Kali's Ski Resort,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 Kali's Ski Resort,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%.