If there is a 30% chance of a 14% return, a 20% chance of an 18% return. a 25% chance of an 19.5% return and a 25% chance of a 12% return, then what is the standard deviation of returns?
Expected return=Respective return*Respective probability
=(0.3*14)+(0.2*18)+(0.25*19.5)+(0.25*12)=15.675%
probability | Return | probability*(Return-Expected Return)^2 |
0.3 | 14 | 0.3*(14-15.675)^2=0.8416875 |
0.2 | 18 | 0.2*(18-15.675)^2=1.081125 |
0.25 | 19.5 | 0.25*(19.5-15.675)^2=3.65765625 |
0.25 | 12 | 0.25*(12-15.675)^2=3.37640625 |
Total=8.956875% |
Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=(8.956875)^(1/2)
=2.99%(Approx)
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