All Averages Are Not Created Equal
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.
In this article
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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.
What are the different “averages,” and how are they calculated?
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Discussion
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".
posted over 2 years ago by Gordon from Colorado
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).
posted about 1 year ago by Jon from Alabama
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%
posted about 1 year ago by John from Pennsylvania
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.
posted about 1 year ago by Opal from California
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
posted about 1 year ago by Jean from Illinois
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
posted about 1 year ago by Jean from Illinois
Where would a weighted average be useful? Calculating the return of the S&P 500 where some companies are far larger than others?
posted about 1 year ago by Rick from Illinois
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. ??
posted about 1 year ago by Dave from Washington
