Question

Based on the following information, what is the variance?

State of Economy	Probability of State of Economy	Rate of Return if State Occurs
Recession	.28	−	10.60%
Normal	.31		12.10%
Boom	.41		23.10%

Answer 1

Expected return=Respective return*Respective probability

=(0.28*-10.6)+(0.31*12.1)+(0.41*23.1)=10.254%

Probability	Return	Probability*(Return-Expected Return)^2
0.28	-10.6	0.28*(-10.6-10.254)^2=121.769008
0.31	12.1	0.31*(12.1-10.254)^2=1.05639196
0.41	23.1	0.41*(23.1-10.254)^2=67.6580836
		Total=190.483484%

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

=(190.483484)^(1/2)

=13.80%(Approx)

Variance=Standard deviation^2

=190.48%(or 0.019048 approx).