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.

State of the Economy	Probability of State Occurring	Stock's Expected Return
Boom	30.00%	19.55%
Normal	51.00%	16.35%
Recession	19.00%	9.50%

Answer 1

Expected return=Respective Return*Respective probability

=(19.55*0.3)+(16.35*0.51)+(9.5*0.19)=16.0085%

probability	Return	probability*(Return-Expected Return)^2
0.3	19.55	0.3*(19.55-16.0085)^2=3.76266675
0.51	16.35	0.51*(16.35-16.0085)^2=0.059477347
0.19	9.5	0.19*(9.5-16.0085)^2=8.048508728
		Total=11.87065283%

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

=3.445%(Approx)

Hence coefficient of variation=Standard deviation/Expected return

=(3.445/16.0085)

=0.22(Approx).