Question

The returns on shares of Valley Transporter are predicted under the following various economic conditions: Recession -0.14 Normal +0.04 Boom +0.18 If each economy state has the same probability of occurring (33.33%), what is the variance of the stock? Place your answer in decimal form using four decimal places.

Answer 1

Expected return=Respective return*Respective probability

=(1/3*-0.14)+(1/3*0.04)+(1/3*0.18)=0.02667

probability	Return	probability*(Return-Expected return)^2
1/3	-0.14	1/3*(-0.14-0.02667)^2=0.00925962963
1/3	0.04	1/3*(0.04-0.02667)^2=0.0000592296333
1/3	0.18	1/3*(0.18-0.02667)^2=0.0078366963
		Total=0.017156(Approx)

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

=(0.017156)^(1/2)

=0.131(Approx)

Variance=Standard deviation^2

=0.0172(Approx)