Question 477491: You have a $2 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?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! here's a reference that describes how it's done.
http://www.investorwords.com/tips/271/calculating-your-portfolios-beta.html
if they're correct, then all you are doing is calculating the average of all your betas based on the relative value of each stock in that portfolio.
you have 20 stocks in your portfolio.
each stock in the portfolio is worth 100,000 dollars.
the portfolio has a beta of 1.1
that would be the average of the beta of all the stocks in your portfolio.
you will be selling one stock that has a beta of .9 and using the proceeds to purchase another stock with a beta of 1.4.
the impact on your portfolios beta should be as follows:
the $100,000 stock is worth 100,000 / 2,000,000 = .05 of your portfolio
your portfolio's beta is 1.1
you subtract .05 * .9 from it and you add .05 * 1.4 to it.
the resulting impact on the portfolio beta should be:
1.1 - .05*.9 + .05*1.4 which becomes:
1.1 - .045 + .07 which becomes:
1.125
your portfolios beta after the transaction is equal to 1.125
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