The mean HPR on stocks is 16.6% and the standard deviation is 1.92
Mean (Expected Return):
Mean = Σ (Probability * HPR)
Standard Deviation (Risk):
Standard Deviation = √Σ [Probability * (HPR - Mean)^2]
For Mean:
= (0.2 * 37%) + (0.6 * 22%) + (0.2 * -20%)
= 7.4% + 13.2% - 4%
= 16.6%
For Standard Deviation:
= √[(0.2 * (37% - 16.6%)^2) + (0.6 * (22% - 16.6%)^2) + (0.2 * (-20% - 16.6%)^2)]
= √[(0.2 * (20.4%)^2) + (0.6 * (5.4%)^2) + (0.2 * (-36.6%)^2)]
= √[(0.2 * 4.1616) + (0.6 * 0.2916) + (0.2 * 13.3956)]
= √[0.83232 + 0.17496 + 2.67912]
= √3.6864
= 1.92.
Full question:
Suppose your expectations regarding the stock market are as follows:
State of Economy Probability HPR
Boom 0.2 37%
Normal growth 0.6 22%
Recession 0.2 -20%
Compute the mean and standard deviation of the HPR on stocks.