Deep Learning Based Residuals in Non-linear Factor Models: Precision Matrix Estimation of Returns with Low Signal-to-Noise Ratio

TL;DR

This paper develops a deep learning-based estimator for the precision matrix of asset returns in large portfolios, effective even with low signal-to-noise ratios, and provides theoretical guarantees and empirical validation.

Contribution

It introduces a novel deep learning estimator for the precision matrix that remains consistent in low signal-to-noise environments and offers new theoretical bounds and error covariance estimation methods.

Findings

Estimator achieves superior accuracy in simulations.

Theoretical bounds on estimation risk are established.

Effective in low signal-to-noise ratio settings.

Abstract

This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with weak factors. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirics.