Kurt's Adventures SA equity is quite cyclical.In a boom economy, the equity 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 SA?
A)10.05%
B)12.60%
C)15.83%
D)17.46%
E)25.04%

Question

Quizplus · Accepted Answer

The expected return can be calculated as follows:
ER = probability of a boom economy * return in a boom economy
   + probability of a recession * return in a recession
   + probability of a normal economy * return in a normal economy
ER = (0.3 * 30%) + (0.15 * -20%) + (0.55 * 12%) = 13.5%
The standard deviation can be calculated as follows:
SD = sqrt[((0.3 * 30% - 13.5%)^2 + (0.15 * -20% - 13.5%)^2 + (0.55 * 12% - 13.5%)^2 )/(3-1)]
SD = 15.83%
Therefore, the best choice is C, as it correctly calculates the standard deviation of the returns on Kurt's Adventures SA.

Kurt's Adventures SA Equity Is Quite Cyclical