Tail-risk spillovers from China to G7 stock market returns during the COVID-19 outbreak: A market and sectoral analysis.

This study uses a combination of copulas and CoVaR to investigate risk spillovers from China to G7 countries before and during the COVID-19 pandemic. Using daily data on stock and equity sectors for the period from January 1, 2013 to June 9, 2021, the main empirical results show that, before the COVID-19 pandemic, stock markets were positively related and systemic risk was comparable for all countries. However, during the COVID-19 outbreak, the level of dependence increased for all G7 countries and the upside-downside risk spillovers become on average higher for all stock markets, with the exception of Japan. Our results also provide evidence of higher market risk exposure to information from China for the technology and energy sectors. Moreover, we find an asymmetric risk spillover from China to the G7 stock markets, with higher intensity in downside risk spillovers before and during COVID-19 spread.

Introduction

The global economy is facing the worst financial crisis, triggered by the COVID-19 outbreak since the US subprime crisis and Great Depression. In addition to dramatic health implications, the severity and spread of COVID-19 poses unprecedented challenges to global value chains and negatively impact investments and consumption patterns. The pandemic induced uncertainty and panic lead to lower cash flow expectations, and higher level of price volatility of financial assets. On February 2020, various U.S. stock market indices including the NASDAQ-100, the S&P 500 Index, and the Dow Jones Industrial Average endured their sharpest declines since 2008. In early March 2020, stock markets have declined over 30%; implied volatilities of equities and oil have spiked to crisis levels (OECD, 2020).1

The official announcements regarding the COVID-19 new cases of infection and fatality ratio, was found to be an important source of financial markets volatility (Albulescu, 2021, Ashraf, 2020, Rehman et al., 2021, Izzeldin et al., 2021). Other authors argue that the pandemic also impacts the stock market through halting industrial, tourism, aviation and other related sectors. Consequently, some industry sectors experienced higher volatility than others, which affect the investment decisions and the potential benefits of portfolio diversification.

Much effort has been made recently to better explain and evaluate how risk spreads across stock markets during turbulent periods (see among others Kang et al., 2019, Akhtaruzzaman et al., 2021, Su, 2020, Abuzayed et al., 2021). However, most of these studies investigate the spillovers by modeling conditional volatility and correlation, often using a GARCH-type model. The major drawback of such an indirect measurement method is that the extreme systemic risk in global stock markets is ignored and therefore the systemic risk spillover will be underestimated (Yu et al., 2018). It appears also from the literature that the study of spillovers between stock sectors have not received much attention compared with the focus on the relationship among international aggregate stock markets.

In this study, we rely on the combination of Copula models and the tail-risk interdependence conditional value at risk (CoVaR) developed by Adrian and Markus (2016). The CoVaR extends the standard regulatory tool of unconditional VaR by carrying about how financial difficulties of one market can increase the tail risk of other markets. Copula models are known to be more flexible and to better characterize the dependence between variables both at the center and the tails of the distribution. This information about the joint behavior of both variables is essential to derive accurate measures of the VaR and CoVaR.

We contribute to the ongoing debate and research regarding the volatility spillover effect across stock markets during the COVID-19 pandemic in the following aspects. First, we extend previous studies on the spillovers among stock returns that often consider mean–variance effects or symmetry in the dependence structure by exploring them at the upper and lower tails of the return distribution, while controlling for other stylized facts like asymmetry and time-varying dependence. This is achieved by fitting copula models and testing for extreme risk spillover effects across markets using the VaR and CoVaR measures. Second, we carry out our study at both market and sectoral levels, before and during the COVID-19 crisis. This provides a more comprehensive understanding of the magnitude and direction of risk spillovers among industry sector groups, which in turn enhances portfolio allocation decisions and trading strategies. Our findings are also valuable for policy makers in terms of building economic resilience strategies by identifying which sectors are most exposed to downside–upside risk spillovers. Our work is thus mostly related to that of Ghorbel et al. (2022) who use ADCC-GARCH models to analyze the risk spillovers between China and G7 stock markets before and during the COVID-19 crisis. However, we differ from it in that we use a large set of static and dynamic copulas, allowing us to flexibly and fully characterize the dependence structure between stock market returns, while avoiding the drawbacks of linear measures of interdependence (e.g., Pearson correlation and dynamic conditional correlation coefficients obtained from a DCC–GARCH model). This information regarding the dependence structure is crucial to compute the value at risk (VaR) of one market conditional on another market or sector fall into financial distress (Reboredo and Ugolini, 2015). Second, we conduct our analysis at both the aggregate market and sectoral levels, specifically to differentiate between the sector reaction and the market reaction as a whole. Finally, since we have studied the risk spillovers between China and G7 stock markets over a more recent period (January 1, 2013 to June 9, 2021), our results complement those of almost all previous works whose study periods cover the first wave of COVID-19 only.

