Putting the squeeze on the sample covariance matrix for portfolio construction

Abstract

ABSTRACTPortfolio construction plays a critical role in adding performance to a fund. Central to portfolio construction are the two primary inputs: the vector of forecast returns and the covariance matrix. Our focus is on the covariance matrix. With guidance from the literature we consider the suitability of two simple estimators, four shrinkage estimators and three blended estimators for mean-variance portfolio construction in the South African environment. Our assessment frameworks comprise a risk-centric framework based on minimum variance portfolios (MVPs) as well as a return-centric framework. Our findings based on a South African equity setting reveal that there are notable differences between the compositions of the MVPs of the covariance estimators. Furthermore, we find that alternative covariance estimators do yield better out-of-period performance in terms of lower realised risks than the sample covariance matrix. In our return-based assessment framework, we considered scenarios of perfect skill and less-than-perfect skill at forecasting returns. In the former case, we found that all of the estimators produced optimal portfolios that substantially outperformed the optimal portfolio derived from the sample covariance matrix. Considering the MVP framework, as well as the return-based framework, we conclude that all of the estimators considered performed better than the sample covariance matrix, effectively reducing the sampling error in the sample covariance without introducing too much specification error. However, no one estimator could be singled out as consistently superior in the South African setting over a range of test metrics considered.