Robust Modeling of Multivariate Financial Data

Coppead Working Paper Series No. 355

32 Pages Posted: 19 Mar 2004

See all articles by Beatriz V.M. Mendes

Beatriz V.M. Mendes

Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Ricardo P. C. Leal

The COPPEAD Graduate School of Business

Date Written: December 2003

Abstract

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.

Keywords: Extreme values, portfolio optimization, asset allocation, robustness

JEL Classification: C51, G11

Suggested Citation

Mendes, Beatriz V.M. and Leal, Ricardo Pereira Câmara, Robust Modeling of Multivariate Financial Data (December 2003). Coppead Working Paper Series No. 355, Available at SSRN: https://ssrn.com/abstract=477321 or http://dx.doi.org/10.2139/ssrn.477321

Beatriz V.M. Mendes

Instituto Nacional de Matemática Pura e Aplicada (IMPA) ( email )

Estrada Dona Castorina 110
Rio de Janeiro, 22460
Brazil

Ricardo Pereira Câmara Leal (Contact Author)

The COPPEAD Graduate School of Business ( email )

Rua Pascoal Lemme
355 - Cidade Universitária
Rio de Janeiro, Rio de Janeiro 21941-918
Brazil
39389871 (Phone)

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