Question

You have a $4 million portfolio consisting of a $100,000 investment in each of 20 different stocks. The portfolio has a beta of 1.1. You are considering selling $100,000 worth of one stock with a beta of 0.9 and using the proceeds to purchase another stock with a beta of 1.4. What will the portfolio’s new beta be after these transactions? Show your work.

Answer 1

1.1125

Step-by-step explanation:

the relative weight of the stocks that you are selling is $100,000/$4,000,000 = 0.025 = 2.5% of the portfolio

this means that their effect on the portfolio's beta was 0.9 x 0.025 = 0.0225

the new stocks that you want to purchase have a beta of 1.4 and their relative effect on the portfolio's beta will be 1.4 x 0.025 = 0.035

the difference between both stocks = 0.035 - 0.0225 = 0.0125

that means that the portfolio's new beta = 1.1 + 0.0125 = 1.1125