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Multi-tail generalized elliptical distributions for asset returns

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  • Sebastian Kring
  • Svetlozar T. Rachev
  • Markus H�chst�tter
  • Frank J. Fabozzi
  • Michele Leonardo Bianchi

Abstract

In the study of asset returns, the preponderance of empirical evidence finds that return distributions are not normally distributed. Despite this evidence, non-normal multivariate modelling of asset returns does not appear to play an important role in asset management or risk management because of the complexity of estimating multivariate non-normal distributions from market return data. In this paper, we present a new subclass of generalized elliptical distributions for asset returns that is sufficiently user friendly, so that it can be utilized by asset managers and risk managers for modelling multivariate non-normal distributions of asset returns. For the distribution we present, which we call the multi-tail generalized elliptical distribution, we (1) derive the densities using results of the theory of generalized elliptical distributions and (2) introduce a function, which we label the tail function, to describe their tail behaviour. We test the model on German stock returns and find that (1) the multi-tail model introduced in the paper significantly outperforms the classical elliptical model and (2) the hypothesis of homogeneous tail behaviour can be rejected. Copyright � 2009 The Author(s). Journal compilation � Royal Economic Society 2009

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Bibliographic Info

Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 12 (2009)
Issue (Month): 2 (07)
Pages: 272-291

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Handle: RePEc:ect:emjrnl:v:12:y:2009:i:2:p:272-291

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Cited by:
  1. Frahm, Gabriel & Jaekel, Uwe, 2010. "A generalization of Tyler's M-estimators to the case of incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 374-393, February.

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