How to use the Average Return Calculator
- Enter each year's percentage return, separated by commas; losses go in as negatives.
- Read the geometric figure as your true annualised return.
- Compare it against the arithmetic average to see the volatility drag.
- Check the cumulative growth line against your actual account statement.
How the calculation works
Arithmetic average adds returns and divides by count; geometric mean multiplies the growth factors and takes the nth root. Only the geometric figure reconciles with the ending balance, because gains and losses compound rather than add.
The gap between the two is volatility drag, approximately half the variance of returns. A portfolio alternating +50% and −50% has a 0% arithmetic average but loses 13.4% a year geometrically — the arithmetic figure is not merely optimistic, it is structurally wrong for multi-period reporting.
This is why marketing materials favour arithmetic averages and why GIPS-compliant performance reporting requires time-weighted, geometrically linked returns.
CAGR = (Π(1 + rᵢ))^(1/n) − 1; Arithmetic = Σrᵢ ÷ nSource: CFA Institute Global Investment Performance Standards (GIPS) return calculation methodology.
Worked example
Returns of 12%, −8%, 21%, 4% and 9%.
- Arithmetic average is 7.6%.
- Growth factors multiply to about 1.4066.
- The fifth root gives roughly 7.06%.
A true annualised return of 7.06% — half a point below the arithmetic figure.
Frequently asked questions
Which figure should I use for projections?+
Geometric for compounding a balance forward; arithmetic only for single-period expected value in a portfolio model.
Why is my fund's advertised return higher?+
Often an arithmetic average, or a period chosen to start after a drawdown. Check the geometric annualised line.
Does it handle contributions?+
No — this is a time-weighted return. With cash flows in and out, use IRR instead.
Last reviewed September 1, 2026. We review this page whenever the underlying formula, tax year, published rate or standard changes.