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Math Help - Very unusual problem - any help highly appreciated

  1. #1
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    Very unusual problem - any help highly appreciated

    Suppose there is a stock (Stock A) and an index (Index A).

    Stock A's price=$150
    Index A's level=2450

    The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

    Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

    Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

    Thanks a lot for all your help.

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  2. #2
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    Quote Originally Posted by gillchandler1 View Post
    Suppose there is a stock (Stock A) and an index (Index A).

    Stock A's price=$150
    Index A's level=2450

    The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

    Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

    Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

    Thanks a lot for all your help.

    Right now you have A(0)/I(0)= .06122 and you believe that at some time in the future, A(t)/I(t) will be 0.07500. That tells you that (A(t)/I(t)) divided by A(0)/I(0) will be [tex]\frac{A(t)/I(t)}{A(0)/I(0)}= \frac{A(t)}{A(0)}{I(0)/I(t)}= .07500/.06122= 1.225. If we think of A= A(t)/A(0) as measuring how well A has "performed" and I= I(t)/I(0) as measuring how well the index has "performed", then we have A/I= 1.225 so we could say that, in some sense, A has "outperformed" the index by 22.5%. I'm not sure that is a useful "sense".
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  3. #3
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    Hello gillchandler1

    Welcome to Math Help Forum!
    Quote Originally Posted by gillchandler1 View Post
    Suppose there is a stock (Stock A) and an index (Index A).

    Stock A's price=$150
    Index A's level=2450

    The current ratio of Stock A/Index A Level = 150/2450 = 0.06122

    Now supposing you look on the historic ratio chart and think that the ratio will increase from the current 0.06122 to say 0.07500 (ie you think stock A will outperform the index).

    Just from knowing the expected ratio (0.07500) and the current ratio level (0.06122), would it be possible to calculate by how much % stock A outperformed the index by ?

    Thanks a lot for all your help.

    The answer is that there isn't a fixed percentage difference, but you can calculate one if you know the other.

    Suppose that the stock is originally valued at $ S and increases by s%; and the index, valued at $ I, increases by i%. Then the values will increase by factors of \left(1+\frac{s}{100}\right) and \left(1+\frac{i}{100}\right) respectively. The ratio of the new values will then be
    \frac{\left(1+\dfrac{s}{100}\right)S}{\left(1+\dfr  ac{i}{100}\right)I}=\left(\frac{100+s}{100+i}\righ  t)\left(\frac{S}{I}\right)
    So if the original ratio, \frac{S}{I}, was 0.06122, and the new one is 0.075, we have
    \left(\frac{100+s}{100+i}\right)\left(0.06122\righ  t)=0.075

    \Rightarrow \left(\frac{100+s}{100+i}\right)=\frac{0.075}{0.06  122}=1.225
    Re-arranging this equation gives:
    s=1.225i+22.5
    which will give the value of s for a given value of i, enabling a comparison to be made. For example:
    If i = 0 (i.e. the index does not rise, s = 22.5; i.e the stock rises by 22.5%.

    If i = 5 (i.e. the index rises by 5%), s = 28.625; the stock rises by 28.625%, outperforming the index by 23.625%.

    ... and so on.
    Grandad
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