Question

You are given the following information:

State of Economy	Probability of State of Economy			Rate of Return If State Occurs
Depression		.12			−.107
Recession		.23			.057
Normal		.46			.128
Boom		.19			.209

Calculate the expected return. (Do not round intermediate calculations. 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. Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Standard deviation              %

Answer 1

Expected Return=Respective return*Respective probability

=(0.12*-10.7)+(0.23*5.7)+(0.46*12.8)+(0.19*20.9)=9.89%(Approx).

probability	Return	probability*(Return-Expected Return)^2
0.12	-10.7	0.12*(-10.7-9.886)^2=50.85400752
0.23	5.7	0.23*(5.7-9.886)^2=4.03019708
0.46	12.8	0.46*(12.8-9.886)^2=3.90604216
0.19	20.9	0.19*(20.9-9.886)^2=23.04855724
		Total=81.838804%

Standard deviation=[Total probability*(Return-Expected Return)^2/Total probability]^(1/2)
=9.05%(Approx)