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Estimating Hedge Ratios with Box–Tiao Canonical Decomposition

Code Stratmill research code

Summary

This method estimates portfolio weights for a spread using the Box–Tiao canonical decomposition. It first reorders the price columns so the selected dependent asset comes first, demeans the data, and fits a first-order vector autoregression. It combines the estimated VAR matrix with the sample covariance matrix, then sorts the resulting eigenvectors by their eigenvalues.

The implementation takes the vector associated with the smallest sorted eigenvalue as the hedge weights, rescales the other assets relative to the dependent asset, and fixes the dependent asset's weight at one. It then constructs the spread residuals from those weights. The document contains code but no empirical example or validation results. Its procedure also assumes the covariance matrix can be inverted and does not discuss stability, data frequency, or how to select assets for the spread.

Key ideas

  • The procedure demeans asset prices and estimates a VAR with one lag.
  • It forms a matrix from the estimated VAR coefficients and the sample covariance matrix.
  • Eigenvectors are ordered by descending eigenvalue, and the last vector is used for the hedge weights.
  • Weights are normalized so the selected dependent asset has a coefficient of one.
  • The resulting weights are used to construct spread residuals.

Tags

Pairs tradingStatisticsPortfolio construction

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