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Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Volatility returns with vengeance: Financial markets vs. commodities Soﬁane Aboura a, Julien Chevallier b,∗ a DRM Finance, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France b IPAG Business School (IPAG Lab), 184 Boulevard Saint-Germain, 75006 Paris, France

a r t i c l e

i n f o

Available online xxx

JEL classiﬁcation: C32 C4 G15 Keywords: Volatility spillovers Financial markets Commodities ADCCX

a b s t r a c t To assess how ﬁnancial markets and commodities are inter-related, this paper introduces a ‘volatility surprise’ component into the asymmetric DCC with one exogenous variable (ADCCX) framework. We develop an econometric model in which returns and volatility allow to inﬂuence pairs of assets, and derive several case studies linking commodities to stocks, bonds and currencies from 1983 to 2013. The innovative feature of our model is that these volatility spillovers are modeled consistently within the correlation dynamics of the ADCCX. We ﬁnd evidence that return and volatility spillovers do exist between commodity and ﬁnancial markets and that in turn, their relative impact on each other is very substantial. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Understanding the origins of volatility has long been a topic of considerable interest to both policy makers and market practitioners. Policy makers are mainly interested in the main (possibly real) determinants of volatility, and in its spillover effects on real activity. Market practitioners – such as investment bankers – are mainly interested in the direct effects time-varying volatility exerts on the pricing and hedging of plain vanilla options and more exotic derivatives. In both cases, forecasting volatility constitutes a formidable challenge, but also a fundamental instrument to manage risks.

∗ Corresponding author. Tel.: +33 01 49 40 73 86; fax: +33 01 49 40 72 55. E-mail addresses: soﬁ[email protected] (S. Aboura), [email protected] (J. Chevallier). http://dx.doi.org/10.1016/j.ribaf.2014.04.003 0275-5319/© 2014 Elsevier B.V. All rights reserved.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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S. Aboura, J. Chevallier / Research in International Business and Finance xxx (2014) xxx–xxx

Since the ﬁnancial crisis of 2008, the topic of international volatility transmission across markets has once more attracted a considerable attention. Recent studies analyze the extent of cross-market linkages over different asset classes: ﬁnancial assets (Straetmans and Candelon, 2013; Wang et al., 2013), and commodities (Chng, 2009; Chan et al., 2011). Cross-sectional effects amongst ﬁnancial and nonﬁnancial assets constitute a central topic in asset pricing. However, we know little about how markets interact. How do shocks go from one market to others? Are these shocks able to contaminate assets belonging to other asset classes? Do commodities have a signiﬁcant inﬂuence on ﬁnancial markets? Whereas commodity markets price different risk factors from a linear asset pricing perspective, extreme events can still trigger contagion effects across markets.1 Spillovers actually encompass two kinds of phenomena: (i) directional shocks as documented recently by Diebold and Yilmaz (2012) and (ii) a contagion effect traditionally deﬁned by Forbes and Rigobon (2002) as a signiﬁcant increase in cross-market linkages after a shock. Regarding cross-market dependencies, the key point in spillover analyses is the equity-to-commodity relationship. Indeed, following the contribution by Gorton and Rouwenhorst (2005), investors have increasingly started to trust the diversiﬁcation effect that commodities could bring to their portfolio. A few spillover analyses have been devoted to the commodity-equity linkage. Most of the literature is based on dynamic correlation models that have been proposed following Engle’s (2002) DCC model and its extensions. These approaches aim at measuring how correlations across markets can move together – which is usually regarded as a measure of contagion. Literature on spillover analyses include, for example, Karolyi and Stulz (1996), Longin and Solnik (2001), Ang and Chen (2002) and Forbes and Rigobon (2002). Chong and Miffre (2010) ﬁnd that the correlation between standard assets and commodities is lower during periods of crisis, i.e. when diversiﬁcation effects are the most sought for. Silvennoinen and Thorp (2010) ﬁnd the exact opposite conclusion. During turbulent periods, these correlations are rising. Such disagreement may come from differences in terms of methodologies, or in terms of the periods covered in each dataset. Buyukshahin et al. (2010) ﬁnd that such correlation increases after 2008, casting some doubt around the commodity diversiﬁcation effect. Dasklaki and Skiadopoulos (2011), Bichetti and Maystre (2012) and Delatte and Lopez (2013) ﬁnd evidence consistent with these conclusions. Other types of econometric methodologies have been designed to capture cross-market linkages. For instance, copulas – a more general dependence structure than the underlying Gaussian model behind the dynamic correlation models – went through an increasing attention, as presented in Patton (2006), Jondeau and Rockinger (2006) and Rodriguez (2007) for standard assets; and in Reboredo (2011) in the case of commodities. Nevertheless, beyond their ability to measure tail dependence – i.e. joint extreme events – turning them into a dynamic measure of dependence turned out to be difﬁcult. Multivariate Markov Switching models also encompass in a certain way the measurement of cross time series dependence, as presented in Khalifa et al. (2012). Their ability to produce switches between two types of dependence structures led to interesting ﬁndings in ﬁnancial markets (Ielpo, 2012). Their numerical complexity when increasing the number of underlying variables is, however, a massive drag to their use to measure cross-market dynamics. This computational burden to estimate sophisticated speciﬁcations of such models in the case of cross-commodity measurement limitates their use. Diebold and Yilmaz (2012) have presented a new approach to measure cross-asset volatility spillovers through the historical cross-series mean reversion parameters. Their approach has been used in Yilmaz (2010), Kocenda et al. (2011) and da Fonseca and Gottschalk (2012), for example. The apparent simplicity and the efﬁciency of the estimates obtained turn this approach into a very promising one. In this article, we advance a methodological contribution related to the ﬁrst strand of literature, e.g. dynamic correlations models. Previous studies have mostly examined the spillovers in multivariate GARCH-type models (Engle et al., 1990; Hassan and Malik, 2007; Cai et al., 2008). In contrast with previous works, this paper focuses on volatility interactions between equities, bonds, foreign exchange rates and commodities, as further evidence is emerging for volatility to be autocorrelated within its

