Calculating a Rolling Z-Score for Cointegrated Stock Pairs

Summary

The document presents a pairs-trading question about two stocks believed to have a long-run cointegrating relationship. It describes fitting a linear relationship between their prices, then standardizing a series associated with that relationship using a rolling mean and standard deviation over a window of length N. The proposed interpretation is that extreme standardized values indicate relative mispricing and may motivate switching exposure between the two stocks as the spread reverts.

The post asks what b and N mean and how to calculate the z-score, but it does not provide an answer. Its notation is ambiguous: in the stated regression, b appears as an intercept, while a standard pairs-trading residual is usually the observed value minus the fitted value. Those quantities are not interchangeable. The text also proposes full-portfolio reallocations at fixed thresholds without discussing hedge ratios, transaction costs, estimation stability, or risk controls. Treat the material as a question framing the calculation, not a complete implementation guide.

Key ideas

• The question concerns standardizing a series derived from a fitted relationship between two stock prices.
• It describes using a rolling mean and standard deviation over a window labeled N.
• The text proposes interpreting extreme z-scores as relative mispricing in a pairs trade.
• It does not answer how to compute the statistic or define its variables precisely.
• Its use of b is ambiguous between regression intercept and spread residual.

Tags

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