A Sparse Approximate Factor Model for High-Dimensional Covariance Matrix Estimation and Portfolio Selection

Abstract

We propose a novel estimation approach for the covariance matrix based on the l1-regularized approximate factor model (AFM). Our sparse approximate factor (SAF) covariance estimator allows for the existence of weak factors and hence relaxes the pervasiveness assumption generally adopted for the standard AFM. We prove the consistency of the covariance matrix estimator under the Frobenius norm as well as the consistency of the factor loadings and the factors. Our Monte Carlo simulations reveal that the SAF covariance estimator has superior properties in finite samples for low and high dimensions and different designs of the covariance matrix. Moreover, in an out-of-sample portfolio forecasting application, the estimator uniformly outperforms alternative portfolio strategies based on alternative covariance estimation approaches and modeling strategies including the 1/N-strategy.