Using CADF Residual Tests to Estimate Pairs Trading Hedge Ratios
Summary
The article presents the Cointegrated Augmented Dickey–Fuller procedure as a way to estimate a regression hedge ratio for two assets and then test whether the resulting spread is stationary. It fits a linear regression, treats its residuals as the candidate spread, and applies an Augmented Dickey–Fuller test. Because ordinary regression is directional, the article fits both possible orientations and compares their test statistics to choose a hedge construction.
A simulated pair illustrates recovery of a known relationship. Historical examples include the EWA and EWC equity ETFs and Royal Dutch Shell share classes, using adjusted prices and a one-lag ADF test. The ETF regressions yield slightly different test statistics, each reported as rejecting a unit root at the 5% level. This is evidence of in-sample stationarity, not proof of profitable mean reversion. The method depends on sample, lag, and regression choices, and the supplied text is truncated before all results are shown.
Key ideas
- Regressing one asset’s prices on another provides a slope that can serve as a candidate hedge ratio.
- Applying an ADF test to regression residuals assesses evidence that the spread is stationary.
- Swapping dependent and independent variables changes the estimated regression and can change the residual test result.
- The examples use simulated data and historical adjusted prices for related ETFs and share classes.
- A detected stationary relationship alone does not establish a profitable trading strategy.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.