Question

calculate the standard deviation

1. Stock A has the following returns for various states of the economy: State of the Economy Recession Below Average Average Above Average Boom Probability 10% 20% 40% 20% 10% Stock A's Return -30% -2% 10% 18% 40%

Answer 1

Expected return=Respective return*Respective probability

=(0.1*-30)+(0.2*-2)+(0.4*10)+(0.2*18)+(0.1*40)=8.2%

Probability	Return	Probability*(Return-Expected Return)^2
0.1	-30	0.1*(-30-8.2)^2=145.924
0.2	-2	0.2*(-2-8.2)^2=20.808
0.4	10	0.4*(10-8.2)^2=1.296
0.2	18	0.2*(18-8.2)^2=19.208
0.1	40	0.1*(40-8.2)^2=101.124
		Total=288.36%

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

=(288.36)^(1/2)

=16.98%(Approx).