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Uncertainty-Adjusted Sorting for Asset Pricing with Machine Learning

Yan Liu, Ye Luo, Zigan Wang, Xiaowei Zhang

TL;DR

This paper addresses how predictive uncertainty can be incorporated into ML-based asset pricing. It introduces uncertainty-adjusted sorting, which uses asset-specific prediction bounds around point forecasts to form long and short portfolios, rather than relying on point predictions alone. The approach is model-agnostic and derived from cross-validated residuals pooled at the asset level, enabling robust performance gains—especially for flexible models—through volatility reduction and improved ranking stability. Empirically on five decades of U.S. equity data, the method improves Sharpe ratios, remains effective under transaction costs, and its benefits hinge on correctly aligning uncertainty with individual assets and market states, rather than on aggregate volatility timing. The findings suggest predictive uncertainty is economically meaningful and should be integrated into cross-sectional portfolio decisions to enhance risk-adjusted performance in ML-driven asset pricing.

Abstract

Machine learning is central to empirical asset pricing, but portfolio construction still relies on point predictions and largely ignores asset-specific estimation uncertainty. We propose a simple change: sort assets using uncertainty-adjusted prediction bounds instead of point predictions alone. Across a broad set of ML models and a U.S. equity panel, this approach improves portfolio performance relative to point-prediction sorting. These gains persist even when bounds are built from partial or misspecified uncertainty information. They arise mainly from reduced volatility and are strongest for flexible machine learning models. Identification and robustness exercises show that these improvements are driven by asset-level rather than time or aggregate predictive uncertainty.

Uncertainty-Adjusted Sorting for Asset Pricing with Machine Learning

TL;DR

This paper addresses how predictive uncertainty can be incorporated into ML-based asset pricing. It introduces uncertainty-adjusted sorting, which uses asset-specific prediction bounds around point forecasts to form long and short portfolios, rather than relying on point predictions alone. The approach is model-agnostic and derived from cross-validated residuals pooled at the asset level, enabling robust performance gains—especially for flexible models—through volatility reduction and improved ranking stability. Empirically on five decades of U.S. equity data, the method improves Sharpe ratios, remains effective under transaction costs, and its benefits hinge on correctly aligning uncertainty with individual assets and market states, rather than on aggregate volatility timing. The findings suggest predictive uncertainty is economically meaningful and should be integrated into cross-sectional portfolio decisions to enhance risk-adjusted performance in ML-driven asset pricing.

Abstract

Machine learning is central to empirical asset pricing, but portfolio construction still relies on point predictions and largely ignores asset-specific estimation uncertainty. We propose a simple change: sort assets using uncertainty-adjusted prediction bounds instead of point predictions alone. Across a broad set of ML models and a U.S. equity panel, this approach improves portfolio performance relative to point-prediction sorting. These gains persist even when bounds are built from partial or misspecified uncertainty information. They arise mainly from reduced volatility and are strongest for flexible machine learning models. Identification and robustness exercises show that these improvements are driven by asset-level rather than time or aggregate predictive uncertainty.
Paper Structure (51 sections, 10 equations, 3 figures, 4 tables)

This paper contains 51 sections, 10 equations, 3 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Machine Learning in Empirical Asset Pricing
  4. Distribution-Free Predictive Inference
  5. The Gap and Our Contribution
  6. Methodology
  7. Panel Prediction Framework and Information Set
  8. Machine Learning Models
  9. Penalized Linear Model: Elastic Net (ENet).
  10. Dimension Reduction Model: Principal Components Regression (PCR).
  11. Dimension Reduction Model: Partial Least Squares (PLS).
  12. Tree-Based Ensemble Method: Random Forest (RF).
  13. Tree-Based Ensemble Method: Gradient Boosting.
  14. Neural Networks (NN1--NN5).
  15. Role of Model Diversity in Uncertainty-Adjusted Sorting.
  16. ...and 36 more sections

Figures (3)

  • Figure 1: Point Predictions with Uncertainty-Adjusted Bounds at Alternative Quantile Levels: A Stock-Level Illustration
  • Figure 2: Flowchart of Asset-Specific Residual Pooling and Uncertainty-Adjusted Bounds Construction Under a 25-Year Rolling Window
  • Figure 3: Scaled Net-Value Paths: Uncertainty-Adjusted Sorting versus Point-Prediction Sorting