Multivariate moments expansion density

Multivariate moments expansion density

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
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© 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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BANCO DE ESPAÑA
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DOCUMENTO DE TRABAJO N.º 1602
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Dow Jones index returns
Ibex35 index returns
20
20
10
10
0
0
-10
-10
96
98
00
02
04
06
08
10
12
14
96
98
Nikkei100 index returns
00
02
04
06
08
10
12
14
08
10
12
14
08
10
12
14
08
10
12
14
10
12
14
Hang Seng index returns
20
20
0
0
-20
-20
96
98
00
02
04
06
08
10
12
14
96
98
00
Deutsche Bank stock returns
02
04
06
BP stock retruns
40
20
20
0
0
-20
-20
96
98
00
02
04
06
08
10
12
14
96
98
00
FX $/£ returns
02
04
06
FX ¥/£ returns
5
10
0
0
-5
-10
96
98
00
02
04
06
08
10
12
14
96
98
00
FX Fr/$ returns
02
04
06
Apple stock returns
10
40
0
0
-10
-40
-20
-80
96
98
00
02
04
06
08
10
12
14
96
98
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02
04
06
08
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DOCUMENTO DE TRABAJO N.º 1602
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DOCUMENTO DE TRABAJO N.º 1602
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DOCUMENTO DE TRABAJO N.º 1602
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