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27 April, 09:07

Suppose you hold a portfolio consisting of a $10,000 investment in each of 8 different common stocks. The portfolio's beta is 1.25. Now suppose you decided to sell one of your stocks that has a beta of 1.00 and to use the proceeds to buy a replacement stock with a beta of 1.35. What would the portfolio's new beta be?

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  1. 27 April, 09:15
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    1.29375

    Explanation:

    Data provided in the question:

    Total investment = $10,000

    Number of different common stock = 8

    Portfolio's beta = 1.25

    Beta of a stock sold = 1.00

    Beta of the replacement stock = 1.35

    Now,

    Change in portfolio beta = weight * (change in security beta)

    also,

    change in security beta

    = Beta of the replacement stock - Beta of a stock sold

    = 1.35 - 1

    = 0.35

    and,

    Weight = Beta : Number of different common stock

    = 1 : 8 = 0.125

    Therefore,

    Change in portfolio beta = 0.125 * 0.35

    = 0.04375

    thus,

    New portfolio beta = Portfolio's beta + Change in portfolio beta

    = 1.25 + 0.04375

    = 1.29375
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