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High-Order Moments and Cumulants of Multivariate Weibull Asset Returns Distributions: Analytical Theory and Empirical Tests: II

Yannick Malevergne
University of St. Etienne - Graduate School of Economics and Business Administration (ISEAG); EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control

Didier Sornette
ETH Zurich

Finance Letters, Vol. 3, No. 1, pp. 54-63, 2005

Abstract:
Using a family of multivariate Weibull distributions to parameterize the non-Gaussian properties of the distributions of asset returns, we offer exact formulas for the moments and cumulants of the distribution of returns of a portfolio made of an arbitrary composition of these assets. Using combinatorial and hypergeometric functions, we are in particular able to extend previous results to the case where the exponents of the Weibull distributions are different from asset to asset and in the presence of dependence between assets. These moments and cumulants can be used as consistent measures of risks to derive (in a companion paper) generalized optimal risk-return portfolio efficient frontiers.

Keywords: Distribution of asset returns, copulas, modified Weibull distribution

JEL Classifications: C16, G10

Accepted Paper Series

Date posted: May 04, 2005 ; Last revised: May 04, 2005

Suggested Citation

Malevergne, Yannick and Sornette, Didier , High-Order Moments and Cumulants of Multivariate Weibull Asset Returns Distributions: Analytical Theory and Empirical Tests: II. Finance Letters, Vol. 3, No. 1, pp. 54-63, 2005. Available at SSRN: http://ssrn.com/abstract=714185

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Contact Information

Didier Sornette (Contact Author) ETH Zurich ( email ) Department of Management, Technology and Economics Kreuzplatz 5 8032 Zurich CH-1015 Switzerland 41446328917 (Phone) 41446321914 (Fax) HOME PAGE: http://www.er.ethz.ch/
Yannick Malevergne University of St. Etienne - Graduate School of Economics and Business Administration (ISEAG) ( email ) 2, Rue Tréfilerie F-42023 St. Etienne Cedex 2 France
EM Lyon (Ecole de Management de Lyon) - Department of Economics, Finance, Control ( email ) 23 av. Guy de Collongue BP 174 69132 Ecully Cedex France HOME PAGE: http://www.em-lyon.com/english/faculty/professors/efc/malevergne/index.aspx