Question

Calculate the expected return, standard deviation, and coefficient of variation for the following probability distribution.

Probability(%) Return(%)

10 12

25 18

45 20

20 -8   

Answer 1

Expected return=Respective return*Respective probability

=(0.1*12)+(0.25*18)+(0.45*20)+(0.2*-8)=13.1%

probability	Return	probability*(Return-Expected Return)^2
0.1	12	0.1*(12-13.1)^2=0.121
0.25	18	0.25*(18-13.1)^2=6.0025
0.45	20	0.45*(20-13.1)^2=21.4245
0.2	-8	0.2*(-8-13.1)^2=89.042
		Total=116.59%

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

=(116.59)^(1/2)

=10.8%(Approx)

Coefficient of variation=Standard deviation/Expected return

=(10.8/13.1)

=0.82(Approx).