Mean-Reversion and Optimization

TL;DR

This paper presents a comprehensive, pedagogical framework for mean-reversion strategies and optimization, covering from basic pair trading to advanced factor models, including practical pitfalls and explicit algorithms.

Contribution

It introduces a systematic approach to mean-reversion and optimization, integrating regression, constraints, and trading costs with detailed algorithms and practical insights.

Findings

Detailed methods for mean-reversion based on regression and demeaning

Explicit algorithms for optimization with costs and constraints

Discussion of pitfalls like Sharpe ratio maximization versus objective minimization

Abstract

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.