# Beta of a Diversified Portfolio

You hold a diversified portfolio consisting of a $5,000 investment in each of 20 different common stocks. The portfolio beta is equal to 1.15. You have decided to sell one of your stocks, a lead mining stock whose b is equal to 1.0, for $5,000 net and to use the proceeds to buy $5,000 of stock in a steel company whose b is equal to 2.0. What will be the new beta of the portfolio?

A. 1.12

B. 1.20

C. 1.22

D. 1.10

https://brainmass.com/business/finance/you-hold-a-diversified-portfolio-consisting-of-a-5-000-investment-in-each-of-20-different-common-sto-154441

#### Solution Preview

Beta of portfolio = sum of weighted betas

For 20 stocks, each having a market value of $5000, the portfolio is worth $100,000 and each stock has the same weight of 1/20 = 0.05 = 5%

Beta of portfolio = SUM(Xi*Bi) = for i = 1 to 20

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#### Solution Summary

This solution shows step-by-step calculations to determine the beta before selling a stock from the diversified portfolio and the new beta after the sale. All workings are shown with brief explanations.