Question

Stuart Company'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? (Hint: Use the formula for the standard deviation of a population, not a sample.)

Economic

Conditions Prob. Return

Strong 30%   22.60%

Normal 40% 10.0%

Weak 30% −16.0%

Select the correct answer.

Answer 1

Expected Return=Respective return*Respective probability

=(0.3*22.6)+(0.4*10)+(0.3*-16)=5.98%

probability	Return	probability*(Return-Expected Return)^2
0.3	22.6	0.3*(22.6-5.98)^2=82.86732
0.4	10	0.4*(10-5.98)^2=6.46416
0.3	-16	0.3*(-16-5.98)^2=144.93612
		Total=234.2676%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=15.31%(Approx).