1 Whereas ‘contagion’ is deﬁned later in the paper, the study of returns ‘co-movements’ begins with Grubel (1968), who explains ﬁrst the beneﬁts from international diversiﬁcation.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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3

own market and also to be cross-correlated with volatility in other asset markets (Hakim and McAleer, 2010)). We propose an alternative for modeling cross-market relations with multivariate volatility processes, on the basis of the asymmetric dynamic conditional correlation model with one exogenous variable (ADCCX) newly deﬁned by Vargas (2008). This model represents a parsimonious speciﬁcation for measuring cross-market relations. It is ﬂexible in the sense that each market’s shock may be ﬁtted separately as a spillover on any combination of bivariate volatility models. Computationally, Vargas (2008) has established the consistency of the estimates in presence of high-dimensional optimization problems. The methodology proposed is applied to commodity and ﬁnancial markets. Our original idea lies in using the ‘volatility surprise’ component to capture cross-market relationships, and to understand how volatility interacts with returns. According to Engle (1993), it is the difference that cannot be forecast between squared residuals and the conditional variance which is worthy of interest. Such a quantity has been coined ‘volatility surprise’. This new concept paved the way for numerous studies (Bae and Karolyi, 1994; Abhyankar, 1995; Chan-Lau and Ivaschenko, 2003; Kim and Rogers, 1995; Niarchos et al., 1999; Tse et al., 2003; Wei et al., 1995). As an extension to the work of Hamao et al. (1990), our key contribution is to document the spillover effects coming from volatility surprises to returns, and vice versa. The two-step econometric methodology consists of (1) computing the mean-zero ‘volatility surprise’ component from univariate GARCH models and (2) plugging it into the ADCCX model. We investigate (i) volatility surprise spillovers on pairwise returns, and (ii) return spillovers on pairwise returns. The dataset includes four aggregate indices from 1983 to 2013. The results provide strong evidence of spillover effects coming from the ‘volatility surprise’ component across markets. We further investigate the reliability of our results in the aftermath of the 2008 ﬁnancial crisis. In addition, asset management implications are derived. To summarize our results, we show that setting the ‘volatility surprise’ component as a spillover variable yields strong volatility transmission effects in the ADCCX framework (especially during 2009–2013). The volatility risk transmission channel can well explain the theoretical underpinnings behind spillovers, whereby asset markets are inter-related through their dynamic conditional correlation structure. The classic impact of a shock channeling through returns is conﬁrmed as well by this empirical study. By examining time-varying correlations, we are able to identify rising interdependencies between ﬁnancial and commodity markets – pointing to the ‘ﬁnancialization of commodity markets’ phenomenon (Tang and Xiong, 2012) – that are especially visible since 2008. This conclusion holds true for both volatility and return shocks. Besides, we attempt to build implications for asset managers. Finally, one central methodological contribution is brought to the attention of practitioners, related to the use of the ‘volatility surprise’ component (alongside other traditional measures of volatility) to apprehend fully the sensitivity of ﬁnancial markets to volatility shocks. The remainder of this paper is organized as follows. Section 2 opens with a presentation of the ADCCX model. Section 3 describes the data. Section 4 contains the empirical results, along with a sensitivity analysis. Section 5 reﬂects on the implications in terms of asset management. Section 6 concludes.

