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Math Help - Average of averages?

  1. #1
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    Average of averages?

    Hello, I need some help with calculating average returns.

    I have a set of 3 portfolios, and they have their own average annual returns. Now how do I calculate the average return for all the portfolios combined?

    I have both arithmetic return and geometric return for the portfolios, can I for example take the arithmetic average of the geometric returns?
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  2. #2
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    Re: Average of averages?

    Hello, actionman777!

    I have a set of 3 portfolios, and they have their own average annual returns.
    Now how do I calculate the average return for all the portfolios combined?

    In general, we must not take the average of a set of averages.

    We have three portfolios, A,B,C. and their average returns: . \bar a,\:\bar b,\:\bar c

    We need a lot more information . . .


    \text{The average }\bar a\text{ comes from:}

    . . \text{the sum of the }a\text{'s, }\sum a_i\:\text{ divided by the number of }a\text{-scores, }n_a


    \text{The average }\bar b\text{ comes from:}

    . . \text{the sum of the }b\text{'s, }\sum b_i\:\text{ divided by the number of }b\text{-scores, }n_b


    \text{The average }\bar c\text{ comes from:}

    . . \text{the sum of the }c\text{'s, }\sum c_i\:\text{ divided by the number of }c\text{-scores, }n_c


    We must know all six of these values.

    The overall average is: . \frac{\sum a_i + \sum b_i + \sum c_i}{n_a+n_b+n_c}
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