Extension of the random matrix theory to the L-moments for robust portfolio selection

In this paper, we propose an approach for selecting stocks from a large investment universe by studying information on the eigenvalues of the correlation matrix. For this purpose, we use a robust measure of moments called L-moments, and their extensions to a multivariate framework. The random matrix theory allows us to extract factors which contain real information from the estimator of the correlation matrix obtained using the L-moments (henceforth the Lcorrelation matrix). An empirical study of the American market shows the coherence of such an approach and highlights the consistency of the Lcorrelation matrix in comparison with the sample correlation matrix. For both estimators of the correlation matrix, it seems that the largest eigenvalue corresponds to the market, and that the other eigenvalues which contain information partition the set of all stocks into distinct sectorial groups. An analysis of the group of stocks shows that the selected stocks obtained from the Lcorrelation matrix outperform those obtained from the sample correlation matrix in terms of the Sharpe ratio, although the sample correlation matrix provides a well-diversified portfolio in terms of volatility in an <italic>out-of-sample</italic> investment approach.