Hedge Ratio Methods for Constructing Mean-Reverting Spreads
Summary
Hedge ratios set the relative sizes of legs in a spread so that price differences do not leave the position unintentionally unbalanced in dollar terms. The document introduces a simple price-ratio method, then describes normalizing weights so the dependent asset has a coefficient of one when constructing a spread. It outlines several alternatives: OLS regression, total least squares, Johansen test eigenvectors, Box-Tiao decomposition, and optimization for minimum mean-reversion half-life or minimum Augmented Dickey-Fuller statistic.
The methods differ in their assumptions and objectives. OLS uses a directional regression and can be sensitive to which asset is treated as dependent; TLS accounts for variation in both legs. Johansen supplies cointegrating vectors, while Box-Tiao seeks a portfolio with predictive properties. The minimum half-life and ADF approaches target spread stationarity measures directly. The document explains these methods conceptually and gives example outputs, but provides no comparative performance evidence. It also cautions that numerical optimization may fail to converge, so its status should be checked.
Key ideas
- Hedge ratios determine the relative exposure of each asset in a spread.
- A simple price ratio can balance the dollar value of differently priced assets.
- OLS hedge ratios can depend on which asset is selected as the dependent variable.
- TLS incorporates variation in both spread legs when estimating their relationship.
- Johansen, Box-Tiao, half-life minimization, and ADF optimization offer distinct ways to choose spread weights.
- Optimization-based estimates may be unstable when the numerical procedure fails to converge.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.