Kalman Filtering for Adaptive Pair Hedge Ratios and Mean Reversion

Summary

This document explains how a Kalman filter can update a pair’s hedge ratio over time, avoiding the need to choose a fixed lookback window or a manually selected observation-weighting scheme. It models one asset’s price as a linear function of the other, with an intercept and slope that evolve as a random walk. Under linearity and Gaussian-noise assumptions, the filter estimates those coefficients and the forecast error’s uncertainty at each observation.

The trading method treats forecast error as deviation of the pair spread from its predicted value. It enters a long spread when the error falls beyond a negative uncertainty-scaled threshold and a short spread when it exceeds a positive threshold; positions close when the error returns past exit thresholds. The text shows example estimates and cumulative returns for an EWC–EWA pair, but gives no numerical performance statistics or robust validation. Results depend on model assumptions, threshold choices, execution costs, and whether the pair’s relationship remains useful.

Key ideas

• A Kalman filter can update a pair’s intercept and hedge ratio as new prices arrive.
• The model assumes a linear price relationship with Gaussian observation noise and evolving coefficients.
• Forecast error and its estimated standard deviation can define mean-reversion entry and exit thresholds.
• Long and short spread positions combine exposure to one asset with an offsetting hedge in the other.
• The illustrated pair results do not establish broad performance, and the method depends on its modeling assumptions.

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