Calculate the average return of an investment from a series of annual returns — both the arithmetic mean and the more accurate geometric mean (CAGR), plus the cumulative total return.
Arithmetic & geometric mean
Enter each year's percentage return, e.g. 12, -8, 22. Negative years are allowed.
There are two ways to average investment returns, and they answer different questions. The arithmetic mean is the simple average of each year's return — useful for estimating a typical year. The geometric mean (also called CAGR, compound annual growth rate) accounts for compounding and is the rate that actually turns your starting balance into your ending balance. The geometric mean is always less than or equal to the arithmetic mean, and the gap widens with volatility.
For example, returns of +12%, −8%, +22%, +5%, +15% have an arithmetic average of 9.2%, but a geometric mean of about 8.7% — the geometric figure is what your money truly compounded at. This is why a fund that gains 50% then loses 50% has a 0% arithmetic average but actually lost 25% of your money (geometric −13.4%). For measuring real, realized investment performance, always use the geometric mean.
The simple average of yearly returns. Good for estimating a single typical year, but it overstates compounded growth.
The true compound growth rate that links your start and end values. The honest measure of realized return.
The more returns swing up and down, the more the geometric mean falls below the arithmetic mean — volatility quietly erodes compounding.
There are two averages for investment returns and they answer different questions. The arithmetic mean adds the yearly returns and divides — it is the right answer for "what return should I expect next year". The geometric mean compounds them and takes the nth root, giving the constant rate that would produce the actual ending balance. The geometric mean is always lower whenever returns vary, and the gap widens with volatility. Quoting the arithmetic mean as a historical performance figure systematically overstates what investors actually earned, which is why regulators require the geometric form.
Arithmetic mean = (r₁ + r₂ + … + rₙ) ÷ nGeometric mean = [ (1+r₁)(1+r₂)…(1+rₙ) ]^(1/n) − 1Approximate gap ≈ variance ÷ 2Geometric ≤ arithmetic always, equal only if all returns are identicalwhere:
Assumptions: Use geometric for reporting past performance and arithmetic for forward expectations. Money-weighted return (IRR) differs again and is the right measure when contributions and withdrawals occurred during the period.
A volatile three-year run, measured both ways, against what actually happened to the money.
ResultArithmetic 11.67% — but the real compound return was 7.00%
The $1,668 gap between the two projections over just three years is the cost of volatility, and it grows with both time and variability. This is also why a 50% loss requires a 100% gain to recover: losses and gains of equal percentage are not symmetric in their effect on capital.