Question

State of the Economy	Probability (%)	Projected Return (%)
Recession	8	-7.29
Moderate	18	3.28
Average	47	9.92
Good	18	13.91
Outstanding	9	22.25

using the table above, compute the standard deviation of the retuns,

The standard deviation is (?)% (Round to two decimal places.)

Answer 1

Expected return=Respective return*Respective probability

=(0.8*-7.29)+(0.18*3.28)+(0.47*9.92)+(0.18*13.91)+(0.09*22.25)=9.1759%

Probability	Return	Probability*(Return-Mean)^2
0.08	-7.29	0.08*(-7.29-9.1759)^2=21.69006902
0.18	3.28	0.18*(3.28-9.1759)^2=6.257094626
0.47	9.92	0.47*(9.92-9.1759)^2=0.26023186
0.18	13.91	0.18*(13.91-9.1759)^2=4.034106506
0.09	22.25	0.09*(22.25-9.1759)^2=15.38388817
		Total=47.62539018%

SD=[Total Probability*(Return-Mean)^2/Total Probability]^(1/2)

=6.90%(Approx).