Systemic risk spillovers between crude oil and stock index returns of G7 economies: Conditional value-at-risk and marginal expected shortfall approaches

Journal Pre-proof Systemic risk spillovers between crude oil and stock index returns of G7 economies: Conditional value-at-risk and marginal expected shortfall approaches

Aviral Kumar Tiwari, Nader Trabelsi, Faisal Alqahtani, Ibrahim D. Raheem PII:

S0140-9883(19)30443-8

DOI:

https://doi.org/10.1016/j.eneco.2019.104646

Reference:

ENEECO 104646

To appear in:

Energy Economics

Received date:

29 August 2018

Revised date:

22 October 2019

Accepted date:

14 December 2019

Please cite this article as: A.K. Tiwari, N. Trabelsi, F. Alqahtani, et al., Systemic risk spillovers between crude oil and stock index returns of G7 economies: Conditional valueat-risk and marginal expected shortfall approaches, Energy Economics(2020), https://doi.org/10.1016/j.eneco.2019.104646

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Journal Pre-proof

Systemic risk spillovers between crude oil and stock index returns of G7 economies: conditional value-at-risk and marginal expected shortfall approaches Aviral Kumar Tiwari Rajagiri Business School, Rajagiri Valley Campus, Kochi, India Email: [email protected] Nader Trabelsia,b Department of Finance and Investment, College of Economics and Administrative Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), PO Box 5701, Riyadh, Saudi Arabia. b University of Sfax, B.P. 3018 Sfax, Tunisia - LARTIGE; e.mail: [email protected]

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Faisal Alqahtani Department of Finance and Economics Taibah University, Saudi Arabia Email: [email protected]

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Ibrahim D. Raheem School of Economics, University of Kent, Canterbury, the United Kingdom Email: [email protected]

Abstract

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In this study, we examine systemic risk and dependence between oil and stock market indices of G7 economies between January 2003 and November 2017. Coincidentally, this timeframe covers different distress periods in financial and energy markets. We use several time-constant, time-varying and time-varying Markov-copula models to examine the dependence. Further, we use the delta conditional value-at-risk (ΔCoVaR) of Adrian and Brunnermeier (2016) and marginal expected shortfall (MES) of Acharya et al. (2012) to captures the risk spillover effects and give evidence of systemic risk. From the copula analysis, we find dissimilar dependence structure between returns series of oil and the G7 stock markets. For France, Germany and Japan, the dependence is Markov-switching time-varying, while it is time-varying for the United States and Canada, constant for the United Kingdom and around zero for Italy. Our empirical evidence on systemic risk indicates that oil price dynamics contributes significantly more to the G7 stock market returns during volatile times than during tranquil times. In particular, the Canada stock market appears more sensitive and vulnerable to negative external shocks emerging from the crude oil market than the other markets. Further, the country risk rankings identified using MES and ΔCoVaR may not be identical. In addition, the analysis results suggest that the crude oil market can be a good diversifier for investors in Japan and France and that the investors in the rest of G7 countries must act more carefully.

JEL Classification: C58; G01; G23; G32 Keywords: CoVaR; MES; Systemic risk; Oil prices; Stock markets; G7

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1. Introduction Throughout history, oil has played a significant role in affecting different aspects of economic development in advanced as well as developing economies. The literature has focused on the effect of oil prices on economic variables. For instance, Hamilton (1983) suggests that a surge in oil prices affects the real gross national product negatively in the United States. Similarly, on considering other advanced economies, Gilbert and Mork (1984) and Mork et al. (1994) find support for Hamilton’s (1983) early findings. A later stream of literature focuses on the impact of oil on aggregate stock

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markets (Phan et al., 2015) and disaggregate stock markets (Tiwari et al., 2018). Ross (1989) is among the earliest to identify that volatilities of different classes of assets

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likely influence each other. Huang et al. (1996) highlight the importance of volatilities, suggesting that oil and stock market relationships could possibly be

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understood through their volatilities. In more detail, according to the equity valuation theory, stock returns are affected by changes in future cash flows and discount rates.

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Hence, a surge in oil prices might have either positive or negative effects on future cash flows of a firm, depending on whether the firm is a producer or consumer of oil

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(Mohanty et al., 2011; Wang & Liu, 2016)

A substantial body of literature has investigated the volatility spillover

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between oil and stock markets in advanced markets (see Arouri & Nguyen, 2010;

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Ewing & Malik, 2016; Kang et al., 2015; Khalfaoui et al., 2015; Mensi et al., 2013; Mohanty et al., 2011; Narayan & Gupta, 2015; Narayan & Sharma, 2014; Phan et al., 2015; Phan et al., 2016), and in emerging markets (see; Arouri & Rault, 2012; Bouri, 2015; Ding et al., 2017; Hamdi et al., 2018; Hammoudeh & Aleisa, 2004; Mohanty et al., 2011; Zheng & Su, 2017). However, no study to date has investigated the tail dependence and the possible systemic impact of oil price fluctuations on the stock market. Tail dependence explains the degree of dependence in the upper and lower quadrant of the tail. The examination of tail dependence offers detailed information on the dependence structure. Such analysis would allow us to determine whether oil price volatility and stock markets are dependent or independent, that is, whether extremely high (low) oil prices are asymmetrically or symmetrically dependent on stock markets.

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Journal Pre-proof Hence, the present study attempts to fill this gap, contributing to the existing body of literature in two ways: at the methodological level and data level. First, at the methodological level, we employ two relatively newly developed approaches, the conditional value-at-risk (CoVaR) and marginal expected shortfall (MES), which were proposed in direct response to the shortcomings of the traditional approaches during the 2007–2009 global financial crisis (GFC; Boucher et al., 2013). CoVaR is a systemic risk measure proposed by Adrian and Brunnermeier (2016)1 . It detects possible spillover of systemic risk between two markets by giving information on the value-at-risk (VaR) of a market, conditional on the other market that is perceived to

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be under financial distress (Reboredo & Ugolini, 2015). We compute CoVaR estimates using quantile regression (Adrian & Brunnermeier, 2016). A few studies attempt to measure the CoVaR between different markets. For instance, Reboredo

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(2015) investigates systemic risk and dependence between oil and renewable energy

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markets in the United States; Reboredo and Ugolini (2015) examine systemic risk in European sovereign debt markets before and during the Greek debt crisis; Reboredo et

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al. (2016) study systemic risk spillovers between currency and stock markets in emerging economies; Petrella et al. (2018) employ the CoVaR method to examine

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the systemic risk in the equity market of the Eurozone, focusing on the contribution of main European firms on the systemic risk; Laporta et al. (2018) use multiple

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extensions of VaR-related models to quantify the systematic risk of seven energy

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commodities; Karimalis and Nomikos (2018) to model systemic risk in the European banking sector; and Borri (2019) use CoVaR to model the conditional tail risk of cryptocurrencies with global assets.

Our second measure for systemic risk is MES, which assesses the short- and long-run expected equity loss of firms when the market falls below a certain level over a given period (Benoit et al., 2013). The short-run MES is defined as a 2% market drop over one day, and the long-run MES (LRMES) is defined as a 40% market drop for six months. Our second

contribution, namely, at the data level, arises from the

international evidence on the effect of oil prices on stocks volatilities. Unlike most of existing evidence that mainly focuses on the U.S. market, the present study examines

1

The early version of this paper was released in 2011

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Journal Pre-proof the effects of oil prices on G7 developed markets, which Feng et al. (2017) highlight. The G7 economies are the most significant and developed economies worldwide, accounting for 64% of the total global wealth as well as 46% of the global gross domestic product (International Monetary Fund, 2016). In addition, their economies show significant variations in regard to policy involvement, economic structure and financial regulations, and hence, the comparative analysis of their stock market responses to oil price shocks is tremendously useful (Bastianin et al., 2016). Unlike the European Union (EU), the G7 is an informal forum of the world’s leading

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industrialized. Despite this difference, the group has deep economic ties, which are

Outlook,

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responsible for a third of the global economic output (source: World Economic International Monetary Fund

(IMF)).

In addition, there is a high

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coordination between these national leads in terms of their policy initiatives such as global economic governance, international security, and energy policy. This means

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that any trouble of any G7 state has a highly significant impact on all other countries.

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The systemic risk is hence increasingly evident. This leads to following research hypothesis:

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Hypothesis: Due to their outstanding importance in the demand of the energy, and

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regardless of their high industry and funds connections, the oil price volatility transmit to the G7 economies by increasing the volatility of stock markets, which

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ultimately increase the systemic dimension of the stock price risk. To account for the fact that stock markets may respond differently to oil price shocks, we have first examined the relationship using time constant, time-varying and time-varying Markov-copula models. Then, to show whether this link is systemic for all the G7 countries, we use the conditional value-at-risk (CoVaR) and marginal expected shortfall such measures are important to evaluate tail dependence during turmoil periods. To the best of our knowledge, our present study is one of the earliest attempts to investigate the systemic risk spillovers between the oil market and stock markets using the aforementioned measures. A deeper understanding of the volatility spillover effect may help investors and policymakers design sound investment and risk management

strategies

and

efficient

macroeconomic

respectively. 4

and

energy

policies,

Journal Pre-proof We find that the dependence structure between tail oil price changes and the G7 stock market returns is dissimilar for the countries under investigation. For France, Germany and Japan the dependence is Markov-switching time-varying, while it is time-varying for the United States and Canada, constant for the United Kingdom and around zero for Italy. Further, the G7 set has a greater risk of spillovers during volatile times than during normal or tranquil times. In particular, the Canada stock market appears more sensitive and vulnerable than the others to the negative external shocks from the crude oil market, owing to its economic dependence on export income from oil.

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The remainder of this paper is organised as follows. Section 2 presents a review of the related literature. Section 3 describes the data and methodology used to analyse the volatility spillover effect of oil prices on G7stock markets. Section 4

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contains the empirical results. Finally, Section 5 concludes the paper.

2. Brief Literature Review

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Only recently, studies have empirically examined the oil and stock market volatility nexus. A vast body of empirical evidence has attempted to comprehend the ways in

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which volatility brings about the effect of oil prices on stock returns in advanced and emerging economies. However, our focus in this section is devoted to prior empirical

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evidence on G7 countries as a whole and individually, to make our empirical findings

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comparable and to extend their findings. In the G7 context as a whole, studies are limited to date and their results are ambiguous. Khalfaoui et al. (2015) study the mean and volatility spillovers between the oil market (WTI) and stock markets using an innovative approach that incorporates bivariate GARCH–BEKK models and wavelet-based MGARCH. Their results indicate the presence of significant volatility spillovers between oil and stock markets. In addition, they find time-varying correlations for several market pairs. Yet, the wavelet coherence results show that the stock markets were led by the WTI market. Feng et al. (2017) revisit the oil–stock nexus in the G7 context using oil volatility risk

premium as the predictor. After controlling for some popular

macroeconomic variables, they find statistically and economically significant effects of oil prices on stock markets both in-sample and out-of-sample.

