Multivariate moments expansion density - Banco de España

MULTIVARIATE MOMENTS EXPANSION DENSITY: APPLICATION OF THE DYNAMIC EQUICORRELATION MODEL Trino-Manuel Ñíguez and Javier Perote

Documentos de Trabajo N.º 1602

2016

MULTIVARIATE MOMENTS EXPANSION DENSITY: APPLICATION OF THE DYNAMIC EQUICORRELATION MODEL

MULTIVARIATE MOMENTS EXPANSION DENSITY: APPLICATION OF THE DYNAMIC EQUICORRELATION MODEL

Trino-Manuel Ñíguez BANCO DE ESPAÑA AND UNIVERSITY OF WESTMINSTER

Javier Perote (*) UNIVERSIDAD DE SALAMANCA

(*) Correspondence to: Javier Perote, Facultad de Economía y Empresa (Edif. FES), Campus de Miguel de Unamuno, Universidad de Salamanca, 37007 Salamanca, Spain; Tel: +34 923 294400 (ext. 3512); E-mail: [email protected]

Documentos de Trabajo. N.º 1602 2016

The Working Paper Series seeks to disseminate original research in economics and finance. All papers have been anonymously refereed. By publishing these papers, the Banco de España aims to contribute to economic analysis and, in particular, to knowledge of the Spanish economy and its international environment. The opinions and analyses in the Working Paper Series are the responsibility of the authors and, therefore, do not necessarily coincide with those of the Banco de España or the Eurosystem.

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Reproduction for educational and non-commercial purposes is permitted provided that the source is acknowledged. © BANCO DE ESPAÑA, Madrid, 2016 ISSN: 1579-8666 (on line)

Abstract

In this study, we propose a new semi-nonparametric (SNP) density model for describing the density of portfolio returns. This distribution, which we refer to as the multivariate moments expansion (MME), admits any non-Gaussian (multivariate) distribution as its basis because it is specified directly in terms of the basis density s moments. To obtain the expansion of the Gaussian density, the MME is a reformulation of the multivariate Gram-Charlier (MGC), but the MME is much simpler and tractable than the MGC when positive transformations are used to produce well-defined densities. As an empirical application, we extend the dynamic conditional equicorrelation (DECO) model to an SNP framework using the MME. The resulting model is parameterized in a feasible manner to admit two-stage consistent estimation, and it represents the DECO as well as the salient non-Gaussian features of portfolio return distributions. The in- and out-of-sample performance of a MME-DECO model of a portfolio of 10 assets demonstrates that it can be a useful tool for risk management purposes. Keywords: density forecasting, dynamic equicorrelation, Gram-Charlier series, multivariate GARCH, semi-nonparametric method. JEL classification: C16, G1.

Resumen

En este estudio, proponemos un nuevo tipo de distribución semi-noparamétrica (SNP) para describir la densidad de los rendimientos de las carteras de activos. Esta distribución, denominada «expansión de momentos multivariante» (MME), admite cualquier distribución (multivariante) no-Gausiana como base de la expansión, ya que está directamente especificada en términos de los momentos de dicha distribución. En el caso de la expansión de una distribución normal, la MME es una reformulación de la distribución Gram-Charlier multivariante (MGC), pero, cuando se utilizan transformaciones de positividad para obtener densidades bien definidas, la MME es más sencilla y manejable que la MGC. Como aplicación empírica, extendemos el modelo de equicorrelación dinámica condicional (DECO) a un contexto SNP utilizando la MME. El modelo resultante presenta una formulación sencilla que admite la estimación consistente en dos etapas e incorpora DECO, así como las características no-Gausianas de la distribución de los rendimientos de cartera. La capacidad predictiva del modelo MME-DECO para una cartera de 10 activos demuestra que puede ser una herramienta útil para la gestión y el control del riesgo de cartera. Palabras clave: equicorrelación dinámica, GARCH multivariante, métodos semi-noparamétricos, predicción de la densidad, series de Gram-Charlier. Códigos JEL: C16, G1.

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Multivariate moments expansion density - Banco de España

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