Question

Barbara is considering investing in a stock and is aware that the return on that investment is particularly sensitive to how the economy is performing. Her analysis suggests that four states of the economy can affect the return on the investment. Using the table of returns and probabilities below calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.) Probability Return Boom 0.4 25.00% Good 0.1 15.00% Level 0.3 10.00% Slump 0.2 -5.00%

Coefficient of variation

Answer 1

Expected return=Respective return*Respective probability

=(0.4*25)+(0.1*15)+(0.3*10)+(0.2*-5)

=13.5%

Probability	Return	Probability*(Return-Expected return)^2
0.4	25	0.4*(25-13.5)^2=52.9
0.1	15	0.1*(15-13.5)^2=0.225
0.3	10	0.3*(10-13.5)^2=3.675
0.2	-5	0.2*(-5-13.5)^2=68.45
		Total=125.25%

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

=(125.25)^(1/2)

=11.19151%(Approx)

Coefficient of variation=Standard deviation/Expected return

=11.19151/13.5

=0.82900(Approx)