Cointegration pairs trading

Motivation

Pairs trading is one of the most-studied statistical arbitrage strategies and a fair test of whether a spread's mean reversion holds up once selection bias and costs are accounted for.

Data

Daily closing prices for 10 liquid large-cap US banks (JPM, BAC, WFC, C, GS, MS, USB, PNC, TFC, COF), 2015-2024, via Yahoo Finance. One sector, so any cointegration reflects shared rate/macro exposure rather than a coincidence.

Methodology

Engle-Granger two-step cointegration test on log prices, run on every pair in the universe (45 combinations) at each re-selection point. The 5 pairs with the lowest p-value below 0.05 are traded; the hedge ratio is fit by OLS on the same formation-window data. Positions are sized on the spread's z-score: enter beyond ±2.0, exit inside ±0.5, stop out beyond ±4.0.

Backtest design

Walk-forward: pairs are re-selected and the hedge ratio re-fit every 63 trading days (one quarter), using only the prior 252 days (one year) — nothing in a trading window ever influences the pair selection or hedge ratio applied to it. Positions are force-closed at the end of each quarter before re-selection. Costs are modeled explicitly: 5bps per leg per trade, plus a 30bps/year borrow cost on the short leg while a position is held — not assumed away.

Results

Robustness checks

Entry threshold sensitivity (z = 1.5 / 2.0 / 2.5) keeps Sharpe in a 0.20-0.36 range — thin but not a knife-edge parameter choice. A 5x cost stress test flips the strategy negative (Sharpe -1.04, CAGR -5.5%), which says the edge is real but genuinely thin relative to trading frictions, not robust to them. Splitting by regime: the strategy lost money 2015-2019 (Sharpe -0.24), did well through the 2020 volatility spike (Sharpe 0.78), and was moderately positive after (Sharpe 0.33) — performance is concentrated in high-dispersion periods, not a steady year-round edge. As a leakage check, re-running the same pipeline but letting pair selection and the hedge ratio see the trading window itself (a deliberate look-ahead leak) pushes Sharpe to 1.91 — confirming the walk-forward split is doing real work, and that 0.20 is the honest number, not a bug suppressing it.

Limitations

Sharpe 0.20 is materially below the buy-and-hold benchmark's 0.55 over this window, on both an absolute and risk-adjusted basis — this strategy did not beat a naive long position here, even though its volatility (5.2%) and max drawdown (-9.2%) are far smaller than buy-and-hold's (28.8% / -50.2%). The universe is small and hand-picked (10 names, one sector), so there's real selection bias and correlated tail risk — the 2023 regional-banking stress is exactly the kind of event that hits every pair in this universe at once. Execution is modeled as same-day with flat per-trade costs; real slippage, short-borrow availability during stress, and wider bid-ask names aren't captured. Only 3 threshold values were checked, with no correction for testing multiple parameters.