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A Mean-Reversion Framework from Pair Trading to Constrained Optimization

Article arXiv papers · Author: Zura Kakushadze
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Summary

These notes build a quantitative treatment of mean-reversion, beginning with pair trading and then progressing through demeaning, regression, weighted regression, constrained optimization, and factor models. The sequence shows how increasingly general methods can be used to construct mean-reversion strategies and portfolios.

The notes also address practical implementation issues, including why maximizing a Sharpe ratio is not equivalent to minimizing an objective function when trading costs are included. They describe algorithms for optimization with linear costs, constraints, and bounds, and flag common application pitfalls. The supplied description does not give the algorithms, assumptions, or performance evidence, so it outlines a learning framework rather than establishing that any particular strategy is profitable.

Key ideas

  • The notes develop mean-reversion methods from pair trading through factor models.
  • Demeaning, regression, and weighted regression lead into constrained optimization.
  • Sharpe ratio maximization can differ from objective minimization when trading costs matter.
  • The framework covers optimization with linear costs, constraints, and bounds.
  • The description does not report empirical performance or specify the algorithms.

Tags

Mean reversionPairs tradingPortfolio constructionExecution
Full text
# Mean-Reversion and Optimization


# Mean-Reversion and Optimization









The purpose of these notes is to provide a systematic quantitative framework - in what is intended to be a "pedagogical" fashion - for discussing mean-reversion and optimization. We start with pair trading and add complexity by following the sequence "mean-reversion via demeaning -> regression -> weighted regression -> (constrained) optimization -> factor models". We discuss in detail how to do mean-reversion based on this approach, including common pitfalls encountered in practical applications, such as the difference between maximizing the Sharpe ratio and minimizing an objective function when trading costs are included. We also discuss explicit algorithms for optimization with linear costs, constraints and bounds.

Shown in full with attribution under the source's licence. Licence: abstract CC0

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