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<p>Cardinality-constrained portfolio optimization aims to determine optimal investment strategies while limiting the total number of stocks. However, the NP-hard nature of cardinality constraints makes this optimization problem intractable in high-dimensional settings. We introduce new portfolio optimization frameworks that use clustering methods to reduce dimensionality while enforcing asset limits within each cluster and optimizing allocation proportions to balance risk and return. We apply hierarchical clustering to group stocks by the correlations of their residual returns, to achieve internally similar clusters. By dividing the complex problem into smaller subproblems, we can approximate the standard optimization in a reduced subspace. Our empirical results on the S&amp;P 500 and Russell 3000 datasets show that the proposed methods are effective in portfolio construction and outperform a range of benchmark strategies. Additionally, by optimizing the number of selected assets and the total cluster weights in each group, we simplify asset selection while achieving performance comparable to traditional mean-variance portfolios. This highlights the potential of strategic clustering as a more effective framework for large-scale portfolio management under real-world constraints.</p>

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Cardinality-constrained portfolio optimization with clustering

  • 期刊论文

  • 发表日期：

    2026年4月8日

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  • Amirmohammad Ebrahimi,
  • Hamed Amini,
  • Hongcheng Liu

摘要

Cardinality-constrained portfolio optimization aims to determine optimal investment strategies while limiting the total number of stocks. However, the NP-hard nature of cardinality constraints makes this optimization problem intractable in high-dimensional settings. We introduce new portfolio optimization frameworks that use clustering methods to reduce dimensionality while enforcing asset limits within each cluster and optimizing allocation proportions to balance risk and return. We apply hierarchical clustering to group stocks by the correlations of their residual returns, to achieve internally similar clusters. By dividing the complex problem into smaller subproblems, we can approximate the standard optimization in a reduced subspace. Our empirical results on the S&P 500 and Russell 3000 datasets show that the proposed methods are effective in portfolio construction and outperform a range of benchmark strategies. Additionally, by optimizing the number of selected assets and the total cluster weights in each group, we simplify asset selection while achieving performance comparable to traditional mean-variance portfolios. This highlights the potential of strategic clustering as a more effective framework for large-scale portfolio management under real-world constraints.