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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2602.21362 |
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| _version_ | 1866910262562390016 |
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| author | Adhikari, Bibhas |
| author_facet | Adhikari, Bibhas |
| contents | In this paper, we develop a time-series-based signed network model for dimensionality reduction in portfolio optimization, grounded in Markowitz's portfolio theory and extended to incorporate higher-order moments of asset return distributions. Unlike traditional correlation-based approaches, we construct a complete signed graph for each trading day within a specified time window, where the sign of an edge between a pair of assets is determined by the relative behavior of their log returns with respect to their mean returns. Within this framework, we introduce a combinatorial interpretation of higher-order moments, showing that maximizing skewness and minimizing kurtosis correspond to maximizing balanced triangles and balanced 4-cliques with specific signed edge configurations respectively. We establish that the latter leads to an NP-hard combinatorial optimization problem, while the former is naturally guaranteed by the structural properties of the signed graph model. Based on this interpretation, we propose a dimensionality reduction method using a combinatorial formulation of the mean-variance optimization problem through a combinatorial hedge score metric for assets. The proposed framework is validated through extensive backtesting on 199 S\&P 500 assets over a 16-year period (2006 - 2021), demonstrating the effectiveness of reduced asset universes for portfolio construction using both Markowitz optimization and equally weighted strategy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21362 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signed network models for dimensionality reduction of portfolio optimization Adhikari, Bibhas Combinatorics Computational Engineering, Finance, and Science In this paper, we develop a time-series-based signed network model for dimensionality reduction in portfolio optimization, grounded in Markowitz's portfolio theory and extended to incorporate higher-order moments of asset return distributions. Unlike traditional correlation-based approaches, we construct a complete signed graph for each trading day within a specified time window, where the sign of an edge between a pair of assets is determined by the relative behavior of their log returns with respect to their mean returns. Within this framework, we introduce a combinatorial interpretation of higher-order moments, showing that maximizing skewness and minimizing kurtosis correspond to maximizing balanced triangles and balanced 4-cliques with specific signed edge configurations respectively. We establish that the latter leads to an NP-hard combinatorial optimization problem, while the former is naturally guaranteed by the structural properties of the signed graph model. Based on this interpretation, we propose a dimensionality reduction method using a combinatorial formulation of the mean-variance optimization problem through a combinatorial hedge score metric for assets. The proposed framework is validated through extensive backtesting on 199 S\&P 500 assets over a 16-year period (2006 - 2021), demonstrating the effectiveness of reduced asset universes for portfolio construction using both Markowitz optimization and equally weighted strategy. |
| title | Signed network models for dimensionality reduction of portfolio optimization |
| topic | Combinatorics Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2602.21362 |