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Signed network models for portfolio optimization

Bibhas Adhikari

TL;DR

The paper addresses the high dimensionality and estimation noise in Markowitz portfolio optimization by proposing a hedge-based dimensionality-reduction framework that leverages time-series of signed graphs to capture hedge relationships among assets. It introduces a hedge-score $H(n,T)$ computed from negative co-movements and formulates an optimization to select a reduced asset set, followed by applying standard allocation within that reduced universe; theory shows that negative edges can reduce portfolio variance via $ w^\dagger \widehat{\Sigma} w \le w^\dagger |\widehat{\Sigma}| w $. Empirical results on two datasets demonstrate that portfolios constructed from the reduced hedge-based set perform comparably to classical Markowitz and equal-weight strategies in many cases, with performance variability linked to the choice of $K$ and potential gains from extending the motif set. Overall, the approach offers a scalable, hedge-aware method for portfolio construction in large asset universes and suggests avenues for future enhancements, including higher-order motifs and potential integration with quantum-era optimization.

Abstract

In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete optimization scheme that reduces the asset selection problem to a desired size by building a time series of signed networks based on asset returns. To benchmark our approach, we consider two standard allocation strategies: Markowitz's mean-variance optimization and the 1/N equally weighted portfolio. Both methods are applied on the reduced universe as well as on the full universe, using two datasets: (i) the Market Champions dataset, consisting of 21 major S&P500 companies over the 2020-2024 period, and (ii) a dataset of 199 assets comprising all S&P500 constituents with stock prices available and aligned with Google's data. Empirical results show that portfolios constructed via our signed network selection perform as good as those from classical Markowitz model and the equal-weight benchmark in most occasions.

Signed network models for portfolio optimization

TL;DR

The paper addresses the high dimensionality and estimation noise in Markowitz portfolio optimization by proposing a hedge-based dimensionality-reduction framework that leverages time-series of signed graphs to capture hedge relationships among assets. It introduces a hedge-score computed from negative co-movements and formulates an optimization to select a reduced asset set, followed by applying standard allocation within that reduced universe; theory shows that negative edges can reduce portfolio variance via . Empirical results on two datasets demonstrate that portfolios constructed from the reduced hedge-based set perform comparably to classical Markowitz and equal-weight strategies in many cases, with performance variability linked to the choice of and potential gains from extending the motif set. Overall, the approach offers a scalable, hedge-aware method for portfolio construction in large asset universes and suggests avenues for future enhancements, including higher-order motifs and potential integration with quantum-era optimization.

Abstract

In this work, we consider weighted signed network representations of financial markets derived from raw or denoised correlation matrices, and examine how negative edges can be exploited to reduce portfolio risk. We then propose a discrete optimization scheme that reduces the asset selection problem to a desired size by building a time series of signed networks based on asset returns. To benchmark our approach, we consider two standard allocation strategies: Markowitz's mean-variance optimization and the 1/N equally weighted portfolio. Both methods are applied on the reduced universe as well as on the full universe, using two datasets: (i) the Market Champions dataset, consisting of 21 major S&P500 companies over the 2020-2024 period, and (ii) a dataset of 199 assets comprising all S&P500 constituents with stock prices available and aligned with Google's data. Empirical results show that portfolios constructed via our signed network selection perform as good as those from classical Markowitz model and the equal-weight benchmark in most occasions.

Paper Structure

This paper contains 4 sections, 1 theorem, 5 equations, 2 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Financial markets as signed graphs
  3. Signed network based hedge-protected portfolio formation
  4. Empirical analysis

Key Result

theorem thmcountertheorem

Let $w=[w_1,\hdots,w_N]^\dagger$ with $w_i\geq 0$ and $\sum_{i=1}^N w_i=1.$ Suppose $G^s(\widehat{\Sigma})$ is the underlying (weighted) signed graph with at least one negative edge. Then $w^\dagger \widehat{\Sigma}w\leq w^\dagger |\widehat{\Sigma}|w,$ where $|\widehat{\Sigma}|=[|\widehat{\Sigma}_{i

Figures (2)

  • Figure 1: (a) Triangles in a signed graph, $T_0,T_1,T_2,T_3$ (from left to right) the green edges are positive and red edges are negative (b) Threshold function harary2002signed for signed network formation. $c_{ij}$ denotes the covariance or correlation strength for the assets $i$ and $j$
  • Figure 2: Hedge scores of all tickers during 2020 to 2024

Theorems & Definitions (4)

  • definition thmcounterdefinition
  • theorem thmcountertheorem
  • proof
  • definition thmcounterdefinition