Enter up to 5 yearly returns to see both the simple arithmetic average and the geometric mean that actually reflects compounded growth.
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.