Bitcoin 'Averaged' +45% a Year and Still Lost Money: Arithmetic vs Geometric Mean Return, Explained
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Bitcoin closed 2021 at $46,328.94. It fell to $16,547.85 by the end of 2022, a drop of 64.28%. Then it rallied to $42,255.12 by the end of 2023, a gain of 155.35%.
Average those two numbers and you get +45.5% a year. That sounds like one of the best two-year runs an investor could ask for.
Anyone who actually held Bitcoin through both years ended up with less money than they started with. Not more. Less. This is the gap between arithmetic vs geometric mean return, and it is not a technicality. It is the difference between a number that flatters a result and a number that describes what actually happened to your money.
Arithmetic mean is the average you learned in school: add the numbers up, divide by how many there are.
(Return₁ + Return₂ + ... + Returnₙ) ÷ n
For Bitcoin's two years, that is (−64.28% + 155.35%) ÷ 2 = +45.5%. The arithmetic is correct. The problem is what the number implies. It treats each year's return as if it applied to the same starting amount, when in reality the second year's huge gain was compounding on top of a balance that had already been cut by nearly two-thirds.
Here is what actually happened to Rp 10,000,000 invested at the start of 2022, using Bitcoin's real closing prices as the return for each year.
| Year | Return | What Rp 10,000,000 becomes |
|---|---|---|
| Start of 2022 | — | Rp 10,000,000 |
| End of 2022 | −64.28% | Rp 3,572,000 |
| End of 2023 | +155.35% | Rp 9,121,000 |
A −64.28% year and a +155.35% year do not cancel out to flat, because the second return is applied to a much smaller base than the first. Rp 10,000,000 falling 64.28% leaves Rp 3,572,000. That amount then growing 155.35% only gets back to about Rp 9,121,000. Still down almost 9% overall, after a year that individually looks spectacular.
Geometric mean multiplies the growth factors together instead of averaging the percentages, then takes the root.
[(1 + Return₁) × (1 + Return₂) × ... × (1 + Returnₙ)]^(1/n) − 1
For Bitcoin: (1 − 0.6428) × (1 + 1.5535) = 0.3572 × 2.5535 ≈ 0.9121. That is a two-year multiplier of 0.9121, meaning the original amount ended at about 91.2% of where it started: an 8.8% loss. Taking the square root of 0.9121 and subtracting 1 gives roughly −4.5% a year, compounded. This is also, not coincidentally, the same figure a CAGR (compound annual growth rate) calculation would give you for the same two years.
If a portfolio returned a steady 10% every single year, arithmetic and geometric mean would land in almost the same place, within a few tenths of a percent. There would be no story here.
The gap opens up specifically because of volatility. A portfolio that swings wildly between deep losses and huge gains will always show a geometric mean noticeably below its arithmetic mean, because a loss and an equal-sized later gain do not cancel out once you account for what the loss did to the base amount. The more extreme the swings, the wider that gap gets. This is sometimes called volatility drag, and Bitcoin's 2022 to 2023 stretch is one of the more dramatic real examples of it on record.
Fund fact sheets, insurance illustrations and investment ads often quote an "average annual return" without specifying which average they mean. A simple arithmetic average of yearly returns will always look better than the geometric mean for any investment with real ups and downs, which is every investment that is not cash. It is not necessarily dishonest, but it is worth checking which figure you are looking at before you compare two products, or before you multiply a quoted average by the number of years you plan to invest.
You can see this same effect on any volatile asset's own price history, including Bitcoin's own price chart on its asset page, where the swings behind these numbers are visible year by year rather than compressed into a single average.
For judging what a past investment actually did to your money: geometric mean, every time. It is the only one of the two that reflects compounding, and compounding is how investment returns actually work.
Arithmetic mean still has a narrow, legitimate use: estimating a single period's expected return when you are modelling many independent future scenarios rather than describing one realised path. For anything backward-looking, meaning anything you are checking against your own results, geometric mean is the honest number.
This is a close cousin of a related mistake covered in why your broker's percentage and your real return often disagree: both come down to a headline number being technically correct while describing something other than what your account actually did.
NetWort computes your portfolio's actual compounded return from your real transaction history, not from an average of period returns that can hide a loss the way Bitcoin's 2022-2023 figures did above. Open the Portfolio Health section of your dashboard and compare your own reported return against a simple arithmetic average of your yearly figures. If the two numbers are far apart, that gap is telling you how much volatility your portfolio actually carried, not just what it earned.