Behavioral Probability Weighting and Portfolio Optimization under Semi-Heavy Tails

ArXiv ID: 2507.04208 “View on arXiv”

Authors: Ayush Jha, Abootaleb Shirvani, Ali M. Jaffri, Svetlozar T. Rachev, Frank J. Fabozzi

Abstract

This paper develops a unified framework that integrates behavioral distortions into rational portfolio optimization by extracting implied probability weighting functions (PWFs) from optimal portfolios modeled under Gaussian and Normal-Inverse-Gaussian (NIG) return distributions. Using DJIA constituents, we construct mean-CVaR99 frontiers, alongwith Sharpe- and CVaR-maximizing portfolios, and estimate PWFs that capture nonlinear beliefs consistent with fear and greed. We show that increasing tail fatness amplifies these distortions and that shifts in the term structure of risk-free rates alter their curvature. The results highlight the importance of jointly modeling return asymmetry and belief distortions in portfolio risk management and capital allocation under extreme-risk environments.

Keywords: Implied probability weighting functions, Mean-CVaR99 frontier, Normal-Inverse-Gaussian (NIG) distribution, Portfolio optimization, Risk management, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical theory (NIG distributions, probability weighting functions, optimization with CVaR) and heavy mathematical derivations in LaTeX, warranting a high complexity score. It is strongly grounded in empirical data with a detailed backtesting methodology, out-of-sample performance diagnostics, and real-world financial data, indicating high empirical rigor.

  flowchart TD
    A["Research Goal<br>Integrate behavioral distortions into<br>rational portfolio optimization"] --> B{"Methodology"}
    
    B --> C["Input: DJIA Constituents<br>Historical Returns"]
    B --> D["Model: NIG Distribution<br>for Tail Asymmetry"]
    
    C --> E["Process: Mean-CVaR99 Optimization<br>Compute Efficient Frontiers"]
    D --> E
    
    E --> F["Extract: Implied Probability<br>Weighting Functions PWFs"]
    
    F --> G{"Key Outcomes"}
    G --> H["Tail Fatness amplifies<br>Behavioral Distortions"]
    G --> I["Risk-Free Rate shifts<br>alter PWF Curvature"]
    G --> J["Joint Modeling essential<br>for Extreme Risk Management"]