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Math Help - the minimum variance of the profit rate

  1. #1
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    the minimum variance of the profit rate

    There are one riskless bond and a bunch of stocks with risk in the market. For the expected profit r>1 (or r=1) the minimum variance of the profit rate for the risk papers is

    σ^2(r)=r^2-2r+2.

    Let's asume that we have a portfolio with both riskless bonds and stocks with risk. When expected profit r=8, the variance of the profit rate is 45. What is the minimum variance of the profit rate when r=2?

    Is there anyone who could help me with this? I have tried to solve this in many ways, but I never get the answer.
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  2. #2
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    is that the entire question, as printed, with no changes or omissions?

    if it is, i am stumped. You are presumably expected to use the first scenario to deduce the return on the bonds; this will let you work out the proportion of the portfolio in bonds and stocks in the second scenario; then you can just plug numbers in to get the variance.


    However, i dont see how to deduce the return on the bonds from the information you posted.
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  3. #3
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    Yes, it is unfortunately all the information I have
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  4. #4
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    Is this the proper way to approach this problem:

    1) Given \sigma^2_{min} = 45 for r=8 implies 7.633% of the return is from stocks and 0.367% is from bonds (i.e. riskless, so contribute zero to the variance).

    2) To have portfolio returning r=2, with bonds only able to contribute 0.367, the stock portion must be 2 - 0.367 = 1.633, thus r=1.633, so \sigma^2_{min}=1.4

    ?
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  5. #5
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    1.4 was my answer on the exam and I got 0 points. I calculated it differently though.
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