Question

q 26 The rate of return on the common stock of a company is expected to be 13.75% in a boom economy, 8.75% in a normal economy, and only 3.25% in a recessionary economy. The probabilities of these economic states are 31.0% for a boom, 48.0% for a normal economy, and 21.0% 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

=(0.31*13.75)+(0.48*8.75)+(0.21*3.25)=9.145%

probability	Return	probability*(Return-Expected Return)^2
0.31	13.75	0.31*(13.75-9.145)^2=6.57386775
0.48	8.75	0.48*(8.75-9.145)^2=0.074892
0.21	3.25	0.21*(3.25-9.145)^2=7.29771525
		Total=13.946475%

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

=(13.946475)^(1/2)

=3.73%(Approx)

Variance=Standard deviation^2

=0.0013946475