Question

# You were analyzing a stock and came up with the following probability distribution of the stock...

You were analyzing a stock and came up with the following probability distribution of the stock returns. What is the coefficient of variation on the company's stock?

 State of the Economy Probability of State Occurring Stock's Expected Return Boom 25.00% 19.90% Normal 51.00% 17.45% Recession 24.00% 8.10%

Expected Return=Respective return*Respective probability

=(0.25*19.9)+(0.51*17.45)+(0.24*8.1)=15.8185%

 probability Return probability*(Return-Expected Return)^2 0.25 19.9 0.25*(19.9-15.8185)^2=4.164660563 0.51 17.45 0.51*(17.45-15.8185)^2=1.357514048 0.24 8.1 0.24*(8.1-15.8185)^2=14.29805814 Total=19.82023275%

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

=4.452%(Approx)

Coefficient of variation=Standard deviation/Expected Return

=(4.452/15.8185)=0.28(Approx).

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