This may sound like a simplistic topic that people will just skip over today, but I assure you it’s a broadly misunderstood concept that comes up quite a bit in my email inbox and that is:

Arithmetic vs Geometric Return

I often hear people say XYZ fund or strategy has made X% in the last number of years, but on further analysis we realize that it’s based on a basic miscalculation of how investment returns actually work.  Let me illustrate.  Imagine a hypothetical fund has the following yearly return for the past 5 years:

Year 1:  20%
Year 2:  30%
Year 3:  25%
Year 4:  -40%
Year 5:  15%

So pretty good performance aside from one year, assume a recession year.  So what I often see people do is just average the numbers out and divide by the number of years.

20%  +  30%  +  25%  –  40%  +  15%  =  50%

 

50%  /  5 years  =  10% per year

 

But did this fund really make 10% a year?  The above calculation is what’s called Arithmetic mean.

Arithmetic mean is appropriate to use when all the variables are independent of each other.  For example the average grade for a classroom full of students or the average age of a group of people.  To calculate it all you do is add up the numbers and divide by how many numbers there are.

However in the financial world the only type of mean that matters is called Geometric mean.  The geometric mean is used to average a series of numbers when the variables are not independent, as is the case with investment returns because they roll forward from year to year.  The formula for calculating geometric mean is below:

 

 

A fund that actually did make 10% a year would be up a lot more money than our fund from the above example:

 

 

That’s a huge difference.  A real person following the yearly returns live would only have 13,455.  That equates to a Geometric average of 6.1% annualized.  It’s still positive, but a far cry from 10%

You would be amazed how often subscription services, especially credit spread and iron condor services use this little Arithmetic vs Geometric trick to make returns look far more impressive than they actually are.

We often see people post performance as a long list of trades, then at the bottom they just add it up and divide by the number of trades.  Or list a bunch of monthly percentage returns and again just add them up and divide by the number of months.

Shame on them!  That’s not how investment returns work.  If they are running a trading business, I’m quite sure they have the basic math skills to know why that makes their performance seem way higher than it actually is.

Arithmetic vs Geometric, it’s not just semantics so be careful of this little statistics trick.

 

 

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