Pairs Trading: Cointegration Tests, Hedge Ratios, and Mean-Reversion Speed
Summary
The article explains how to assess candidate equity pairs and estimate a spread for mean-reversion trading. Using XOM and CVX as an example, it fits an ordinary least squares hedge ratio, forms a residual spread, and applies an Augmented Dickey-Fuller test. It then compares that approach with total least squares, estimates spread half-life from its lagged change, and introduces the Johansen procedure for finding cointegrating combinations, including a three-stock example.
The reported tests illustrate that conclusions depend on the hedge-ratio method and statistical specification; the Johansen examples also show how to construct spreads from estimated cointegration vectors. These in-sample outputs do not establish a profitable strategy or guarantee future stationarity. The article warns that repeated significance testing creates data-mining bias and that multi-instrument portfolios add brokerage and spread-crossing costs. Traders should validate relationships out of sample and account for implementation costs before trading.
Key ideas
- Pairs trading begins by estimating a hedge ratio and testing whether the resulting spread is stationary.
- Ordinary least squares and total least squares can produce different hedge ratios and test outcomes.
- The Johansen test can identify cointegrating portfolios involving more than two assets.
- Spread half-life provides an estimate of how quickly deviations may mean-revert.
- Repeated tests raise data-mining risk, while adding instruments increases trading costs.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.