Behavioral Probability Weighting and Portfolio Optimization under Semi-Heavy Tails

2025-07-05

AI Summary

This paper addresses the nonlinear impact of behavioral biases—such as fear and greed—on investment decisions under extreme risk, proposing a unified framework integrating behavioral probability weighting with rational portfolio optimization. Methodologically, it derives implicit weighting functions from Gaussian and Normal Inverse Gaussian distributions to capture belief distortions arising from heavy-tailed return distributions and return asymmetry; it further implements mean-CVaR₉₉ efficient frontiers, Sharpe ratio maximization, and CVaR minimization strategies, calibrated empirically using Dow Jones Industrial Average constituents. The key contribution is the first empirical demonstration that tail thickness amplifies behavioral biases, and that shifts in the risk-free rate term structure significantly modulate the curvature of the weighting function—enabling quantitative modeling of market sentiment. Empirical results show that jointly modeling return asymmetry and belief distortion substantially improves asset allocation efficiency and capital management robustness during extreme market stress.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Cognitive Modeling & Cognitive Systems: Adaptive Behavior

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Security and Privacy: Large-scale security measurements

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.

Problem

• Integrate behavioral distortions into rational portfolio optimization
• Extract implied probability weighting functions from optimal portfolios
• Model return asymmetry and belief distortions under extreme-risk

Innovation

• Extracts implied probability weighting functions from portfolios
• Models portfolios under Gaussian and NIG distributions
• Analyzes impact of tail fatness on behavioral distortions