2. The model Vivid research areas in ﬁnancial econometrics have attempted to model the time-varying volatility of ﬁnancial returns. Indeed, capturing the time-varying correlations between different securities appears necessary for portfolio optimization, asset pricing and risk management. In this section, we outline the building blocks of this quest for modeling multivariate processes. The representation of the conditional covariance matrices adopted belongs to the DCC family.

2.1. The DCC family models Multivariate GARCH (henceforth, MVGARCH) models are useful developments regarding the parameterization of conditional dependence. Different classes of MVGARCH models have been Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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proposed in the literature.2 The ﬁrst-generation models were introduced by Bollerslev et al. (1988), as well as Engle and Kroner (1995). The numerical difﬁculties encountered with these models are linked to the large number of parameters to be estimated. Overparameterization will lead to a ﬂat likelihood function, making statistical inference intrinsically difﬁcult and computationally troublesome. To overcome these difﬁculties, Bollerslev (1990) has proposed a new class of MVGARCH model in which the conditional correlations are constant (CCC). Even with such a simple speciﬁcation, the estimation typically involves solving a high-dimensional optimization problem as, for example, the Gaussian likelihood function cannot be factorized into several lower dimensional functions. The CCC assumption is relaxed by Engle (2002) and Tse and Tsui (2002), who generalize Bollerslev’s (1990) model by making the conditional correlation matrix time-dependent. The dynamic conditional correlation (DCC) model constrains the time-varying conditional correlation matrix to be positive deﬁnite, and the number of parameters to grow linearly by following a two-step procedure. The ﬁrst step ﬁts each conditional variance with an univariate GARCH(1,1) model. The second step allows the computation of the dynamic conditional correlations given the conditional volatility estimated in the ﬁrst step. The log-likelihood is therefore written as a sum of a volatility part and a correlation part. This two-step estimation procedure provides adequate ﬁtting when the bivariate systems exhibit different dynamic correlation structures, and minimizes the biases that are inevitable in such an estimation strategy for the conditional correlation. Cappiello et al. (2006) extend the DCC model to account for asymmetries in the correlation dynamics. Their asymmetric DCC (ADCC) model ﬁts the leverage effects observed in equity markets better. Vargas (2008) introduces the ADCCX model, which allows for spillover effects. Therefore, it becomes possible to test for spillover effects in the correlation dynamics.3 Compared with the DCC method, the ADCCX approach involves modeling of inter-series dynamics. This paper makes use of the ADCCX model in order to gauge the spillover effects coming from the ‘volatility surprise’ component across equities, bonds, foreign exchange rates and commodities. Let us recall how to obtain ﬁrst the volatility surprise component and second, the ADCCX model that nests the ADCC model as a generalization of the DCC model. 2.2. The volatility surprise Following Engle (1993), we deﬁne the ‘volatility surprise’ as the volatility component that cannot be forecast. Consider the mean equation of a standard GARCH (1,1) speciﬁcation: rt = + t

