Signed network models for dimensionality reduction of portfolio optimization

2026-02-24

AI Summary

This study addresses the challenges of computational complexity and noise in high-dimensional portfolio optimization. Building upon the Markowitz mean-variance framework, it proposes a time-driven dimensionality reduction method based on signed networks: edge signs are defined by the relative behavior of asset log returns with respect to their means, and—novelly—higher-order moments (skewness and kurtosis) are mapped onto balanced triangles and 4-cliques in the signed graph, revealing their intrinsic connection to investment objectives. A combinatorial hedging-score-based NP-hard reduction mechanism is then devised and validated through rolling-window backtesting. Empirical results on 199 S&P 500 constituents from 2006 to 2021 demonstrate that the reduced asset sets significantly enhance risk-adjusted returns under both Markowitz and equally weighted strategies.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Machine Learning: Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

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.

Problem

• portfolio optimization
• dimensionality reduction
• signed network
• higher-order moments
• asset selection

Innovation

• signed network
• higher-order moments
• combinatorial optimization
• portfolio dimensionality reduction
• balanced cliques