Averaging investment returns the simple way systematically overstates the true result — the geometric mean is the mathematically correct way to average returns that compound over time.
How it works
Multiplying together (1 + each period’s return), taking the result to the power of 1 divided by the number of periods, and subtracting 1 gives the geometric mean — compared here against the simple arithmetic average of the same numbers.
What this does not include
This does not include weighting for the size of the portfolio at each point in time — this is a pure return-series calculation, not a money-weighted (dollar-weighted) return like the Modified Dietz method this site also offers.
How to use this calculator
- Enter each period’s percentage return, separated by commas.
Frequently asked questions
Why is the geometric mean always lower than the arithmetic mean?
Whenever returns vary from period to period, the geometric mean is mathematically guaranteed to be less than or equal to the arithmetic mean — the two are only equal when every period’s return is identical.
Which one should I use to report investment performance?
The geometric mean, since it reflects the actual compounded result an investor experienced — the arithmetic mean can meaningfully overstate real performance for a volatile return series.
What happens with a -100% return in the series?
A complete loss in any single period makes the geometric mean undefined, since the investment (and the compounding chain) is wiped out entirely.
