# Multivariate Approximations to Portfolio Return Distribution

Mora-Valencia, A., Ñíguez, T.M. and Perote, J. 2017. Multivariate Approximations to Portfolio Return Distribution. Computational and Mathematical Organization Theory. 23 (3), pp. 347-361. https://doi.org/10.1007/s10588-016-9231-3

Title Multivariate Approximations to Portfolio Return Distribution Journal article Mora-Valencia, A., Ñíguez, T.M. and Perote, J. 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. European stock indices; Gram-Charlier expansion; Method of moments; Portfolio returns. Computational and Mathematical Organization Theory 23 (3), pp. 347-361 1381-298X 2017 Springer CMOT-D-13-00001R3_FINAL VERSION.pdf https://doi.org/10.1007/s10588-016-9231-3 02 Aug 2016 02 Aug 2016 Sep 2017

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