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22 January, 03:13

You have $13,000 to invest in a stock portfolio. Your choices are Stock X with an expected return of 13 percent and Stock Y with an expected return of 8 percent. Assume your goal is to create a portfolio with an expected return of 11.45 percent. How much money will you invest in Stock X and Stock Y

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  1. 22 January, 03:19
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    You should invest $8,970 in stock X and $4,030 in stock Y.

    Explanation:

    These can be estimated as follows:

    PER = (ERX * wX) + (ERY * wY) ... (1)

    Where,

    PER = Portfolio expected return = 11.45%, or 0.1145

    ERX = Expected return of X = 13%, or 0.13

    ERY = Expected retun of Y = 8%, or 0.08

    wX = Weight of X = ?

    wY = Weight of Y = 1 - wX = ?

    Substituting the values into equation (1), we have:

    0.1145 = [0.13 * wX] + [0.08 * (1 - wX) ]

    0.1145 = 0.13wX + [0.08 - 0.08wX]

    0.1145 = 0.13wX + 0.08 - 0.08wX

    0.1145 - 0.08 = 0.13wX - 0.08wX

    0.0345 = 0.05wX

    wX = 0.0345 / 0.05

    wX = 0.69

    Since wY = 1 - wX

    Therefore,

    wY = 1 - 0.69

    wY = 0.31

    Total amount to invest = $13,000

    Investment in stock X = Amount to invest * 0.69 = $13,000 * 0.69 = $8,970

    Investment in stock Y = Amount to invest * 0.31 = $13,000 * 0.31 = $4.030

    Therefore, you should invest $8,970 in stock X and $4,030 in stock Y.
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