Question

The rate of return on the common stock of a company is expected to be 12.75% in a boom economy, 7.75% in a normal economy, and only 2.25% in a recessionary economy. The probabilities of these economic states are 27.0% for a boom, 56.0% for a normal economy, and 17.0% for a recession. What is the variance of the returns on the common stock of the company?

Answer 1

Expected return=Respective return*Respective probability

=(0.27*12.75)+(0.56*7.75)+(0.17*2.25)=8.165%

probability	Return	probability*(Return-Expected Return)^2
0.27	12.75	0.27*(12.75-8.165)^2=5.67600075
0.56	7.75	0.56*(7.75-8.165)^2=0.096446
0.17	2.25	0.17*(2.25-8.165)^2=5.94782825
		Total=11.720275%

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

=(11.720275)^(1/2)

=3.42%(Approx)

Variance=Standard deviation^2

=0.0011720275