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The smooth, constant rate of growth that gets you from start to end. The honest annualization.
CAGR is the constant annualized growth rate that turns a starting value into an ending value over a given time period, assuming compound interest. It is the geometric mean of period returns and the standard way to report multi-year performance. CAGR smooths out year-to-year volatility into a single, comparable number.
CAGR = (V_end / V_start)^(1/years) − 1CAGR = (Vend / Vstart)1/n − 1You take the ratio of end to start, raise it to one over the number of years, subtract one. There is no iteration — closed-form formula.
CAGR is honest because it is geometric. The arithmetic average return is mathematically a lie: a portfolio that goes +50% then −50% has an arithmetic mean of 0% but actually lost 25%. The geometric mean catches that drag. The gap is roughly half the variance.
CAGR assumes one starting amount and one ending amount with no cash flows in between. The moment you contribute or withdraw, you need XIRR instead.
You invested $10,000 in 2020 and let it ride. By 2026 it was worth $18,000, six years later.
CAGR = (18,000 / 10,000)1/6 − 1 = (1.8)0.1667 − 1 = 10.3% per year
Total return: +80%. CAGR: +10.3%. Those are the same fact stated two different ways.
Long-run CAGR by asset class (US data, 1928–present, nominal):
| Asset | Long-run CAGR |
|---|---|
| 3-month T-bills | ~3.3% |
| 10-year Treasuries | ~4.9% |
| Investment-grade corporate bonds | ~6.2% |
| S&P 500 (total return) | ~10.2% |
| US small caps | ~11.5% |
| Gold | ~5.0% (very regime-dependent) |
Subtract roughly 3% for inflation to get the real CAGR (purchasing-power growth), which is what actually matters for retirement math. See Real Return.
Annualized Return · TWR (Time-Weighted Return) · XIRR · Real Return
Average is arithmetic mean — it mathematically overstates compound growth. CAGR is the geometric mean and is the only correct annualization for multi-period returns.
CAGR for one-buy/one-sell investments with no cash flows in between. XIRR for any portfolio with contributions or withdrawals.
Yes — if the ending value is less than the starting value, CAGR is negative. The geometric mean handles losses correctly without the misleading arithmetic-mean issue.
CAGR is a special case of IRR with only two cash flows: start and end. IRR/XIRR generalizes to any number of intermediate cash flows.
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