You have a 2 million portfolio consisting of a 100,000 investment in each of 20 different stocks

Finance Sep 23, 2020

You have a 2 million portfolio consisting of a 100,000 investment in each of 20 different stocks. The portfolio has a beta equal to 1.1. You are considering selling $100,000 worth of one stock which has a beta equal to 0.9 and using he process to purchase another stock which has a beta equal to 1.4. What will be the new beta of your portfolio following the transaction?

Expert Solution

The beta of a portfolio is the weighted average beta of individual stocks. The weight of each stock in the total portfolio is 100,000/2,000,000=5%.
The beta of portfolio will be 5%Xbeta 1+ 5% Xbeta2+.......+ 5% X beta 20=1.1
We are removing a stock with a beta of 0.9. The beta weight of this stock will be 0.9X5%=0.045.
We are adding a stock with a beta of 1.4. The beta weight of the stock will be 1.4X5%=0.07
The new portfolio beta is 1.1-0.045+0.07=1.125

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