Question

Consider the following information:

		Rate of Return if State Occurs
State of	Probability of State
Economy	of Economy	Stock A	Stock B
Recession	.23	.025	–.28
Normal	.58	.105	.18
Boom	.19	.170	.41

Requirement 1:

Calculate the expected return for the two stocks. (Do not round intermediate calculations. Enter your answers as a percentage rounded to 2 decimal places (e.g., 32.16).)

	Expected return
E(RA)	%
E(RB)	%

Requirement 2:

Calculate the standard deviation for the two stocks

Answer 1

Expected return=Respective return*Respective probability

A:

Expected return=(0.23*2.5)+(0.58*10.5)+(0.19*17)=9.90%(Approx)

Probability	Return	Probability*(Return-Mean)^2
0.23	2.5	0.23*(2.5-9.895)^2=12.57778575
0.58	10.5	0.58*(10.5-9.895)^2=0.2122945
0.19	17	0.19*(17-9.895)^2=9.59139475
		Total=22.381475%

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

=4.73%(Approx).

B:

Expected return=(0.23*-28)+(0.58*18)+(0.19*41)=11.79%

Probability	Return	Probability*(Return-Mean)^2
0.23	-28	0.23*(-28-11.79)^2=364.146143
0.58	18	0.58*(18-11.79)^2=22.367178
0.19	41	0.19*(41-11.79)^2=162.112579
		Total=548.6259%

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

=23.42%(Approx).