A novel regularization-based optimization approach to sparse mean-reverting portfolios selection

The construction of profitable mean-reverting portfolios, with fewer assets, but enough volatility is a real challenge for financial investors. Although they offer an ideal investment opportunity, they are very difficult to construct, especially with real-time data. To design such portfolios, one has to optimize their mean-reverting strength while maintaining sparsity constraints and a volatility threshold. Most of the existing approaches are framed as an eigenvector issue with a sparsity constraint. In this paper, we propose two optimization approaches to design a sparse mean-reverting portfolio. The idea is to optimize the predictability using a regularization technique that combines l1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{1}$$\end{document} and l2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$l_{2}$$\end{document}-norms. Computer simulations are performed on market data extracted from the 10 Fama–French industrial portfolios, the 49 Fama–French industrial portfolios, and from the SP500 index. The obtained numerical results prove the effectiveness of the proposed methods compared with the existing approaches.