Question

A stock will have a loss of 10.9 percent in a bad economy, a return of 10.7 percent in a normal economy, and a return of 24.6 percent in a hot economy. There is 31 percent probability of a bad economy, 38 percent probability of a normal economy, and 31 percent probability of a hot economy. What is the variance of the stock's returns?

Multiple Choice

A. .03977

B. .14101

C. .01988

D. .02982

E. .01491

Answer 1

Expected return=Respective return*Respective probability

=(-10.9*0.31)+(10.7*0.38)+(24.6*0.31)=8.313%

Probability	Return	Probability*(Return-Expected Return)^2
0.31	-10.9	0.31*(-10.9-8.313)^2=114.433204
0.38	10.7	0.38*(10.7-8.313)^2=2.16515222
0.31	24.6	0.31*(24.6-8.313)^2=82.2325744
		Total=198.830931%

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

=(198.830931)^(1/2)

=14.10%(Approx)

Variance=Standard deviation^2

=0.01988(Approx).