(1)

with rt the asset price returns, the unconditional mean, and t = zt t the innovations. zt denotes a strong white noise, with E(zt ) = 0 and E(zt2 ) = 1. t denotes the conditional variance: V (rt |rt−1 ) = t2 , with rt−1 the historical information available at time t − 1. The purpose of the time-varying conditional t is to capture as much of the conditional variance in the residual t as follows: 2 t2 = ω + ˛2t−1 + ˇt−1

(2)

More speciﬁcally, Engle (1993) deﬁnes the so-called ‘volatility surprise’, ς , as the difference between the squared residuals 2t and the conditional variance t2 . For scaling purposes, we normalize ˜ , is given by: this quantity by the conditional variance t2 . The ‘normalized volatility surprise’, ς

ς˜t =

2t − t2 t2

(3)

2 One of the most general multivariate generalized auto-regressive conditional heteroskedasticity GARCH(p, q) models is the BEKK representation (Engle and Kroner, 1995). Although the form of this model is quite general, it suffers from overparameterization. Hence, we do not detail further BEKK-type models. For a survey, see Bauwens et al. (2006). 3 Sheppard (2008) proposes an alternative approach, whereby the conditional covariance matrix is a linear function of one or more exogenous variables, by using spectral decomposition. However, in this paper, we wish to employ Vargas’s (2008) model.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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The volatility surprise component for each univariate time series can be computed accordingly. It is easy to see that, once we have speciﬁed ς˜t , we obtain E(ς˜t |rt−1 ) = t2 .

E(2t |rt−1 )

|r )−t2 E(2 t t−1 t2

= 0, since by

= Hence, we are able to verify that – as a pre-requisite for an input to construction any MVGARCH model – the ‘volatility surprise’ computed in Eq. (3) is indeed mean-zero. 2.3. The ADCCX model ˜ ) represent, respectively, the price returns and the volatility surprise component. Let (rt ) and (ς The returns are computed as the logarithmic ﬁrst difference of the asset price, i.e. rt = log(Pt /Pt−1 ). Let xt be a n × 1 vector of spillover variables, be a n × 1 vector of parameters, and I be an n × n identity matrix. The variables (x1 , x2 , . . ., xn ) correspond to the cross-market spillover effects coming from the volatility surprises computed in Eq. (3). Let us consider the vectorial process t as representing the n × 1 vector of unpredictable observations (t or ς˜t ) at time t, which is assumed to be conditionally normal with mean zero and covariance n × n matrix Ht : t | t−1 ∼N(0, Ht )

(4)

with t−1 the information set at time t − 1. The conditional covariance matrix Ht can be decomposed as follows: Ht = Dt Rt Dt with Rt the n × n time-varying correlation matrix. Dt = diag

h1,t , . . .,

hi,t , . . .,

hn,t

(5) is the n × n

diagonal matrix of time-varying standard deviations extracted from univariate GARCH models with hi,t = i,t on the ith diagonal. The dynamic conditional correlation structure in matrix form is given by: Rt = Qt∗−1 Qt Qt∗−1

(6)

An element of Rt has the following form:

ij,t = Qt∗ = diag

qij,t

(7)

qii,t qjj,t

qii,t

is a diagonal matrix composed of the square root of the diagonal elements of

the covariance matrix Qt . The covariance matrix Qt of the ADCCX model evolves according to:

¯ − I x¯ + A et−1 e Qt = Q¯ − A Q¯ A − B Q¯ B − N t−1 A + B (Qt−1 ) B + t−1 t−1 + I xt−1

(8) where the unconditional covariance matrix Q¯ is composed of the n × n vector of standardized residu als ei,t = i,t computed from the ﬁrst stage procedure for which ei,t → N (0, Rt ). t = 1[et

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Contents lists available at ScienceDirect

Research in International Business and Finance j o ur na l ho me pa ge : w w w . e l s e v i e r . c o m / l o c a t e / r i b a f

