Question

Hayek Corporation has a 0.5 probability of a return of 0.00, a 0.2 probability of a rate of return of 0.08, and the remaining probability of a 0.40 rate of return. What is the variance in the expected rate of return of Hayek Corporation?

Answer 1

remaining probability=1-0.5-0.2=0.3

Expected return=Respective return*Respective probability

=(0.5*0)+(0.2*0.08)+(0.3*0.4)=0.136

probability	Return	probability*(Return-Expected Return)^2
0.5	0	0.5*(0-0.136)^2=0.009248
0.2	0.08	0.2*(0.08-0.136)^2=0.0006272
0.3	0.4	0.3*(0.4-0.136)^2=0.0209088
		Total=0.030784

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

=0.1755(Approx).

Variance=Standard deviation^2

=0.030784.