We found evidence of a positive relationship between China and G7 stock markets, with dependence level and structure differed across subperiods. A similar conclusion was reached for the relationship between China and G7 stock sectors. Our empirical results reveal also that systemic risk spillover is intensified during the COVID-19 period and show an asymmetric behavior with downside movements greater than upside movements. In particular, we conclude that during the pandemic, the downside risk spillover from China was of most intensity for Italy, Germany, France and UK stock markets. At the same time, we found that the energy, financials, technology and basic materials stock sectors were heavily exposed to the downside tail risk, while telecommunication and non cyclical goods sectors have been relatively spared.

This paper proceeds as follows. Section 2 presents a review of the related literature on the financial contagion. Section 3 develops the methodology. Section 4 presents the data and the preliminary analysis. In Section 5, the empirical results are reported and interpreted. Finally, Section 6 draws conclusions concerning the main themes covered in this paper.

Table 6

Marginal estimation results for stock returns.

	G7	China	Germany	Canada	USA	Italy	France	Japan	UK
Mean
ϕ_0	0,043 (0.013)	0.038 (0.026)	0.020 (0.021)	0.023 (0.015)	0.055^∗(0.014)	0.035 (0.027)	0.028 (0.026)	0.023 (0.021)	0.007 (0.354)
ϕ_1	0,048^∗∗(0.023)	0.081^∗(0.021)	−0.035^∗∗∗(0.021)	0.041^∗∗∗(0.022)	−0.072^∗(0.022)	−0.060^∗(0.022)	−0.035 (0.026)	−0.147^∗(0.023)	−0.020 (0.360)
ϕ_2	0,003 (0.026)		−0.010 (0.021)	−0.002 (0.021)	0.004 (0.019)	0.000 (0.012)	−0.020 (0.032)
ϕ_3				0.030 (0.022)
Variance
ω	0.021^∗(0.005)	0.065^∗∗(0.029)	0.028^∗∗(0.012)	0.012^∗(0.004)	0.030^∗(0.006)	0.049^∗∗(0.020)	0.032^∗(0.011)	0.051^∗∗(0.020)	0.045^∗(0.016)
α	0.015 (0.014)	0.030^∗(0.011)	0.000 (0.010)	0.015 (0.012)	0.017 (0.020)	0.011 (0.012)	0.014 (0.015)	0.034^∗∗(0.016)	0.027 (0.041)
β	0.828^∗(0.024)	0.879^∗(0.034)	0.920^∗(0.024)	0.906^∗(0.017)	0.804^∗(0.025)	0.902^∗(0.026)	0.880^∗(0.026)	0.848^∗(0.039)	0.840^∗(0.118)
λ	0.258^∗(0.046)	0.096^∗(0.033)	0.116^∗(0.032)	0.126^∗(0.023)	0.312^∗(0.05)	0.122^∗(0.029)	0.164^∗(0.033)	0.162^∗(0.048)	0.193^∗(0.041)
Asym.	−0.147^∗(0.029)	−0.048^∗∗∗(0.025)	−0.121^∗(0.027)	−0.175^∗(0.029)	−0.157^∗(0.031)	−0.125^∗(0.030)	−0.154^∗(0.035)	−0.127^∗(0.031)	−0.126 (0.301)
Tail	5.634^∗(0.720)	7.173^∗(1.140)	5.134^∗(0.301)	8.553^∗(1.472)	5.352^∗(0.668)	5.874^∗(0.750)	5.860^∗ (0.747)	6.039^∗(0.699)	5.202^∗(1.110)
LogLik	2164.69	6922.98	3173.49	2656.47	2420.32	3639.51	3069.07	3077.69	2876.93
Lj	8.772 [0.643]	8.004 [0.713]	12.652 [0.317]	9.827 [0.546]	7.135 [0.788]	12.581 [0.322]	8.489 [0.669]	11.650 [0.390]	15.564 [0.158]
Lj2	8.505 [0.668]	12.930 [0.298]	8.520 [0.666]	9.101 [0.613]	10.030 [0.528]	21.664 [0.027]	10.788 [0.461]	13.187 [0.281]	15.211 [0.173]
ARCH	8.473 [0.747]	13.433 [0.338]	8.837 [0.717]	8.864 [0.715]	9.960 [0.620]	22.303 [0.034]	11.289 [0.504]	13.007 [0.369]	15.603 [0.210]