5

Journal Pre-proof Bastianin et al. (2016) examine the impact of oil price shocks on the volatility of the stock market of the G7 economies. They find that the volatility of the stock markets does not react to oil supply shocks. In contrast, oil demand shocks influence the volatility of the G7 stock markets significantly. On the contrary, Lee et al. (2012)—in their study that covers the 1991–2009 period—find that oil price changes do not significantly influence the index in each G7 member country. Nevertheless, they find that stock price fluctuations in the United States, the United Kingdom and Germany lead to oil price fluctuations. Empirical evidence for the United States offers inconclusive findings. Some

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studies find significant volatility spillovers from oil prices to stock markets. Choi and Hammoudeh (2010) examine the effects of oil price volatility on the S&P500 index using dynamic conditional correlations (DCCs). They find that high and low volatility

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regimes exist, which then they use to draw implications for investors. Narayan and

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Gupta (2015) analyse monthly data for over 150 years using a predictive regression model. They reveal that oil price predicts stock returns in both in-sample and out-of-

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sample. They also find that negative oil shocks predict stock returns relatively better. Narayan and Sharma (2014) study whether oil prices influence stock return volatility

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of 560 firms listed on the New York Stock Exchange using the GARCH (1,1) model as well as a variance predictive regression model. They find that oil price is a

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significant predictor of firm return volatility, concluding that investors can earn

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significant gains in returns by employing oil prices to forecast. Liu et al. (2017) use a wavelet-based GARCH–BEKK model to qualify the spillover effect between oil and the American stock market in multiple frequency dimensions. They find that the volatility spillover between oil and the stock market is changing to short term but is fading in the long term. In a more recent study, Bastianin and Manera (2018) examine the influence of oil price shocks on the U.S. stock market volatility using a structural vector autoregressive model. In their analysis, the authors distinguish between three types of oil price shocks: aggregate demand, oil supply and oil-specific demand. Their findings indicate that the U.S. stock market responds significantly to oil price shocks triggered by unexpected changes in aggregate and oilspecific demand but not oil supply shocks. Other studies on the United States, such as Kang et al. (2015), find the volatility to be bidirectional. Vo (2011) studies the interdependence between the S&P500 index and WTI oil price volatilities over 1999–2008. Unlike previous 6

Journal Pre-proof studies, the author reveals the presence of mutual interdependence between both market volatilities. Similar findings are obtained by Mensi et al. (2013), who study oil–stock volatility using WTI as well as Brent oil prices. They reveal that positive bidirectional effects exist between S&P500 and WTI volatilities, but their findings do not hold in the case of the Brent volatility. More recently, Ewing and Malik (2016) showed affirmed this with similar findings of Vo (2011) and Mensi et al. (2013). They find strong cross-market volatility effects. Comparable results are reported for the futures markets of crude oil, S&P500 and NASDAQ as well, confirming the presence of cross-market volatility impact (Phan et al., 2016).

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Finally, as regards Europe, Arouri and Nguyen (2010) investigate volatility spillovers between oil and stock markets in several European economies through GARCH-type models. They find bidirectional volatility spillovers between oil prices

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3. Data and Methodology

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and stock markets; however, the spillovers from oil to stock markets are stronger.

3.1. Data and descriptive statistics

We examine daily data from January 01/03/2003 to 30 November 2017. Based we calculate continuously compounded returns,

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on daily closing prices,

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for each G7 stock market i at day t. This sample period is marked by several extreme events and turbulences including the mid-2003 Iraq invasion, the

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2007–2009 GFC and the 2009–2012 eurozone debt crisis. This period is also characterised by higher oil price volatility. To measure oil price, we used data of West Texas Intermediate (WTI), Brent Blend and Dubai/Oman) collected from the US Energy Information Administration (EIA) globally accepted benchmarks measures. While Brent is the reference for about two-thirds of the oil traded around the world, with WTI the dominant benchmark in the U.S. and Dubai/Oman influential in the Asian market. Since, we have data of stock indices of all other developed markets and we wanted to provide a comparison between US and other G7 we preferred to use WTI as benchmark. Further, we also preferred to use WTI as benchmark oil price because prior to 2011, WTI traded at a dollar or two premium over Brent and another dollar or two premium over the OPEC basket and only after 2011 Brent is traded at higher price than WTI. Besides, our data start from 2003 justifying the choice of use of WTI oil price as benchmark.

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Journal Pre-proof Following the extant literature, we used the conventional/traditional stock indices for the G-7 countries (for instance, see Khalfaoui et al. 2015 and Feng et al. 2017). In essence, the indices used are: S&P500 (United States); FTSE100 index (United Kingdom); NIKKEI 225 (Japan); CAC40 Index (France); DAX 30 performance index (Germany); FTSE MIB (Italy) and S&P/TSX (Canada). Table 1 reports the descriptive statistics over the period. [Insert Table 1 here]

The statistics relating to oil and stock market indices are quite similar. At the

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country level, we find an insignificant difference, especially in terms of couple meanrisk returns. The higher risk is attributed to the oil market. This can be because of the oil price instability in the past decades, particularly the two upward crises or supply

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crises, in late 2003 (the price rose above US$30 following the Iraq invasion) and

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during 2009–2012 (the oil price sharply rebounded after the crisis and hit $100 a barrel on 31 January 2011). The oil market has also experienced two substantial

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downward crises or demand crisis, in late 2008 (the oil price fell from its July 2008 record of US$147.30 to US$32 in December 2008) and from mid-2014 to late 2016 (after

2014).

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a slightly higher period from 2009 to late 2013, the oil price fell again to US$40 in mid-

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Conversely, negative values for skewness are more pronounced for stocks than for

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the oil market. All return series show a coefficient of kurtosis significantly in excess of the normal distribution reference value. This means that data have a heavy tail. In fact, the Jarque–Bera test strongly rejects normality of unconditional distribution for all series. The results of the unit root test (Dickey and Fuller, 1979) and the KPSS stationary test confirm the stationarity. Additionally, Pearson’s Chi-square test reveals a high chi-square value and a p-value of more than 0.10 significance level. Therefore, we accept the null hypothesis and conclude that G7 stock market returns and daily oil price changes do not have, in the median, a significant relationship. This can also be confirmed by the unconditional correlation measures with constant values near zero. However, it is known that the relation between financial asset returns is not stable over time but rather time-varying. In addition, there is strong evidence that the link between financial series tends to be more pronounced during downturns rather than upturns. For that reason, our analysis now focuses on dependence models with timevarying properties on down days. 8

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3.2. Econometric models There are three main parts in our methodology. First, we introduce the Asymmetric Spline-GARCH model of Engle and Rangel (2008) used to analyse our oil and G7 stock market datasets. Secondly, we present the fundamental properties of the copula and then propose the application of the time-varying Markov-switching copula to evaluate the dependence structure between markets. In this stage, the fitted models of the first stage (i.e., Asymmetric Spline-GARCH parameters) are used to construct the joint distribution. Thirdly, we introduce two cross sectional distribution of marginal

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systemic risk measures such as, Delta Conditional Value-at-Risk and Marginal

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expected Shortfall (MES). These measures are used as a second alternative to provide clear and consistent information on interactions between Oil and stock returns in the

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G4 economies.

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3.2.1. The model of marginal distribution

Appendix 2),

the univariate

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We propose, among the known multivariate GARCH models available (see Asymmetric Spline-GARCH model of Engle and

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Rangel (2008) with Skewed-t innovations2 to estimate oil and G7 stock market returns. This model also has the potential to capture both short- and long-term dynamic

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behaviour of market volatility. This is formulated for each series

,

√

where

∑

,

and

as:

(1)

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∑

with

(2) (3)

are the AR and MA parameters with m and n lags, respectively.

is

the unconditional variance that changes smoothly as a function of time. The factor is an exponential quadratic spline function with k knots multiplied by another available GARCH (p, q) component: ∑ (

( ∑

) [

∑

∑ ] ),

2

,

(4) (5)

From Appendix 2, the comparison between different models with three different distributio n errors, reveals (1) skew-t distribution in our model outperforms across all the series (except the America series). (2) some models are good for some series but not for others, then using different marginal models for different series will complicate the issue when we must compare our results and draw findings. (3) there are in certain cases a convergence problem, serial correlation and ARCH effect. Thus, using Skew-Student-t distribution innovations and making adjustments to the knots we could solve these issues.

9

Journal Pre-proof where ω,

,

and

for i = 0,1,…,k are parameters,

{ {

= 0,

,…,

(6) } are time indices partitioning the time span into k equally spaced

intervals. In this study, the number is limited to five knots. The specification of

may be chosen among other available GARCH equations

provided that E( ) = 1 (which implies an identification constraint for the intercept). A slightly different specification than the above equation is implemented. Indeed, the spline function is specified as follows: + ),

(7)

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*

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∑

(

where the trend variables have been re-scaled to fall between 0 and 1 to avoid numerical

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problems during optimisation. Note that the optimal numbers of m, n, p and q lags of each series are selected according to Akaike information criterion (AIC) and the Log-Likelihood

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function (LL).

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3.2.2. Copula approach

Karimalis et al. (2014) and Reboredo and Ugolini (2015), among others, show that the

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study of dependence is well suitable in the framework of the copula approach. This

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approach provides greater flexibility to specify the models for the dependence structure from marginal distributions. Particularly, it is related to some dependence

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concepts (e.g. linear correlation, concordance, tail dependence, positive quadrant dependency, etc.) and some other statistical measures such as Kendall’s tau, Pearson’s rho, and index of tail dependency (Cherubini et al., 2004; Hu, 2006). The famous theorem of Sklar (1959) yields the connection between marginal distributions and copulas to the joint distribution. If F X and FY denote the marginal distributions, then there exists a two-dimensional copula cumulative distribution function C on [0, 1], such that for all (x, y)

̿

FX Y(x, y) = C(FX(x), FY(y)),

(8)

For continuous FX and FY, C is uniquely determined by C(u, v) = FX Y (F−1 X(u), F−1 Y(v) ),

(9)

where u = FX(x) and v = FY(y) (i.e., obtained by the probability integral transform) are uniformly distributed on [0,1], and F−1 X(u) and F−1 Y(v) are the generalised inverse distribution functions of the marginal F X and FY. 10

Journal Pre-proof To identify the copula functions that lead to the best fit to our data, we focus on tail dependence measures that describe the degree of dependence in the upper and lower quadrant tail. Formally, Sibuya (1959) and Joe (1997) define the upper and lower tail dependence coefficients as follows: (

)

(10)

(

)

(11)

and

[

where

] denote upper and lower tail dependence, respectively. For

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there is no tail dependence.

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In this study, apart from the application of a battery of copula specifications with different feature dependencies and static and time-varying parameters3 , we focus on the

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Engle and Rangel (2008) conditional copula model including a hidden Markov chain.

