On the impact of some distributional factors in large scale portfolio problems

In this paper, we examine the possibility to estimate the return distributions using a principal component analysis applied to different semidefinite positive correlation matrices. Using a recent classification of semidefinite positive correlation measures we are able to value the impact of different distributional factors in the choices under uncertainty conditions. In particular we investigate the opportunity to reduce the complexity of large scale portfolio selection problems using some concordance measures. We first analyze the large scale static problem and then we discuss a first extension to the dynamic portfolio problem. Finally we propose an empirical application to the large scale portfolio problem.