All Averages Are Not Created Equal

All Averages Are Not Created Equal Splash image

Turn to any listing of mutual fund returns, or even stocks, and you will likely see a “summary” of those results, referred to as the “average” return. For example, a listing of mutual funds in a particular category may show the average return for the fund in that category. A different listing may show a particular fund’s returns for each of the last five years, and an average annual return over that five-year period.

Many individuals assume those averages are all calculated in the same way. In fact, they are not.

The dictionary definition of an average is: A single value that summarizes or represents the general significance of a set of unequal values. But there are a number of different ways to present a “summary” of values, depending on what you are seeking to measure.

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Discussion

Gordon from Colorado posted over 3 years ago:

You have a typo in the opening definition of the arithmatic average, i.e.,

"Most people ....., which adds ......, and then dividends by the number of listings.

Should be "divide", not "dividends".


Jean from Illinois posted over 2 years ago:

Thank you; the error has been fixed. Jean at AAII.


Jon from Alabama posted over 2 years ago:

Shouldn't the geometric average be calculated this way???

(1.1 * 1.15 * 1.12 * 1.02 * .7) ^ (1/5) - 1

= .0023 = 0.23%


The article mentions taking the n'th root, but the chart shows simply multiplying by (1/5).



John from Pennsylvania posted over 2 years ago:

The geometric problem states the third year return is 0.02% which in the calculation should be 1.0002 yielding a final answer of -.16%


Opal from California posted over 2 years ago:

So when I see the term "average annual return" on a fund, am I seeing the geometric average? I had always wondered why the figures never added up to the actual result over a period of several years.


Jean from Illinois posted over 2 years ago:

Jon - We've fixed the box so that the geometric average is now showing to take the nth root. Thanks for pointing that error out. Jean from AAII


Jean from Illinois posted over 2 years ago:

John - The third year return is 0.2%, which is correctly shown in the box as 1.002 in the geometric average calculation. Jean from AAII


Rick from Illinois posted over 2 years ago:

Where would a weighted average be useful? Calculating the return of the S&P 500 where some companies are far larger than others?


Dave from Washington posted over 2 years ago:

I am not "embarrassed" to admit it, but I can't wrap my head around how +100%, +100%, -100% is equal to a 50% average return.
100+100-100=100/3 = 33.3% return over the 3 years. ??


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