Solving cardinality constrained mean-variance portfolio problems via MILP

Nasim Dehghan Hardoroudi, Abolfazl Keshvari, Markku Kallio, Pekka Korhonen

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)


Controlling the number of active assets (cardinality of the portfolio) in a mean-variance portfolio problem is practically important but computationally demanding. Such task is ordinarily a mixed integer quadratic programming (MIQP) problem. We propose a novel approach to reformulate the problem as a mixed integer linear programming (MILP) problem for which computer codes are readily available. For numerical tests, we find cardinality constrained minimum variance portfolios of stocks in S&P500. A significant gain in robustness and computational effort by our MILP approach relative to MIQP is reported. Similarly, our MILP approach also competes favorably against cardinality constrained portfolio optimization with risk measures CVaR and MASD. For illustrations, we depict portfolios in a portfolio map where cardinality provides a third criterion in addition to risk and return. Fast solution allows an interactive search for a desired portfolio.
Original languageEnglish
Pages (from-to)47-59
JournalAnnals of Operations Research
Issue number1-2
Early online date2017
Publication statusPublished - Jul 2017
MoE publication typeA1 Journal article-refereed


  • Portfolio optimization
  • Cardinality constraints
  • Mean-variance theory
  • CVaR
  • MASD
  • MILP

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