Robust Modeling of Multivariate Financial Data

The bottom line in many statistical analysis in finance is the basic issue of modeling a set of multivariate data. Financial data are characterized by their fat tails containing some proportion of extreme observations. We propose a simple model able to capture these main characteristics, and to provide a good fit for the bulk of the data as well as for the atypical observations. Basically, we use a robust covariance estimator to define the center and orientations of the data, and the classical sample covariance to estimate how inflated could this distribution be by the effect of extreme observations. Estimation of the model is done either empirically or by maximum likelihood based on elliptical distributions. Simulation experiments verified the adequacy of the model to real data. We provide illustrations of the usefulness of the proposed procedure, in particular when constructing efficient frontiers. We show that robust portfolios may yield higher cumulative returns and have more stable weights