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?
Homework Answers
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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Outcome Probability Return
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