Extension of Random Matrix Theory to the L-moments for Robust Portfolio Allocation

In this paper, we propose a methodology for building an estimator of the covariance matrix. We use a robust measure of moments called L-moments (see hosking, 1986), and their extension into a multivariate framework (see Serfling and Xiao, 2007). Random matrix theory (see Edelman, 1989) allows us to extract factors which contain real information. An empirical study in the American market shows that the Global Minimum L-variance Portfolio (GMLP) obtained from our estimator well performs the Global Minimum Variance Portfolio (GMVP) that acquired from the empirical estimator of the covariance matrix.