Advances in Estimating Covariance Matrices

Vol. 19, No. 3, 2021

Jose Menchero and Lei Ji

Correlation matrices are widely used in finance both for risk forecasting and for portfolio optimization. It is well known that the sample correlation matrix is unreliable for portfolio optimization. However, we show that for purposes of predicting portfolio risk, the sample correlation matrix is close to optimal. In this paper, we present a technique for estimating correlations that is well suited both for risk forecasting and for portfolio optimization. We apply our technique to estimate factor correlation matrices spanning different asset classes. We find that our technique produces improved correlation estimates compared to an alternative widely used approach.