Bitcoin: four models, scored on the past

Bitcoin has no earnings, so the only thing its price can be held against is a trend. We run four models of that trend: the power law, a growth rate that keeps slowing, an older hand-written view, and a new maturity model fitted on the whole history since 2010. Then we went back to every month-end since 2013, let each model forecast using only the data known that day, and scored it against what happened. The blend weights come from that score.

Price against two trends

Weekly closes in USD, log scale. The shaded band runs from half to twice the power-law trend. The maturity trend bends slightly below it and carries the halving cycle. Both are drawn five years forward.

Bitcoin Power-law trend Maturity trend, with the halving cycle

Source: nxtdev.sk NXTlab · data: Coin Metrics community API

How fast the trend actually grew, against what the power law says

Growth a year over the trailing four years, measured on the 365-day average price so the cycle mostly drops out.

Actual, trailing 4 years Power-law trend, same window

Five years of simulated price, by model

Median 25th and 75th percentile shaded: 5th to 95th percentile

The median path of every model

EUR, log scale. Half the simulated paths end above each line and half below.

Which model forecast best

Horizon Start dates

Error: how far the forecast was from the outcome, counting its spread, in log points (CRPS; 0.30 ≈ typically 30% off). Lower is better. In 80% range: how often the outcome landed inside the forecast's middle 80%; honest ranges hit about 80%. Bias: outcome minus the forecast's median, in log points; negative means the model forecast too high.

What €10,000 does, model by model

Holding period

Risk over the whole five years

Drawdown is the deepest fall below the entry price at any point in the five years, before tax. Sharpe is the yearly return above EUR cash divided by its volatility, before tax.

Margin-of-safety price

Why the model is built this way

A trend is the only anchor there is. A share can be valued on the profits it will earn. Bitcoin earns nothing, so its price can only be compared with a trend, and the whole question is how fast that trend grows. The model does not pick one answer. It runs four and shows how far apart they land.
Four models. The power law is the best-known bitcoin model. Decaying growth is the simplest reading of the last decade: every cycle grew more slowly than the one before. The scenario table is the older hand-written view from our portfolio model, kept so the change can be seen. The maturity model is new and is described below.
One model for the whole history. Measured by bitcoin's age, three things have held since 2010. Volatility falls as one over the square root of age: weekly moves scaled that way have had the same spread in 2010–15, 2016–20 and 2021–26. Growth slows a little faster than the power law says, so the maturity trend may bend (fitted bend , where 1 is the power law). And the gap to the trend follows the four-year halving cycle, whose swings shrink as bitcoin ages. Each simulated path also draws its own trend, bend and cycle, because none of them is known exactly.
Scored on the past, weighted by the score. At every month-end since 2013 each model was refitted on the data known that day and asked for 1, 3 and 5 years. The blend gives each model the weight that would have forecast best over three years, pulled halfway toward equal weights because the test covers only one or two cycles.
Same weeks for the first three models. Their paths are stitched together from real bitcoin weeks of the last five years (51% a year), in random stretches averaging two months, so any difference between them is the trend, never luck. The maturity model draws its weeks from all of history since 2010, each scaled to bitcoin's age.
A chance that it breaks. Both measured trends are fitted on a coin that survived. Neither can see the risk that it stops working. Each year there is a 1% chance of a permanent 80% fall, after which the price has no trend at all.
The investor's outcome, not the coin's. Everything is in EUR, after Slovak 2026 tax on crypto (no holding-period exemption, 19–35% plus a 16% health levy), so the numbers say what a euro investor keeps.

Strong and weak sides

What you can trust

The risk numbers. Drawdowns, volatility and the chance of halving come from real weeks, and they hardly change between models: . Expect to sit through a fall of more than half.
The comparison. Shared weeks mean the gap between models is a fair measure of how much the answer depends on the trend you believe.
The tax gap. It is plain arithmetic: .
The maturity model forecast best when tested on past years. It is also almost free of bias, while every power-law version forecast too high at five years.
The power law's record is real. Fitted only on data up to 2020, the next six years averaged of that trend. In the backtest it is the second-best model throughout.
Nothing is hidden. Each assumption is one number in a config file, and the sensitivity tables below show what each one moves.

Where it is weak

Every trend comes from the price itself. Nothing outside the chart (adoption, fund flows, a share of gold) pins them down. With three and a half cycles of data many curves fit the past, and they part ways in the future.
The backtest is short. Monthly start dates overlap: from 2017 they cover about two independent cycles at three years and one at five. We also scored about 20 versions of the maturity model on the same years, so part of its lead comes from picking the best one.
The maturity model leans on the halving cycle repeating. The cycle is what makes it expect a weak year first and a rise after the 2028 halving. It has repeated only three or four times. Its five-year ranges also turned out too wide in the backtest.
The power law's pull back to trend is partly built in. The speed of the pull is measured around a trend fitted on the same data, and a fitted line always has the data scattered evenly around it. That flatters the power law, which loses money only if bitcoin breaks.
The peaks above the trend keep shrinking (11×, 6.6×, 3.6×, 1.4×), and actual growth has trailed the law's own growth for five years. The law is holding on its floor, not its peaks.
Decaying growth rests on little data. About ten years of heavily overlapping four-year windows: two or three independent observations. Growth could also slow faster than the curve we chose.
The blend weights rest on that short test. Taken at face value, the backtest gives the decaying-growth model and the scenario table no weight at all; we keep 12.5% each.
The 1% a year chance of a break is an assumption, not a measurement. FX is held constant.
Even the blend assumes the market misprices a $1.6 trillion asset. If it does not, the right row is "no premium", and the model cannot rule that out.

How to read it. Treat the risk numbers as estimates and the return numbers as scenarios. On the backtest-weighted blend today's price passes, but only because the trend models, which forecast best in the past, outweigh the rest. If you think bitcoin's trend is over, the right row is "no premium", and no backtest on a survivor can rule that out.

The evidence behind the trends

Maturity model.

Refitted using only the data up to each date. Bend 1 = the power law; above 1, growth slows faster. With 2014's data the bend could not be measured (the range runs 0.7–1.2), which is why each path draws its own.

Power law.

Power law refitted using only the data up to each date. The slope barely moves, and every version puts today's trend above the price.

Out of sample: fitted up to a date, then the later price compared with that trend. Ratio = price ÷ trend.

Price ÷ trend, highest and lowest each year.

Decaying growth.

Growth of the 90-day average price from one halving to the next. The last row is the cycle so far.

Context, not inputs.

Sensitivity

The chance a year of a permanent 80% fall. The scenario table already contains its own break scenario.

Which years supply the weekly moves (power law and decaying growth; the maturity model always uses all years, scaled by age). Medians barely change; drawdowns, the mean and the safety price change a lot.

Method and data

Model code: btc-eval-model, built on our equity valuation framework (simulation, tax, safety rule). Prices: Coin Metrics community API and Yahoo Finance; rates: ECB AAA curve. This is a draft and not investment advice.