Question

Expected Return, Variance, Std. Deviation and Cofficient of Variation:
Magee Inc.'s manager believes that economic conditions during the next year will be strong, normal, or weak, and she thinks that the firm's returns will have the probability distribution shown below. What's the standard deviation of the estimated returns?

Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72.

State of the Economy	Probability of State Occurring	Stock's Expected Return
Boom	30%	25.35%
Normal	45%	14.85%
Recession	25%	–11.70%

A. 18.25%

B. 14.04%

C. 10.53%

D. 15.44%

E. 12.64%

Answer 1

Expected Return=Respective Return*Respective probability

=(0.3*25.35)+(0.45*14.85)+(0.25*-11.7)

=11.3625%

probability	Return	probability*(Return-Expected Return)^2
0.3	25.35	0.3*(25.35-11.3625)^2=58.69504688
0.45	14.85	0.45*(14.85-11.3625)^2=5.473195313
0.25	-11.7	0.25*(-11.7-11.3625)^2=132.9697266
		Total=197.1379688%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)

=(197.1379688)^(1/2)

=14.04%(Approx).