Question

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?

Round your answer to two decimal places. For example, if your answer is $345.6671 round as 345.67 and if your answer is .05718 or 5.7182% round as 5.72.

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%

Answer 1

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).