Question

Based on the following information, what is the standard deviation of returns? State of Economy Recession Normal Boom Probability of State of Economy .30 .33 .37 Rate of Return if State Occurs -.104 .119 .229 Multiple Choice 19.31% 0 13.68% 13.68% 24.95%

Answer 1

Expected rate of return

Expected Return = Sum[Returns x Probability]

= [-10.40% x 0.30] + [11.90% x 0.33] + [22.90% x 0.37]

= -3.12% + 3.93% + 8.47%

= 9.28%

Variance of the returns

Variance of the returns = [(-10.40 – 9.28)² x 0.30] + [(11.90 – 9.28)² x 0.33] + [(22.90 – 9.28)² x 0.37]

= [387.30 x 0.30] + [6.86 x 0.33] + [185.50 x 0.37]

= 116.19 + 2.27 + 68.64

= 187.09

Standard deviation of returns

Standard Deviation of the return = Square Root of 187.09 or [187.09]^1/2

= 13.68%

“Hence, the standard deviation of the returns will be 13.68%”