Notes: The table summarizes the GJR-GARCH estimation results. The values between brackets represent the standard error of the parameters. LogLik is the log-likelihood statistic. Lj and Lj2 denote the Ljunk–Box statistics with 12 lags for serial correlation in the residual and the squared residual models, respectively. ARCH is the Lagrange multiplier test for autoregressive conditional heteroskedasticity effect in the residuals up to 12th order. -values associated with the tests are reported in square brackets.

Literature review

A review of major theoretical and empirical studies focusing on financial market comovement emphasize the fact that a significant increase in cross-market linkages after a shock is an indicator of the presence of contagion (Forbes and Rigobon, 2002, Dimitriou et al., 2013, Flavin and Sheenan, 2015, Andriosopoulos et al., 2017, Gkillas et al., 2019, Fang et al., 2021, Li, 2021).

Since the seminal work of Markowitz (1952), a large number of useful techniques have been developed and used to investigate the relationship between financial time series data. For instance, Pearson and Spearman’s correlation represent the most common technique used to evaluate linkages among financial markets (e.g., Bonanno et al., 2004, Durante and Pappadà, 2014). However, when the usual assumption of multivariate normality is in question, applying this technique to measure the dependence between returns could lead to underestimate the joint risk of extreme events.

The proposed connectedness approach of Diebold and Yilmaz (2008) and Diebold and Yılmaz (2014), based directly on the notion of variance decompositions in vector autoregressions, is another useful tool that has been applied in many related studies (Caloia et al., 2019, Mensi et al., 2021, He and Hamori, 2021). Aloui et al. (2011) used copula functions to examine the contagion effects between the US and BRIC stock markets and conclude that the dependency on the US is larger for countries with higher sensitivity to commodity-price changes. Jung and Maderitsch (2014) explored the volatility transmission between stock markets in Europe, Hong Kong, and the United States over the period 2000–2011. Using heterogeneous autoregressive distributed lag model, the authors reveal time-variation and structural breaks in volatility spillovers during the financial crisis of 2007. Shen et al. (2015) examined the contagion influence of the European debt crisis on China’s stock market by the Kalman filter approach. The proposed model confirms that crisis contagion definitely happens between countries that trade more often with each other. Mensi et al. (2017) combined variational mode decomposition (VMD) method and copula functions to examine the dependence structure between crude oil prices and major regional developed stock markets under different investment horizons. The findings show that there is tail dependence between oil and all stock markets for the raw return series. More recently, Davidson (2020) proposed a novel model switching approach to analyze contagion from the US to Argentina, Brazil and Mexico. Empirical results show that contagion exists during the global financial crisis while early crises exhibit interdependence only. Elgammal et al. (2021) examine the dynamic relationships, at both return and volatility levels, between global equity, energy and gold markets prior to and during the COVID-19 crisis. Under the COVID-19 regime, the authors provide evidence of bidirectional return spillover effects between equity and gold markets and unidirectional spillovers from energy markets to the equity and gold returns.

