Sparsity and Performance Enhanced Markowitz Portfolios Using Second-Order Cone Programming

Noam Goldberg, Ishy Zagdoun

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


A mixed-integer second order cone program (MISOCP) formulation is proposed for solving Markowitz’s asset portfolio construction problem under a cardinality constraint. Compared with a standard alternative big-M linearly constrained formulation, our reformulation is solved significantly faster using state-of-the-art integer programming solvers. We consider learning methods that are based on the MISCOP formulation: cardinality-constrained Markowitz (CCM) solves the MISCOP for a given cardinality k and training set data of asset returns. We also find reinforcing evidence for factor model theory in the selection of factors to form optimal CCM portfolios. For large datasets in the absence of a hard-cardinality constraint, we propose a method (CCM-R) that is based on the continuous relaxation of our MISCOP, where k selected by rolling time window validation. In predictive performance experiments, based on historical stock exchange data, our learning methods usually outperform a competing extension of the Markowitz model that penalizes the L1 norm of asset weights.

Original languageEnglish
Title of host publicationOptimization of Complex Systems
Subtitle of host publicationTheory, Models, Algorithms and Applications, 2019
EditorsHoai An Le Thi, Hoai Minh Le, Tao Pham Dinh
PublisherSpringer Verlag
Number of pages11
ISBN (Print)9783030218027
StatePublished - 2020
Event6th World Congress on Global Optimization, WCGO 2019 - Metz, France
Duration: 8 Jul 201910 Jul 2019

Publication series

NameAdvances in Intelligent Systems and Computing
ISSN (Print)2194-5357
ISSN (Electronic)2194-5365


Conference6th World Congress on Global Optimization, WCGO 2019

Bibliographical note

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.


  • Markowitz
  • Perspective reformulation
  • SOCP
  • Sparsity


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