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

ArXiv ID: 2505.16019 “View on arXiv”

Authors: Shaobo Li, Ben Sherwood

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.

Keywords: Quantile Regression, Group Penalty, Selection Consistency, Equity Premium Prediction, Huberized Loss, Equities

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.2/10
• Quadrant: Holy Grail
• Why: The paper employs advanced statistical theory including selection consistency, group LASSO penalties, and Huberized quantile loss, indicating high mathematical density. It also provides simulation studies and empirical backtesting with benchmarks and OOS evaluation, demonstrating significant implementation and data-driven rigor.

  flowchart TD
    Goal["Research Goal<br>Equity Premium Prediction<br>vs. Traditional Mean Regression"] --> Inputs["Data Inputs<br>Equity Premium Data<br>Predictor Variables"]
    
    Inputs --> Method["Key Methodology<br>Novel Penalized Quantile Regression<br>Huberized Quantile Loss"]
    
    Method --> Process1["Computational Process<br>Simultaneous Estimation<br>Group Penalty for Cross-Quantile Consistency"]
    
    Process1 --> Process2["Computational Process<br>Augmented Data Approach<br>for Efficiency"]
    
    Process2 --> Results["Outcomes<br>Enhanced Interpretability<br>No Crossing Quantiles<br>Outperforms Benchmarks"]
    
    Results --> Insights["Key Findings<br>Variable Relationships Reverse<br>from Lower to Upper Quantiles"]