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Multivariate approximations to portfolio return distribution

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Abstract

This article proposes a three-step procedure to estimate portfolio return distributions under the multivariate Gram–Charlier (MGC) distribution. The method combines quasi maximum likelihood (QML) estimation for conditional means and variances and the method of moments (MM) estimation for the rest of the density parameters, including the correlation coefficients. The procedure involves consistent estimates even under density misspecification and solves the so-called ‘curse of dimensionality’ of multivariate modelling. Furthermore, the use of a MGC distribution represents a flexible and general approximation to the true distribution of portfolio returns and accounts for all its empirical regularities. An application of such procedure is performed for a portfolio composed of three European indices as an illustration. The MM estimation of the MGC (MGC-MM) is compared with the traditional maximum likelihood of both the MGC and multivariate Student’s t (benchmark) densities. A simulation on Value-at-Risk (VaR) performance for an equally weighted portfolio at 1 and 5 % confidence indicates that the MGC-MM method provides reasonable approximations to the true empirical VaR. Therefore, the procedure seems to be a useful tool for risk managers and practitioners.

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Acknowledgments

Javier Perote acknowledges financial support from the Spanish Ministry of Economics and Competitiveness, through the project ECO2013-44483-P, and from the Junta de Castilla y León, through the proyect SA072U16. Andrés Mora-Valencia acknowledges financial support from FAPA-Uniandes through the project P16.100322.001.

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Authors and Affiliations

  1. School of Management, Universidad de los Andes, Bogotá, Colombia

    Andrés Mora-Valencia

  2. Westminster Business School, University of Westminster, 35 Marylebone Road, London, NW1 5LS, UK

    Trino-Manuel Ñíguez

  3. Monetary and Financial Studies Department, Research Division, Bank of Spain, Alcala 48, 28014, Madrid, Spain

    Trino-Manuel Ñíguez

  4. University of Salamanca (IME), Campus Miguel de Unamuno (Edif. F.E.S.), 37007, Salamanca, Spain

    Javier Perote

Authors
  1. Andrés Mora-Valencia
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  2. Trino-Manuel Ñíguez
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  3. Javier Perote
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Correspondence to Javier Perote.

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Mora-Valencia, A., Ñíguez, TM. & Perote, J. Multivariate approximations to portfolio return distribution. Comput Math Organ Theory 23, 347–361 (2017). https://doi.org/10.1007/s10588-016-9231-3

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