Question

Consider the following information:

  

		Rate of Return if State Occurs
State of Economy	Probability of State of Economy	Stock A	Stock B	Stock C
Boom	0.74	0.07	0.29	0.09
Bust	0.26	0.15	0.15	0.05

  

Requirement 1:

What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)

Requirement 2:

What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.)

Answer 1

Solution:

1)Calculation of Expected return of each stock

Expected Return=Probability*Rate of return

Stock A=(0.74*0.07)+(0.26*0.15)=0.0908 or 9.08%

Stock B=0.74*0.29+0.26*0.15=0.2536 or 25.36%

Stock C=0.74*0.09+0.26*0.05=0.0796 or 7.96%

Weight of each stock=1/3=0.3333

Expected return of Portfolio=Expected return of Stock*Weight of stock

=(9.08*0.3333)+(25.36%*0.3333)+(7.96%*0.3333)

=14.132%

2.Calculation of Variance

a)Return of portfolio in each state

Boom=0.20*0.07+0.20*0.29+0.60*0.09=0.126 or 12.60%

Bust=0.20*0.15+0.20*0.15+0.60*.05=0.09 or 9%

Expected return of portfolio

=0.74*12.60%+0.26*9%=11.664% or 0.11664

Variance=Probability*(Return-expected return)^2

=0.74(0.1260-0.11664)^2+0.26(0.09-0.11664)^2

=0.000250