Question

Your investment has a 9% chance of earning a 55% return, a 25% chance of earning an 17% rate of return, a 31% chance of earning an 9.25% rate of return, a 20% chance of losing 16%,and a 15% chance of losing 30%. What is the standard deviation of this investment? Enter your answer rounded to two decimal places. Do not enter % in the answer box. For example, if your answer is 0.12345 or 12.345% then enter as 12.35

Answer 1

Expected return=Respective return*Respective probabiity

=(0.09*55)+(0.25*17)+(0.31*9.25)+(0.2*-16)+(0.15*-30)=4.3675%

probabiity	Return	probabiity*(Return-Expected Return)^2
0.09	55	0.09*(55-4.3675)^2=230.7285051
0.25	17	0.25*(17-4.3675)^2=39.89501406
0.31	9.25	0.31*(9.25-4.3675)^2=7.390029938
0.2	-16	0.2*(-16-4.3675)^2=82.96701125
0.15	-30	0.15*(-30-4.3675)^2=177.1687584
		Total=538.1493187%

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

=(538.1493187)^(1/2)

which is equal to

=0.23(Approx).