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Efficient computation of mean reverting portfolios using cyclical coordinate descent

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  • T. Griveau-Billion
  • B. Calderhead

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&P500, FX and ETF futures data.

Suggested Citation

  • T. Griveau-Billion & B. Calderhead, 2021. "Efficient computation of mean reverting portfolios using cyclical coordinate descent," Quantitative Finance, Taylor & Francis Journals, vol. 21(4), pages 673-684, April.
  • Handle: RePEc:taf:quantf:v:21:y:2021:i:4:p:673-684
    DOI: 10.1080/14697688.2020.1803497
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    Cited by:

    1. Philippe Goulet Coulombe & Maximilian Goebel, 2023. "Maximally Machine-Learnable Portfolios," Papers 2306.05568, arXiv.org, revised Apr 2024.
    2. Philippe Goulet Coulombe & Maximilian Gobel, 2023. "Maximally Machine-Learnable Portfolios," Working Papers 23-01, Chair in macroeconomics and forecasting, University of Quebec in Montreal's School of Management, revised Apr 2023.

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