Answer:
a. STOCK A
State of nature R(%) P ER R-ER R - ER2.P
Recession 0.010 0.20 0.002 -0.1015 0.00206045
Normal 0.090 0.55 0.0495 -0.0215 0.0002542375
Boom 0.240 0.25 0.06 0.1285 0.0041280625
ER 0.1115 Variance 0.00644275
STOCK B
State of nature R(%) P ER R - ER R - ER2.P
Recession -0.35 0.20 -0.07 -0.5375 0.05778125
Normal 0.25 0.55 0.1375 0.0625 0. 0021484375
Boom 0.48 0.25 0.12 0.2925 0.021389062
ER 0.1875 Variance 0.08131875
Expected return of stock A = 0.1115 = 11.15%
Expected return of stock B = 0.1875 = 18.75%
b. Standard deviation of stock A = √0.00644275 = 0.0802
Standard deviation of stock B = √0.08131875= 0.2852
Explanation:
In the first case, there is need to calculate the expected return of each stock by multiplying the return by probability.
In the second case, we need to obtain the variance. The square root of variance gives the standard deviation. Variance is calculated by deducting the expected return from the actual return, then, raised the difference by power 2 multiplied by probability.
