k-Covariance: An Approach of Ensemble Covariance Estimation and Undersampling to Stabilize the Covariance Matrix in the Global Minimum Variance Portfolio

Abstract

A covariance matrix is an important parameter in many computational applications, such as quantitative trading. Recently, a global minimum variance portfolio received great attention due to its performance after the 2007–2008 financial crisis, and this portfolio uses only a covariance matrix to calculate weights for assets. However, the calculation process of that portfolio is sensitive with outliers in the covariance matrix, for example, a sample covariance matrix estimation or linear shrinkage covariance matrix estimations. In this paper, we propose the use of an undersampling technique and ensemble learning to stabilize the covariance matrix by reducing the impacts of outliers on the output of a covariance estimation. Experimenting on an emerging stock market using three performance metrics shows that our approach significantly improves the sample covariance matrix and also a linear shrinkage to the single-index model to a level of two shrinkage estimations, a shrinkage to identity matrix and shrinkage to constant correlation model.