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Currently you have $6,000 in a portfolio with a beta of 1.4. If you invest an...

Currently you have $6,000 in a portfolio with a beta of 1.4. If you invest an additional $4,000 in a stock, what will the beta of the stock have to be to make your portfolio beta equal to 1.24?

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Answer #1

Amount in the existing portfolio = $ 6000

Amount in the additional stock = $ 4000

Weight of the existing portfolio = 6000 / (6000 + 4000) = 0.6

Weight of the additional stock = 4000 / (6000 + 4000) = 0.4

Portfolio Beta = weight of existing portfolio * Beta of portfolio + weight of additional stock * Beta of stock

or , 1.24 = 0.6 * 1.4 + 0.4* Beta of stock

= 0.84 + 0.4 * Beta of stock

Hence Beta of stock = (1.24 - 0.84) / 0.4

= 0.40/0.4

= 1

The beta of stock =1

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