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You own a portfolio that has a total value of $155,000 and a beta of 1.33....

You own a portfolio that has a total value of $155,000 and a beta of 1.33. You have another $64,000 to invest and you would like the beta of your portfolio to decrease to 1.26. What does the beta of the new investment have to be in order to accomplish this?

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Answer #1

Existing portfolio weight in new portfolio = $155000/($155000+$64000)

New Portfolio Beta = Existing portfolio Beta*Weight of existing portfolio in the new portfolio + Beta of new investment*weight of new investment

1.26 = 1.33*[$155000/($155000+$64000)] + Beta of new investment*[$64000/($155000+$64000)]

1.26 = 0.941234 + Beta of new investment*0.292237

Beta of new investment*0.292237 = 1.26-0.941234

Beta of new investment = 0.318676/0.292237

Beta of new investment = 1.09

Therefore to accomplish the portfolio Beta of 1.26, the Beta of new investment should be 1.09

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