What is the standard deviation of the returns on this stock?
State of the Economy Probability E(R)
Boom 0.33 24%
Normal 0.55 12%
Recession 0.12 -60%
Expected return=Respective return*Respective probability
=(0.33*24)+(0.55*12)+(0.12*-60)=7.32%
probability | Return | probability*(Return-Expected Return)^2 |
0.33 | 24 | 0.33*(24-7.32)^2=91.813392 |
0.55 | 12 | 0.55*(12-7.32)^2=12.04632 |
0.12 | -60 | 0.12*(-60-7.32)^2=543.837888 |
Total=647.6976% |
Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=(647.6976)^(1/2)
=25.45%(Approx).
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