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

Joint with: Javier Mencia, Bank of Spain

We show that the distribution of any portfolio whose components jointly follow a location-scale mixture of normals can be characterized 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 standardized 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, Spanning Tests, Tail Dependence.

JEL: C52, C32, G11

For more information, contact Frank Schorfheide.