Robust Covariance Matrix Estimation And Portfolio Allocation: The Case Of Non-Homogeneous Assets

This paper presents how the most recent improvements made on covariance matrix estimation and model order selection can be applied to the portfolio optimisation problem. The particular case of the Maximum Variety Portfolio is treated but the same improvements apply also in the other optimisation problems such as the Minimum Variance Portfolio. We focus on the fact that the assets should preferably be classified in homogeneous groups before applying the proposed procedure which is to whiten the data before estimating the covariance matrix using the robust Tyler M-estimator and the Random Matrix Theory (RMT). The proposed procedure is applied and compared to standard techniques on real market data showing promising improvements.