Question

Based on the following information, what is the standard deviation of returns? State of Economy Probability of State of Economy Rate of Return if State Occurs Recession .31 − .099 Normal .38 .114 Boom .31 .224

Answer 1

Expected return=Respective return*Respective probability

=(0.31*-0.099)+(0.38*0.114)+(0.31*0.224)=0.08207

Probability	Return	Probability(Return-Expected Return)^2
0.31	-0.099	0.31*(-0.099-0.08207)^2=0.0101637669
0.38	0.114	0.38*(0.114-0.08207)^2=0.000387419462
0.31	0.224	0.31*(0.224-0.08207)^2=0.00624467872
		Total=0.0167958651

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

=[0.0167958651]^(1/2)

=0.1296(or 12.96% approx)