Question

Given the following probability distribution of security N's return, what is the standard deviation of the security? (Expresss your answer in percentage and round it two decimal places, but do not include the percent sign, %, i.e., 4.65) State Probi rn Bad 0.3 3% Neutual 0.4 9% Good 0.3 15%

Answer 1

Expected return=Respective return*Respective probability

=(0.3*3)+(0.4*9)+(0.3*15)=9%

probability	Return	probability*(Return-Expected Return)^2
0.3	3	0.3*(3-9)^2=10.8
0.4	9	0.4*(9-9)^2=0
0.3	15	0.3*(15-9)^2=10.8
		Total=21.6%

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

=(21.6)^(1/2)

=4.65(Approx).