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Math Help - Calculating portfolio weight with a certain expected return

  1. #1
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    Calculating portfolio weight with a certain expected return

    You are considering investing $1000 in a complete portfolio. The complete portfolio is compose of t-bills that pay 5% and a risky portfolio, P, constructed with 2 risky securities X and Y. The weight of X and Y in P are 60% and 40% respectively. X has an E[r] of 14% and Y has an E[r] of 10%. To form a complete portfolio with an E[r] of 11%, how much of your complete portfolio should be invested in t-bills?

    I'm sort of stumped and don't know where to begin. I want to find the variance I think, but to do so, that means I have to know actual returns, right? Which is not given.

    I did start by finding the return on the risky portfolio by doing: (Wx * rx) + (Wy * ry) = (.6 * .14) + (.4 * .1) = 12.4% I'm not entirely sure what to do with this.

    Past problems that I have done similar to this have had the std dev given, and I really don't know where to start. Some help would be appreciated.
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  2. #2
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    At all times:

    First Moment = \sum pr(value) \cdot value = Expected Return = M

    Second Moment = \sum pr(value) \cdot value^{2} = N

    Can you find the variance given those two items?

    Invest $R t-bills and ($1,000 - $R) in the risky portfolio and see how far you get.
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