Question

If there is a 30% chance of a 14% return, a 20% chance of an 18% return. a 25% chance of an 19.5% return and a 25% chance of a 12% return, then what is the standard deviation of returns?

Answer 1

Expected return=Respective return*Respective probability

=(0.3*14)+(0.2*18)+(0.25*19.5)+(0.25*12)=15.675%

Probability	Return	Probability*(Return-Expected Return)^2
0.3	14	0.3*(14-15.675)^2=0.8416875
0.2	18	0.2*(18-15.675)^2=1.081125
0.25	19.5	0.25*(19.5-15.675)^2=3.65765625
0.25	12	0.25*(12-15.675)^2=3.37640625
		Total=8.956875%

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

=(8.956875)^(1/2)

=2.99%(Approx).