MULTIVARIATE LOCATION-SCALE MIXTURES OF NORMALS AND MEAN-VARIANCE-SKWNESS PORTFOLIO ALLOCATION

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-varianceskewness 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 meanvariance-skewness frontier generated by the ten Datastream US sectoral indices, and conduct spanning tests.