Question

Suppose you hold a portfolio consisting of a $10,000 investment in each of 10 different common stocks. The portfolio’s beta is 1.25. Now suppose you decided to make two changes to your portfolio as follows: 

a) sell stock X that has a beta of 1.0 and replace it with stock Y that has a beta od 1.5, and

b) sell stock W that has a beta of 1.2 and replace it with stock Z that has a beta of 2.1. What would the portfolio’s new beta be after you make the two changes?

Answer 1

a.

Let new portfolio be b,

100,000(b) = 90,000(1.25) + 10,000(1.50) - 10,000(1)

b = 1.175

b.

Let new portfolio be b,

100,000(b) = 90,000(1.25) + 10,000(2.10) - 10,000(1.20)

b = 1.215