Question

The rate of return on the common stock of a company is expected to be 15.50% in a boom economy, 10.50% in a normal economy, and only 5.00% in a recessionary economy. The probabilities of these economic states are 38.0% for a boom, 34.0% for a normal economy, and 28.0% 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

=(0.38*15.5)+(0.34*10.5)+(0.28*5)=10.86%

probability	Return	probability*(Return-Expected Return)^2
0.38	15.5	0.38*(15.5-10.86)^2=8.181248
0.34	10.5	0.34*(10.5-10.86)^2=0.044064
0.28	5	0.28*(5-10.86)^2=9.615088
		Total=17.8404%

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

=(17.8404)^(1/2)

=4.22%(Approx)

Variance=Standard deviation^2

=0.00178404