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What does the beta of the replacement stock have to be to produce a new portfolio of 1.55?

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Imagine you are managing a portfolio of 10 stocks which are held in equal amounts. The current beta of the portfolio is 1.64, and the beta of Stock A us 2.0. If Stock A is sold, what does the beta of the replacement stock have to be to produce a new portfolio of 1.55?

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This solution contains step-by-step calculations for the beta of the replacement stock.

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Hello

As the stocks are held in equal amounts, weight of each stock is equal to 1/10 = 0.1.

Beta of portfolio = 0.1*beta of stock 1 + 0.1*beta of stock 2 + ........+ ...

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