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3 November, 16:36

You own a portfolio that has a total value of $200,000 and it is invested in Stock D with a beta of. 94 and Stock E with a beta of 1.36. The beta of your portfolio is equal to the market beta. What is the dollar amount of your investment in Stock D?

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  1. 3 November, 16:48
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    Answer: BP = BD (WD) + BE (WE)

    1 = 0.94WD + 1.36WE

    1 = 0.94 (1-WE) + 1.36WE

    1 = 0.94 - 0.94WE + 1.36WE

    1 = 0.94 + 0.42WE

    -0.42WE = 0.94 - 1

    -0.42WE = - 0.06

    0.42WE = 0.06

    WE = 0.06/0.42

    WE = 0.1428571428

    Thus, WD = 1 - WE

    WD = 1 - 0.1428571428

    WD = 0.8571428572

    The dollar amount of investment in stock D = 0.8571428572 x $200,000

    = $171,428.57

    Explanation: The Beta of the portfolio is equal to 1, which is the same as the market Beta. The weight of stock D = 1 - weight of stock E. Thus, there is need to equate the beta of the portfolio to the Beta of each stock and their corresponding weights and the solve mathematically by making weight of stock E the subject of the formula. After obtaining the weight of stock E, then, we need to calculate the weight of stock D by applying the formula 1 - WE. Finally, there is need to multiply the weight of stock D by $200,000, which is the total value of the investment in order to obtain the dollar amount of stock D.
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