Forecasting of dependence, market, and investment risks of a global index portfolio

• Date: 01 April 2020
• DOI: http://doi.org/10.1002/for.2641
• Published date: 01 April 2020

RESEARCH ARTICLE

Forecasting of dependence, market, and investment risks of

a global index portfolio

Jose Arreola Hernandez

1

| Mazin A.M. Al Janabi

2

1

Department of Accounting and Finance,

Rennes School of Business, Rennes,

France

2

EGADE Business School, Tecnologico de

Monterrey, Santa Fe Campus, Mexico

City, Mexico

Correspondence

Jose Arreola Hernandez, Department of

Accounting and Finance, Rennes School

of Business. Rennes 35065, France.

Email: jose.arreola-hernandez@rennes-sb.

com

Abstract

This paper undertakes an in-sample and rolling-window comparative analysis of

dependence, market, and portfolio investment risks on a 10-year global index

portfolio of developed, emerging, and commodity markets. We draw our empiri-

cal results by fitting vine copulas (e.g., r-vines, c-vines, d-vines), IGARCH(1,1)

RiskMetrics value-at-risk (VaR), and portfolio optimization methods based on

risk measures such as the variance, conditional value-at-risk, conditional

drawdown-at-risk, minimizing regret (Minimax), and mean absolute deviation.

The empirical results indicate that all international indices tend to correlate

strongly in the negative tail of the return distribution; however, emerging mar-

kets, relative to developed and commodity markets, exhibit greater dependence,

market, and portfolio investment risks. The portfolio optimization shows a clear

preference towards the gold commodity for investment, while Japan and Canada

are found to have the highest and lowest market risk, respectively. The vine cop-

ula analysis identifies symmetry in the dependence dynamics of the global index

portfolio modeled. Large VaR diversification benefits are produced at the 95%

and 99% confidence levels by the modeled international index portfolio. The

empirical results may appeal to international portfolio investors and risk man-

agers for advanced portfolio management, hedging, and risk forecasting.

KEYWORDS

commodities, emerging and developed markets, forecasting, portfolio investment risk, value-at-

risk, vine copulas

1|INTRODUCTION

Global index portfolios attract the attention of investors

because they provide diversification benefits, in terms of

geographical location and financial security types, that

single equity-based domestic portfolios cannot provide.

Global index portfolios are also of interest to investors

because they can capture in aggregate the performance of

the entire stock markets. In the current world of globali-

zation, global index portfolios widen the portfolio diversi-

fication horizon to individual and institutional investors

by offering a wide array of international equity

investment opportunities that can vary according to the

characteristics of individual stock markets. For instance,

some emerging market stock markets, while displaying

negative correlations with major developed market stock

markets, have been acknowledged for the attractive

returns they offer (Erb, Harvey, & Viskanta, 1998;

Salomons & Grootveld, 2003). Developed market stock

markets, on the other hand, have been observed to pro-

vide investment stability and medium- to long-term

growth, while being indirectly linked to emerging stock

markets through dependence and contagion effects

(Arestis, Caporale, Cipollini, & Spagnolo, 2005).

Received: 10 May 2019 Revised: 4 November 2019 Accepted: 25 November 2019

DOI: 10.1002/for.2641

512 © 2019 John Wiley & Sons, Ltd. Journal of Forecasting. 2020;39:512–532.wileyonlinelibrary.com/journal/for

This study, aware of the important role global invest-

ment positions play in the diversification spectrum of port-

folio investors and risk managers, undertakes an in-sample

and rolling-window analysis of nonlinear dependence, mar-

ket, and portfolio investment risks. To that end, we show

the usefulness of our modeling approach by implementing,

to a global index portfolio of developed, emerging and com-

modity markets, vine copulas techniques (such as regular

vines (r-vines), canonical vines (c-vines), and drawable

vines (d-vines)), IGARCH (1,1) RiskMetrics value-at-risk

(VaR), and portfolio optimization methods based on the

variance, conditional value-at-risk (CVaR), conditional

drawdown-at-risk (CDaR), minimizing regret (Minimax),

and mean absolute deviation (MAD). The main objectives

of this paper are to identify the block of global market indi-

ces and single global indices that have the highest (lowest)

dependence, market, and portfolio investment risk expo-

sures. Some studies have been proposed in the relevant lit-

erature that implement the methodology we use in this

research study to different datasets (see, e.g., Abad, Benito,

& López, 2014; Alexander & Baptista, 2004, 2008; Arreola-

Hernandez, 2014; Arreola-Hernandez, Hammoudeh,

Khuong, Al Janabi, & Reboredo, 2017; Bekiros, Arreola-

Hernandez, Hammoudeh, & Khuong, 2015; Brechmann,

Czado, & Aas, 2012; Campbell, Huisman, & Koedijk, 2001;

Dissmann, Brechmann, Czado, & Kurowicka, 2013; Jorion,

2001; Ghalanos, 2013).

