Signed network models for dimensionality reduction of portfolio optimization

TL;DR

This paper introduces a novel signed network model for dimensionality reduction in portfolio optimization, leveraging higher-order moments and combinatorial optimization to improve asset selection and portfolio performance.

Contribution

It develops a signed graph approach incorporating higher-order moments and formulates a new combinatorial optimization method for portfolio reduction.

Findings

Effective reduction of asset universe improves portfolio performance.

Validated on 16 years of S&P 500 data with positive results.

Demonstrates advantages over traditional correlation-based 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.