Expected Shortfall Panel Regression

TL;DR

This paper develops a panel data expected shortfall regression model with a latent factor structure, providing robust estimation methods and theoretical guarantees, and demonstrating improved performance in simulations and empirical analysis.

Contribution

It introduces a novel panel ES regression framework with latent factors, along with a two-stage estimation procedure and theoretical properties, addressing cross-sectional and temporal dependencies.

Findings

Proposed estimators are consistent and asymptotically normal.

Simulation shows improved parameter and factor estimation accuracy.

Empirical application reveals ES factors contain unique pricing information.

Abstract

Expected Shortfall (ES) is a coherent measure of tail risk that captures the average loss beyond a quantile threshold. Despite the growing literature on ES regression conditional on covariates, no existing work considers ES modeling in panel data settings where both cross-sectional and temporal dependencies are present. This paper introduces the panel ES regression model with a latent factor structure to capture cross-sectional dependence. We develop a two-stage estimation procedure robust to heavy-tailed errors, recovering the conditional quantile in the first stage and iteratively estimating the ES factor model in the second stage. Theoretically, we establish the consistency and asymptotic normality of the proposed two-step ES estimators and derive non-asymptotic error bounds for both the panel quantile and ES estimators. We also provide a non-asymptotic normal approximation for the standardized ES regression estimator, bridging asymptotic theory and finite-sample practice. Simulation evidence shows that the proposed method delivers substantial gains in both parameter estimation and factor recovery, particularly in the presence of latent tail dependence. An empirical application further indicates that the extracted ES factors carry distinct pricing information that is not captured by conventional mean or quantile-based approaches.