CAGR gets described as "your average annual return," which is close enough to be dangerous. CAGR is a geometric mean, computed only from your starting value, ending value and the time between them — it is mathematically guaranteed to be less than or equal to the arithmetic average of your yearly percentage returns, and the gap is driven entirely by volatility. A portfolio can average a positive return every year on paper and still have a negative real CAGR.
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CAGR = (End / Start)^(1 / Years) − 1
O Calculadora CAGR on this site runs exactly this formula. Crucially, CAGR is a geometric mean of the implied per-period growth factors, not the arithmetic mean of the actual yearly percentage returns. Those are two different kinds of average, and for anything other than a perfectly flat, identical-every-year return stream, they give two different numbers — with the geometric one (CAGR) always the smaller of the two.
Take $1,000 through two years: +50% in year one, -50% in year two. The arithmetic average of those two returns is a clean 0%. Here is what actually happens to the money:
| Ano | Retornar | Valor |
|---|---|---|
| Start | — | $1,000.00 |
| Year 1 | +50% | $1,500.00 |
| Year 2 | −50% | $750.00 |
$1,000 → $750 over 2 years. CAGR = (750/1000)^(1/2) − 1 = √0.75 − 1 = −13,40% a year, every year, compounding. The arithmetic average of the two yearly returns said "0%, you broke even." The actual money says you lost a quarter of your capital and your real annualized rate is a steep negative number. Neither figure is wrong — they are answering different questions — but only CAGR tells you what happened to your dollars.
This is not a quirk of round numbers. A milder, more realistic version makes the same point: three years of +20% followed by one year of −50% averages to a healthy-looking +2.5% a year arithmetically, yet $1,000 ends at $864 — a CAGR of −3.59%. An investment that "averaged a positive return every single year" still lost money, annualized.
The mechanism is simple once you see it: a loss of X% requires a larger-than-X% gain to get back to even, because the loss shrinks the base you're gaining from next. −50% needs +100% to recover, not +50%. Averaging +50% and −50% arithmetically pretends the gain and the loss were the same size relative to the money at risk — they weren't, because the −50% happened on a bigger pile ($1,500) than the +50% started from ($1,000).
Formally, this is the AM-GM inequality applied to growth factors: the geometric mean of a set of positive numbers is never greater than their arithmetic mean, and the two are equal only when every number in the set is identical. Zero volatility between periods (every year returns exactly the same amount) is the one case where CAGR and the arithmetic average coincide. Any variation between periods — any volatility at all — pulls CAGR below the simple average, and it pulls harder the more volatile the path is.
For a return stream with annualized volatility σ and arithmetic drift μ, the standard approximation for the resulting compound growth rate is:
CAGR ≈ exp(μ − σ²/2) − 1
The σ²/2 term is usually called arrasto de volatilidade ou variance drain — the structural cost that volatility itself imposes on compounding, separate from and in addition to whatever the asset actually does on average. It grows with the quadrado of volatility, so it stays small for low-volatility assets and becomes dominant for the kind of volatility crypto routinely produces:
| Annual volatility (σ) | Drag at 10% drift | Approx. real CAGR |
|---|---|---|
| 10% | −0.03pp | ≈ 9.97% |
| 20% | −1.67pp | ≈ 8.33% |
| 40% | −7.98pp | ≈ 2.02% |
| 60% | −17.69pp | ≈ −7.69% |
| 80% (typical altcoin) | −29.75pp | ≈ −19.75% |
| 100% | −42.97pp | ≈ −32.97% |
At 10% drift and 80% volatility — not an unusual combination for an altcoin — the drag alone is larger than the drift, turning a plausible-sounding "10% a year on average" pitch into a real expected CAGR around −20%. This exact relationship, including leverage, is what the volatility drag calculator models (set leverage to 1× to reproduce the table above directly); leverage multiplies the drift linearly but the drag by the quadrado of leverage, which is why leveraged tokens decay so much faster than their unleveraged counterparts even with zero net price change.
CAGR (compound annual growth rate) is the single constant rate that would have turned your starting value into your ending value over the period — it is a geometric mean, derived only from the two endpoints. Average return is usually the arithmetic mean of each period's percentage return. They are different calculations, and CAGR is always less than or equal to the arithmetic average, never greater, except in the special case where every period's return is identical.
Because percentage gains and losses are not symmetric around your capital. A +50% year followed by a -50% year averages to 0% arithmetically, but $1,000 that grows to $1,500 and then drops 50% ends at $750 — a real loss. The CAGR over those two years is -13.40%, not 0%, because CAGR is computed from what actually happened to the capital, not from averaging the percentages.
Approximately, CAGR is lower than the arithmetic average return by about half the variance of the returns (volatility squared, divided by two) — a relationship sometimes called volatility drag or variance drain. At 20% annual volatility the drag is roughly 2 percentage points a year; at 80% annual volatility (common for altcoins) it grows to roughly 30 percentage points a year, which is enough to turn a healthy-looking average return into a negative real CAGR.
No. This follows from the AM-GM inequality: the geometric mean of a set of positive growth multipliers can never exceed their arithmetic mean, and the two are equal only when every period's return is exactly the same. Any volatility at all — any variation between periods — pushes CAGR strictly below the simple average, which is why a steady 8% compounder can out-earn a wilder asset with a higher average annual return.
⚠️ Educational only — not financial advice. Past CAGR does not guarantee future compounding, and leveraged products carry liquidation risk on top of volatility drag.