Volatility returns with vengeance: Financial markets vs. commodities Soﬁane Aboura a, Julien Chevallier b,∗ a DRM Finance, Université Paris Dauphine, Place du Maréchal de Lattre de Tassigny, 75775 Paris Cedex 16, France b IPAG Business School (IPAG Lab), 184 Boulevard Saint-Germain, 75006 Paris, France

a r t i c l e

i n f o

Available online xxx

JEL classiﬁcation: C32 C4 G15 Keywords: Volatility spillovers Financial markets Commodities ADCCX

a b s t r a c t To assess how ﬁnancial markets and commodities are inter-related, this paper introduces a ‘volatility surprise’ component into the asymmetric DCC with one exogenous variable (ADCCX) framework. We develop an econometric model in which returns and volatility allow to inﬂuence pairs of assets, and derive several case studies linking commodities to stocks, bonds and currencies from 1983 to 2013. The innovative feature of our model is that these volatility spillovers are modeled consistently within the correlation dynamics of the ADCCX. We ﬁnd evidence that return and volatility spillovers do exist between commodity and ﬁnancial markets and that in turn, their relative impact on each other is very substantial. © 2014 Elsevier B.V. All rights reserved.

1. Introduction Understanding the origins of volatility has long been a topic of considerable interest to both policy makers and market practitioners. Policy makers are mainly interested in the main (possibly real) determinants of volatility, and in its spillover effects on real activity. Market practitioners – such as investment bankers – are mainly interested in the direct effects time-varying volatility exerts on the pricing and hedging of plain vanilla options and more exotic derivatives. In both cases, forecasting volatility constitutes a formidable challenge, but also a fundamental instrument to manage risks.

∗ Corresponding author. Tel.: +33 01 49 40 73 86; fax: +33 01 49 40 72 55. E-mail addresses: soﬁ[email protected] (S. Aboura), [email protected] (J. Chevallier). http://dx.doi.org/10.1016/j.ribaf.2014.04.003 0275-5319/© 2014 Elsevier B.V. All rights reserved.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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S. Aboura, J. Chevallier / Research in International Business and Finance xxx (2014) xxx–xxx

Since the ﬁnancial crisis of 2008, the topic of international volatility transmission across markets has once more attracted a considerable attention. Recent studies analyze the extent of cross-market linkages over different asset classes: ﬁnancial assets (Straetmans and Candelon, 2013; Wang et al., 2013), and commodities (Chng, 2009; Chan et al., 2011). Cross-sectional effects amongst ﬁnancial and nonﬁnancial assets constitute a central topic in asset pricing. However, we know little about how markets interact. How do shocks go from one market to others? Are these shocks able to contaminate assets belonging to other asset classes? Do commodities have a signiﬁcant inﬂuence on ﬁnancial markets? Whereas commodity markets price different risk factors from a linear asset pricing perspective, extreme events can still trigger contagion effects across markets.1 Spillovers actually encompass two kinds of phenomena: (i) directional shocks as documented recently by Diebold and Yilmaz (2012) and (ii) a contagion effect traditionally deﬁned by Forbes and Rigobon (2002) as a signiﬁcant increase in cross-market linkages after a shock. Regarding cross-market dependencies, the key point in spillover analyses is the equity-to-commodity relationship. Indeed, following the contribution by Gorton and Rouwenhorst (2005), investors have increasingly started to trust the diversiﬁcation effect that commodities could bring to their portfolio. A few spillover analyses have been devoted to the commodity-equity linkage. Most of the literature is based on dynamic correlation models that have been proposed following Engle’s (2002) DCC model and its extensions. These approaches aim at measuring how correlations across markets can move together – which is usually regarded as a measure of contagion. Literature on spillover analyses include, for example, Karolyi and Stulz (1996), Longin and Solnik (2001), Ang and Chen (2002) and Forbes and Rigobon (2002). Chong and Miffre (2010) ﬁnd that the correlation between standard assets and commodities is lower during periods of crisis, i.e. when diversiﬁcation effects are the most sought for. Silvennoinen and Thorp (2010) ﬁnd the exact opposite conclusion. During turbulent periods, these correlations are rising. Such disagreement may come from differences in terms of methodologies, or in terms of the periods covered in each dataset. Buyukshahin et al. (2010) ﬁnd that such correlation increases after 2008, casting some doubt around the commodity diversiﬁcation effect. Dasklaki and Skiadopoulos (2011), Bichetti and Maystre (2012) and Delatte and Lopez (2013) ﬁnd evidence consistent with these conclusions. Other types of econometric methodologies have been designed to capture cross-market linkages. For instance, copulas – a more general dependence structure than the underlying Gaussian model behind the dynamic correlation models – went through an increasing attention, as presented in Patton (2006), Jondeau and Rockinger (2006) and Rodriguez (2007) for standard assets; and in Reboredo (2011) in the case of commodities. Nevertheless, beyond their ability to measure tail dependence – i.e. joint extreme events – turning them into a dynamic measure of dependence turned out to be difﬁcult. Multivariate Markov Switching models also encompass in a certain way the measurement of cross time series dependence, as presented in Khalifa et al. (2012). Their ability to produce switches between two types of dependence structures led to interesting ﬁndings in ﬁnancial markets (Ielpo, 2012). Their numerical complexity when increasing the number of underlying variables is, however, a massive drag to their use to measure cross-market dynamics. This computational burden to estimate sophisticated speciﬁcations of such models in the case of cross-commodity measurement limitates their use. Diebold and Yilmaz (2012) have presented a new approach to measure cross-asset volatility spillovers through the historical cross-series mean reversion parameters. Their approach has been used in Yilmaz (2010), Kocenda et al. (2011) and da Fonseca and Gottschalk (2012), for example. The apparent simplicity and the efﬁciency of the estimates obtained turn this approach into a very promising one. In this article, we advance a methodological contribution related to the ﬁrst strand of literature, e.g. dynamic correlations models. Previous studies have mostly examined the spillovers in multivariate GARCH-type models (Engle et al., 1990; Hassan and Malik, 2007; Cai et al., 2008). In contrast with previous works, this paper focuses on volatility interactions between equities, bonds, foreign exchange rates and commodities, as further evidence is emerging for volatility to be autocorrelated within its

