Vol 3, Issue 17. Quarter 4 – 2026. 

One problem that D-I-Y investors have is that it’s easy to get distracted by some sales pitch that uses terms and language that we don’t use in everyday English. Let us address one of these elements here so that you are not overly impressed when you see it in some brochure or seminar. In previous posts we have spoken about the meaning of a simple “Average”. I add up n numbers, get a sum, and divide that sum by n to get an average. No big deal. However, it is easy to lose sight of the fact that just because this is what normal people mean by the word Average, that doesn’t mean that it’s the right meaning for your money. In fact, this is only one of many definitions of thebterm. This simple version is what is formally known as an Arithmetic average since it stems from simple arithmetic.

However, in many settings when you are discussing finances, this is not the average that really matters, even though it typically the average that the salesman point to. Consider this toy example. Let’s say that the returns on my portfolio over the past 5 years matched the total returns of the S&P 500. In other words, they were roughly 27%, -19%, 26%, 25%, and 18%. The first thing that we probably notice is that this was a VERY good run. If you followed the advice consistently given on this site, many of you almost doubled your money over that span. The arithmetic average of these figures is about 15.4%. But what if I told you that you really saw a return rate of 13.8%? You would probably say something like, huh?

The way that you need to look at it is like this. Start with $1. Have it earn 27% in Year 1, lose 19% in Year 2 and so on. In this case you end up with 1 * 1.27 * 0.81 * 1.26 * 1.25 * 1.18 = $1.91. Your dollar grew by a total of 91%. Now 91%/5 = 18.2%. This is a different type of average that a smart salesman will pull out when making his pitch. Of course, this is meant to lead you to believe that you made over 18% per year, but you did not. 

You need to consider a different type of average. The geometric average is found by calculating 191%^(1/5) = 13.8%. This tells us that if I were to invest $1 and have it grow at 13.8% per year, with no variation for 5 years, I would end up with the same $1.91. Some articles will refer to this as the Compound Annual Growth Rate. The key point is that this geometric rate tells you what you can compare your returns to in a world with no variability to make an apples to apples comparison. If I have n return levels, I multiply (1+ Return₁) * (1 +  Return₂) etc. This yields a final value. I then take the n’th root of this value, and subtract 1 to get the geometric mean. The key points are that the geometric mean is always less than the arithmetic mean and is a better depiction of what really happened with your money.

In fact, the more variance we see in the returns, the more misleading the Arithmetic mean actually is. Consider this extreme example. Let’s say you saw a -50% return in one year (which we see about once every 10 years) and a +100% return in the next. So your $1 went to $0.50, and then back to $1.00. Clearly, there was no net gain here. However, the arithmetic mean would be (-50 + 100)/2 = 25%. This is highly misleading. But if I look at the geometric mean I get (0.5 * 2)^0.5 = 1, and 1 – 1 = 0% which is clearly the relevant growth rate over this period. 

Here is the take away for you. Don’t get overly excited about an arithmetic mean return when high variability and some negative values are part of the mix. What you really end up with is better described by a Geometric mean. If you keep these ideas straight in your mind, you can make better comparisons between strings of return figures and make better assessments about what is truly impressive.