Sparse index tracking has emerged as a prominent passive portfolio management strategy, leveraging sparse portfolios to replicate the performance of financial benchmarks. However, while investors often exhibit behavioral biases that influence portfolio selection, existing research has yet to incorporate investor preference information. This paper investigated the cardinality-constrained index tracking problem by integrating investor preferences and enforcing sparsity through a minimal subset of selected assets. Specifically, we proposed a novel approach that incorporates fuzzy preference relations into the sparse tracking model via an additive consistency under priority vectors. This framework captures investor preference heterogeneity while harmonizing subjective inputs with objective tracking performance. An effective matrix decomposition method was employed to address the cardinality-constrained optimization, yielding a precise lower bound and substantially decreasing computational demands. By combining the supergradient method with a branch-and-bound algorithm, our model enhances the efficiency of optimal portfolio selection. Extensive numerical experiments demonstrated that the proposed method outperforms existing lower-bound techniques and mixed-integer programming solvers in tracking efficiency. Furthermore, the preference-aware model balances customization and risk-adjusted returns, achieving superior risk-return performance across multiple tracking metrics. These findings provide practical insights for investor decision-making in portfolio management.
Citation: Chun Wang, Zhongming Wu, Wei Xu, Yu Yuan. An exact algorithm for a cardinality-constrained index tracking model considering investment preferences in portfolio optimization[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 612-641. doi: 10.3934/jimo.2026023
Sparse index tracking has emerged as a prominent passive portfolio management strategy, leveraging sparse portfolios to replicate the performance of financial benchmarks. However, while investors often exhibit behavioral biases that influence portfolio selection, existing research has yet to incorporate investor preference information. This paper investigated the cardinality-constrained index tracking problem by integrating investor preferences and enforcing sparsity through a minimal subset of selected assets. Specifically, we proposed a novel approach that incorporates fuzzy preference relations into the sparse tracking model via an additive consistency under priority vectors. This framework captures investor preference heterogeneity while harmonizing subjective inputs with objective tracking performance. An effective matrix decomposition method was employed to address the cardinality-constrained optimization, yielding a precise lower bound and substantially decreasing computational demands. By combining the supergradient method with a branch-and-bound algorithm, our model enhances the efficiency of optimal portfolio selection. Extensive numerical experiments demonstrated that the proposed method outperforms existing lower-bound techniques and mixed-integer programming solvers in tracking efficiency. Furthermore, the preference-aware model balances customization and risk-adjusted returns, achieving superior risk-return performance across multiple tracking metrics. These findings provide practical insights for investor decision-making in portfolio management.
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Chun Wang, Zhongming Wu, Wei Xu, Yu Yuan. An exact algorithm for a cardinality-constrained index tracking model considering investment preferences in portfolio optimization[J]. Journal of Industrial and Management Optimization, 2026, 22(1): 612-641. doi: 10.3934/jimo.2026023
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