Enter up to 5 yearly returns to see both the simple arithmetic average and the geometric mean that actually reflects compounded growth.
The page opens with five yearly returns: 12%, −5%, 18%, 7%, 10%. Add them and divide by five — the arithmetic mean — and you get 8.40%. But compound those same five returns one after another and solve for the single steady rate that would have produced the identical result — the geometric mean, also called CAGR — and you get 8.12%.
The gap is only 0.28 points here because none of the individual years was extreme. It is not always this small.
Take a portfolio that gains 50% one year and loses 50% the next. The arithmetic mean is exactly 0% — it looks like breaking even. What actually happened: 00 grows to 50, then that 50 falls by half to 5. A quarter of the money is gone, against an average that claimed nothing changed. The geometric mean reports this correctly, at −13.40% — because losses and gains are not symmetric once they compound: a 50% loss needs a 100% gain just to get back to even, not another 50%.
This gap has a name — volatility drag — and it grows with how much a return sequence swings, not with how good or bad the returns are on average. Two portfolios can share an identical arithmetic mean and compound to very different ending balances if one of them is far more volatile.
The geometric mean is always less than or equal to the arithmetic mean for any series that is not perfectly constant, and the two only converge when volatility is zero. Any investment return you see advertised is worth checking against this distinction — an "average annual return" quoted without saying which kind is being described is easy to overstate.
Multiplication does not care what order its factors come in, so 12%, then −5%, then 18% compounds to the identical ending value as −5%, then 18%, then 12%. Both the arithmetic and geometric means of a fixed set of returns are unaffected by the sequence they occurred in. What sequence does change is the outcome for someone adding or withdrawing money along the way — a large withdrawal right after a bad year does lasting damage that the same withdrawal after a good year would not, even though the average return across the whole period is identical either way. That is sequence-of-returns risk, and it is a different concept from the averaging question this calculator answers.
The arithmetic average simply adds up each year's return and divides by the count, treating every year as an independent, unrelated number. The geometric mean instead compounds each year's return onto the last — exactly the way real investment growth works — then finds the single constant annual rate that would have produced the same ending value. Whenever returns vary from year to year, the geometric mean is always equal to or lower than the arithmetic average, and the gap widens the more the returns swing.
Use the geometric mean. It reflects actual compounding and the real effect of volatility on an account balance, while the arithmetic average overstates how fast a volatile investment actually grows. The more the yearly returns swing up and down around their average, the bigger the gap between the two numbers becomes — see the Compound Interest Calculator for projecting growth forward at a single assumed rate.
Volatility drag is the gap between the arithmetic average and the geometric mean caused purely by the ups and downs of returns — a 50% loss needs a 100% gain just to break even, so swings hurt compounded growth asymmetrically more than a steady return of the same average would. In the worked example below, the arithmetic average is 8.40% but the geometric mean is only 8.12% — that 0.28-point gap is volatility drag, purely from the returns bouncing between -5% and 18% instead of holding steady.
No — for a single lump sum with no additional deposits or withdrawals along the way, multiplying the same set of yearly returns together in any order produces exactly the same final value, since multiplication is commutative. Order only starts to matter once regular contributions or withdrawals enter the picture, because then early gains or losses interact differently with cash flows that happen at different times.
Worked example: yearly returns of 12%, −5%, 18%, 7%, and 10%. Arithmetic average = (12 − 5 + 18 + 7 + 10) ÷ 5 = 8.40%. Geometric mean = ((1.12 × 0.95 × 1.18 × 1.07 × 1.10)1/5 − 1) ≈ 8.12%. A $10,000 lump sum compounding through that exact sequence ends at $14,777.47 — noticeably less than the $14,967.40 the 8.40% arithmetic average alone would suggest.