A Partially Isotropic Reduced Pca Model for Large Equity Portfolios

Abstract

We estimate joint stock return probability distributions for large portfolios of stocks via a method that can accommodate fat-tailed, dependent, covariates with an ill-conditioned covariance matrix. Our method strikes a balance between fidelity to the training data and regularization, with the goal of producing a model that generalizes well out-of-sample. We benchmark our approach against other methods.

Keywords: Multivariate Stock Return Distribution, Multivariate Probability Distribution, Copula, Principal Components, Partially Isotropic, Fat-tailed, Dependence, Ill-Conditioned