Mean-Reversion and Optimization

Journal of Asset Management 16(1) (2015) 14-40

41 Pages Posted: 11 Aug 2014 Last revised: 15 Feb 2016

See all articles by Zura Kakushadze

Zura Kakushadze

Quantigic Solutions LLC; Free University of Tbilisi

Date Written: September 22, 2014


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.

Keywords: Mean-reversion, optimization, pair trading, regression, Sharpe ratio, objective function, trading costs, constraints, bounds, factor models

JEL Classification: G00

Suggested Citation

Kakushadze, Zura, Mean-Reversion and Optimization (September 22, 2014). Journal of Asset Management 16(1) (2015) 14-40, Available at SSRN: or

Zura Kakushadze (Contact Author)

Quantigic Solutions LLC ( email )

680 E Main St #543
Stamford, CT 06901
United States
6462210440 (Phone)
6467923264 (Fax)


Free University of Tbilisi ( email )

Business School and School of Physics
240, David Agmashenebeli Alley
Tbilisi, 0159

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