Classify whether the covered assets are trading with, or independent of, Bitcoin
Answers how the covered assets are behaving relative to Bitcoin. It reads 30 days of daily prices for the covered assets plus Bitcoin and Ethereum, computes rolling correlation and beta to BTC, and classifies the regime as risk-on (high correlation and beta), decorrelating, defensive, or standard, with per-asset correlation and beta. It shows whether each asset has moved closely with BTC over the window.
A single-benchmark regression, taught as the market model rather than as asset pricing.
Beta is the slope of an ordinary least squares regression of an asset's returns on the benchmark's, with an intercept: beta = cov(R_asset, R_btc) / var(R_btc), defined when BTC return variance is non-zero. Read it as the fitted difference in the asset's return associated with a one-percentage-point difference in BTC's return over the sample - an association within the window, not a causal or forward-looking statement, and one that ignores the intercept.
Correlation and beta are related but different, and separating them is the point of this analysis. Correlation is scale-free and bounded in [-1, 1]; beta carries the ratio of the two volatilities, so an asset can have a high beta with modest correlation, or the reverse.
Sample size: 30 daily prices yield at most 29 return observations. That is a small regression sample - the standard error on the slope can be wide, and a single influential observation can materially move it - so any label built on it should be read with that uncertainty in mind.
On terminology: this is a MARKET-MODEL beta against a chosen benchmark. It is not the Capital Asset Pricing Model. CAPM - Sharpe (1964), with Lintner and Mossin, and Treynor's earlier unpublished work - concerns EXPECTED EXCESS returns relative to the market portfolio. This computes a realised-return regression against Bitcoin, which is a convention rather than a theoretically justified market proxy. The word 'beta' is inherited from that literature; the quantity here is the regression slope, and conflating the two is the error to avoid.
The risk-on / decorrelating / defensive / standard labels are thresholds on correlation and beta. Read the run's published classification rule for the cut-offs, how individual readings are aggregated and how conflicts between the two measures are resolved. They are retrospective heuristic classifications of the sample window, not calibrated regime probabilities or forecasts.
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