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

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Mencía, Javier; Sentana, Enrique

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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.
Classification Economic Statistics, Econometrics, Business Informatics
Free Keywords C52; C32; G11; Generalised hyperbolic distribution; Maximum likelihood; Portfolio frontiers; Sortino ratio; Spanning tests; Tail dependence
Document language English
Publication Year 2009
Page/Pages p. 105-121
Journal Journal of Econometrics, 153 (2009) 2
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)