Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation

50 Pages Posted: 9 Jun 2009

See all articles by Javier Mencia

Javier Mencia

Banco de España

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI); Financial Markets Group; Centre for Economic Policy Research (CEPR)

Multiple version iconThere are 2 versions of this paper

Date Written: June 2, 2009

Abstract

We show that the distribution of any portfolio whose components jointly follow a location-scale mixture of normals can be characterised solely by its mean, variance and skewness. Under this distributional assumption, we derive the mean-variance-skewness frontier in closed form, and show that it can be spanned by three funds. For practical purposes, we derive a standardised distribution, provide analytical expressions for the log-likelihood score and explain how to evaluate the information matrix. Finally, we present an empirical application in which we obtain the mean-variance-skewness frontier generated by the ten Datastream US sectoral indices, and conduct spanning tests.

Keywords: generalized hyperbolic distribution, maximum likelihood, portfolio frontiers, Sortino ratio, spanning tests, tail dependence

JEL Classification: C52, C32, G11

Suggested Citation

Mencia, Javier and Sentana, Enrique, Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation (June 2, 2009). Banco de Espana Working Paper No. 0909. Available at SSRN: https://ssrn.com/abstract=1413060 or http://dx.doi.org/10.2139/ssrn.1413060

Javier Mencia (Contact Author)

Banco de España ( email )

Alcala 50
Madrid 28014
Spain
+34 91 338 5414 (Phone)
+34 91 338 6104 (Fax)

HOME PAGE: http://www.bde.es/investigador/staff/66.htm

Enrique Sentana

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
Spain
+34 91 429 0551 (Phone)
+34 91 429 1056 (Fax)

HOME PAGE: http://www.cemfi.es/~sentana/

Financial Markets Group

Houghton Street
London School of Economics & Political Science (LSE)
London WC2A 2AE
United Kingdom
+44 20 7955 7002 (Phone)
+44 20 7852 3580 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom

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