Efficient computation of mean reverting portfolios using cyclical coordinate descent

TL;DR

This paper introduces a fast, scalable method for computing sparse mean reverting portfolios using cyclical coordinate descent and data from a heterogeneous graphical dynamic linear model, applicable to large asset universes.

Contribution

It formulates the mean reversion problem as a quasi-convex minimization, enabling efficient exact solutions with a novel algorithm and leveraging H-SGDLM data for sparsity control.

Findings

Method is flexible and scalable to large asset sets.

Demonstrates speed and efficiency on S&P 500, FX, and ETF futures data.

Provides exact sparse solutions for mean reversion portfolios.

Abstract

The econometric challenge of finding sparse mean reverting portfolios based on a subset of a large number of assets is well known. Many current state-of-the-art approaches fall into the field of co-integration theory, where the problem is phrased in terms of an eigenvector problem with sparsity constraint. Although a number of approximate solutions have been proposed to solve this NP-hard problem, all are based on relatively simple models and are limited in their scalability. In this paper we leverage information obtained from a heterogeneous simultaneous graphical dynamic linear model (H-SGDLM) and propose a novel formulation of the mean reversion problem, which is phrased in terms of a quasi-convex minimisation with a normalisation constraint. This new formulation allows us to employ a cyclical coordinate descent algorithm for efficiently computing an exact sparse solution, even in a large universe of assets, while the use of H-SGDLM data allows us to easily control the required level of sparsity. We demonstrate the flexibility, speed and scalability of the proposed approach on S\&P$500$, FX and ETF futures data.