Minimum Half-Life Hedge Ratios for Mean-Reverting Spreads

Summary

The method selects hedge ratios for a basket spread by minimizing the absolute estimated half-life of mean reversion. It treats one price series as the target and the remaining series as explanatory assets, forming the spread as the target minus their weighted prices. A numerical optimizer searches for weights, starting from ratios based on the initial target price relative to the other assets.

The function returns the hedge ratios, input series, resulting spread residuals, and the optimizer’s result object. It also warns when optimization does not converge, since the resulting ratios may be unstable. The code provides an implementation outline, but no empirical comparison, validation procedure, or safeguards for unstable half-life estimates; minimizing estimated half-life alone does not establish that the spread is tradable or robust out of sample.

Key ideas

• The hedge ratio is chosen to minimize the absolute half-life of the resulting spread.
• The spread subtracts weighted prices of the explanatory assets from the target asset price.
• Initial weights are derived from the target’s initial price relative to each explanatory series.
• The routine reports a warning if the numerical optimizer fails to converge.
• A short estimated half-life does not by itself demonstrate a stable or profitable trading relationship.

Tags

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