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3.2.3. Time-varying Markov-switching copula approach

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A wide consensus exists in the literature that preceding financial crises have additionally increased the dependence structure between assets (see, e.g., Baur, 2013;

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Delatte & Lopez, 2013; Garcia & Tsafack, 2011; Lombardi & Ravazzolo, 2016). One approach to account for the different levels of dependence is to switch between

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different copula models. In this study, we use two different conditional copula

two

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approaches, a version without regime-switching (i.e., different

states

[

) and one that allows for

] (with

Considering

transition

Probabilities

,a

two-dimensional

time series vector, the copula model may be expressed as the form ( where

)

(12)

is the copula function with time-varying dependence parameter ,

and

are the univariate distributions specified in the first stage by

the spline-GARCH model. The dependence parameter,

, of copula C, is allowed to

vary through time t. As Patten (2006), the time evolution can be captured by a restricted ARMA(1,10) process. The intercept term can switch according to a firstorder Markov chain, that is, 3

See Appendix 1 for more details.

11

Journal Pre-proof ( where

)

(12)

is a logistic transformation of each copula function that constrains the

dependence parameter in the interval [0, 1]. For the Student-t and Normal copulas, we use , and for the Archimedean copulas,

.

We compare the performance of our proposed approach with regime switching with that without regime switching, which implies dependence parameter

in Eq. (12). The

is determined by a constant

autoregressive term,

that switches, a first-order

and a forcing variable,

, whose representation

(

(

)

∑

)

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{ The forcing variable

(

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∑

)

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∑

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depends on the copula:

is necessary to account for possible time variation in dependence.

In line with Patton (2006), a two-stage maximum likelihood (ML) approach is

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used to estimate parametric copulas.4

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3.2.4. Systemic risk analysis: ΔCoVaR and MES measures Recall that we follow two ways to measuring the contribution of the Oil market to the overall risk of the G7 stock markets. The first approach is related to copula approach, while the second deals with the two popular systemic risk measures, called and MES measures. ΔCoVaR As originally proposed by Adrian and Brunnermeier (2016), CoVaR detects the possible risk of spill over between two markets by giving information on the VaR of a stock market, conditional on the other stock market being under extreme events

4

See Appendix 4 for more details about the Copula estimation procedure.

12

Journal Pre-proof (Reboredo & Ugolini, 2015). The unconditional VaR, used to define for example the risk of the i’s stock market at the q-quantile of the conditional distribution5 , is simply: (

)

(13)

is typically a negative number, which can be defined by the marginal models as

, where

using eq. (1)-(7), and where

and

are the mean and variance, computed

designed to capture the q-quantile of the data from

the skewed t-distribution. According to Adrian and Brunnermeier (2016), the CoVaR measure is expressed for

P(Xi

| Xoil

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each t as: ) = q,

(14)

changes, Δ

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While CoVaR estimates the size of the tail distribution of the i’s stock market and how it can be used to capture particular G7 stock market returns (denoted by

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i) when the crude oil market (denoted by oil) experiences a return equal to the q-quantile of

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its unconditional return distribution. By definition,

is the difference between its 6

CoVaR when the crude oil market is, or is not, in distress : −

(15)

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MES

=

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Δ

Our second measure for marginal systemic risk is MES. Originally, Acharya,

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Pedersen, Phillipon and Richardson (2010) define this measure of market ‘i’ as its expected equity loss conditional on the other stock market incurring a loss greater than its VaR(q) or the average return of market ‘i’ on the α% worse days when the other market is on the tail of its distribution. In this study, the MES for each G7 stock market ‘i’ corresponds to the conditional mean of the stock return market return

based on the oil

being at or less the sample q-quantile. (16)

Higher levels of MES imply that the G7 stock market ‘i’ is more likely to be undercapitalised and thus more exposed to bad states of the oil market. The short- and long-run MES analyses are performed in line with Benoit, Colletaz, Hurlin and Pérignon (2013). The short-run MES (denoted by MES) permits 5

6

See Kupiec (2002) and Jorion (2006) for overviews. In this study, we retain CoVaR in absolute value in line with previous studies. A high or positive argues the exposition of G7 economies to oil market distress.

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Journal Pre-proof assessment of daily G7 equity loss when crude oil market truncated below a certain level or threshold fixed to the unconditional oil market daily VaR(q). The long-run MES (denoted by LRMES) is deduced from the short-run MES measure by using the expected loss over a six-month horizon. For the threshold value C = −2%, Acharya, Engle and Richardson (2012) proposed an approximation of the LRMES without simulation exercises. This approximation represents the expected loss over a sixmonth horizon, obtained conditionally on the whole market falling by more than 40% within the subsequent six months. A growing body of literature has proposed numerous alternatives to the CoVaR

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and MES quantitative measures using different approaches and data. In this study, estimators are computed using a parametric method recognised by the DCC-GARCH model (Girardi & Ergün, 2013). For the robustness check of our results, we also

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consider two other methods: the quantile regression as developed by Adrian and

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Brunnermeier (2016) and the standard ordinary least squares (OLS) method.7 It is important to understand which country is systemically important during the

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period of oil price distress. For that, we perform two tests: the significance test and

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4. Empirical Analysis

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the Dominance test (see Appendix 6).

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4.1. Dependence structure results In our methodology, we need to ensure first that the marginal distributions are well specified, before modelling the dependence structure in the second step through copulas. Therefore, we propose first applied asymmetric Spline-GARCH model skewed t innovations (see Eqs. 1-7). Table 2 summarises the maximum log-likelihood estimate results (detailed in Appendix 4) for all the time series included in our analysis. [Insert Table 2 here]

It is visually clear that coefficients of the Spline-GARCH components are in general statistically significant. For instance, it is well documented that oil and G7 stock market indices present ARCH and fat-tailed. The alpha1 coefficients are in general significant for all series. Nonetheless, the alpha2 coefficient is significant for only three cases (i.e., oil, 7

Please see Appendix 5 for more details about the estimation procedure.

14

Journal Pre-proof Canada and Italy series). The GARCH volatility effects are also statistically significant and, in this case, they are positive, except for Japan and Italy. Moreover, the volatility of the suggesting data is not constant and tends to cluster. Another important stylised fact of volatility is that there is a leverage effect for most data (except the financial markets of Japan and Italy). In this case, a large negative return shock of oil or stock index increases volatility by much more than a positive return shock of the same magnitude. The knot coefficients are also almost statistically significant. Specifically, the assumption suggesting that volatility reverts towards a constant is not appealing to describe long-run volatility behaviour for most

oo

f

cases, except Japan that presents a significant Spline-GARCH parameter with knot 2. Indeed, results are lying only for five interior knots, suggested to characterise the frequency component of the market volatility or the changes in the curvature of the

pr

time trend.

e-

The bottom part of Table 2 presents diagnostic tests. We can see that there is no autocorrelation, nor is there squared autocorrelation, in the residual terms, as we can

Pr

infer by the Ljung–Box Q statistic, indicating that the model for the marginal distributions is not misspecified. Additionally, the McLeod–Li test results reject the

al

null hypothesis in almost all cases (except Japan). These results corroborate the inference that the data contains nonlinearities, and in particular, provides a strong

rn

indication for nonlinearity in conditional variance.

Jo u

In this study, we retain copula functions as adequate indicators of the possible comovement between the series of daily returns of oil and each stock market in the G7 country set. Table 3 summarises the parameters of the best copula suggested to fit the structure of dependence. The numerical computation of the maximum log-likelihood and estimated copula parameters are reported in detail in Appendix 3. For each country, one can find estimated parameters of 23 bivariate copulas including common copula functions, such as elliptical and Archimedean forms, with static, time-varying Pattonlike, and with and without Markov-switching parameters (see section 3.2.3). The ranking of the model fit is based on the smallest log-likelihood measure. [Insert Table 3 here]

It can be seen from Table 3 that the dependence structure differs from country to country. For instance, the most suitable dependence model of the U.S. and Canada stock markets to oil shocks is the time-varying Student-t copula followed by the 15

Journal Pre-proof Markov-switching dynamic normal copula. This result reveals temporal variations in the dependence structure of the considered markets. The degree of freedom is [

]. This result indicates that the symmetric nonzero tail dependence is a

feature characteristic of the relationship between oil and US and Canada financial markets. This dependence model implies that ceteris paribus, bad news in the oil market has a similar impact as good news on extreme returns. More interestingly, estimate parameters show very high and significant persistence (βu > 1). Therefore, their dependence processes are likely to be very explosive. Further, Ψ0 is negative for the U.S. and positive for Canada, which is not a surprise

oo

f

given that the former is a major oil-importing country whereas the latter is a major oilexporting country. That is, when the oil price plunges it leads to low performance for the Canada stock market and high performance for the US stock market.

pr

Table 3 further shows that the static Student-t copula confirms its superiority for

e-

the U.K. and Italy financial markets. These countries are highly dependent on both types of shocks in the oil market. More importantly, an average and positive

Pr

dependence is found between the oil and UK stock markets. We also find an average and negative dependence between the oil and Italy stock markets. This negative

al

dependence is close to zero, indicating the presence of diversification opportunities in these two markets. This also suggests strong evidence of the lower and upper tail

rn

dependence between the aforementioned countries (i.e. US, Canada, UK and Italy),

Jo u

highlighting the importance of contagion during oil trading imbalances. The Markov-switching dynamic normal copula gives a better fit for the remaining G7 countries (i.e., France, Germany and Japan) according to the LL measure. This is a no-lower and upper dependence structure. For these cases, we observe that the estimates of β are significant, indicating that the dependence varies with time. In addition, we see a substantial change in intercept ω according to the two regimes. Moreover, these regimes are persistent with p + q = 1. [Insert Figure 1 here]

Figure1 shows the smoothed probabilities concerning the high and the low dependence regimes. While France and Germany possess similar features in term of the volatility of p and q, Japan appears relatively different. [Insert Figure 2 here]

16

Journal Pre-proof From Figure 2, we can see the dependence dynamic (i.e., the linear correlation) captured by the normal copula parameters. It is also clear to see the change of the dependence among country and in view to considering regime. Precisely, France and Germany show similar plots. For the low dependence regime, we see a substantial pick of dependence value in 2003 caused by the significant increase in oil price following the Iraq invasion event. During the GFC, dependence value appears higher volatile but not higher amplitude. The same behaviour is observed for the high dependence regime. In sum, these results indicate that the dependence structure between oil price

oo

f

changes and the G7 stock indices returns is not similar. For France, Germany and Japan, the dependence is Markov-switching time-varying, while it is time-varying for the US and Canada, constant for the UK and low for Italy.

pr

From these results, it is clear that oil is an important factor for these economies.

e-

This comes from their development companies related to oil and gas industries, with cash-flows largely altered by oil price volatility. As another possible explanation is

Pr

that the underlying business of most non-oil and non-gas firms in this group is closely associated to oil price changes than the business of other firms.

al

These findings are also confirmed by studies of Arrouri and Nguyen (2010), Khalfaoui (2015), Feng et al.

