Question

A stock will have a loss of 10.5 percent in a bad economy, a return of 10.3 percent in a normal economy, and a return of 24.2 percent in a hot economy. There is 27 percent probability of a bad economy, 42 percent probability of a normal economy, and 31 percent probability of a hot economy. What is the variance of the stock's returns

Answer 1

Expected return=Respective return*Respective probability

=(-10.5*0.27)+(10.3*0.42)+(24.2*0.31)=8.993%

probability	Return	probability*(Return-Expected Return)^2
0.27	-10.5	0.27*(-10.5-8.993)^2=102.593803
0.42	10.3	0.42*(10.3-8.993)^2=0.71746458
0.31	24.2	0.31*(24.2-8.993)^2=71.6883832
		Total=174.999651%

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

=(174.999651)^(1/2)

=13.23%(Approx)

Variance=Standard deviation^2

=0.0175(Approx)