Compound Annual Growth Rate (CAGR) — Definition and Formula
CAGR is the constant annual rate that would grow a beginning value into an ending value over a given period. Definition, formula, when it applies, and when TWR is preferred.
- CAGR is the smoothed annualised rate that takes a starting value to an ending value over n years.
- It is only meaningful when there are no external cash flows during the period.
- For portfolios with deposits or withdrawals, time-weighted return is the correct manager-level metric.
Definition
The compound annual growth rate (CAGR) is the constant annual rate of return that, if applied each year, would compound a beginning value V0 into an ending value Vn over n years. CAGR is a smoothed figure: it ignores the path the value took and tells you only the geometric mean of the annual growth.
Formula
CAGR = (V_n / V_0)^(1 / n) - 1
where:
V_0 = beginning value
V_n = ending value
n = number of years (fractional values allowed)Worked example
An account starts at 50,000 and ends at 80,000 four years later, with no deposits or withdrawals in the interim. CAGR = (80,000 / 50,000)^(1/4) − 1 = 1.6^0.25 − 1 ≈ 12.47% per year. Note that the actual annual returns may have been wildly uneven — for example +40%, −10%, +20%, +5% — but CAGR collapses them into a single equivalent compounding rate.
When CAGR is appropriate
CAGR is correct only when there is a single contribution at the start and a single valuation at the end. The moment any external cash flow enters or leaves the account, CAGR becomes a misleading summary because it cannot tell investment growth apart from funding events. For a portfolio with regular deposits and withdrawals — the typical case for traders — time-weighted return is the manager-level standard, and internal rate of return is the investor-level standard.
CAGR versus arithmetic average
A common reporting error is to confuse CAGR with the arithmetic mean of annual returns. They are equal only when annual returns are constant. Whenever returns vary year to year, the arithmetic mean exceeds the geometric mean (CAGR). Example: a portfolio that returns +50% in year one and −50% in year two has an arithmetic mean of 0% but a CAGR of (0.5)^0.5 − 1 ≈ −13.4% per year — the investor is meaningfully poorer at the end. Honest performance reporting always uses the geometric quantity.
Related terms
- Time-weighted return (TWR)
- Internal rate of return (IRR)
- Geometric mean return
- Annualised return