(2017) and Bastianim and Manera (2018), among

rn

others. Moreover, these findings related to G7 economies differ slightly to others

Jo u

related to transition and developing markets. For instance, Aloui et al. (2013) focused on the oil–stock market relationship for six major transition markets (namely Bulgaria, Czech Republic, Hungary, Poland, Romania, and Slovenia), found that oil and these CEE stock markets exhibit time-varying interdependence in both the middle and lower tail quantiles. Next, Sukcharoen et al. (2014) found no dependence of oil price changes with many developing stock markets, whereas weak but significant for most of the developed stock markets. Therefore, it is worth to mention that the tail dependencies are relatively strong for the stock markets of large oil consuming and producing countries (US and Canada).

17

Journal Pre-proof

4.2. Systemic risk results 4.2.1. Volatility, Correlation and VaR analysis Figure 3 exhibits the daily time-varying volatility and correlation as well as VaR measures for each time series using the Spline-GARCH fitted parameters. We show that throughout the sample period, the level of volatility is varying (see panel A). For the oil market, we find that considerable volatility occurred in late 2003, between 2008–2009 and 2011–2013 and from mid-2014 to late 2016. These periods are also

f

associated with high VaR values (in absolute value) with abrupt changes during GFC

oo

periods. In addition, most of the G7 stock returns follow a similar pattern for volatility and VaR changing over the study period (see panel B). These results can offer us a

pr

preliminary idea about the risk of spillovers from the oil market to a G7 economy set or from the G7 economy set to the oil market. However, the plots of the conditional

e-

correlation show that the crude oil returns are not strongly correlated with most G7

Pr

countries, although the Canada stock market shows the strongest correlation but only during the recent crisis from mid-2014 when the oil price fell approximately 80%. Thus, no significant relationship exists between these major oil-consuming countries

al

and the oil price changes. This finding appears opposite to those of previous studies

rn

(e.g. Choi and Hammoudeh (2010) Khalfaoui et al. (2015), Bastianin and Manera (2018), among others), which support that negative oil shocks can affect negatively

Jo u

developed stock markets rather than positive shocks. This is, in part, why we suggest in this study other more sophisticated methods, such as ΔCoVaR and MES measures, to evaluate the strength of the systemic risk. [Insert Figure 3 here]

4.2.2. MES and ΔCoVaR results The results, shown in Table 4, suggest that the estimated average of short-run MES is significantly

positive

and

varies slightly from one country to

another.

Not

surprisingly, the largest value of MES is assigned to the Canada stock market followed by the Italy, Germany, UK and US markets. This finding implies that there are significant loss returns in these markets on days when the oil market experiences a return that is in the q% left-hand tail within the sample period. The loss in the oil and gas companies listed (e.g., BP and Shell in the United Kingdom, DEA in Germany 18

Journal Pre-proof and Blackbird Energy Inc. in Canada) in these markets is, in general, greater compared with the benefice of the other stock sectors when the oil market experienced downward periods. For the France and Japan, crude oil negative shocks of about 2% affect, however, positively their short-term returns (i.e. increase their welfare gains). The average value of LRMES is much larger (in absolute value) than that of others (i.e., short-run MES and ΔCoVaR measures) because it measures the long-run shortfall condition on the long-run tail events, while the others correspond to the short-run shortfall and short-run tail events. Additionally, we show that in the long

oo

f

run, MES is, on average, negatively higher for all G7 stock markets. This result means that since these countries are considered the largest oil consumers account for nearly 50% of the world’s oil consumption, there is a long-term profit in their economy

pr

when the oil price falls by more than 40%. Conversely, the Canada stock market

e-

appears the less sensitive among the G7 set markets by the long-term crude oil market downward. Indeed, Canada is the unique oil-exporting country in the G7 set of

Pr

countries and its economy seems very susceptible to oil incomes.

al

[Insert Table 4 here]

rn

Further investigation of Table 4 shows the average of ΔCoVaR measures calculated

Jo u

using the DCC-GARCH method and conditioning to the events that the crude oil market returns are less or equal to its q% VaR value. The results related to quantile and OLS regressions are also reported in Table 4. The comparison suggests the presence of a high correspondence between OLS and DCC estimation methods but with high value when the ΔCoVaR is estimated with a DCC model. This implies that the different methods of ∆CoVaR expression have little influence on the estimation results of ∆CoVaR. Conversely, there is a high correspondence between the time series average of ΔCoVaR computed using quantile regression ( see Eqs. 18-21) and short-term MES (see Eqs. 22-26). As for DCC method of Girardi & Ergün (2013), the cross-country comparison to the response to crude oil lower-tail events shows that Canada has the greater positive ΔCoVaR, followed by Germany and the United Kingdom. ΔCoVaR is an estimation of how much crude oil shock adds to the VaR of G7 stock index when the system moves from the median state to the q%-VaR level. Then, the positive ΔCoVaR (CoVaR considered in absolute value) results reflect that 19

Journal Pre-proof crude oil shocks have added on average to the VaR of the Canada stock market. This market does not seem resistant to oil shocks. Conversely, crude oil shocks do not add to the VaR of the US, France, Italy and Japan, which show negative values of −1.59%, −2.62%, −2.04% and −5.44%, respectively. Figure 4 shows the plots of daily ΔCoVaR and MES for each individual country, using the DCC model (panel A) and the plots of daily ΔCoVaR corresponding to the quantile regression method (panel b). A preliminary observation of the graphs of panel A suggests that the two lines match almost perfectly. In particular, we distinguish four high turbulent phases (see the encircled periods in Figure 4), which

oo

f

correspond to the four aforementioned oil shocks. The important systemic risk values are those related to GFC. Conversely, and more interestingly, the computational value of ΔCoVaR and MES are positively time-varying for the Canada and UK stock

pr

markets (and are negative otherwise) but the magnitude is stronger for the former than

e-

for the latter. In addition, there is evidence of significant cross-volatility effects (i.e., more risk of spillover effects) between these markets and the crude oil market during

Pr

the previous oil crisis that commenced in mid-2014.

Table 5 reports the KS statistics and the associated p values under the null

al

hypothesis of no difference between the CoVaR during a period of crude oil distress and the CoVaR in normal oil price condition i.e. 𝛥CoVaR = 0 (see Appendix 6). One

rn

can see that the probability is low than 1% significance level which can give us some

Jo u

confidence that we can reject the null hypothesis. This means that all countries impact significantly on the entire G7 economic system during a period of oil price distress and thus they contribute to systemic risk. In addition, we compare the conditional density functions (CDFs) of the 𝛥CoVaRs on country-level with the dominance test. Table 6 presents the summary statistics under the null hypothesis that the i’s 𝛥CoVaR, in absolute value, is larger than the j’s 𝛥CoVaR (see Appendix 6). Therefore, the i-th country dominates the -th country if and only if the

value is large and the

value is close to zero. Even for

the Dominance test, the null hypothesis is tested at the 1% significance level (see Eqs. 29-30).8 [Insert Tables 5, 6 here]

8

One can find the results related only for DCC model. The Quantile model results are available upon request.

20

Journal Pre-proof The results of Table 6 allow to construct a consistent country ranking. We can see a significant dominance of the US and Canada against the France, Italy and Japan contributions to systemic risk during period of crude oil distress. Concerning the japan and the UK, they are the last ranking countries. These results appear in line to our analysis of Table 4. 4.3. Robustness check: GO-GARCH model Multivariate GARCH specifications are typically determined by means of practical considerations, such as the ease of estimation, which often results in a serious loss of

f

generality. Hence, we propose the generalisation Orthogonal GARCH (GO-GARCH)

oo

model or principal components GARCH model, as an additional estimation model of the oil and G7 return series.9

pr

Figure 5 shows the conditional volatility, VaRs and conditional correlation of each series using the standardised GO-GARCH residuals. The plots of this Figure and

e-

those of Figure 3 related to DCC-GARCH model show no significant difference,

Pr

except that the plot of the conditional correlations estimated by GO-GARCH are much less volatile, mainly for the France and Germany stock markets. The effect of the use of the GO-GARCH model for an improved description of the process is also

al

observed in the MES and ΔCoVaR systemic risk measures.

rn

[Insert Figure 5 here]

Jo u

Table 7 summarises the results of MES and ΔCoVaR systemic risk measures based on the GO-GARCH estimation model. For the short-run MES measure, the important results are related to the France and Japan stock markets, in which their sectors and companies bring a welfare gains with the falling of crude oil prices. These results look the same as those reported in Table 4 and based on the DCC-GARCH model. Concerning the average MES result of other countries, no significant difference is also found. In fact, Canada ranks first among the countries in losing revenues at the short-term during oil market distress. For LMES, the strong predictability result holds 9

For other results on the marginal distribution, one can see Khalfaoui et al. (2015) who use the GARCH–BEKK model to investigate the mean and volatility spillovers between the oil market (WTI) and the G7 stock markets. Moreover, it is important to note that Lee et al. (2014) investigate the volatility spillover between G7 stock price and oil price with the dynamic conditional correlation (DCC), constant conditional correlation (CCC) and BEKK models. The empirical results show that DCC model is better than the CCC and BEKK models. Hence, we used DCC model for analysis and or the purpose of comparison we used GO-GARCH model which is also more robust particularly when we are dealing with many series at a time.

21

Journal Pre-proof for Italy country, since the two models (i.e., GO-GARCH and the multivariate GARCH models) provide opposite results. [Insert Table 7 here] For ΔCoVaR measure, one can see that Figures 6 and 7 duplicate the same results provided by the DCC-GARCH model, except for Japan and France quantile regression estimators, which exhibit the opposite sign. Precisely, Figure 7 plots the time evolution of the estimated Japan and France ΔCoVaR below zero but these are above zero in Figure 4. Overall, MES and ΔCoVaR estimated by DCC-GARCH or

oo

f

GO-GARCH have captured the presence of a time-varying exposure of G7 stock markets to the oil market shocks. Concerning the sign of the co-movement between the stock markets in the G7 set and the oil market, the results seem decisive only for

e-

significant short and long-term dependence.

pr

three countries, namely Canada, France and the Japan, where they provide a

[Insert Figures 6, 7 here]

Pr

Moreover, the spillover risk in the G7 set is more during volatile times than during normal or tranquil times. In particular, the Canada stock market appears the

al

most sensitive and vulnerable to the negative external shocks emerging from the crude oil market, owing to its economic dependence on export income from oil. Conversely,

rn

the country risk rankings identified by MES and ΔCoVaR may not be the same.

Jo u

Overall, our results confirm previous studies that show no consensus that there is a defined relationship between oil prices and stock markets across different countries. Particularly, our results are in line with Park and Ratti (2008) who find that oil price shocks have a statistically significant impact on real stock returns in the US and thirteen European countries.

