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2 February, 05:37

4. You own a Portfolio that is invested 43 percent in Stock A, 16 percent in Stock B, and 41 percent in Stock C. The "Expected Returns" on Stocks A, B, and C are: 9.1 percent, 16.7 percent, and 11.4 percent, respectively. A.) What is the "Expected Return" of the Portfolio? B.) What is the "Variance" of the Portfolio? C.) What is the "Standard Deviation" of the Returns on this Stock?

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  1. 2 February, 06:38
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    A.) The "Expected Return" of the Portfolio is 11.26%

    B.) The "Variance" of the Portfolio is 6.749238

    C.) The "Standard Deviation" of the Returns on this Stock is 2.5979%

    Explanation:

    A.) Expected return on portfolio = 0.43x9.10 + 0.16x16.70 + 0.41x11.40

    = 11.26%

    Therefore, The "Expected Return" of the Portfolio is 11.26%

    B.)

    "Variance" of the Portfolio = probability * (deviation) ^2

    Stock A:

    probability = 0.43

    (deviation) ^2 = (9.1 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4)) ^2

    = (9.1 - (3.913 + 2.672 + 4.674)) ^2

    = (9.1 - 11.259) ^2

    = (-2.159) ^2

    = 4.6613

    Stock B:

    probability = 0.16

    (deviation) ^2 = (9.1 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4)) ^2

    = (16.7 - (3.913 + 2.672 + 4.674)) ^2

    = (16.7 - 11.259) ^2

    = (5.441) ^2

    = 29.6045

    Stock C:

    probability = 0.41

    (deviation) ^2 = (11.4 - (0.43*9.1 + 0.16*16.7 + 0.41*11.4)) ^2

    = (11.4 - (3.913 + 2.672 + 4.674)) ^2

    = (11.4 - 11.259) ^2

    = (0.141) ^2

    = 0.0199

    "Variance" of the Portfolio = 0.43x4.6613 + 0.16x29.6045 + 0.41x0.0199

    = 2.004359 + 4.73672 + 0.008159

    = 6.749238

    Therefore, The "Variance" of the Portfolio is 6.749238

    C.) "Standard Deviation" = square root of variance

    Stock A = 1.4158

    Stock B = 2.1764

    Stock C = 0.0906

    "Standard Deviation" of the Returns on this Stock = 1.4158 + 2.1764 + 0.0906

    = 2.5979%

    Therefore, The "Standard Deviation" of the Returns on this Stock is 2.5979%
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