Bitcoin cycle analysis and the limits of four observations

Bitcoin has completed four price cycles. That sample supports a narrower set of conclusions than the cycle literature generally draws from it, and the conclusions it does support are mostly about measurement rather than about price.

Over the first week of August we ran six preregistered studies on bitcoin's full tradeable history, spliced from public sources back to August 2010 and validated against an independent series on the overlapping period to a median ratio error of zero. Each study fixed its hypotheses, thresholds and disqualification criteria before any result was computed. What follows is what survived.

The four-year period is not separable from an autocorrelated null

A spectral analysis of detrended log price returns a dominant period of 1,452 days, or 3.98 years, close enough to the halving interval that it is routinely read as confirmation of one. Benchmarked against an AR(1) surrogate matched to the series' own persistence, that peak carries p = 0.16; against a block-bootstrap surrogate, p = 0.73. Any trending, volatile, strongly autocorrelated series produces spectral peaks of this magnitude, and four cycles cannot distinguish a genuine oscillation from that background.

Everything below has to be read under that constraint. Cycle templates remain useful as scenario arithmetic, and they are not evidence of periodicity.

Shrinking drawdowns are falling volatility

Claims that bitcoin's crashes are getting shallower usually rest on a sequence of trough depths. Re-derived from price across the four completed cycles, those depths are −89.6%, −79.7%, −83.4% and −76.4%, which is not monotone: the 2017 trough was deeper than the 2013 trough. Sequences that appear monotone typically omit the 2013 to 2015 cycle. A permutation test on the ordering of the four gives p = 0.125 against an attainable floor of 0.042, so the declining trend is not established at conventional significance and could not have been on four observations.

Normalising by volatility identifies the mechanism and reverses the interpretation. Annualised volatility across the same cycles fell from 2.46 to 0.66, a decline of 73%, while depth fell about 15%. Drawdown per unit of volatility therefore ran −0.92, −1.42, −2.12, −2.18 — it more than doubled, monotonically. Volatility accounts for more than the entire observed shrinkage, and the residual points the other way: risk-adjusted, bitcoin's drawdowns have deepened.

Declining cycle multiples survive seven of eight denominators

Successive cycle tops have risen by 35.06×, 17.19×, 3.47× and 1.85× over the prior top. The standard explanations attribute the decline to the growing base, to the monetary environment, or to maturation. Each of those is a claim about the correct denominator, so we tested eight of them against a flattening criterion fixed in advance: a denominator explains the decline if it reduces the slope of the log-multiple sequence by at least half.

Denominator	Slope vs nominal	Explains?
Price per active address	15%	Yes
Price per stock-to-flow	83%	No
Price per unit hashrate	94%	No
Nominal, baseline	100%	—
Annual issuance value	100%	No
Consumer-price deflated	104%	No
Market value over broad money	115%	No
Market capitalisation	117%	No

Deflating by consumer prices moves the slope by 4%, which places currency debasement as a level effect rather than a cycle effect. Normalising by broad money or by market capitalisation makes the decline steeper rather than flatter, so neither liquidity nor base growth removes it. The single denominator that does flatten the sequence is price per active on-chain address, and its own denominator has been falling since 2017, from roughly 958,000 to 595,000, over a period in which custody centralised and exchange-traded holdings began generating no on-chain activity at all. A ratio whose denominator shrinks mechanically will flatten almost any numerator, so that result is at least as consistent with proxy degradation as with economics.

The most recent cycle did not match its own supply reduction

Each halving cuts issuance exactly in half. Under a flow-balance accounting benchmark, constant dollar demand against half the new supply implies a price response of 2.00×. Dividing the observed multiples by that benchmark gives the demand contribution net of supply mechanics: 17.53, 8.60, 1.73 and 0.92. The 2021 to 2025 cycle is the first in which the price gain did not reach what the supply reduction alone implies. The dollar value of annual issuance tells the same story from the miners' side, peaking at $22.2 billion in 2021 and falling to $20.5 billion in 2025, so the sell pressure from new supply has stopped growing.

Flow balance is an accounting identity rather than an economic law, and the stock-to-flow model built on it has failed out of sample. The arithmetic above does not depend on that model being correct; it uses the halving only as a fixed reference against which to measure the residual.

Interest rates and inflation

Policy was materially tighter over the recent cycle than in any before it, with mean effective fed funds of 3.88% against 0.12%, 0.39% and 1.15% in the three prior cycles, and mean consumer inflation of 4.64% against 2.16%, 1.29% and 2.32%. The natural inference is that the policy environment suppressed the return.

