BTC & Liquidity: the Honest Fair Value
Why the popular "liquidity fair value" chart misleads — with the test it never passes.
BTC vs. Liquidity Fair Value
Four traps of the liquidity fair-value chart
1.Levels, not changes
Two series that both rise for years almost always correlate in levels — even when unrelated. What matters is the relationship in the changes (returns R²), and that is ≈0.
2.No cointegration test
A pretty R² without a cointegration test is worthless: the ADF test (p≈0.999) rejects any stable equilibrium relationship. Without cointegration, "fair value" is undefined.
3.In-sample fitting
Fit the regression over the WHOLE history and the line looks perfect — it knows the future. The honest walk-forward estimate (past only) is far noisier.
4."X% above fair value" as a signal
The naive deviation is sold as a buy/sell signal. Without a valid fair value that number is not interpretable — it only describes how far two drifting series currently sit apart.
This does NOT mean liquidity is irrelevant to Bitcoin — only that it does not yield a mechanical "fair price" from which over- or undervaluation could be derived. Both series drift up together; that is a descriptive co-trend, not an equilibrium relationship. Not a trading signal.
Methodology: Cointegration, not Correlation
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Liquidity series = G3 central-bank balance sheets (Fed WALCL + ECB + BoJ, in USD, monthly; Big-5 M2 is discontinued on free FRED, hence "G3", not literally global). Model: log(BTC) = α + β·log(liquidity), estimated walk-forward (expanding, 24-month warmup) — the walk-forward line knows only the past. For contrast we also show the naive in-sample fit (fitted over the whole history, contains look-ahead) — the line popular charts present. The cointegration test (Engle-Granger: OLS residuals → ADF, MacKinnon critical values) decides whether a "fair value" exists at all. Empirically 2010–2026: not cointegrated (ADF ≈ −1.84, p ≈ 0.999, Durbin-Watson ≈ 0.06). The levels R² (~0.85) is spurious; the returns R² (≈0) proves it. Hence: no interpretable fair value, only a descriptive co-trend. Descriptive, not a forecast, not investment advice.
As a machine-readable knowledge object: /knowledge/btc_liquidity_fair_value/BTC
BTC vs. Liquidity Fair Value — the Cointegration Test It Fails
The 'Bitcoin liquidity fair value' chart is everywhere: overlay BTC on global liquidity, fit a line, declare BTC 'X% above fair value'. It looks compelling because both series drift up together. But over 170 months against G3 central-bank liquidity (Fed+ECB+BoJ), BTC and liquidity are not cointegrated — so there is no statistically valid fair value, only a descriptive co-trend.
- Levels R² (price level)
- 0.854 (looks perfect)
- Returns R² (changes)
- 0.011 (no relationship)
- Cointegration (ADF)
- −1.84, p≈0.999 → not cointegrated
- Durbin-Watson
- 0.06 (residuals not stationary)
A high levels R² between two trending series is the textbook signature of a spurious regression: two things that both rise over a decade will correlate in levels whether or not one drives the other. The honest question is whether they move together in their changes — the returns R² — and here it is essentially zero. The Engle-Granger cointegration test (OLS residuals fed into an ADF regression, MacKinnon critical values) confirms it: the residuals are not stationary (Durbin-Watson ≈ 0.06, ADF p ≈ 0.999), so no stable equilibrium — no fair value — exists.
We plot two model lines against BTC. The naive in-sample fair value is fitted over the entire history and therefore contains look-ahead — it is the seductive line popular charts show. The walk-forward fair value re-estimates using only past data at each point and is far noisier. The implied "X% above fair value" number from the naive fit is not interpretable without cointegration. This page is descriptive and educational — not financial advice and not a buy/sell signal. The same result is exposed as a machine-readable knowledge object at /knowledge/btc_liquidity_fair_value/BTC.