You were analyzing a stock and came up with the following probability distributi

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.

Probability of State Occurring

Stock's Expected Return

30.00%

20.60%

51.00%

15.65%

19.00%

7.95%

State of the Economy

Probability of State Occurring

Stock's Expected Return

Boom

30.00%

20.60%

Normal

51.00%

15.65%

Recession

19.00%

7.95%

Explanation / Answer

Expected return=Respective return*Respective probability

=(0.3*20.6)+(0.51*15.65)+(0.19*7.95)=15.672%

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

=(18.615366)^(1/2)

=4.315%(Approx)

Coefficient of variation=Standard deviation/ExpectedReturn

=(4.315/15.672)

which is equal to

=0.28(Approx).

probability Return probability*(Return-Expected Return)^2 0.3 20.6 0.3*(20.6-15.672)^2=7.2855552 0.51 15.65 0.51*(15.65-15.672)^2=0.00024684 0.19 7.95 0.19*(7.95-15.672)^2=11.32956396 Total=18.615366%

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