Question

You currently own a portfolio valued at $52,000 that has a beta of 1.16. you have another $10,000 to invest and would like to invest it in a manner such that the portfolio beta decreases to 1.15. what does the beta of the new investment have to be?

Answer 1

The beta of the new investment must be 1.098.

We need to use the concept of weighted averages to solve this problem.

We find the ratios of the dollar value of existing to the total new portfolio and additional investments to the total new portfolio and find the weights.

We then find the product of the beta of the existing portfolio and its respective weight calculated in the earlier step, with the given data.

We derive the product of the additional investment and beta by subtracting the answer from the earlier step from the new portfolio's beta (1.15).

Then we work backwards to arrive at the the beta for the additional investment.