A study of covariance matrix estimators for Markowitz mean-variance portfolio optimization

Abstract

This paper aims to compare the performance of 3 covariance matrix estimators with respect to sample covariance matrix in terms of portfolio optimisation using historical return data of 30 top stocks traded at Singapore market from May 2012 to October 2014. The comparison shows that the improvement of covariance matrix estimators relies largely upon the allowance or forbid of short selling, upon the ratio of estimation time horizons T and stocks number N, as well as upon the evaluators. When there is short selling, sample covariance matrix performs worst; and all other estimators achieve a huge improvement in terms of reduced realized risk, improved risk reliability and reduced short selling amount, especially when T/N =1. Nevertheless, when there is no short selling, the improvement with respect to sample covariance matrix is not that significant. Sample covariance matrix even has a comparable performance as other enhanced methods in area of portfolio realised risk, portfolio risk reliability and portfolio diversification when T/N>1 while still underperforms other estimators when T/N<1.