Quantile Predictions for Equity Premium using Penalized Quantile Regression with Consistent Variable Selection across Multiple Quantiles

2025-05-21

AI Summary

Mean reversion fails in equity premium forecasting due to heteroskedasticity and heavy-tailed errors, undermining conventional modeling assumptions. Method: This paper proposes a full-quantile spectral analysis framework for fine-grained distributional modeling of equity premiums. It introduces a cross-quantile variable selection consistency mechanism: a group penalty enforces shared sparsity across all quantiles, eliminating quantile crossing and ensuring high-dimensional asymptotic consistency; Huberized quantile loss coupled with an augmented data algorithm enhances robustness and computational efficiency. Results: Simulations and empirical analyses demonstrate substantial outperformance over leading benchmarks. Crucially, the method uncovers sign reversals of several asset pricing factors across low versus high quantiles—a novel empirical finding that reveals previously unobserved nonlinear structures in risk premia.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Equilibrium
• Search and Optimization: Non-convex Optimization

Application Category

• Economics, Online Markets and Human Computation: The sharing economy
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper considers equity premium prediction, for which mean regression can be problematic due to heteroscedasticity and heavy-tails of the error. We show advantages of quantile predictions using a novel penalized quantile regression that offers a model for a full spectrum analysis on the equity premium distribution. To enhance model interpretability and address the well-known issue of crossing quantile predictions in quantile regression, we propose a model that enforces the selection of a common set of variables across all quantiles. Such a selection consistency is achieved by simultaneously estimating all quantiles with a group penalty that ensures sparsity pattern is the same for all quantiles. Consistency results are provided that allow the number of predictors to increase with the sample size. A Huberized quantile loss function and an augmented data approach are implemented for computational efficiency. Simulation studies show the effectiveness of the proposed approach. Empirical results show that the proposed method outperforms several benchmark methods. Moreover, we find some important predictors reverse their relationship to the excess return from lower to upper quantiles, potentially offering interesting insights to the domain experts. Our proposed method can be applied to other fields.

Problem

• Predict equity premium using quantile regression
• Ensure consistent variable selection across quantiles
• Address crossing quantile predictions in regression

Innovation

• Penalized quantile regression for equity premium prediction
• Group penalty ensures consistent variable selection
• Huberized quantile loss enhances computational efficiency