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 l(1) and l(2)-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.