Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation

• Autores: Javier Mencía, Enrique Sentana Iváñez
• Localización: Documentos de trabajo - Banco de España, ISSN 0213-2710, Nº 9, 2009, págs. 9-51
• Idioma: inglés
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• Resumen

  • 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.