Question

The rate of return on the common stock of a company is expected to be 11.25% in a boom economy, 6.25% in a normal economy, and only 0.75% in a recessionary economy. The probabilities of these economic states are 21.0% for a boom, 68.0% for a normal economy, and 11.0% for a recession. What is the variance of the returns on the common stock of the company?

Question 4 options:

	0.000754
	0.000775
	0.000796
	0.000817
	0.000838

Answer 1

Expected return=Respective return*Respective probability

=(0.21*11.25)+(0.68*6.25)+(0.11*0.75)=6.695%

probability	Return	probability*(Return-Expected Return)^2
0.21	11.25	0.21*(11.25-6.695)^2=4.35708525
0.68	6.25	0.68*(6.25-6.695)^2=0.134657
0.11	0.75	0.11*(0.75-6.695)^2=3.88773275
		Total=8.379475%

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

=(8.379475)^(1/2)

=2.89%(Approx)

Variance=Standard deviation^2

=0.000838(Approx)