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27 February, 14:31

An investor wishes to construct a portfolio consisting of a 70% allocation to a stock index and a 30% allocation to a risk free asset. The return on the risk-free asset is 4.5% and the expected return on the stock index is 12%. The standard deviation of returns on the stock index 6%. Calculate the expected return on the portfolio and the expected standard deviation of the portfolio.

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  1. 27 February, 14:57
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    9.75%

    4.2%

    Explanation:

    Given:

    Stock index portfolio = 70% = 70/100 = 0.70

    Risk free asset = 30% = 30/100 = 0.30

    Return on the risk-free asset = 4.5% = 4.5/100 = 0.045

    Return on the stock index = 12% = 12/100 = 0.12

    Standard deviation (Return on the stock index) = 6% = 6/100 = 0.06

    Computation of expected return on the portfolio:

    Expected return = [Risk free asset * Return on the risk-free asset ] + [Stock index portfolio * Return on the stock index ]

    = [0.3 * 4.5] + [0.7 * 12]

    = [1.35 + 8.4]

    = 9.75%

    Computation of expected standard deviation of the portfolio:

    Expected standard deviation = [Stock index portfolio * Standard deviation (Return on the stock index) ]

    = 0.7 * 6

    = 4.2%
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