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26 November, 23:40

You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 18% and a standard deviation of 21% and a Treasury bill with a rate of return of 4%. How much money should be invested in the risky asset to form a portfolio with an expected return of 13%?

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  1. 27 November, 03:38
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    The amount of money invested in risky asset = $6428.57

    Explanation:

    The portfolio return is made up of the returns of the individual returns of securities in a portfolio multiplied by their weight in the portfolio.

    Thus the formula for portfolio retyurn is,

    Portfolio return = wA * rA + wB * rB + ... + wX * rX and so on

    Where,

    w represents weight of security in portfolio r represents the return on that security

    Plugging in the values in the formula,

    let x be the weight of investment in risky asset

    then x-1 is weight of investment in risk free asset

    0.13 = x * 0.18 + (1-x) * 0.04

    0.13 = 0.18x + 0.04 - 0.04x

    0.13 - 0.04 = 0.14x

    0.09 / 0.14 = x

    x = 9/14 or 0.6429 or 64.29%

    The amount of money invested in risky asset is 9/14 * 10000 = $6428.57
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