1

For instance, Arreola-Hernandez (2014) models the

dependence risk and resource allocation characteristics

of two 20-stock coal–uranium and oil–gas sector portfo-

lios from the Australian market in the context of the

global financial crisis (GFC). The implemented modeling

framework consists of pair vine copulas and linear and

nonlinear portfolio optimization methods with respect to

five risk measures The combined modeling approach,

consisting of a pair c-vine copula and the nonlinear

mean–variance quadratic portfolio optimization method,

produces the highest return relative to risk. In a similar

vein, Bekiros et al. (2015) propose an integrated frame-

work to model relatively large dependence matrices using

pair vine copulas and minimum risk optimal portfolios

with respect to five risk measures within the context of

the GFC. Their paper addresses the dependence charac-

teristics and risks of Australian gold and iron ore–nickel

stock portfolios under specific market conditions. To that

end, an integrated modeling framework of the pair vine

copulas and portfolio optimization with respect to the

variance risk measure is implemented with the purpose

of improving the accuracy of the estimations. On the

other hand, Arreola-Hernandez et al. (2017) use the regu-

lar vine (r-vine), canonical vine (c-vine), and drawable

vine (d-vine) copulas to examine the dependence risk

characteristics of three 20-stock portfolios from the retail,

manufacturing, and gold-mining equity sectors of the

Australian market in the periods before, during, and after

the GFC. The authors broaden the related literature by

providing a detailed analysis of the portfolios' multivari-

ate dependence structure and dependence risk dynamics

by means of a copula counting technique.

The specific type of vine copula modeling undertaken

in this study is broadly linked to the research studies pur-

sued by Berg and Aas (2009) and Fischer, Kock, Schluter,

and Weigert (2009), where comparisons between pair

vine copulas such as the Student t, Gaussian, Gumbel,

Clayton, and nested Archimedean constructions are

established. The first study finds the vine copulas to be

more flexible than the Archimedean constructions, while

the latter study indicates that Student tpair vine copula

outperforms the implemented alternative vine copula

models. Other studies that connect in a more specific

manner to the vine copula modeling of dependence struc-

ture we undertake in this paper are Chollete, Heinen,

and Valdesogo (2009) and Dissmann et al. (2013). The

former study employs a mixed c-vine copula with regime

switching and skewed-tgeneralized autoregressive condi-

tional heteroskedasticity (GARCH) features to model the

skewness and asymmetric dependence of an index portfo-

lio consisting of the G5 and three Latin American coun-

tries. The latter study explores the flexibility of r-vines

relative to c-vines and d-vines under varied distributional

scenarios, and acknowledges the greater flexibility of the

r-vines when fitted to a portfolio of equity, fixed income,

and commodity index securities. The implementation of

a vine copula autoregressive model for asymmetric

dependence, negative skewness, and nonlinear depen-

dence estimation of financial datasets carried out by

Brechmann et al. (2012) is also related to our dependence

modeling technique. The modeling of market risk that

we realize in this paper using the IGARCH(1,1) Risk-

Metrics VaR is broadly linked to the studies undertaken

by, among others, Jorion (2001), Abad et al. (2014),

Berkowitz and O'Brien (2002), Artzner, Delbaen, Eber,

and Heath (1999), and Garcia, Renault, and Tsafack

(2007), where the forecasting accuracy of standard VaR

models is examined. The multiple risk measures for port-

folio optimization that we undertake is in tandem with

studies conducted by Arreola-Hernandez (2014), Arreola-

1

In a different modeling technique, Al Janabi, Arreola-Hernández,

Berger, and Nguyen (2017) propose a portfolio optimization

methodology based on the integration of DCC (dynamic conditional

correlation), t-copula and LVaR models to enhance asset allocation

decisions under illiquid market conditions. Their empirical findings

prove the superiority of the DCC–copula–LVaR modeling technique

over the traditional Markowitz (1959) optimization procedure for a

portfolio composed of international stock market indices, gold, and

crude oil across various trading scenarios.

ARREOLA HERNANDEZ AND AL JANABI 513