5. Conclusion We examine the systemic risk and nonparametric dependence between oil and stock market indices of the G7 economies for the period January 2003 to November 2017 using several time-constant, time-varying and Markov-switching copula models as well as conditional VaR (CoVaR) of Adrian and Brunnermeier (2016) and marginal

22

Journal Pre-proof expected shortfall (MES) of Acharya et al. (2012). We use the asymmetric SplineGARCH model with skewed t-innovations as a marginal model and obtain standard residuals, which we then smooth and use in copula analysis. From the marginal analysis, we find that all series exhibit fat-tail, leverage effects and volatilities are unstable and tend to cluster. From the copula analysis, we find that the dependence structure is dissimilar for most of the countries. Overall, the results show that the most suitable dependence model of the US and Canada markets is the time-varying Student-t copula followed by the Markov-switching dynamic normal copula whereas the static Student-t copula

oo

f

outperforms for the UK and Italy financial markets. The Markov-switching dynamic normal copula gives a better fit for France, Germany and Japan. Further evidence from the copula analysis shows that the symmetric nonzero tail

pr

dependence is a feature characteristic of the relationship between oil and the US and

e-

Canada financial markets, which indicates that, ceteris paribus, bad news in the oil market has a similar impact as good news on extreme returns. For the UK and Italy

negative

dependence close to

Pr

markets, respectively, on average, positive and negative dependence are found, while zero

indicates the presence of diversification

al

opportunities between the UK and Italy. For France, Germany and Japan, we find time-varying dependence with regime-switching with the absence of a lower and

rn

upper dependence structure.

Jo u

Last but not least, from the risk analysis we find that the largest MES value is for the Canada stock market followed by those of the UK and Germany. This finding implies that there are a significant loss returns in these markets on days when the oil market experiences a return that is in q-% left-hand tail within the sample period. Further evidence shows that in the long run, MES is, on average, negatively higher all the G7 stock market, implying that there is a long-term profit in these economies when oil prices fall by more than 40%. Moreover, we find evidence of significant cross-volatility effects (i.e., more spillover risk) between these markets and the crude oil market during the past oil crisis that commenced in mid-2014. We examine the robustness of the analyses through GO-GARCH, which shows that findings as obtained from MES and ΔCoVaR estimated by DCC-GARCH are quite consistent and the results seem decisive only for three countries, namely Canada, France and the Japan, where they provide a significant short and long-term interdependence with oil market. 23

Journal Pre-proof These results seem important to investors. Precisely, the crude oil market can be a good diversifier opportunity for Japan and France investors. For countries with significant positive reactions to oil shocks, such as Canada, the oil shocks may cause investors to act more carefully, which can, in turn, lower investments in these countries over time. These investors can hedge against expected oil changes by using financial instruments, such as derivatives, but they cannot hedge against unexpected oil shocks. Therefore, during the oil market turbulences and for avoiding unforeseen losses, investors in Canada should reduce their investment. This study can be extended by using more advanced models which can

oo

f

incorporate multiple structural breaks or nonlinearity. One can also consider analysing the risk and spillover analysis at different frequencies of data or using spectral or wavelet decomposition analysis or using denoised data (by most appropriate method)

e-

pr

can be possible direction of the future research.

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Appendix Appendix 1. Archimedean and elliptical Copulas In this paper, we use the following copula functional forms: A) Archimedean Copulas  The Clayton (1978) copula (C)—has only lower tail dependence, and is represented by

[

with

-,

f

)

oo

,(

. The degree of dependence is in the lower tail and perfect dependence for

pr

, where impendence is obtained for

. There is zero tail dependence in the upper tail, i.e.

. If we assume

e-

that co-movements increase more in financial turbulence periods, then the Clayton copula is recommended.

Pr

 The Rotated Clayton copula (RC)—has only upper tail dependence, and is

[

. The degree of dependence is in the upper tail

rn

with

,

al

represented by

and in the lower tail

.

Jo u

 The Gumbel (1960) copula (G)—has only upper tail dependence, and is presented by ( ((

with

[

))

], where the special case

nests the independence copula,

which indicates no tail dependence, and The upper tail dependence is

),

yields perfect tail dependence. and

in the lower tail.

 The Rotated Gumbel copula (RG)—has only lower tail dependence and is given by , with

[

. The lower tail dependence is

. If we assume that

co-movements increase more in financial turbulence periods, then the rotated Gumbel copula is recommended.  The Symmetrized Joe–Clayton copula (SJC)—is explained as follows (Patton (2006)):

27

Journal Pre-proof ( ) where

is the Joe-Clayton copula, also known as BB7 which may be defined as [

( )

]

[

]

, with ,

, and

.

The SJC has both upper and lower tail dependence, its own dependence and

are the measures of the dependence of the upper and lower

tail, respectively. Furthermore, =

range freely and not dependent on each

the dependence is symmetric.

oo

other. For

and

f

parameters

Elliptical Copulas:

 The bivariate Gaussian copula (N)—it has no tail dependence, hence

pr

=

= 0.

e-

Therefore, modeling the dependence structure of the series by a Gaussian (normal) copula is consistent with the estimation of this dependence by the linear

Pr

correlation coefficient such that

where

∫

{

√

}

rn

∫

al

e.g. Cherubini et al. (2004))

. The copula density is given by (see

represents the univariate standard normal distribution function with .

Jo u

correlation

 The Student-t copula (ST)—it also has a correlation coefficient such that however, it shows some tail dependence. Specifically, it has symmetric tail dependence. It may be expressed as follows (see e.g. Cherubini et al. (2004)): ∫ where

∫

{

√

is a univariate Student-t distribution function with

freedom and

} degrees of

. The symmetric tail dependence is ( √

√

√

)

. As the Student-t copula allows

for symmetric non-zero dependence in the tails and it represents a generalization of the Gaussian copula.

28

Journal Pre-proof Appendix 2. A comparison of GARCH models for the marginal distribution Mode l

LL

AIC

Schwarz America 2.59 2.55 2.54

Hannan-Quinn

Q 2 (10))

ARCH(5)

2.59 2.54 2.53

0.02 0.13 0.08

0.12 0.28 0.21

-4855.55 -4772.08 -4756.89

2.58 2.54 2.53

GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINEGARCH(1,1-ts SPLINEGARCH(1,1)-GED SPLINEGARCH(1,1)-Sts

-4761.69 -4778.19 -4698.95 -4694.67

2.53 2.54 2.50 2.50

2.54 2.55 2.51 2.51

2.54 2.55 2.51 2.50

0.14 0.03 0.06 0.05

0.29 0.25 0.24 0.24

-4676.23 -4833.95

2.49 2.58

2.50 2.59

2.49 2.58

0.04 0.00

0.18 0.05

-4758.78

2.54

2.55

2.54

0.06

0.19

-4744.19

2.53

2.55

2.53

0.02

0.11

-4749.30

2.53

2.55

2.54

0.07

0.21

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINEGARCH(1,1-ts SPLINEGARCH(1,1)-GED SPLINEGARCH(1,1)-Sts

-4993.42 -4891.77 -4900.59 -4871.12 -4977.42 = 4878.94 -4889.08

2.65 2.59 2.60 2.58 2.64 2.59 2.59

UK 2.65 2.60 2.61 2.58 2.65 2.60 2.60

2.65 2.60 2.60 2.59 2.64 2.59 2.60

0.58 0.54 0.60 0.39 0.39 0.83 0.63

0.44 0.67 0.80 0.47 0.96 0.38 0.75

-4862.69 -4967.19

2.58 2.63

2.58 2.64

0.12 0.81

0.14 2.64

-4869.85

2.58

2.60

2.59

0.70

0.78

-4880.39

2.59

2.61

2.60

0.80

0.90

-4847.62

2.57

2.59

2.58

0.48

0.51

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINEGARCH(1,1-ts SPLINEGARCH(1,1)-GED SPLINEGARCH(1,1)-Sts

-6522.34 -6465.96 -6472.98 -6449.37 -6490.58 -6436.29 -6446.33

3.44 3.41 3.41 3.40

0.18 0.16 0.19 0.15

0.57 0.38 0.50 0.37

3.39 3.40

0.29 0.32

0.35 0.40

rn

Jo u

oo pr

e-

al

Pr

2.59 2.65

Italy 3.43 3.44 3.40 3.41 3.41 3.42 3.40 3.41 Weak convergence 3.39 3.40 3.40 3.41

f

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED

-6419.32 -6494.96

3.38 3.42

3.39 3.44

3.39 3.43

0.27 0.13

0.34 0.58

-6448.16

3.40

3.42

3.40

0.12

0.41

-6454.04

3.40

3.42

3.41

0.14

0.53

-6433.30

3.39

3.41

3.40

0.11

0.38

29

Journal Pre-proof LL

AIC

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)-GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINE-GARCH(1,1-ts SPLINE-GARCH(1,1)-GED SPLINE-GARCH(1,1)-Sts

-6373.21 -6306.19 -6311.23 -6299.37 -6335.39 -6275.40 -6281.72 -6266.63 -6358.70 -6299.36 -6292.20 -6286.21

3.36 3.32 3.32 3.32 3.34 3.31 3.31 3.30 3.35 3.32 3.32 3.32

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)-GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINE-GARCH(1,1-ts SPLINE-GARCH(1,1)-GED SPLINE-GARCH(1,1)-Sts

-6146.94 -6105.16 -6111.45 -6096.40 -6117.64 -6082.17 -6088.79 -6066.70 -6137.41 -6095.85 -6102.83 -6087.32

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N EGARCH(1,1-ts EGARCH(1,1)-GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINE-GARCH(1,1-ts SPLINE-GARCH(1,1)-GED SPLINE-GARCH(1,1)-Sts

-6363.22 -6304.06 -6309.68 -6297.57 -6317.94 -6258.69 -6269.72 -6249.43 -6340.66 -6283.73 -6291.71 -6278.12

GARCH(1,1)-N GARCH(1,1-ts GARCH(1,1)-GED GARCH(1,1)-Sts EGARCH(1,1)-N

-5582.38 -5561.64 -5564.96 -5534.06 -5554.78

Hannan-Quinn

Q 2(10)

ARCH(5)

3.36 3.32 3.33 3.32 3.34 3.31 3.31 3.31 3.36 3.33 3.32 3.32

0.35 0.95 0.94 0.95 0.96 0.98 0.97 0.98 0.91 0.95 0.98 0.23

0.90 0.92 0.91 0.90 0.88 0.93 0.90 0.94 0.89 0.92 0.95 0.95

3.36 3.34 3.34 3.34

0.01 0.00 0.00 0.00

0.00 0.00 0.00 0.00

3.33 .NaN 3.32 3.36 3.34 3.34 3.34

0.35 0.49 0.59 0.04 0.00 0.01 0.00

0.22 0.35 0.44 0.03 0.00 0.01 0.00

3.33 3.30 3.30 3.30 3.31 3.28 3.28 3.27 3.32 3.30 3.30 3.29

0.59 0.46 0.55 0.44 0.99 0.95 0.98 0.94 0.48 0.36 0.46 0.34

0.53 0.28 0.40 0.26 0.93 0.85 0.91 0.85 0.48 0.24 0.38 0.23

2.98 2.97 2.97 2.95 2.97

0.29 0.29 0.29 0.29 0.17

0.32 0.35 0.35 0.32 0.30

Pr

e-

pr

oo

3.36 3.33 3.33 3.33 3.35 3.32 3.32 3.32 3.37 3.34 3.34 3.33 Japan 3.36 3.36 3.34 3.34 3.34 3.35 3.33 3.34 No convergence 3.32 3.34 .NaN .NaN 3.32 3.33 3.36 3.37 3.33 3.35 3.34 3.36 3.33 3.35 France 3.33 3.33 3.30 3.30 3.30 3.31 3.29 3.30 3.30 3.31 3.27 3.29 3.28 3.29 3.27 3.28 3.32 3.33 3.29 3.31 3.29 3.31 3.29 3.31 Canada 2.98 2.98 2.97 2.97 2.97 2.98 2.95 2.96 2.96 2.97

al

rn

Jo u

EGARCH(1,1-ts EGARCH(1,1)-GED EGARCH(1,1)-Sts SPLINE-GARCH (1, 1)-N SPLINE-GARCH(1,1-ts SPLINE-GARCH(1,1)-GED SPLINE-GARCH(1,1)-Sts