1 Whereas ‘contagion’ is deﬁned later in the paper, the study of returns ‘co-movements’ begins with Grubel (1968), who explains ﬁrst the beneﬁts from international diversiﬁcation.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

G Model RIBAF-307; No. of Pages 21

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3

own market and also to be cross-correlated with volatility in other asset markets (Hakim and McAleer, 2010)). We propose an alternative for modeling cross-market relations with multivariate volatility processes, on the basis of the asymmetric dynamic conditional correlation model with one exogenous variable (ADCCX) newly deﬁned by Vargas (2008). This model represents a parsimonious speciﬁcation for measuring cross-market relations. It is ﬂexible in the sense that each market’s shock may be ﬁtted separately as a spillover on any combination of bivariate volatility models. Computationally, Vargas (2008) has established the consistency of the estimates in presence of high-dimensional optimization problems. The methodology proposed is applied to commodity and ﬁnancial markets. Our original idea lies in using the ‘volatility surprise’ component to capture cross-market relationships, and to understand how volatility interacts with returns. According to Engle (1993), it is the difference that cannot be forecast between squared residuals and the conditional variance which is worthy of interest. Such a quantity has been coined ‘volatility surprise’. This new concept paved the way for numerous studies (Bae and Karolyi, 1994; Abhyankar, 1995; Chan-Lau and Ivaschenko, 2003; Kim and Rogers, 1995; Niarchos et al., 1999; Tse et al., 2003; Wei et al., 1995). As an extension to the work of Hamao et al. (1990), our key contribution is to document the spillover effects coming from volatility surprises to returns, and vice versa. The two-step econometric methodology consists of (1) computing the mean-zero ‘volatility surprise’ component from univariate GARCH models and (2) plugging it into the ADCCX model. We investigate (i) volatility surprise spillovers on pairwise returns, and (ii) return spillovers on pairwise returns. The dataset includes four aggregate indices from 1983 to 2013. The results provide strong evidence of spillover effects coming from the ‘volatility surprise’ component across markets. We further investigate the reliability of our results in the aftermath of the 2008 ﬁnancial crisis. In addition, asset management implications are derived. To summarize our results, we show that setting the ‘volatility surprise’ component as a spillover variable yields strong volatility transmission effects in the ADCCX framework (especially during 2009–2013). The volatility risk transmission channel can well explain the theoretical underpinnings behind spillovers, whereby asset markets are inter-related through their dynamic conditional correlation structure. The classic impact of a shock channeling through returns is conﬁrmed as well by this empirical study. By examining time-varying correlations, we are able to identify rising interdependencies between ﬁnancial and commodity markets – pointing to the ‘ﬁnancialization of commodity markets’ phenomenon (Tang and Xiong, 2012) – that are especially visible since 2008. This conclusion holds true for both volatility and return shocks. Besides, we attempt to build implications for asset managers. Finally, one central methodological contribution is brought to the attention of practitioners, related to the use of the ‘volatility surprise’ component (alongside other traditional measures of volatility) to apprehend fully the sensitivity of ﬁnancial markets to volatility shocks. The remainder of this paper is organized as follows. Section 2 opens with a presentation of the ADCCX model. Section 3 describes the data. Section 4 contains the empirical results, along with a sensitivity analysis. Section 5 reﬂects on the implications in terms of asset management. Section 6 concludes.

