Question

The rate of return on the common stock of a company is expected to be 11.75% in a boom economy, 6.75% in a normal economy, and only 1.25% in a recessionary economy. The probabilities of these economic states are 23.0% for a boom, 64.0% for a normal economy, and 13.0% for a recession. What is the variance of the returns on the common stock of the company? 0.000878 0.000902 0.000926 0.000949 0.000973

Answer 1

Expected return=Respective return*Respective probability

=(0.23*11.75)+(0.64*6.75)+(0.13*1.25)=7.185%

probability	Return	probability*(Return-Expected Return)^2
0.23	11.75	0.23*(11.75-7.185)^2=4.79302175
0.64	6.75	0.64*(6.75-7.185)^2=0.121104
0.13	1.25	0.13*(1.25-7.185)^2=4.57914925
		Total=9.493275%

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

=(9.493275)^(1/2)

=3.08%(Approx)

Variance=Standard deviation^2

=0.000949(Approx)