Estimating ETF Pair Hedge Ratios with a Kalman Filter
Summary
The article explains how a Kalman filter can estimate a changing linear relationship between two related assets. In a pairs trading setup, the regression intercept and slope define the spread and hedge ratio; treating them as hidden states allows the estimates to update as new price observations arrive. The model uses a random walk for the coefficients and separates state noise from observation noise. This offers an alternative to rolling regression, which requires choosing a lookback window.
The example applies the method to two US Treasury bond ETFs with different durations, showing a time-colored price scatterplot and plots of the estimated slope and intercept. These visualizations illustrate how the relationship can vary through the sample, but the provided text does not establish profitability or report a completed trading performance evaluation. Results depend on model and noise assumptions, initialization, data quality, and subsequent decisions about spread signals, costs, and execution.
Key ideas
- A Kalman filter can update regression coefficients as new paired price observations arrive.
- Modeling the intercept and slope as hidden random-walk states allows the hedge ratio to vary over time.
- Rolling regression also adapts coefficients but introduces a lookback-window choice.
- The example uses two related Treasury bond ETFs to illustrate changing regression behavior.
- Estimated coefficients alone do not demonstrate a profitable strategy; signal rules and trading costs still need evaluation.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.