Question

The rate of return on the common stock of a company is expected to be 13.25% in a boom economy, 8.25% in a normal economy, and only 2.75% in a recessionary economy. The probabilities of these economic states are 29.0% for a boom, 52.0% for a normal economy, and 19.0% 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

=(0.29*13.25)+(0.52*8.25)+(0.19*2.75)=8.655%

probability	Return	probability*(Return-Expected Return)^2
0.29	13.25	0.29*(13.25-8.655)^2=6.12306725
0.52	8.25	0.52*(8.25-8.655)^2=0.085293
0.19	2.75	0.19*(2.75-8.655)^2=6.62511475
		Total=12.833475%

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

=(12.833475)^(1/2)

=3.58%(Approx)

Variance=Standard deviation^2

=0.0012833475