A Unified Framework for Estimation of High-dimensional Conditional Factor Models

TL;DR

This paper introduces a unified high-dimensional conditional factor model estimation framework using nuclear norm regularization, with theoretical guarantees, efficient algorithms, and improved empirical performance in stock return prediction.

Contribution

It provides a general, flexible estimation framework for conditional factor models, unifying various existing methods and deriving new asymptotic results.

Findings

Imposing homogeneity improves out-of-sample predictability of stock returns

The proposed method outperforms existing alternatives in empirical tests

Efficient algorithms and cross-validation enhance practical applicability

Abstract

This paper presents a general framework for estimating high-dimensional conditional latent factor models via constrained nuclear norm regularization. We establish large sample properties of the estimators and provide efficient algorithms for their computation. To improve practical applicability, we propose a cross-validation procedure for selecting the regularization parameter. Our framework unifies the estimation of various conditional factor models, enabling the derivation of new asymptotic results while addressing limitations of existing methods, which are often model-specific or restrictive. Empirical analyses of the cross section of individual US stock returns suggest that imposing homogeneity improves the model's out-of-sample predictability, with our new method outperforming existing alternatives.