The returns on the common stock of New Image Products are quite cyclical. In a boom economy, the stock is expected to return 32 percent in comparison to 14 percent in a normal economy and a negative 28 percent in a recessionary period. The probability of a recession is 25 percent while the probability of a boom is 10 percent. What is the standard deviation of the returns on this stock?
19.94 percent
E(r) = (0.10 0.32) + (0.65 0.14) + (0.25 -0.28) = 0.053
Var = 0.10 (0.32 - 0.053)2 + 0.65 (0.14 - 0.053)2 + 0.25 (-0.28 - 0.053)2 = 0.039771
Std dev = 0.039771 = 19.94 percent
