Precision Matrix Estimation for the Global Minimum Variance Portfolio

We use the Minimum Regularised Covariance Determinant Estimator (MRCD) to limit weights' misspecification within the Global Minimum Variance Portfolio (GMVP) framework. Estimating the precision matrix is a key step that often generates misspecification which translates to resulting portfolio weights, directly affecting the GMVP out-of-sample performance. This effect is exacerbated when data are high-dimensional and non-Normal. To this extent, we propose using the MRCD because is well-designed to deal with high-dimensionality and non-Normality. We perform an extensive Monte Carlo simulation analysis to check the effectiveness of the proposed approach in comparison to the sample estimator. Our analysis demonstrates that the out-of-sample performance of the GMVP benefits from the use of the MRCD estimator: results suggest a reduction in the portfolio turnover at no cost for the portfolio variance and an increase in the portfolio Sharpe ratio.