A famous example of the gap
Alternating returns of +50% and −50% produce an arithmetic average of exactly 0% — yet the actual balance shrinks every cycle, since a 50% loss needs a 100% gain just to break even. The geometric average correctly shows a loss; the arithmetic average hides it completely.
With the default returns shown above
Returns of 12%, −8%, 18%, 5%, 10% give a simple average of 7.40%, but a true geometric average of about 7.03% — a 0.37 percentage point gap from volatility alone.
Frequently asked questions
Why are these two averages ever different?
Arithmetic mean simply adds the percentages and divides — it ignores how compounding actually works. Geometric mean multiplies the growth factors together, which is what your money actually experienced. They match only when returns never vary year to year.
What is 'volatility drag'?
It's the gap created purely by the ups and downs of returns, separate from the average level of return itself. Two investments with the same arithmetic average can end up with very different real (geometric) growth if one is far more volatile than the other.
Which number should I actually use to judge an investment?
The geometric mean — it's the rate that, applied consistently, would have produced the same actual ending balance from the same starting balance. The arithmetic mean can make a volatile investment look better than it really performed.
This calculator provides estimates for general informational purposes only and is not financial advice.