Question

Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. Assume that all three states are equally likely. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Security Return if State State of Economy Recession Normal Occurs -9.00% 16.00 Boom 25.00 Standard deviation

Answer 1

Expected return = sum of (probability of state * return of state)

= 1/3 * -9% + 1/3 * 16% + 1/3 * 25%

= 10.67%

E(X^2) =  sum of (probability of state * return of state^2)

= 1/3 * (-9%)^2 + 1/3 * (16%)^2 + 1/3 * (25%)^2

= 0.03206666666

variance = E(X^2) - (E(X))^2

= 0.03206666666 - (10.67%)^2

= 0.02068177666

Standard deviation = sqrt(variance)

= sqrt(0.02068177666)

= 14.38%