Research · Altcoins · Quant Research

Estimating beta to Bitcoin

Beta is the slope of a regression of an asset's returns on Bitcoin's returns. It is a single number standing in for a relationship that changes with the market regime, and this page sets out how it is estimated, what the estimate assumes, and why a beta measured in one period is a poor guide to the next.

Last reviewed 2026-09-21Source: Methodology reference; no dataset is published on this pageRegression setup follows standard practice; no beta figure is asserted.

The regression setup

Beta is estimated by regressing an asset's return on Bitcoin's return over the same window. The asset's return is the dependent variable, Bitcoin's return is the independent variable, and the slope of the fitted line is the beta. A beta of one means the asset tended to move one per cent for each one per cent move in Bitcoin. A beta above one means it moved more than proportionally, and a beta below one means it moved less. The intercept of the regression is the average return the asset produced that Bitcoin's return does not explain, and it is usually reported alongside the slope because a high beta with a negative intercept describes a very different asset from a high beta with a positive one.

The regression is run on returns rather than prices, for the same reason a correlation is. Two price series that both trend upward will produce a high slope whether or not they are related, because the regression is fitting the trend. Differencing the series removes the trend and leaves the day-to-day co-movement, which is what beta is meant to describe. The return definition, the observation frequency and the window all have to be stated, because each one changes the slope.

The coefficient of determination, usually reported as R-squared, is the share of the asset's return variance that the regression explains. It is as important as the beta and is more often omitted. A beta of two with an R-squared of five per cent means Bitcoin's return explained almost none of the asset's movement, and the slope is close to noise. A beta of two with an R-squared of eighty per cent means the two series moved together closely. The same beta describes two completely different relationships, and only the pair of numbers distinguishes them.

Why beta is regime-dependent

A beta estimated over a long window is an average of the betas that held within it, weighted by where the variance was. Because crypto volatility is concentrated in a small number of turbulent periods, the estimate is often dominated by those periods. An asset that traded independently through a quiet stretch and fell with everything else through a crash will show a beta that describes the crash. That is not a flaw in the estimator; it is what an average does when the underlying quantity moves.

The regimes that matter are recognisable. In a broad risk-off episode, correlations across the asset class tend to rise toward one, because the common factor — the withdrawal of risk capital — dominates every asset-specific story. In a quiet, range-bound market, correlations tend to fall, because there is no common shock to synchronise the assets and idiosyncratic news dominates. Beta therefore tends to be higher in exactly the periods when a reader most wants to know it, and lower in the periods when the estimate is most stable.

There is a second source of instability that is specific to crypto: the asset's own liquidity and venue structure change over time. An asset that trades on one venue with thin depth behaves differently from the same asset after it is listed on several large venues with derivatives markets attached. The change is not a change in the asset's design; it is a change in the market it trades in, and it moves the beta without any change in the underlying relationship.

What a beta does and does not say

Beta is a measure of co-movement, not of causation. A high beta to Bitcoin does not mean Bitcoin moved the asset. It means the asset's returns and Bitcoin's returns moved together in a way a straight line describes well over the window measured. The mechanism behind that co-movement is a separate question, and the regression cannot answer it. The plausible mechanisms — shared exposure to risk appetite, shared leverage and collateral, shared market-makers — are described on the correlation page and apply here unchanged.

Beta is also not a measure of risk on its own. A beta of one and a half describes how the asset moved relative to Bitcoin, not how much it moved in absolute terms. An asset can have a high beta to Bitcoin and low absolute volatility if Bitcoin itself was calm over the window, and a low beta and high absolute volatility if the asset's movements were mostly idiosyncratic. The two measures answer different questions, and a risk comparison needs both.

Finally, beta is not a forecast. A beta estimated over the last year is a description of the last year. Using it to size a position assumes the relationship persists, and the evidence is that it does not persist reliably across regimes. The defensible use of a beta is as a description of a past period, reported with its window, its R-squared and its sensitivity to the window, and read alongside the regime the window contained.

Method, dataset and limitations

The regression choices a beta study has to state, and what each one changes about the estimate.
Choice	Options	What it changes
Dependent variable	Asset return; excess return over a cash rate	Using raw returns measures co-movement; using excess returns measures co-movement after the return available on cash, which is the convention in equity beta.
Observation frequency	Daily; weekly; monthly	Daily data gives more observations and more microstructure noise; monthly data gives fewer, more stable observations and a longer required window.
Window length	90 days; 365 days; full history	Short windows capture the current regime and are unstable; long windows are stable and average across regimes. The window is part of the claim.
Intercept	Reported; suppressed	The intercept is the average return Bitcoin's return does not explain. Suppressing it hides whether the asset out- or under-performed the relationship.
Goodness of fit	R-squared reported; omitted	R-squared is the share of variance the regression explains. A slope without it cannot be distinguished from noise.
Regime treatment	Single full-sample estimate; sub-period estimates	Sub-period estimates show whether the relationship was stable. A single estimate over a window containing two regimes is an average of two relationships.

Last reviewed 2026-09-21Source: Methodology reference; standard regression practiceNo dataset is published on this page and no beta figure is asserted.

The dataset is the same panel of daily closes described on the correlation page: a public price aggregator as the primary series, cross-checked against at least one independent source, with the retrieval date recorded. The period is bounded by the shortest history in the panel, and the window used for the regression is stated on every table.

The limitations are the ones above. Beta is a linear summary of a relationship that changes with the regime, estimated over a window that is a choice, on a panel selected by current market capitalisation, with unequal histories. It is a useful description of a past period and a poor forecast of the next one, and it should never be reported without its R-squared and its window.

Sources and references

The regression setup follows standard practice. The series a study would use are named and linked below.

Daily price series for the four assets. CoinGecko, CoinGecko API documentation: the historical daily close series used to build the return panel, with the retrieval date recorded on each study.
Reference and cross-check series. Coin Metrics, Community Network Data: an independent daily series used to check that a price move is not an artefact of a single venue's quote.
On-chain and market-structure context. Glassnode, Glassnode API documentation: the realised-capitalisation and supply series used to describe the market each asset trades in, not to compute the return panel.
Asset-level reference data. Messari, Messari API documentation: a third series used where the first two disagree, so the disagreement can be reported rather than hidden.
Bitcoin's own record, for the baseline. Bitcoin Data Guide, Bitcoin Price History and Data Sources & Methodology: the site's own compiled daily record and the provenance rules that apply to it.

Beta and the capital asset pricing model. William Sharpe, Capital Asset Prices: A Theory of Market Equilibrium: the original definition of beta as the slope of a return regression.
Regime dependence in asset betas. Ang and Chen, Asymmetric Correlations of Equity Portfolios: evidence that correlations rise in down markets, which is the mechanism behind a regime-dependent beta.
Bitcoin's own record, for the baseline. Bitcoin Data Guide, Bitcoin Price History and Risk-Adjusted Returns: the daily record and the ratio definitions used across this site.

Last reviewed 2026-09-21. No live market data is fetched or displayed on this page.