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.

翻译：本文基于马科维茨投资组合理论，构建了一种基于时间序列的符号网络模型，用于投资组合优化中的降维问题，并将其扩展至资产收益率分布的高阶矩。与传统基于相关性的方法不同，我们在指定时间窗口内的每个交易日构建一个完全符号图，其中任意一对资产间连边的符号由其对数收益率相对于各自均值收益率的表现关系决定。在此框架下，我们提出了高阶矩的组合解释，证明最大化偏度和最小化峰度分别对应于最大化具有特定符号边构型的平衡三角形和平衡4-团。我们论证后者导致一个NP难组合优化问题，而前者由符号图模型的结构性质自然保证。基于此解释，我们通过资产的组合对冲得分度量，提出一种利用组合形式的均值-方差优化问题实现降维的方法。该框架通过对199只标普500资产在16年期间（2006-2021年）的广泛回测验证，证明了采用马科维茨优化和等权重策略时，降维资产池在投资组合构建中的有效性。