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

Author

Listed:
  • 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.

Suggested Citation

  • Javier Mencía & Enrique Sentana, 2009. "Multivariate location-scale mixtures of normals and mean-variance-skewness portfolio allocation," Working Papers 0909, Banco de España.
    • Handle: RePEc:bde:wpaper:0909
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    More about this item

    Keywords

    Generalised Hyperbolic Distribution; Maximum Likelihood; Portfolio Frontiers; Sortino Ratio; Spanning Tests; Tail Dependence;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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