Mitigating Extremal Risks: A Network-Based Portfolio Strategy

ArXiv ID: 2409.12208 “View on arXiv”

Authors: Unknown

Abstract

In financial markets marked by inherent volatility, extreme events can result in substantial investor losses. This paper proposes a portfolio strategy designed to mitigate extremal risks. By applying extreme value theory, we evaluate the extremal dependence between stocks and develop a network model reflecting these dependencies. We use a threshold-based approach to construct this complex network and analyze its structural properties. To improve risk diversification, we utilize the concept of the maximum independent set from graph theory to develop suitable portfolio strategies. Since finding the maximum independent set in a given graph is NP-hard, we further partition the network using either sector-based or community-based approaches. Additionally, we use value at risk and expected shortfall as specific risk measures and compare the performance of the proposed portfolios with that of the market portfolio.

Keywords: Portfolio Optimization, Extreme Value Theory, Complex Networks, Risk Diversification, Extremal Dependence, Equities

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.5/10
  • Quadrant: Holy Grail
  • Why: The paper employs advanced mathematics including extreme value theory, multivariate regular variation, and graph-theoretic NP-hard problems, placing it in the high math category. It also demonstrates empirical rigor by using real market data, implementing a specific algorithm with risk metrics (VaR, ES), and conducting backtest-like performance comparisons.
  flowchart TD
    A["Research Goal: Mitigate Extremal Risks in Portfolio Construction"] --> B["Data: Daily Equity Returns & Market Indices"]
    B --> C["Key Methodology: Extreme Value Theory & Network Modeling"]
    C --> D["Computational Process: Threshold-Based Network & Structural Analysis"]
    D --> E["Computational Process: Heuristic Network Partitioning<br>(Sector/Community) & Max Independent Set Approximation"]
    E --> F["Key Outcome: Proposed Portfolio Strategies"]
    F --> G["Comparison: Risk-Adjusted Performance<br>vs. Market Portfolio<br>using VaR & Expected Shortfall"]