Paper: arXiv 2409.12208

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.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 6.0/10 (capped from 6.5: transaction costs not modelled; see penalty flags)
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: 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.

Research Flowchart

  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"]

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and 39 more
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  2. Regularly varying multivariate time series (2009)
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  10. Extreme dependence and risk spillovers across north american equity markets (2019)
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0 of 47 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.