Question

Outcome Probability Return Boom 60% 0.26 Normal 25% 0.19 Recession 10% 0.14 Depression 5% 0.10 What...

Outcome Probability Return

Boom 60% 0.26

Normal 25% 0.19

Recession 10% 0.14

Depression 5% 0.10

What is the variance of this asset's returns?

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Answer #1

Expected return=Respective return*Respective probability

=(0.6*0.26)+(0.25*0.19)+(0.1*0.14)+(0.05*0.1)=0.2225

probability Return probability*(Return-Expected Return)^2
0.6 0.26 0.6*(0.26-0.2225^2=0.00084375
0.25 0.19 0.25*(0.19-0.2225)^2=0.0002640625
0.1 0.14 0.1*(0.14-0.2225)^2=0.000680625
0.05 0.1 0.05*(0.1-0.2225)^2=0.0007503125
Total=0.00253875

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

=(0.00253875)^(1/2)

=0.0504(Approx)

Variance=Standard deviation^2

=0.00253875(Approx)

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