Evidence of extreme risk spillovers between stock markets has been well documented in the literature, especially during periods of market turbulence. Focusing on the COVID-19 period, Bissoondoyal-Bheenick et al. (2021) show that both stock return and volatility connectedness increase across the different phases of the pandemic for the G20 members. They also find that this connectedness is intensified as the severity of the pandemic increases. Akhtaruzzaman et al. (2021) show that dynamic conditional correlations (DCCs) between Chinese and G7 financial and nonfinancial stock returns increased significantly during the COVID-19 period. The empirical results indicate also the importance of financial firms in financial contagion transmission. So Mike et al. (2020) used dynamic financial networks based on correlations and partial correlations of stock returns to assess the impacts of the COVID-19 pandemic on the connectedness of the Hong Kong financial market. The results show an increase in both the network density and clustering in the partial correlation networks during the COVID-19 crisis. Azimli (2020) applied a quantile regression to investigate the COVID-19 pandemic’s effect on the degree and structure of risk-return dependence in the US. They conclude that the pandemic changed the dependence and structure of risk-return relationship. Izzeldin et al. (2021) used a smooth transition HAR model in order to examine the impact of COVID-19 on G7 stock markets and sectors. They conclude that the Health Care and Consumer services sectors were most affected by the crisis, while the Technology sector was hit least severely. Tiwari et al. (2022) use various techniques: Diebold and Yılmaz (2014) (DY, hereafter) spillover indices and TVP-VAR, LASSO-VAR to examine the connectedness between energy sector stocks of 20 regional blocs. They conclude that during the US subprime crisis and COVID-19 pandemic, energy stock market spillovers have increased substantially. Caselli et al. (2020) investigated the impact of the COVID-19 pandemic on G20 stock markets using the spillover index approach by Diebold and Yilmaz (2008) and Diebold and Yılmaz (2014). The findings show that the developed markets are the main spillover transmitters while the emerging markets are the main spillover receivers in volatility transmissions.

The complex nature of financial systems highlights the needs of more sophisticated tools when considering tail risk between financial markets or institutions. To extend the traditional measure of market risk VaR, Adrian and Markus (2016) introduced the conditional value at risk (CoVaR) as the VaR of a specific market conditional on the fact that another market is in distress. Using a combination of CoVaR and copula models, Reboredo and Ugolini (2015) studied the systemic risk in European sovereign bond markets before and during the Greek debt crisis. The authors find that, before the debt crisis, sovereign bond markets were all dependent and financial risk was comparable for all considered countries. However, with the onset of the debt crisis, systemic risk decreased for all countries in crisis, except Spain. Reboredo et al. (2016) examine tail risk spillovers between exchange rates and stock prices and conclude that downside and upside spillovers are asymmetric with greater spillovers from and to the USD than from and to the EUR. Ji et al. (2018) used a time-varying copula based CoVaR model to examine the impact of uncertainties on energy prices. The empirical findings reveal an asymmetry in upside and downside risk spillovers, with energy prices being more affected by an increase in uncertainty. Tian and Ji (2021) analyze the risk spillovers from four financial markets to the developed market’s financial system using a GARCH copula quantile regression-based CoVaR model. Their findings show that risk spillovers are substantially bigger during the COVID-19 epidemic than during the banking and sovereign debt crises. Hanif et al. (2021) have used Copula and Conditional Value at Risk approaches to examine the impacts of COVID-19 outbreak on the spillover between ten US and Chinese equity sectors. Their results show time varying bidirectional asymmetric risk spillovers from the US to China and vice versa. Moreover, the risk spillover is higher from the US to China before COVID-19 and from China to the US during COVID-19 spread. Zehri (2021) employ a GARCH-Copula CoVaR approach to investigate the tail spillovers from the US to Asian stock returns and conclude that there is a large spillover effect from the US to East Asian stock markets especially during the COVID-19 period. Ghorbel et al. (2022) used VAR-ADCC models and CoVaR to examine extreme risk spillovers between G7 stock markets and China. Their results show that during the COVID-19 pandemic a significant and asymmetrical two-way risk transmission exists between the majority of the considered pair markets. Also, their findings suggest that downward and upward movements are significantly larger before the COVID-19 pandemic in almost all cases.