S chwarz Germany

f

Model

-5540.67 -5543.42

2.96 2.96

2.97 2.97

2.96 2.96

0.25 0.20

0.43 0.37

-5567.06 -5548.69 -5552.17 -5520.41

2.97 2.96 2.96 2.95

2.99 2.98 2.98 2.97

2.98 2.97 2.97 2.95

0.45 0.43 0.45 0.43

0.40 0.42 0.42 0.39

Notes: The N, GED, ts and Sts correspond to normal, Generalized, student and skew t-student errors distribution, respectively. LL and AIC indicate Log-Likelihood and Akaike Information criteria measures. Q(10) and ARCH (5) are the p-value of the rejection of the null hypothesis related to serial correlation of squared residuals and ARCH effects, respectively.

30

Journal Pre-proof Appendix 3. Estimates for the bivariate copula models

0.036 -2.481

-0.002 -0.013

-0.007 -0.104

0.016 -0.539

0.070 -9.023

0.032 -2.102

0.014 -0.420

0.052 -5.191

0.031329 -1.7343

0.006925 -0.0974

0.00114 -0.0024

0.008 -0.136

1.139755 -3.2733

0.990513 -0.0179

0.967276 -0.2164

1.072 -0.9576

0.246 -3.085

0.000 0.0002

0.000 0.000

0.134

1.100 17.9153

1.1 37.536

1.1 43.0649

1.100 29.6712

1.1 4.8895

1.100001 28.9066

1.1 36.3447

1.1 15.0653

-0.00383 8.221061 -27.0765

-0.00891 13.84556 -9.5286

0.02183 8.68698 -23.1287

3.13E-08

3.13E-08

5.37E-07

0.000468

0.001094

-0.6816

2.2269

-3.6445

-0.912

f

0.040469 7.719297 -31.2986

3.13E-08

4.68E-07

0.019903

0.000498

0.006211

0.044562

-0.00735

-0.00255

0.040234

0.005253

0.03389

-0.04411

-0.06629

0.087064

0.02162

-0.13428

1.923891

1.802668

0.456038

0.956152

-1.76668

1.856238

-0.00401

-26.169

-0.4645

-4.3679

-0.5892

-4.6337

-2.4239

0.137302

0.067638

-0.27008

0.012369

0.271787

1.480474

-2.45144

0.717879

0.290103

0.172244

1.360948

0.455383

-0.37742

0.58507

-1.72344

-1.52415

-0.81002

1.380363

-35.3721

TVP Rotated Clayton 0.571102  0

U

-1.8301

U

-1.13468

e-9.414

-4.8643

-4.7325

-6.0669

0.721074

-0.18279

-0.53817

0.099635

-0.20841

0.616638

0.487025

-2.69227

0.567881

1.388276

-2.39449

-1.49507

-1.45549

0.815468

1.509818

-0.06737

0.662614

-1.44387

-0.8856

-4.5369

-0.1046

-0.3252

-1.2245

-2.50036 2.371929 0.396856 -1.8597

1.53785 -1.89142 1.389465 -5.0173

-2.31959 2.416842 -0.06237 -2.0468

1.749752 -2.00648 0.843678 -1.4486

0.570566 -1.00705 1.308656 -3.487

-0.29052

-0.24535

-1.70184

-1.95103

2.503709

-0.98114

0.731475

0.134255

1.800566

1.99872

-2.69357

1.019528

-0.71186

0.55324

0.080775

0.131268

1.038356

0.264481

-47.6922

-4.7448

-13.4239

-5.0398

-6.9557

-8.385

-37.8266 -0.25853 0.721204 -0.79558 -50.5304

Jo u

0.638187 2 -1.29624 1 Log-lik. -3.7014 TVP Gumbel -0.25521 0.745266 -1.1288 Log-lik. -9.5 TVP Rotated Gumbel copula 2.440022 U

-4.9695

al

-9.7825

-9.4092

Pr

0.537648

-1.42327

rn

Log-lik.

UK

0.000246

Log-lik. -0.8708 TVP Clayton 0.828288  0 2 1

Japan

0.003564

Log-lik. -1.8597 -28.8996 0.9537 Panel B: Parameter estimates for time-varying copulas. TVP-Normal -0.00067 0.009528 -0.0075  0 2 1

Italy

pr

SJC copula  7.41E-07 U  0.000366 L

Germany

oo

America Canada France Panel A: Parameter estimates for time-invariant copulas. Normal copula  -0.008 0.083 -0.004 Log-lik. -0.149 -13.119 -0.0359 Clayton copula 0.037 0.113 0.026 Log-lik. -2.8372 -21.5923 -1.3679 Rotated Clayton 0.009 0.095 0.0001 Log-lik. -0.205 -15.118 0.0007 Plackett copula 0.976793 1.269 0.994074 Log-lik. -0.1011 -10.359 -0.007 Frank copula 0.000 0.439 0.000 Log-lik. 0.000 -9.510 0.000 Gumbel copula 1.100 1.1 1.1 Log-lik. 29.2812 -20.7249 44.3809 Rotated Gumbel copula 1.100001 1.1 1.100001 Log-lik. 19.5618 -24.8781 31.1243 Student-t copula  -0.00604 0.075729 -0.00278  5.580332 5.37948 9.985071 Log-lik. -52.6595 -66.6298 -17.9366

Log-lik. TVP-SJC U

-13.9839 -17.6722

2.670557

-18.647

-15.3934

-18.4857

-19.0178

-17.9137

U

-1.90751

-23.6066

-0.83585

-0.38479

-0.85285

-0.87692

-1.39105

U

-0.00426

-0.62379

-0.00238

-0.0012

-0.00214

-0.00235

-0.00387

L

-19.5839

0.092994

-21.3106

-15.5487

-21.3532

-20.0649

-17.863

L L

-5.93072

-13.2601

-4.23981

20.28012

-4.94321

-3.62215

-3.0276

-0.01501

2.860819

-0.01769

6.862112

-0.01764

-0.01376

-0.01832

-50.4283

7.3716

-10.1575

4.6145

8.5464

0.35

0.004544

-0.00818

0.033301

-0.01287

-0.00157

0.035344

-0.01195

0.043999

0.008345

-0.05296

1.211158

-1.77569

1.883369

0.498387

0.033301 -24.9684

4.999995 -19.0404

4.999997 10.1578

4.999995 -14.7878

-0.36793 0.579566 0.765843 -0.08273 0.577246 0.422754 -31.7596

-1.56498 1.164163 -1.86412 0.066848 0.348704 0.651296 -26.3141

-0.05787 3.022367 -2.00442 -0.17407 0.347503 0.652497 -9.5678

0.040214 7.455228 -0.00385 -0.13427 0.619725 0.380275 -4.0647

Log-lik 2.2159 TVP Student-t -0.02633*  0

0.054062* 0.018267 -0.04546 2 -1.99659* 1.887547 -0.12436 1    4.998292* 4.990415 4.999999 Log-lik. -53.4805 -79.9234 -5.1784 Panel C: Parameter estimates for time-varying Markov copula Time-varying Normal Markov copula -1.50701 -0.07972 -1.65876 2.186844 2.24831 0.893619 -2.1649 -1.13861 -1.83594 0.167111 -0.33492 -0.12794 0.701852 0.384928 0.178951 0.298148 0.615072 0.821049 Log-lik. -53.4068 -69.2915 -18.1368 Time-varying Clayton Markov copulas

31

Journal Pre-proof 0.213736 -1.33009 0.364819 -0.92042 0.362549 0.637451 -3.7549

0.06475 -0.57919 1.081159 -0.37681 0.918619 0.081381 -8.7533

-0.11429 -0.62835 -0.44682 0.330485 1.147301 -0.1473 -0.5829

0.055664 -0.81539 -0.18949 -0.24149 0.37281 0.62719 -4.1184

0.508058 -0.44754 0.858851 -1.47663 0.605742 0.394258 -1.5416

0.403119 0.572322 -0.65667 0.293631 0.520412 0.479588 -2.0562

1.608992 1.241597 -1.52219 0.727875 0.602166 0.397834 -1.944

0.409942 0.560606 -0.86146 1.132552 0.498034 0.501966 -3.8834

1.217038 1.025429 -1.16738 -0.12763 0.332782 0.667218 -5.1413

0.702167 0.918166 -0.79578 -0.31703 0.595275 0.404725 -8.2634

0.306308 0.578588 -0.12208 -0.96133 0.505596 0.494404 -11.2427

6.479838 3.739219 -20.0939 -19.7622 -3.99329 -8.38612 -12.7163 -11.7998 0.395992 0.604008 4.2738

3.501481 3.116862 -9.80978 -9.71625 -4.7663 -4.31965 -9.64195 -7.73203 0.620451 0.379549 0.5153

