  Recent studies stressed the fact that covariance matrices computed from
empirical financial time series appear to contain a high amount of noise. This
makes the classical Markowitz Mean-Variance Optimization model unable to
correctly evaluate the performance associated to selected portfolios. Since the
Markowitz model is still one of the most used practitioner-oriented tool,
several filtering methods have been proposed in the literature to fix the
problem. Among them, the two most promising ones refer to the Random Matrix
Theory or to the Power Mapping strategy. The basic idea of these methods is to
transform the correlation matrix maintaining the Mean-Variance Optimization
model. However, experimental analysis shows that these two strategies are not
adequately effective when applied to real financial datasets.
  In this paper we propose an alternative filtering method based on
Combinatorial Optimization. We advance a new Mixed Integer Quadratic
Programming model to filter those observations that may influence the
performance of a portfolio in the future. We discuss the properties of this new
model and we test it on some real financial datasets. We compare the
out-of-sample performance of our portfolios with the one of the portfolios
provided by the two above mentioned alternative strategies. We show that our
method outperforms them. Although our model can be solved efficiently with
standard optimization solvers the computational burden increases for large
datasets. To overcome this issue we also propose a heuristic procedure that
empirically showed to be both efficient and effective.
