Question

Use the following information on states of the economy and stock returns to calculate the standard deviation of returns. (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.)

State of Economy	Probability of State of Economy		Security Return if State Occurs
Recession	.35		−10.00	%
Normal	.50		7.00
Boom	.15		17.00

Answer 1

Expected return=Respective return*Respective probability

=(0.35*-10)+(0.5*7)+(0.15*17)

=2.55%

probability	Return	probability*(Return-Expected Return)^2
0.35	-10	0.35*(-10-2.55)^2=55.125875
0.5	7	0.5*(7-2.55)^2=9.90125
0.15	17	0.15*(17-2.55)^2=31.320375
		Total=96.3475%

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

=(96.3475)^(1/2)

=9.82%(Approx)