3.277417 2.429028 -21.046 -22.9583 -4.26291 -5.48727 -10.7523 -10.2656 0.339859 0.660141 0.2956

oo

f

-0.04998 -1.76265 0.121902 -0.30598 0.143213 0.856787 -2.8136

pr

Pr

e-

-0.1752 0.297269 0.240268 -0.11882 -1.34702 -0.98114 -1.18278 -0.88464 0.964661 0.162343 0.060837 1.108774 -0.60793 -0.1723 -0.85109 -0.5137 0.408226 0.422913 -0.10939 0.362002 0.591774 0.577087 1.109389 0.637998 Log-lik 8.2087 -50.3513 -5.4196 -12.8285 Time-varying Rotated Clayton Markov copulas 0.196326 0.108597 0.106728 0.280119 -1.57637 -1.25023 -5.11544 -0.6212 0.193836 0.413458 0.359573 0.911872 -0.42504 0.083529 -0.41325 -1.34198 0.299821 0.417217 0.628943 0.313996 0.700179 0.582783 0.371057 0.686004 Log-lik. -6.467 -48.0418 -0.5152 -1.9766 Time-varying Gumbel Markov copulas 0.211955 1.38771 -2.28799 0.078227 0.4272 0.260158 -2.21387 0.629122 -0.68997 -0.44254 2.152348 -0.37371 0.774907 0.125674 0.305781 -0.72012 0.708951 0.590417 0.485321 2.708854 0.291049 0.409583 0.514679 -1.70885 Log-lik. -10.3066 -63.9504 -0.7503 -12.047 Time-varying Rotated Gumbel Markov copulas 0.412446 1.814326 -0.23942 1.129302 0.210844 0.880746 -0.05841 0.795569 -0.67299 -0.59847 0.419532 -0.57286 0.659165 -0.2294 -0.78033 -1.15844 0.427789 0.602471 0.490689 0.398468 0.572211 0.397529 0.509311 0.601532 Log-lik -12.157 -67.7605 -4.8703 -14.0955 Time-varying SJC Markov copulas 4.420982 1.914885 4.59532 5.77319 5.275563 2.622018 3.681912 1.997992 -18.7342 -19.7942 -19.4813 -21.0792 -18.6446 -7.60822 -18.9597 -23.8406 -10.6787 -2.9773 -0.81369 -6.01923 -5.37911 -4.67372 1.318161 -6.08669 -25 -7.58692 -11.6533 -10.295 -24.9999 -8.48382 -18.321 -9.74397 0.592708 0.560658 0.394584 0.403986 0.407292 0.439342 0.605416 0.596014 Log-lik. -7.879 -75.1746 6.9301 -7.7117 Time-varying T Markov copulas Convergence was not achieved in any of the models hence results are not presented

Jo u

rn

al

Note: All copula coefficients are significant at 1% level of significance. Bold values are insignificant at 10% level of significance.

32

Journal Pre-proof Appendix 4. Copula estimation procedure The log-likelihood function can be expressed as:

∑

(

(

|

(

|

)

)∏

)

= ∑

(

)

(

)

∑

∑

),

(

) and

∑

)

.

e-

(

(

pr

∑

where

)

oo

(

f

.

These are the log-likelihood functions used to estimate the parameters of the

).

(

Reformulating we have

∑

(∑

As States

) considering

al

decomposing

rn

(

Pr

marginal models at the first stage. Thus, we can now move to the evolution of nonobservable

[

variables

]).

and

(17)

are nonobservable, to assess the log-likelihood in Eq. (17) we [

] for

and

since we consider a set

Jo u

might compute the weights

of two states only. Applying Kim’s filter, we obtain the following algorithm, which should be iterated through the sample (a) Prediction of

[ For

]

∑

and

the

probabilities between States

transition

and .

(b) Filtering by [ where for

=

]

∑ In

, the filter is initialised stationary probabilities of

. Thus, we obtain the probability distribution of

33

given the

Journal Pre-proof information

set

[

]

by .

Further,

the

smoothed

∑

probabilities are

regarding

obtained

and

can be calculated recursively from the filtered probabilities. This smoothing process works like a backward-smoothing algorithm as follows. 1. Given the aforementioned filtering process, we obtain

for l = 1,

2 and t = 1,…,T. 2. Then, we can initialise the smoothing algorithm in recursively, with 3. For

being equal to the filtered probability in

each

the

smoothed

pr

∑

oo

∑ =

are the transition probabilities between States

e-

and

, the smoothing algorithm yields

from which we can start

Pr

At all

probability distribution

f

is given by:

where

and go backwards

the optimisation procedure. Thus, we calculate the forward-filtering-backwardsmoothing algorithm and we can then maximise Eq. (17) in relation to the model

al

parameters directly in a numerical fashion.

rn

We use the block bootstrap approach as described by Politis and White (2004) and Politis et al. (2007) to estimate adequately the standard errors for our estimations.

Jo u

A brief explanation of this approach is as follows: 1. Obtain parameters via two-step ML method, that is, the inference for margins method (see Joe & Xu, 1996). 2. Sample

subsamples (with replacement) from the observed time series and

create a set of time series with size

, where is the block size.

3. Re-estimate the parameters using standard time series. 4. Repeat steps (2) and (3) K times 5. Using the covariance matrix

∑

̂

̂ ̂

the estimated parameter vector for each replication

̂ , where ̂

and ̂ is the parameter

vector obtained in step (1), calculate the standard errors for the parameters.

34

is

Journal Pre-proof

Appendix 5. CoVaR and MES estimation procedure Girardi and Ergün (2013) follow a three-step procedure to estimate CoVaRs conditioned by

, which we adopt: First, we apply the distribution

function for the oil and G7 stock market returns as given by the marginal model in Eqs. (1)–(5) and calibrate the standard normal distribution, to estimate the isolated time series of VaRs. Subsequently, the bivariate-Spline-GARCH model with DCC specification (Engle, 2002) is used to estimate the time-varying conditional variance

oo

returns–oil pair is incorporated in the computation of

f

and correlation. Finally, the estimated joint distribution of each G7 country stock

& Ergün, 2013 for more details).

. (please see Girardi

pr

Adrian and Brunnermeier (2016) propose the quantile regression technique to

e-

estimate the location of percentiles of the conditional distribution. The model can be written as:

Pr

Xi = α + β Xoil + ε

(18)

The quantile regression estimates a different set of coefficients associated with each value of Xoil, is:

al

percentile of interest. Therefore, the estimate of the q th percentile of Xi, given the ̂

̂

rn

̂

(19)

(regress stock index daily changes on WTI daily changes)

Jo u

Estimate αq and βq for some lower-tail value of q, and then choose the q% VaR values for Xoil. Hence, the fitted Xi variable is the estimate of the q-quantile of Xi, given that Xoil = VaR(q).10 We compute

via historical simulation and find the median of each ̂

̂

:11

(20)

̂

(21)

Since the CoVaR measure is essentially a measure of downside risk, its main interest is in the behaviour of the left tail. In particular, q%-VaR is expected to be a negative value and is usually less than 50%-VaR.

10

̂ q% reflects the estimated

Since we focus on the left-tail risk, we set q to be 1%. OLS regressions estimate the mean of the distribution of the dependent variable Xi , given the explanatory variables Xoil . 11

35

Journal Pre-proof response of the G7 stock market returns to the extreme crude oil returns, which is expected to be a positive value. Consequently, the predictions of quantile regressions should derive a negative value of ΔCoVaR. The higher a stock market ΔCoVaR (in absolute value), the higher is its co-movement or exposition to crude oil distress. Brownless and Engle (2011) argue that the estimation of MES can be reduced into the estimations of three components: volatility, correlation and tail expectation. Their linear market model can be summarised as follows: (22) √

where

satisfies

, and

(24) and D denotes the

pr

joint distribution of the standardised innovations.

oo

f

(23)

e-

Following these assumptions, the MES can be expressed as a function of the G7 stock return volatility, its correlation with the oil market and the co-movement of the tails of

Pr

the distribution as follows:

al

(

(

where

(

rn

√

)

) ),

(

and

(25) ) are

the

conditional

Jo u

expectations under tail quintiles that are not captured by the correlation. We consider in (25) an unconditional threshold C equal to the unconditional VaR of the oil market. Therefore, under the assumption that standardised innovations and

are i.i.d., and according to the DCC-GARCH model, the nonparametric

estimation of MES is defined as: ̂

̂ ̂ ̂

̂ √

̂ ̂

(26)

where ̂

is deduced from ̂

(2012), ̂

using the approximation proposed by Acharya et al. ̂

(

36

).

Journal Pre-proof

Appendix 6. Significance and Dominance tests for ΔCoVaR For the significance test, we propose for comparing the testing approach introduced by Bernal et al. (2014). This approach is based on the boostrap Kolmogorov-Simirnov (K-S) test developed by Abadie (2002). The method consists in testing the hypothesis of equality in two cumulative distribution functions (CDFs). In this case, the twosample Kolmogorov-Smirnov statistics is defined as follows: 𝒎𝒏

𝟐

) 𝐬𝐮𝐩 𝑭𝒎

𝒎 𝒏

(27)

𝒏

f

(

and 𝐆𝐧 𝐱 are the CDFs of the 𝐂𝐨𝐕𝐚𝐑𝐢𝐪𝐨𝐢𝐥 and the 𝐂𝐨𝐕𝐚𝐑𝐢𝐭 𝐨𝐢𝐥𝟓 𝐭

oo

𝑲𝒎 𝒏 𝝉

Where 𝐅𝐦 𝐱

pr

respectively, and m and n are the size of the two samples. In particular, we test the following null hypothesis: 𝐂𝐨𝐕𝐚𝐑𝐢𝐪𝐨𝐢𝐥 𝐭

𝐂𝐨𝐕𝐚𝐑𝐢𝐭 𝐨𝐢𝐥𝟓

e-

𝐇 : 𝚫𝐂𝐨𝐕𝐚𝐑𝐢𝐭 𝛕𝐨𝐢𝐥

(28)

Pr

The alternative hypothesis is that 𝚫𝐂𝐨𝐕𝐚𝐑𝐢𝐭 𝐨𝐢𝐥 𝐪

For the Dominance test, the statistics is expressed as follows: 𝐦𝐧

(𝐦

𝟐

𝐧

(29)

𝐁𝐧 𝐱

𝐢 𝐨𝐢𝐥

and 𝐁𝐧 𝐱 are the CDFs of the 𝚫𝐂𝐨𝐕𝐚𝐑 𝐭 𝐪

𝐣 𝐨𝐢𝐥

and the 𝚫𝐨𝐕𝐚𝐑 𝐭 𝛕

rn

Where 𝐀𝐦 𝐱

) 𝐬𝐮𝐩𝐱 𝐀𝐦 𝐱

al

𝐊𝐦 𝐧 𝛕

respectively, and m and n are the size of the two samples and i and j represent the i-th

Jo u

and the j 𝒕𝒉 country. Here the null hypothesis tested is: 𝐢 𝐨𝐢𝐥

𝐇 :|𝚫𝐂𝐨𝐕𝐚𝐑 𝐭 𝐪 |

𝐣 𝐨𝐢𝐥

|𝚫𝐨𝐕𝐚𝐑𝐭 𝐪 |

(30)

These two tests are sufficient for us to be able to determine which countries of G7 set contribute more to the systemic risk than others during oil market distress.

