Pairs Trading with Cointegration, Spread Z-Scores, and ADF Testing

Summary

The document introduces pairs trading as a market-neutral approach that buys one security and shorts another when their relationship diverges. It distinguishes correlation from cointegration: correlated prices can continue trending apart, whereas a stationary linear combination of log prices offers a basis for expecting the spread to revert. The hedge ratio is estimated by regression, and an Augmented Dickey-Fuller test is used to assess whether the resulting spread is stationary.

For signal generation, the spread is standardized with rolling mean and standard deviation to obtain a z-score. Threshold crossings indicate potential entries, with positions reversed as the spread returns toward its mean; the article discusses thresholds in the vicinity of one and a half to two standard deviations. It also identifies practical limitations, including unstable relationships, commissions, and execution risk when small margins require large trades. Stationarity tests and historical mean reversion do not ensure future convergence, and the discussion does not establish robust performance after trading costs.

Key ideas

• Pairs trading combines a long position in one security with a short position in another.
• Correlation alone is not sufficient because correlated prices may diverge without reverting.
• Regression can estimate a hedge ratio for a spread constructed from log prices.
• An ADF test can assess whether the spread behaves as a stationary time series.
• Rolling spread z-scores provide thresholds for identifying unusually large deviations.
• Commissions, fills, and failure of the relationship to persist can undermine the strategy.

Tags

Cited by

• Strategies PEP/KO Heteroskedastic Filtered-Spread Re-entry
• Hypotheses PEP/KO Heteroskedastic Filtered-Spread Re-entry

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.