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Cardinality-constrained distributionally robust portfolio optimization

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  • Kobayashi, Ken
  • Takano, Yuichi
  • Nakata, Kazuhide

Abstract

This paper studies a distributionally robust portfolio optimization model with a cardinality constraint for limiting the number of invested assets. We formulate this model as a mixed-integer semidefinite optimization (MISDO) problem by means of the moment-based ambiguity set of probability distributions of asset returns. To exactly solve large-scale problems, we propose a specialized cutting-plane algorithm that is based on bilevel optimization reformulation. We prove the finite convergence of the algorithm. We also apply a matrix completion technique to lower-level SDO problems to make their problem sizes much smaller. Numerical experiments demonstrate that our cutting-plane algorithm is significantly faster than the state-of-the-art MISDO solver SCIP-SDP. We also show that our portfolio optimization model can achieve good investment performance compared with the conventional robust optimization model based on the ellipsoidal uncertainty set.

Suggested Citation

  • Kobayashi, Ken & Takano, Yuichi & Nakata, Kazuhide, 2023. "Cardinality-constrained distributionally robust portfolio optimization," European Journal of Operational Research, Elsevier, vol. 309(3), pages 1173-1182.
    • Handle: RePEc:eee:ejores:v:309:y:2023:i:3:p:1173-1182
    DOI: 10.1016/j.ejor.2023.01.037
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