Improving Portfolio Allocation Through Covariance Matrix Filtering

Abstract

The sample covariance matrix is known to contain substantial statistical noise, making it inappropriate for use in financial decision making. Leading researchers have proposed various filtering methods that attempt to reduce the level of noise in the covariance matrix estimator. In most cases, these methods can be interpreted by analysing how they adjust the eigen-structure of the sample correlation matrix. This paper compares the filtering methods using a theoretical eigen-framework as well as a practical South African experiment. By focussing on the eigen-structure, the sources of statistical noise are identified. The sample correlation matrix suffers from excess dispersion in its eigenvalues and excess dispersion in its pairwise correlations. Bayesian shrinkage estimators that effectively remove the excess dispersion provide superior performance in terms of out-of-sample portfolio risk and turnover. Specifically, the optimal filtering method is a blend between the sample covariance matrix, its diagonal elements and the covariance matrix based on the constant correlation model.