Question

The rate of return on the common stock of a company is expected to be 14.25% in a boom economy, 9.25% in a normal economy, and only 3.75% in a recessionary economy. The probabilities of these economic states are 33.0% for a boom, 44.0% for a normal economy, and 23.0% for a recession. What is the variance of the returns on the common stock of the company?

Question 11 options:

	0.001393
	0.001431
	0.001468
	0.001506
	0.001544

Answer 1

Expected return=Respective return*Respective probability

=(0.33*14.25)+(0.44*9.25)+(0.23*3.75)=9.635%

probability	Return	probability*(Return-Expected Return)^2
0.33	14.25	0.33*(14.25-9.635)^2=7.02841425
0.44	9.25	0.44*(9.25-9.635)^2=0.065219
0.23	3.75	0.23*(3.75-9.635)^2=7.96564175
		Total=15.059275%

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

=(15.059275)^(1/2)

=3.88%(Approx)

Variance=Standard deviation^2

=0.001506(Approx)