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Math Help - Finance Portfolio Theory

  1. #1
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    Mar 2009
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    Finance Portfolio Theory

    consider the two (excess retrun) index model regression results from stocks A and B. The risk free rate over the period was 6% and the market's averge return was 14%. Performance is measured using an index model regression on excess return:

    Stock A
    inxel model regression equation: 1% + 1.2(rM-rf)
    R-square: 0.576
    residual standard deviation: 10.3%
    standard deviation of excess returns: 21.6%

    Stock B
    inxel model regression equation: 2% + 0.8(rM-rf)
    R-square: 0.436
    residual standard deviation: 19.1%
    standard deviation of excess returns: 24.9%

    How do i calculate:

    1) Alpha:
    2) Information ratio:
    3) Sharpe measure:
    4) Treynor measure:

    Can someone just show me how you determine the answers by showing me the full workings so i can sit down and properly understand it.

    I have this information from the solution guide but i have no idea how to use it:

    *To compute the Sharpe measure, note that for each stock, (rP – rf ) can be computed from the right-hand side of the regression equation, using the assumed parameters rM = 14% and rf = 6%. The standard deviation of each stock’s returns is given in the problem.
    ** The beta to use for the Treynor measure is the slope coefficient of the regression equation presented in the problem.
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  2. #2
    Member
    Joined
    Jan 2009
    From
    Punjab, Pakistan
    Posts
    88
    Sharpe Measure

    Stock A
    S = \frac{R_p-R_f}{\sigma}
    R_p = 1\% + 1.2 (R_m - R_f )
    R_m=14\%
    R_f=6\%
    \sigma=21.6\%
    R_p=1\% + 1.2(14\%-6\%)
    R_p=1\% + 1.2(8\%)
    R_p=1\% + 9.6\%
    R_p=10.6\%
    S = \frac{10.6\%-6\%}{21.6\%}
    S = \frac{4.6\%}{21.6\%}
    S = 0.2129

    Stock B
    S = \frac{R_p-R_f}{\sigma}
    R_p=2\% + 0.8(R_m-R_f)
    R_m=14\%
    R_f=6\%
    \sigma=24.9\%
    R_p=2\% + 0.8(14\%-6\%)
    R_p=2\% + 0.8(8\%)
    R_p=2\% + 6.4\%
    R_p=8.4\%
    S = \frac{8.4\%-6\%}{21.6\%}
    S = \frac{2.4\%}{21.6\%}
    S = 0.1111


    Treynor measure:

    T = \frac{R_p-R_f}{\beta}

    Stock A

    T = \frac{10.6\%-6\%}{1.2}
    T = \frac{4.6\%}{1.2}
    T = 0.038333

    Stock B

    T = \frac{8.4\%-6\%}{0.8}
    T = \frac{2.4\%}{0.8}
    T = 0.03000

    Jensen's Alpha

    Stock A
    \alpha_p = 10.6\% - [6\% + 1.2 (14\% - 6\%)]
    \alpha_p = 10.6\% - [6\% + 1.2 (8\%)]
    \alpha_p = 10.6\% - [6\% + 9.6\%]
    \alpha_p = 10.6\% - [6\% + 9.6\%]
    \alpha_p = 10.6\% - 15.6\%
    \alpha_p = -0.05

    Stock B
    \alpha_p = 8.4\% - [6\% + 0.8 (14\% - 6\%)]
    \alpha_p = 8.4\% - [6\% + 0.8 (8\%)]
    \alpha_p = 8.4\% - [6\% + 6.4\%]
    \alpha_p = 8.4\% - [6\% + 6.4\%]
    \alpha_p = 8.4\% - 12.4\%
    \alpha_p = -0.04
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