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10 February, 20:38

You are considering investing $1,000 in a complete portfolio. The complete portfolio is composed of Treasury bills that pay 5% and a risky portfolio, P, constructed with two risky securities, X and Y. The optimal weights of X and Y in P are 60% and 40% respectively. X has an expected rate of return of 14%, and Y has an expected rate of return of 10% what percentage of your complete portfolio should you invest in treasury bills?

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  1. 10 February, 22:49
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    34.78% should be invested.

    Explanation:

    Expected return of portfolio constructed with stock X and Y

    = Rate of return on stock X * Weight of stock X + Rate of return on stock Y + Weight of stock Y

    = 18*0.40 + 10*0.60 i. e 13.20

    Calculation of percentage to be invested in treaury bill

    10% = 4% * X + 13.20% (1-X)

    0.10 = 0.04X + 0.1320 - 0.1320X

    0.10-0.1320 = - 0.092X

    X = 34.7826%
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