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16 February, 23:57

Assume the standard deviation of the U. S. market portfolio is 18.2%, the standard deviation of the non-U. S. portion of the world portfolio is 17.1%, and the correlation between the U. S. and non-U. S. market portfolios is. 47. Suppose you invest 25% of your money in the U. S. stock market and the other 75% in the non-U. S. portfolio. What is the standard deviation of your portfolio?

a) 16.7% b) 15.5% c) 17.1% d) 18.6%

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  1. 16 February, 23:58
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    b) 15.5%

    Explanation:

    Let U. S. market portfolio be represented by variable "U"

    And let Non - U. S. market portfolio be represented by variable "N"

    σP = SQRT [ w²U*σ²U + w²N*σ²N + 2*wS * wN*σU*σN*correl. ]

    whereby,

    w = weight of ...

    σ² = variance of ...

    σP=SQRT[0.25²*0.182² + 0.75²*0.171² + 2*0.25 * 0.75 * 0.182 * 0.171 * 0.47 ]

    σP = SQRT[ 0.002070 + 0.0164 + 0.005485]

    = SQRT (0.023955)

    = 0.15477 or 15.5%

    = As a percentage, the standard deviation of your portfolio is 15.5%
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