37

Journal Pre-proof

Tables & Figures Table 1. Statistical properties

-44.72 0.03*

1

France 0.01 12.34 -11.44 1.57 -0.03 10.55 8933*

Germany 0.04 12.57 -9.31 1.55 -0.11 9.03 5708.5*

Italy 0.00 12.35 -14.16 1.65 -0.24 9.59 6841.8*

Japan 0.02 10.72 -11.26 1.46 -0.41 8.13 4119.3*

UK 0.00 6.92 -10.59 1.06 -1.22 11.59 12506.7*

-45.65 0.09*

-44.09 0.06*

-44.20 0.11*

-47.72 0.08*

-37.62 0.16**

-0.00 Inf. (0.24)

0.09 Inf. (0.24)

-0.01 Inf. (0.24)

-0.00 Inf. (0.24)

-0.00 Inf. (0.24)

0.01 Inf. (0.24)

Jo u

rn

al

Pr

e-

Note: * denotes significant at the 1% level of significance.

f

ADF KPSS (with drift and trend Alte rnative nonstationary) Correlation Pe arson's Chi-squared test

Canada 0.02 11.99 -12.24 1.37 -0.58 13.02 15921.86 * -43.45 0.06*

oo

Me an Maximum Minimum Std. De v. Skewness Kurtosis Jarque-Bera

US 0.02 10.95 -9.46 1.15 -0.34 14.86 22089.08 * -45.8 0.08*

38

0.03 Inf. (0.24)

pr

O il 0.01 16.41 -15.19 2.41 -0.00 7.39 3028.38*

Journal Pre-proof Table 2. Estimates of the marginal distribution models (AR-SPLINE-GARCH model) Germany

Italy

Japan

0.05***

Canada France Mean equation 0.04* 0.05*

Cst(M)

0.04

AR(1)

-0.04

0.07*

0.05

0.04*

0.04*

-0.08***

- 0.04*

-0.02

-0.03

-0.15**

0.15*

Cst(V)

2.92***

1.53*

Variance equation 0.95* 2.00*

2.68*

1.41*

1.90

0.38*

Spline_0 (V)

11.33***

1.17

-8.57**

-8.20*

-6.80

2.38

12.56*

Spline_1 (V)

-38.06**

Spline_2 (V)

57.71*

-10.28**

2.40

27.55**

22.08

-12.45

-43.93*

38.28*

6.41

-12.45

-1.97

-4.67

30.02*

80.51*

Spline_3 (V)

-61.61*

-62.60*

-61.53*

-62.96*

-64.65*

-53.77**

-43.14

-84.97*

Spline_4 (V)

118.67***

61.10*

126.17*

89.87*

87.72*

56.52

46.65

77.20*

Spline_5 (V)

-185.83***

-89.15*

-170.33*

-119.08*

-126.28*

-71.79

-55.46

-45.33

ARCH(Alpha1)

0.09***

0.09*

0.03***

0.07*

0.06*

0.07*

0.11*

0.09*

ARCH(Alpha2)

-0.04**

GARCH(Beta1)

0.93***

0.88*

0.89*

0.88*

Asymmetry

-0.06***

-0.10*

-0.17*

-0.08*

Tail

8.35***

6.24*

15.94*

8.65*

-0.04*

21.46*

UK

f

US

0.88*

0.91*

-0.13*

-0.04

0.83*

-0.08*

9.63*

0.89*

-0.13*

7.90*

1.41*

-0.11*

7.31*

pr

0.05**

oo

O il

Diagnostic tests -8033.67 -4737.66 -5513.12 -6273.94 -6285.18 -6430.40 -6043.15 -4801.01 4.28 2.52 2.94 3.28 3.32 3.39 3.33 2.55 14.39 2.55 2.97 3.31 4.31 3.42 3.34 4.31 4.29 2.54 2.96 3.29 4.30 3.40 3.32 4.29 6.34 14.31 12.68 9.38 14.46 15.09 6.98 46.88 [0.70] [0.11] [0.17] [0.31] [0.10] [0.08] [0.63] [0.00] Q(10)(2) 8.53 13.83 4.82 16.51 1.96 12.60 14.03 6.52 [0.28] [0.08] [0.68] [0.17] [0.98] [0. 12] [0.05] [0.58] 1.60 2.79 0.21 1.43 0.13 0.05 4.61 0.29 McLe od-Li(1) [0.20] [0.06] [0.80] [0.20] [0.87] [0.94] [0.01] [0.74] Notes: T he lags p, q, r, and m are selected using the AIC, BIC and HQIC for different combinations of values ranging from 0 to 2. Q(10) and Q(10)(2) are the Ljung-Box statistics for serial correlation in the model residuals and squared residuals, respectively, computed with 10 lags. T he p-values (in square brackets) below 0.05 indicate the rejection of the null hypothesis. *, **, *** denote, respectively, significance at the 1%, 5%, and 10% levels.

Jo u

rn

al

Pr

e-

Log-Likelihood AIC BIC HQ IC Q(10)

39

Journal Pre-proof

Table 3. Best copula estimation results TVP Student-t

Dependence structure

US

Canada

-0.026*

0.004*

-1.995* 0.054* 4.998*

1.887* 0.018* 4.990*

-53.480 -106.959 -106.952 Italy -0.003* 8.221* -27.076 -54.151 -54.148

-79.923 -159.845 -159.838 UK 0.0218* 8.686* -23.128 -46.256 -46.253

Ψ0 Time -varying of the same lower and upper tail dependence

Ψ1 Ψ2 ν LL AIC BIC Static Student-t

 

Same lower and upper tail dependence (constant)

oo

f

LL AIC BIC

France -1.658* 0.893* -1.835* -0.127* 0.1789* 0.821* -18.136

Germany -0.367* 0.579* 0.765* -0.082* 0.577* 0.422* -31.759

Japan -0.057* 3.022* -2.004* -0.174* 0.347* 0.652* -9.567

-36.270 -36.260

-63.515 -63.506

-19.132 -19.122

pr

Time -varying Normal Markov copula

No lower and upper tail dependence

e-

P Q LL

Pr

AIC BIC

America 0.0158

Ave rage MES

France

Germany

Italy

Japan

UK

0.2663

-0.1634

0.0873

0.1007

-0.2335

0.0359

-3291.26

-210511699.6

-18118.90

-6347822

-134.830

-0.0159

0.1395

-0.0262

0.0480

-0.0204

-0.0544

0.0211

0.1043

0.1933

-0.0903

0.0258

0.0255

-0.0801

-0.0067

0.1870

-0.0305

0.0735

-0.0113

-0.0082

rn

Jo u

Ave rage ΔCoVaR (DCC) Ave rage ΔCoVaR (quantile regression) Ave rage ΔCoVaR (O LS regression)

Canada

-33.8499

-379987.12

Ave rage LRMES

al

Table 4. Risk analysis summary: SPLINE-GARCH model

40

0.0187 0.0195

Journal Pre-proof

Table 5: Significant test for DCC and OLS regression Significance Test for ΔCoVAR- DCC model

T est value

America

Canada

France

Germany

Italy

Japan

UK

0.4009*

0.4285*

0.4417*

0.4697*

0.3939*

0.3942*

0.4718*

0.4104*

0.5034*

Significance Test for delta CoVAR quantile regression T est value

0.5192*

0.5356*

0.4006*

0.5052*

0.5051*

Table 6: Dominance test for DCC model France

0.4797*

Ame rica

Germany

0.1407*

0.5965*

0.0205

Italy

Japan

UK

0.0133

0.0005

0.5125*

0.1894*

0

0

0.1656*

0.2848*

0.0740*

0.8359*

0.0051

0

0.0032

0.0035

0.5708*

pr

Canada

e-

America

oo

f

Notes. * Probability less than 1%.

Canada

0

France

0.3280*

0.6976*

Germany

0.0117

0.3581*

0

Italy

0.0623*

0.5084*

0.1462*

0.6533*

Japan

0.2763*

0.6323*

0.3717*

0.8124*

0.2566*

UK

0.0379*

0.5144*

0

0.4868*

0.0467*

0.7638* 0

al

Pr

0.8808*

Jo u

rn

Notes. T hese results are only for DCC model. For Quantile model results are available upon request. * Probability less than 1%.

Table 7: Risk analysis summary: GO-GARCH model America

Canada

France

Germany

Italy

Japan

0.0245

0.2569

-0.1041

0.0438

0.1124

Ave rage LRMES

-0.5571

-585.161

-346.999

-1.3393

0.8200

Ave rage ΔCoVaR (DCC)

-0.0078

0.1396

-0.0421

0.0881

-0.0141

-0.0309

0.0124

0.1043

0.1945

-0.0903

0.0260

0.0255

-0.0802

0.0187

-0.0067

0.1882

-0.0305

0.0739

-0.0113

-0.0082

0.0196

Ave rage MES

Ave rage ΔCoVaR (quantile re gression) Ave rage ΔCoVaR (OLS re gression)

41

-0.1800

UK

-30569.71

0.0716 -0.1424

Journal Pre-proof

Figure 1. Smoothed probabilities for high and low dependence regimes

oo

f

a) France

c) Japan

Jo u

rn

al

Pr

e-

pr

b) G ermany

42

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Figure 2. Time-varyi ng Normal Markov copula: Dependence dynamic for France, Germany, and Japan

France

e-

pr

oo

f

G ermany

rn

al

Pr

Japan

Jo u

Figure 3. Time-varying conditional Volatility, conditional correlation, and VaR: GARCH-DCC method Panel A. Conditional volatility plots Oil

US

Canada

France

43

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Germany

Italy

UK

pr

oo

f

Japan

Panel B. VaRs plots

Canada

Jo u

rn

al

Pr

e-

Oil

France

Germany

Italy

44

US

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UK

Pr

e-

pr

oo

f

Japan

Panel C. Conditional Correlation plots

Canada

France

Jo u

rn

al

US

Germany

45

Journal Pre-proof Italy

Japan

e-

pr

oo

f

UK

Pr

Figure 4. Comparison between MES and ΔCoVaR measures

Panel A. DCC method

Canada

Jo u

rn

al

US

Germany

France

46

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Italy

Japan

e-

pr

oo

f

UK

Pr

Panel B.: Quantile regression

Canada

Jo u

rn

al

US

France

Germany

47

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Japan

f

Italy

Pr

e-

pr

oo

UK

US

Jo u

Oil

Conditional volatility plots

rn

Panel A.

al

Figure 5. Time-varying conditional Volatility, conditional correlation, and VaR: GO-GARCH method

Canada

France

Germany

Italy

Japan

UK 48

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Panel B.

VaRs plots US

pr

oo

f

Oil

France

Germany

Jo u

rn

al

Pr

e-

Canada

Italy

Japan

UK

49

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DCC plots

US

Canada

Germany

pr

oo

f

France

Japan

UK

Jo u

rn

al

Pr

e-

Italy

Figure 6. Comparison between MES and ΔCoVaR : GO-GARCH method US

Canada

50

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France

Germany

Japan

Pr

e-

pr

oo

f

Italy

Jo u

rn

al

UK

51

Journal Pre-proof Figure 7. ΔCoVaR with GO-GARCH method: quantile regression US

Canada

Germany

Pr

e-

pr

oo

f

France

rn

al

Japan

Jo u

Italy

UK

52

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Jo u

rn

al

Pr

e-

pr

oo

f

Highlights 1. Systemic risk spillovers between crude oil and stock index returns of G7 is examined 2. Conditional value-at-risk and marginal expected shortfall approaches are used 3. Crude oil can be a good diversifier for investors in the Japan, US and Italy 4. The investors in Canada, Germany and the UK have to act more carefully in diversification opportunities

53