Inferential Theory for Pricing Errors with Latent Factors and Firm Characteristics

2025-11-04

AI Summary

This paper addresses the modeling challenge of pricing errors in factor models that jointly incorporate latent factors and firm characteristics. Methodologically, it proposes a novel, identifiable, estimable, and inferential framework that decomposes mispricing into two distinct alpha components: “internal alpha”—driven by characteristics and reflecting their systematic impact on expected returns—and “external alpha”—orthogonal to both factors and characteristics, capturing unmodeled idiosyncratic shocks. The framework unifies statistical modeling with characteristic-based genetic factor structures, employing low-rank matrix estimation and explicit debiasing to resolve issues of non-orthogonality, basis dependence, and unit sensitivity. It enables asymptotic inference in high-dimensional, multi-characteristic settings and yields closed-form estimators with rigorous theoretical guarantees. Empirically, using U.S. equity data from 2000–2019, both alpha components are statistically significant: internal alpha exhibits industry-level comovement, while external alpha reflects heterogeneous shocks beyond fundamentals.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Other Foundations of Cognitive Modeling & Systems

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: Incentives in network design for Web infrastructures and ecosystems

Abstract

We study factor models that combine latent factors with firm characteristics and propose a new framework for modeling, estimating, and inferring pricing errors. Following Zhang (2024), our approach decomposes mispricing into two distinct components: inside alpha, explained by firm characteristics but orthogonal to factor exposures, and outside alpha, orthogonal to both factors and characteristics. Our model generalizes those developed recently such as Kelly et al. (2019) and Zhang (2024), resolving issues of orthogonality, basis dependence, and unit sensitivity. Methodologically, we develop estimators grounded in low-rank methods with explicit debiasing, providing closed-form solutions and a rigorous inferential theory that accommodates a growing number of characteristics and relaxes standard assumptions on sample dimensions. Empirically, using U.S. stock returns from 2000-2019, we document strong evidence of both inside and outside alphas, with the former showing industry-level co-movements and the latter reflecting idiosyncratic shocks beyond firm fundamentals. Our framework thus unifies statistical and characteristic-based approaches to factor modeling, offering both theoretical advances and new insights into the structure of pricing errors.

Problem

• Modeling pricing errors with latent factors and firm characteristics
• Decomposing mispricing into inside alpha and outside alpha components
• Developing estimators for pricing errors with rigorous inferential theory

Innovation

• Combining latent factors with firm characteristics
• Decomposing mispricing into inside and outside alpha
• Using low-rank methods with explicit debiasing