Behavioral Probability Weighting and Portfolio Optimization under Semi-Heavy Tails

TL;DR

This paper introduces a framework that incorporates behavioral probability distortions into portfolio optimization, accounting for tail risk and belief biases under different return distributions, with empirical analysis on DJIA data.

Contribution

It presents a novel method to extract probability weighting functions from optimal portfolios considering semi-heavy tails, integrating behavioral biases into risk management models.

Findings

Tail fatness increases probability distortions.

Shifts in risk-free rates affect the curvature of probability weighting functions.

Joint modeling of return asymmetry and belief distortions is crucial for risk management.

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.