Shrinkage = Factor Model

TL;DR

This paper discusses a specific type of regularization for sample covariance matrices, framing it as a factor model that combines risk factors and principal components, and proposes a scheme to reduce out-of-sample instability.

Contribution

It clarifies that shrinkage is a form of factor model and introduces a regularization scheme less susceptible to instabilities compared to traditional methods.

Findings

Shrinkage can be viewed as a special factor model.

A new regularization scheme reduces out-of-sample instability.

Contextualization within multifactor models enhances understanding.

Abstract

Shrunk sample covariance matrix is a factor model of a special form combining some (typically, style) risk factor(s) and principal components with a (block-)diagonal factor covariance matrix. As such, shrinkage, which essentially inherits out-of-sample instabilities of the sample covariance matrix, is not an alternative to multifactor risk models but one out of myriad possible regularization schemes. We give an example of a scheme designed to be less prone to said instabilities. We contextualize this within multifactor models.