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

TL;DR

This paper introduces the Panel Coupled Matrix-Tensor Clustering (PMTC) model, which jointly uses tensor and matrix data sources to improve asset grouping and factor estimation, outperforming existing methods in accuracy and interpretability.

Contribution

The paper proposes a novel PMTC model that integrates tensor and matrix data for asset clustering, with efficient algorithms that enhance accuracy and interpretability over traditional single-source approaches.

Findings

PMTC outperforms single-source methods in simulations.

Empirical results show higher out-of-sample R^2.

PMTC yields more interpretable factor loadings.

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.