# pairs_coint_perp / 1

Hypothesis. BTC and ETH share a common stochastic trend: log ETH − β · log BTC is stationary over a couple of weeks, so a stretched spread comes back. Holding the spread (one leg long, the other short) removes most of the market direction; what is left is the bet on the spread. The spot version (pairs_rotation/1) could only tilt between two long positions and kept the full market risk.

Mechanism. At each bar, ordinary least squares of log ETH on log BTC over the 336 bars ending at that bar gives the hedge ratio β, the z-score of the last residual and the Dickey–Fuller t-statistic of the residuals. Enter when the residuals look stationary (t < −3.04, the 10 % Engle–Granger critical value for two series) and |z| > 2: short the spread if z > 0 (short ETH, long BTC), long it if z < 0. Exit when z is back inside ±0.5. Stop when |z| > 4 or β turns non-positive, and stay out until z is back inside ±0.5. Notional weights: ETH ± gross / (1 + β), BTC ∓ gross · β / (1 + β) — β-weighted, so the position is neutral to a common move of the two logs (and close to dollar-neutral when β ≈ 1). The rule is replayed over the last 96 bars, each with its own window, because the function keeps no memory.

What would refute it. The stationarity test failing most of the time (then the strategy barely trades and says nothing), or losses on the trades it does take: a spread that looked stationary in-sample and then drifts is the standard failure of pairs trading, and the stop turns it into a realised loss. Both legs pay fee and slippage (four fills per round trip) and each leg pays or receives its own funding: the funding differential between ETH and BTC is a carry the z-score knows nothing about. β is estimated on 336 points with strongly autocorrelated residuals; the t-statistic is only an indication.

Parameters were written before any backtest on the Hyperliquid data and are not tuned on the test split.