Risk-based portfolio sensitivity to covariance estimation

Risk-based portfolio construction methods focus on optimally extracting information from the covariance matrix of asset returns, as opposed to utilising forecasts of expected returns, in determining the portfolio allocation. This improves their robustness to estimation error in means, but this does not mean that they are immune to errors in estimating volatilities and correlations. Using a covariance matrix decomposition that allows separately estimated volatility and correlation models to be recomposed into different models of the covariance matrix, this study examines the empirical performance impact of using an enhanced estimator of the covariance matrix, relative to using the historical sample covariance estimator in the context of six risk-based portfolio optimisations, in a long-only constrained equity market setting. It finds that sensitivity to covariance estimation varies significantly among risk-based portfolio types and that outperformance of the sample historical covariance estimator is possible, but rare. As components of the covariance estimate, among volatility models the EWMA volatilities perform best and GARCH models, poorly. Among correlation models, the Rotationally Invariant Estimator of Bouchaud, Bun, and Potters (2016) shows strong performance, along with the classic Ledoit and Wolf (2003) Single Market Model Estimator.