Adjusting for the rate environment directly does not support that inference. Compounding the policy rate daily across each cycle gives the cash return an investor forwent, and expressing the multiples net of it yields 35.34, 16.93, 3.31 and 1.59. Because the hurdle rose, adjusting for the rate environment reduces the most recent multiple by 14.1% rather than rescuing it. Rank correlation between mean policy rate and log cycle multiple is −1.000, which is the strongest available and still uninformative: the critical value at four observations is 0.950 on the Pearson statistic, which the observed −0.863 does not reach, and the cycle index correlates +0.905 with the policy rate, so controlling for it flips the partial correlation positive.

At monthly frequency, where the sample runs to 190 observations, the picture is different from the narrative in a specific way. Regressed on forward three-month log returns with Newey-West standard errors, the policy rate level gives t = −1.05, the real policy rate gives t = +1.57 with a positive sign, and the twelve-month change in policy rates gives t = −0.29. The one macroeconomic variable that clears the threshold is realised consumer inflation, at t = −3.15, and its sign is negative: higher inflation has been followed by lower bitcoin returns over the subsequent quarter. That result survives a Bonferroni correction across the four predictors tested at that horizon, though the correction was not specified in advance and is disclosed rather than claimed.

Projections and the choice of lens

Extrapolating the same observations is where all of this acquires practical consequence. For the trough, ten methods — arithmetic drawdown on closes and on lows, log drawdown, recovery multiple, a bounded logit transform, a volatility-adjusted estimate, an analytic estimate scaled by the measured fat-tail excess, and realised-price anchors — span a range of 1.43× between the lowest and highest. Drawdown is bounded below by total loss, and bounded quantities transform consistently.

For the subsequent peak, five methods on the same four multiples span 16.18×. Price has no upper bound, so a multi-year multiplicative extrapolation inherits whatever its functional form assumes about adoption, and the assumptions differ by an order of magnitude. One of those forms was disqualified by a criterion set before the results were seen: fitting log multiples linearly implies they decline without limit, which projects the asset to roughly a thousand dollars within two further cycles. A form that produces an absurdity two steps out should not be trusted one step out, and it was the form in general use.

Asymmetry between the two is the usable finding. A cycle trough can be characterised; the peak that follows it cannot, and the spread between methods is the honest measure of that. Neither range should be read as a forecast, and the point of reporting them together is that one of them is an order of magnitude less informative than the other.

How this compares to the models in circulation

The public models rest on independent variables that are monotone in time, which guarantees in-sample fit against a monotone price series and guarantees nothing beyond it.

Stock-to-flow regresses log market value on the ratio of supply to annual issuance, reports very high in-sample correlation, and has limited to no out-of-sample predictive ability, with its explanatory power confounded by the log-time trend. The power law regresses log price on log time since inception and currently implies a fair value near $378,000 against a market price near $60,000; recent work characterises it as having weak structure and comparatively good forecasts, which is an unusually candid position, and Broido and Clauset found genuine power-law structure in roughly 4% of about a thousand real-world networks, so the prior on any particular series exhibiting one is low. Metcalfe-type models value the network by the square of its participants and now face the measurement problem described above, since the participant proxy has been falling while value rose. Network-value-to-transactions and market-value-to-realised-value are relative indicators rather than valuations, and in our own cross-correlation the latter lags price by roughly 240 days. Cost-of-production models are undermined by the direction of causality, since mining difficulty adjusts to price rather than anchoring it, and price per unit of hashrate has fallen in every cycle.

Academic asset-pricing work has largely declined to produce fair-value models at all, asking instead which factors price the cross-section and the time series. None of the models above has been adopted by it.

What four cycles support

Supply is arithmetic and needs no model: annual issuance is now 0.86% against United States broad money growth of 6.04% and consumer inflation of 3.73%, and the crossover below money growth dates to April 2024. That is a statement about dilution, and it carries no implication about price, which demand determines.

Beyond it, the defensible conclusions are negative. The four-year period fails its own significance test. Shrinking drawdowns are falling volatility with the risk-adjusted residual running backwards. Declining multiples survive normalisation by inflation, liquidity, base size and supply mechanics. The peak is not estimable at a 16× spread across methods. And the one macroeconomic variable with demonstrable predictive content over investable horizons is inflation, with the sign opposite to the hedging argument.

Across the whole tradeable history the maximum leverage at which a position entered at any point would have avoided liquidation is 1.076×, set by the June 2011 peak and the 92.4% decline that followed it. That number is a property of the worst path rather than of the average return, and it is the one result here that requires no model at all.