Sparse portfolio selection via the sorted ℓ1-Norm

Research output: Contribution to journalArticle


We introduce a financial portfolio optimization framework that allows to automatically select the relevant assets and estimate their weights by relying on a sorted ℓ1-Norm penalization, henceforth SLOPE. To solve the optimization problem, we develop a new efficient algorithm, based on the Alternating Direction Method of Multipliers. SLOPE is able to group constituents with similar correlation properties, and with the same underlying risk factor exposures. Depending on the choice of the penalty sequence, our approach can span the entire set of optimal portfolios on the risk-diversification frontier, from minimum variance to the equally weighted. Our empirical analysis shows that SLOPE yields optimal portfolios with good out-of-sample risk and return performance properties, by reducing the overall turnover, through more stable asset weight estimates. Moreover, using the automatic grouping property of SLOPE, new portfolio strategies, such as sparse equally weighted portfolios, can be developed to exploit the data-driven detected similarities across assets.


External organisations
  • Hanyang University
  • University of Trento
  • Wroclaw University
  • Prime Capital AG, Frankfurt am Main
  • EBS Universität für Wirtschaft und Recht
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Economics


  • Alternating direction method of multipliers, Markowitz model, Portfolio management, Sorted ℓ-Norm regularization
Original languageEnglish
Article number105687
JournalJournal of Banking and Finance
Publication statusPublished - 2020
Publication categoryResearch