Not an implementation claim. The classic distance-method pairs strategy famously decayed after its academic documentation; this guide teaches the mechanics and failure modes — the things that determine whether any modern variant deserves attention.
Definition. Pairs trading: find two instruments whose prices move together, trade the spread when it diverges, profit on reconvergence. It’s stat-arb’s minimal unit, and its clean structure makes every failure mode legible — which is why it remains the field’s best teaching example even as its classic form retired.
The three assumptions, and what tests them
1. The relationship is real. Two testing traditions: distance/correlation (simple, finds co-movers, can’t distinguish “related” from “were both trending”) and cointegration (Engle-Granger, Johansen — tests for a stationary spread, the actual tradeable object). The trap in both: selection across a large universe manufactures relationships. Test 500 stocks pairwise and 5% of ~125,000 pairs pass at 5% significance by construction — the multiple-testing problem wearing its most classic costume. Any pairs paper not correcting for search breadth across pairs is reporting luck’s order statistics.
2. It persists. Cointegration measured in-sample is a historical statement; the economic linkage behind it (same industry, dual listing, holding structure) is what persists or doesn’t. Pairs with a mechanical linkage (share classes, ADRs, index-vs-constituents) have persistent relationships and tiny, crowded spreads; pairs with only statistical linkage have wide spreads and relationships that break with regimes. That inverse relation between persistence and profitability is the strategy’s central trade-off, and papers silent on which type they trade are averaging over it.
3. Reversion arrives before capital leaves. A stationary spread reverts eventually; your margin, borrow, and patience operate on deadlines. The half-life estimate (from an OU/error-correction fit) is the load-bearing number — and it’s estimated with wide error bars from limited data. A “20-day half-life” pair that draws a 6-month divergence isn’t misbehaving statistically; you just met the distribution’s tail with leverage on.
The worked micro-example
Spread = A − β·B, β from cointegrating regression. Enter at ±2σ, exit at 0. Three quiet leaks even here: β is estimated (its error means your “hedged” position carries directional exposure that compounds with the divergence itself); σ is regime-dependent (a 2σ entry in calm vol is a 0.8σ entry in crisis vol — entries cluster exactly when spreads are structurally widening); and the exit at 0 assumes β still holds at exit time. Rolling re-estimation helps and adds its own turnover and whipsaw.
Common ways this fails in production
- The false pair: passed cointegration by search; diverges permanently on the first idiosyncratic event. Post-mortem always shows there was never an economic linkage.
- The broken pair: real linkage, then M&A, index deletion, spin-off, or delisting severs it — corporate actions are the pair-killer papers rarely model, and the short leg’s version is worst.
- The crowded unwind: statistical pairs share membership across every quant book; a deleveraging event widens all spreads simultaneously — the correlation-when-it-matters failure.
- Short-leg mechanics: borrow recalls and buy-ins force-close the profitable side of the trade at the worst time.
- The 2σ trap in vol terms: entry thresholds in fixed σ units auto-concentrate entries in high-vol regimes unless vol-scaled.
Questions to ask a pairs paper
- How many pairs were searched, and what correction was applied?
- Mechanical or statistical linkage — and does the P&L come from the type claimed?
- What happens to the equity curve if the worst 3 divergences run twice as long?
- Is the sample pre- or post-decay era, and does the paper engage with the decay literature at all?
What our scoring captures
Cointegration papers split sharply on our axes: methodology papers (new tests, new spread models) sit in Lab Rats, and the rigor axis rewards exactly what this genre skips — search-breadth honesty, divergence-tail accounting, and cost-inclusive results. The stat-arb map’s pairs branch shows the ranking.
The general machinery: signal to portfolio → · The statistics: multiple testing → · regime breaks → · From the corpus: ARDL models: appropriate use vs p-hacking →