Question

Based on the following information: State of Economy Probability of State of Economy Rate of Return if State Occurs Depression .15 ?.100 Recession .20 .064 Normal .50 .135 Boom .15 .216 Calculate the expected return. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.) Expected return % Calculate the standard deviation. (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Answer 1

expected return=Respective returns*Respective probability

=(0.15*-10)+(0.2*6.4)+(0.5*13.5)+(0.15*21.6)=9.77%

probability	Return	probability*(Return-Mean)^2
0.15	-10	0.15*(-10-9.77)^2=58.627935
0.20	6.4	0.2*(6.4-9.77)^2=2.27138
0.5	13.5	0.5*(13.5-9.77)^2=6.95645
0.15	21.6	0.15*(21.6-9.77)^2=20.992335
		Total=88.8481%

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

which is equal to

=9.43%(Approx).