2. The model Vivid research areas in ﬁnancial econometrics have attempted to model the time-varying volatility of ﬁnancial returns. Indeed, capturing the time-varying correlations between different securities appears necessary for portfolio optimization, asset pricing and risk management. In this section, we outline the building blocks of this quest for modeling multivariate processes. The representation of the conditional covariance matrices adopted belongs to the DCC family.

2.1. The DCC family models Multivariate GARCH (henceforth, MVGARCH) models are useful developments regarding the parameterization of conditional dependence. Different classes of MVGARCH models have been Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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proposed in the literature.2 The ﬁrst-generation models were introduced by Bollerslev et al. (1988), as well as Engle and Kroner (1995). The numerical difﬁculties encountered with these models are linked to the large number of parameters to be estimated. Overparameterization will lead to a ﬂat likelihood function, making statistical inference intrinsically difﬁcult and computationally troublesome. To overcome these difﬁculties, Bollerslev (1990) has proposed a new class of MVGARCH model in which the conditional correlations are constant (CCC). Even with such a simple speciﬁcation, the estimation typically involves solving a high-dimensional optimization problem as, for example, the Gaussian likelihood function cannot be factorized into several lower dimensional functions. The CCC assumption is relaxed by Engle (2002) and Tse and Tsui (2002), who generalize Bollerslev’s (1990) model by making the conditional correlation matrix time-dependent. The dynamic conditional correlation (DCC) model constrains the time-varying conditional correlation matrix to be positive deﬁnite, and the number of parameters to grow linearly by following a two-step procedure. The ﬁrst step ﬁts each conditional variance with an univariate GARCH(1,1) model. The second step allows the computation of the dynamic conditional correlations given the conditional volatility estimated in the ﬁrst step. The log-likelihood is therefore written as a sum of a volatility part and a correlation part. This two-step estimation procedure provides adequate ﬁtting when the bivariate systems exhibit different dynamic correlation structures, and minimizes the biases that are inevitable in such an estimation strategy for the conditional correlation. Cappiello et al. (2006) extend the DCC model to account for asymmetries in the correlation dynamics. Their asymmetric DCC (ADCC) model ﬁts the leverage effects observed in equity markets better. Vargas (2008) introduces the ADCCX model, which allows for spillover effects. Therefore, it becomes possible to test for spillover effects in the correlation dynamics.3 Compared with the DCC method, the ADCCX approach involves modeling of inter-series dynamics. This paper makes use of the ADCCX model in order to gauge the spillover effects coming from the ‘volatility surprise’ component across equities, bonds, foreign exchange rates and commodities. Let us recall how to obtain ﬁrst the volatility surprise component and second, the ADCCX model that nests the ADCC model as a generalization of the DCC model. 2.2. The volatility surprise Following Engle (1993), we deﬁne the ‘volatility surprise’ as the volatility component that cannot be forecast. Consider the mean equation of a standard GARCH (1,1) speciﬁcation: rt = + t

