Question

Kate recently invested in real estate with the intention of selling the property one year from today. She has modeled the returns on that investment based on three economic scenarios. She believes that if the economy stays healthy, then her investment will generate a 30 percent return. However, if the economy softens, as predicted, the return will be 10 percent, while the return will be -25 percent if the economy slips into a recession. If the probabilities of the healthy, soft, and recessionary states are 0.3 , 0.4 , and 0.3 , respectively, then calculate the coefficient of variation for the investment? (Round intermediate calculations and answer to 5 decimal places, e.g. 0.07680.)

Coefficient of variation ?

Answer 1

Expected return=Respective return*Respective probability

=(0.3*30)+(0.4*10)+(0.3*-25)

=5.5%

probability	Return	probability*(Return-Expected Return)^2
0.3	30	0.3*(30-5.5)^2=180.075
0.4	10	0.4*(10-5.5)^2=8.1
0.3	-25	0.3*(-25-5.5)^2=279.075
		Total=467.25%

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

=(467.25)^(1/2)

=21.61597%(Approx)

Coefficient of variation=Standard deviation/Expected return

=21.61597/5.5

=3.93018(Approx)