Question

(13-1) You are trying to make a forward assessment of the risk and return of a stock that you are considering. You have developed what you consider a reasonable model of the performance of this stock based on five States of the World. Below are your estimates of the probabilities of the States of the World and the associated returns on the shares. State of the World Probability Return Boom 10% 25% Healthy 20% 15% Normal 40% 7% Weak 20% 2% -10% Bust 10% Based on this framework, calculate the expected return on these shares, and the variance and standard deviation of the returns

Answer 1

Expected return=Respective return*Respective probability

=(0.1*25)+(0.2*15)+(0.4*7)+(0.2*2)+(0.1*-10)=7.7%

probability	Return	probability*(Return-Expected Return)^2
0.1	25	0.1*(25-7.7)^2=29.929
0.2	15	0.2*(15-7.7)^2=10.658
0.4	7	0.4*(7-7.7)^2=0.196
0.2	2	0.2*(2-7.7)^2=6.498
0.1	-10	0.1*(-10-7.7)^2=31.329
		Total=78.61%

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

=(78.61)^(1/2)

=8.87%(Approx).

Variance=Standard deviation^2

=78.61%