MiesOnChartsBitcoin power-law fair value
Log-log regression of price against days since the genesis block (Jan 3, 2009), fitted on the entire tradable history — July 2010 to the latest candle — and refitted every time this page loads. The shaded ±1σ and ±2σ bands narrow over time: residual volatility is modeled as a decaying function of Bitcoin's age rather than assumed constant.
Price vs. Modeled fair value — log scale
Model: log10(price) = a + b·log10(days since genesis), ordinary least squares on the full daily history — CoinMetrics data from July 2010 through August 2017 (bundled; historical facts don't change), then Binance daily closes fetched live. Fit stats: exponent –, R² –, residual σ today – (log10). The bands account for Bitcoin's declining volatility: residual magnitude is regressed on log-age (σ(t) = √(π/2)·(c + d·log10(days))), so ±1σ/±2σ converge toward the fair value line instead of staying a fixed width. Calibration on history: – of days closed inside ±1σ and – inside ±2σ (Gaussian targets: 68% / 95%). Dashed extension projects the fit 12 months forward. This is a curve fit, not a valuation; treat the bands as descriptive, not predictive.
Coefficient stability — does the fair-value line repaint?
The line does refit on every load, so in principle it repaints. But the point of a power law is that it shouldn't move much: each row below is an independent fit using only the data available at that past year-end, with "fair value today" being that older fit projected to the present. If the exponent barely changes as years of data accumulate, the repaint is cosmetic — the model is a stable law, not a curve chased to recent price.
| Fit using data through | Exponent (b) | Implied fair value today | Days in fit |
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Data table — start-of-year snapshots
| Date | Price | Fair value | Deviation |
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