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

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  • Javier Mencía

    ()
    (Banco de España)

  • Enrique Sentana

    ()
    (Centro de Estudios Monetarios y Financieros)

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.

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Bibliographic Info

Paper provided by Banco de Espa�a in its series Banco de Espa�a Working Papers with number 0909.

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Length: 50 pages
Date of creation: Jun 2009
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Handle: RePEc:bde:wpaper:0909

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Keywords: Generalised Hyperbolic Distribution; Maximum Likelihood; Portfolio Frontiers; Sortino Ratio; Spanning Tests; Tail Dependence;

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