the variance: Var(R) = 0.30*(0.30-0.099)^2 + 0.55*(0.12-0.099)^2 + 0.15*(-0.20-0.099)^2 = 0.02506. The standard deviation is the square root of the variance: √0.02506 = 0.1583 or 15.83%.