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Math Help - Finance - Riskless Rate and Expected Return Question

  1. #1
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    Finance - Riskless Rate and Expected Return Question

    I have no idea where to begin for this problem in order to get a riskless rate of 8.7% and 11.7% for the expected return on the market. Any ideas where I can start. Thank you in advance!



    Wal-Mart Company stock has beta of 1.1 and its expected return is 12%, whereas Dell Company stock has beta of 1.2 and its expected return is 12.3%. Find the riskless rate and the expected return on the market.
    (8.7%, 11.7%)
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  2. #2
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    Turn it into a "two-equation, two-unknown" setup, and knock it out that way.

    With m playing the role of the market expected return, and r starring as the risk-free rate, Wal-Mart's expected return sets up as...

    0.12 = r + 1.1(m - r)

    ...and Dell's equation is

    0.123 = r + 1.2(m - r)

    Solve that system for m and for r, and you'll see it agrees with the given answers. Cheers!
    Last edited by LochWulf; July 22nd 2010 at 11:27 AM. Reason: edit typo
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  3. #3
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    I am a little fuzzy on how to solve from this point. What is the first step? It will probably jump start my thinking as to how to approach this. Thanks again for your help!
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  4. #4
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    Glad to help, comrade. In a couple of algebraic steps WalMart's equation simplifies to

    0.12 = 1.1m - 0.1r

    and Dell's to

    0.123 = 1.2m - 0.2r

    Now multiply WalMart's simplifed version above by (-2), and add the resulting equation to Dell's. r falls away leaving you with an equation with m as the sole variable, which you can then solve for m.

    Then plug that value for m back into either of the original equations to solve for r. Verify that your discoveries both agree with the given answers, and then knock the top off of a cold Guinness.
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