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	.26	−	9.40%
Normal	.43		10.90%
Boom	.31		21.90%

Answer 1

Expected return=Respective return*Respective probability

=(0.26*-9.4)+(0.43*10.9)+(0.31*21.9)=9.032%

probability	Return	probability*(Return-Expected Return)^2
0.26	-9.4	0.26*(-9.4-9.032)^2=88.3320422
0.43	10.9	0.43*(10.9-9.032)^2=1.50045232
0.31	21.9	0.31*(21.9-9.032)^2=51.3314814
		Total=141.163976%

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

=(141.163976)^(1/2)

=11.88%(Approx)

Variance=Standard deviation^2

=0.01412(Approx)