Panel Coupled Matrix-Tensor Clustering Model with Applications to Asset Pricing

2025-12-29

AI Summary

In asset pricing, jointly estimating group structures and factor loadings under sparse, high-noise settings remains challenging: conventional regression imposes coefficient homogeneity, while single-source clustering lacks robustness. This paper proposes the Panel-coupled Matrix-Tensor Clustering (PMTC) model—the first to jointly leverage return matrices and feature tensors, enabling cross-source collaborative learning that accommodates both group heterogeneity and factor dynamics. Methodologically, PMTC integrates high-order tensor decomposition, spectral clustering optimization, and regularized multi-task learning, with a scalable iterative algorithm. Simulation studies demonstrate significantly higher clustering accuracy and factor loading estimation precision compared to single-source benchmarks. Empirical analysis on U.S. equities shows improved out-of-sample total R² and uncovers economically meaningful differences in industry- and style-factor exposures across clusters.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Data Mining & Knowledge Management: Scalability, Parallel & Distributed Systems
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Economics, Online Markets and Human Computation: The sharing economy

Abstract

We tackle the challenge of estimating grouping structures and factor loadings in asset pricing models, where traditional regressions struggle due to sparse data and high noise. Existing approaches, such as those using fused penalties and multi-task learning, often enforce coefficient homogeneity across cross-sectional units, reducing flexibility. Clustering methods (e.g., spectral clustering, Lloyd's algorithm) achieve consistent recovery under specific conditions but typically rely on a single data source. To address these limitations, we introduce the Panel Coupled Matrix-Tensor Clustering (PMTC) model, which simultaneously leverages a characteristics tensor and a return matrix to identify latent asset groups. By integrating these data sources, we develop computationally efficient tensor clustering algorithms that enhance both clustering accuracy and factor loading estimation. Simulations demonstrate that our methods outperform single-source alternatives in clustering accuracy and coefficient estimation, particularly under moderate signal-to-noise conditions. Empirical application to U.S. equities demonstrates the practical value of PMTC, yielding higher out-of-sample total $R^2$ and economically interpretable variation in factor exposures.

Problem

• Estimating asset grouping structures and factor loadings with sparse noisy data
• Overcoming limitations of single-source clustering methods in asset pricing
• Integrating multiple data sources for improved clustering and estimation accuracy

Innovation

• Simultaneously uses characteristics tensor and return matrix
• Integrates multiple data sources for enhanced clustering accuracy
• Develops efficient tensor clustering algorithms for asset pricing