(1)

with rt the asset price returns, the unconditional mean, and t = zt t the innovations. zt denotes a strong white noise, with E(zt ) = 0 and E(zt2 ) = 1. t denotes the conditional variance: V (rt |rt−1 ) = t2 , with rt−1 the historical information available at time t − 1. The purpose of the time-varying conditional t is to capture as much of the conditional variance in the residual t as follows: 2 t2 = ω + ˛2t−1 + ˇt−1

(2)

More speciﬁcally, Engle (1993) deﬁnes the so-called ‘volatility surprise’, ς , as the difference between the squared residuals 2t and the conditional variance t2 . For scaling purposes, we normalize ˜ , is given by: this quantity by the conditional variance t2 . The ‘normalized volatility surprise’, ς

ς˜t =

2t − t2 t2

(3)

2 One of the most general multivariate generalized auto-regressive conditional heteroskedasticity GARCH(p, q) models is the BEKK representation (Engle and Kroner, 1995). Although the form of this model is quite general, it suffers from overparameterization. Hence, we do not detail further BEKK-type models. For a survey, see Bauwens et al. (2006). 3 Sheppard (2008) proposes an alternative approach, whereby the conditional covariance matrix is a linear function of one or more exogenous variables, by using spectral decomposition. However, in this paper, we wish to employ Vargas’s (2008) model.

Please cite this article in press as: Aboura, S., Chevallier, J., Volatility returns with vengeance: Financial markets vs. commodities. Res. Int. Business Finance (2014), http://dx.doi.org/10.1016/j.ribaf.2014.04.003

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5

The volatility surprise component for each univariate time series can be computed accordingly. It is easy to see that, once we have speciﬁed ς˜t , we obtain E(ς˜t |rt−1 ) = t2 .

E(2t |rt−1 )

|r )−t2 E(2 t t−1 t2

= 0, since by

= Hence, we are able to verify that – as a pre-requisite for an input to construction any MVGARCH model – the ‘volatility surprise’ computed in Eq. (3) is indeed mean-zero. 2.3. The ADCCX model ˜ ) represent, respectively, the price returns and the volatility surprise component. Let (rt ) and (ς The returns are computed as the logarithmic ﬁrst difference of the asset price, i.e. rt = log(Pt /Pt−1 ). Let xt be a n × 1 vector of spillover variables, be a n × 1 vector of parameters, and I be an n × n identity matrix. The variables (x1 , x2 , . . ., xn ) correspond to the cross-market spillover effects coming from the volatility surprises computed in Eq. (3). Let us consider the vectorial process t as representing the n × 1 vector of unpredictable observations (t or ς˜t ) at time t, which is assumed to be conditionally normal with mean zero and covariance n × n matrix Ht : t | t−1 ∼N(0, Ht )

(4)

with t−1 the information set at time t − 1. The conditional covariance matrix Ht can be decomposed as follows: Ht = Dt Rt Dt with Rt the n × n time-varying correlation matrix. Dt = diag

h1,t , . . .,

hi,t , . . .,

hn,t

(5) is the n × n

diagonal matrix of time-varying standard deviations extracted from univariate GARCH models with hi,t = i,t on the ith diagonal. The dynamic conditional correlation structure in matrix form is given by: Rt = Qt∗−1 Qt Qt∗−1

(6)

An element of Rt has the following form:

ij,t = Qt∗ = diag

qij,t

(7)

qii,t qjj,t

qii,t

is a diagonal matrix composed of the square root of the diagonal elements of

the covariance matrix Qt . The covariance matrix Qt of the ADCCX model evolves according to:

¯ − I x¯ + A et−1 e Qt = Q¯ − A Q¯ A − B Q¯ B − N t−1 A + B (Qt−1 ) B + t−1 t−1 + I xt−1

(8) where the unconditional covariance matrix Q¯ is composed of the n × n vector of standardized residu als ei,t = i,t computed from the ﬁrst stage procedure for which ei,t → N (0, Rt ). t = 1[et