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，并扩展至资产收益分布的高阶矩，提出了一种用于投资组合优化降维的时序符号网络模型。与传统的相关性方法不同，我们在指定时间窗口内为每个交易日构建一个完整符号图，其中资产对之间边的符号由其对数收益相对于均值收益的相对行为决定。在此框架下，我们引入高阶矩的组合解释，表明最大化偏度与最小化峰度分别对应于最大化具有特定符号边配置的平衡三角形与平衡4-团。我们证明后者属于NP难组合优化问题，而前者则自然由符号图模型的结构性质保证。基于这一解释，我们通过资产的组合对冲得分度量，提出一种利用均值-方差优化问题组合表述的降维方法。通过2006年至2021年间199只标普500资产的16年回测验证，该框架证明了在运用马科维茨优化与等权重策略构建投资组合时，缩减资产池的有效性。