Covariance Averaging for Improved Estimation and Portfolio Allocation

We propose a new method for estimating the covariance matrix of a multivariate time series of nancial returns. The method is based on estimating sample covariances from overlapping windows of observations which are then appropriately weighted to obtain the nal covariance estimate. We extend the idea of (model) covariance averaging oered in the covariance shrinkage approach by means of greater ease of use, exibility and robustness in averaging information over different data segments. The suggested approach does not suer from the curse of dimensionality and can be used without problems of either approximation or any demand for numerical optimization.