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Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks

Qian Hui, Tiandong Wang

TL;DR

This work tackles systemic risk from extreme market events by quantifying pairwise extremal dependence with the extremal dependence measure (EDM) and representing inter-institution connections as extremal dependence networks. By applying a maximum independent set (MIS) approach on these networks, the authors construct portfolios that minimize tail risk, validated with Delta CoVaR and expected shortfall (ES) metrics. Empirical analysis on 2023 data for Chinese and U.S. bank/insurance stocks reveals structural differences in network topology and contagion pathways, guiding market-specific MIS portfolios that demonstrate stable risk-return behavior in early 2024. The study offers a data-driven framework for regulators and investors to mitigate systemic risk through topology-aware diversification, with potential extensions to dynamic networks and graph-based deep learning models.

Abstract

The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies.

Systemic Risk Management via Maximum Independent Set in Extremal Dependence Networks

TL;DR

This work tackles systemic risk from extreme market events by quantifying pairwise extremal dependence with the extremal dependence measure (EDM) and representing inter-institution connections as extremal dependence networks. By applying a maximum independent set (MIS) approach on these networks, the authors construct portfolios that minimize tail risk, validated with Delta CoVaR and expected shortfall (ES) metrics. Empirical analysis on 2023 data for Chinese and U.S. bank/insurance stocks reveals structural differences in network topology and contagion pathways, guiding market-specific MIS portfolios that demonstrate stable risk-return behavior in early 2024. The study offers a data-driven framework for regulators and investors to mitigate systemic risk through topology-aware diversification, with potential extensions to dynamic networks and graph-based deep learning models.

Abstract

The failure of key financial institutions may accelerate risk contagion due to their interconnections within the system. In this paper, we propose a robust portfolio strategy to mitigate systemic risks during extreme events. We use the stock returns of key financial institutions as an indicator of their performance, apply extreme value theory to assess the extremal dependence among stocks of financial institutions, and construct a network model based on a threshold approach that captures extremal dependence. Our analysis reveals different dependence structures in the Chinese and U.S. financial systems. By applying the maximum independent set (MIS) from graph theory, we identify a subset of institutions with minimal extremal dependence, facilitating the construction of diversified portfolios resilient to risk contagion. We also compare the performance of our proposed portfolios with that of the market portfolios in the two economies.

Paper Structure

This paper contains 19 sections, 23 equations, 8 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Data example
  3. Extremal dependence measure
  4. Stock network model based on extremal dependence
  5. The statistical properties of the network
  6. Average degree and degree distribution
  7. Average path length
  8. Clustering coefficient
  9. Network diameter
  10. Graph density
  11. Network construction and important characteristics
  12. Choice of threshold
  13. Community structure of the extremal dependence network via GN algorithm
  14. Centrality measure of the extremal dependence network
  15. Stock portfolio based on extremal dependence networks and maximum independent set
  16. ...and 4 more sections

Figures (8)

  • Figure 1: Log-log plots of the complementary cumulative distribution function (1-CDF) for the degrees at different thresholds in the Chinese A-shares market.
  • Figure 2: Log-log plots of the complementary cumulative distribution function (1-CDF) for the degrees at different thresholds in the U.S. S&P 500 market.
  • Figure 3: Community structures in extremal dependence networks. (a) The GN algorithm partitions 48 vertices into 16 communities in the Chinese A-shares market, with vertex colors marking community affiliation. (b) A coarse-grained view condenses each community into a single node whose diameter reflects its vertex count, while edges denote collaborations between communities.
  • Figure 4: Community structures in extremal dependence networks. (a) The GN algorithm partitions 37 vertices into 9 communities in the U.S. S&P 500 market, with vertex colors marking community affiliation. (b) A coarse-grained view condenses each community into a single node whose diameter reflects its vertex count, while edges denote inter-community collaborations between communities.
  • Figure 5: The MIS of each network graph, and they are denoted by white nodes.
  • ...and 3 more figures

Theorems & Definitions (3)

  • Definition 1
  • Definition 2
  • Definition 3