Multivariate Location-Scale Mixtures of Normals and Mean-Variance-Skewness Portfolio Allocation
50 Pages Posted: 9 Jun 2009
Date Written: June 2, 2009
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: Suggested Citation