Pairs Trading — Cointegration & Z-Score

Universe overview

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All Long-spread (z < -2) Short-spread (z > +2) Mean-reverted (|z| < 0.5) Cointegrated only

Live Pairs

z-score interpretation: z > +2 → spread extreme high → short t1 / long t2; z < -2 → spread extreme low → long t1 / short t2; |z| < 0.5 → mean-reverted → exit any open pair. Conviction scales with |z|. Cointegration test runs ADF on the spread; non-cointegrated pairs are noise — ignore the z-score.

Pair	z-score ↓	Spread ⇅	β (hedge) ⇅	Cointegrated? ⇅	Verdict	Action	Conviction ⇅

Methodology

Hedge ratio β estimated by OLS slope of c1 = α + β·c2 + ε over 60-bar lookback. Spread s_t = c1_t − (α + β·c2_t). z-score z = (s_t − μ_s) / σ_s where μ, σ computed on the lookback window. Cointegration test wraps THV2V42.cointegrationTest (Engle-Granger / ADF on residuals) over a 90-bar lookback. Default candidate universe in THV2V92.CANDIDATE_PAIRS covers intra- and cross-asset relationships (energy / bank / tech / ETF / commodity / crypto / cross-asset).

Academic basis: Engle & Granger (1987) "Co-integration and Error Correction" — foundation of cointegration testing; Dickey & Fuller (1979) — ADF unit-root test; Gatev, Goetzmann & Rouwenhorst (2006) "Pairs Trading: Performance of a Relative-Value Arbitrage Rule" — the canonical empirical pairs-trading study.

Limitations: ADF p-values rely on stable beta — structural breaks invalidate the relationship. Cointegration is a rolling property; pairs that pass at t may fail at t+30. We re-run the ADF test on every refresh and flag pairs with p-value drift > 0.10. Z-score reversion assumes mean stationarity; in trending regimes (risk-off transitions) spreads can persist outside ±2σ for extended periods, producing extended drawdowns. Position sizing should account for cap-tier-aware microstructure friction (see Scoring Card § Size factor).

See: Scoring · 5-gate Playbook · Calibration