Table 8

Copulas estimation results in the precrisis period for China and G7 countries.

	G7	Germany	Canada	USA	Italy	France	Japan	UK
Panel A: static copulas
Gaussian
ρ	0.393 (0.019)	0.369 (0.025)	0.310 (0.020)	0.331 (0.020)	0.306 (0.022)	0.366 (0.023)	0.295 (0.02)	0.402 (0.019)
AIC	−276.32	−254.573	−172.548	−193.310	−172.377	−248.694	−155.809	−300.661
Student-t
ρ	0.394 (0.020)	0.371 (0.025)	0.313 (0.022)	0.332 (0.022)	0.307 (0.023)	0.367 (0.021)	0.292 (0.024)	0.405 (0.021)
v	25.195 (12.597)	13.419 (4.728)	23.353 (12.781)	26.686 (18.175)	14.243 (5.528)	23.397 (12.08)	10.779 (3.025)	13.802 (4.924)
AIC	−284.846	−264.910	−175.692	−195.370	−180.093	−251.893	−168.011	−309.699
Gumbel
θ	1.308 (0.028)	1.271 (0.026)	1.219 (0.022)	1.246 (0.023)	1.210 (0.021)	1.259 (0.027)	1.204 (0.020)	1.307 (0.027)
AIC	−247.557	−209.122	−143.905	−171.750	−138.975	−191.550	−130.553	−247.204
Rotated Gumbel
θ	1.295 (0.026)	1.291 (0.024)	1.219 (0.021)	1.228 (0.022)	1.227 (0.022)	1.284 (0.024)	1.210 (0.022)	1.328 (0.025)
AIC	−245.890	−256.009	−155.447	−163.564	−181.117	−246.746	−163.887	−299.224
Clayton
θ	0.191 (0.012)	0.198 (0.012)	0.156 (0.013)	0.158 (0.012)	0.165 (0.013)	0.195 (0.012)	0.156 (0.012)	0.217 (0.012)
AIC	−215.635	−237.477	−142.692	−146.893	−168.050	−231.831	−151.443	−274.044
Symmetric Joe–Clayton
λ_U	0.204 (0.035)	0.184 (0.032)	0.107 (0.035)	0.160 (0.035)	0.069 (0.033)	0.096 (0.035)	0.078 (0.034)	0.138 (0.037)
λ_L	0.161 (0.031)	0.238 (0.029)	0.145 (0.032)	0.128 (0.031)	0.188 (0.030)	0.239 (0.029)	0.165 (0.028)	0.268 (0.029)
AIC	−264.863	−258.933	−163.537	−182.824	−182.874	−247.323	−169.496	−300.587
Panel B: dynamic copulas
TVP-Gaussian
α	0.009 (0.004)	0.013 (0.006)	0.010 (0.004)	0.007 (0.003)	0.030 (0.012)	0.023 (0.048)	0.004 (0.025)	0.025 (0.012)
β	0.990 (0.006)	0.982 (0.011)	0.987 (0.006)	0.992 (0.004)	0.919 (0.040)	0.961 (0.113)	0.156 (0.259)	0.898 (0.042)
AIC	−312.365	−282.004	−191.855	−218.902	−187.094	−281.441	−153.735	−306.314
TVP-Student-t
α	0.010 (0.005)	0.014 (0.006)	0.010 (0.004)	0.009 (0.004)	0.030 (0.012)	0.024 (0.030)	0.000 (0.016)	0.024 (0.012)
β	0.988 (0.007)	0.981 (0.011)	0.986 (0.007)	0.990 (0.006)	0.921 (0.039)	0.963 (0.069)	0.729 (0.048)	0.905 (0.047)
v	29.505 (25.918)	15.059 (5.903)	31.727 (17.134)	28.132 (30.383)	14.915 (5.663)	27.859 (26.238)	11.033 (3.217)	14.290 (5.350)
AIC	−312.657	−287.580	−191.641	−219.016	−185.566	−281.977	−164.380	−312.376
TVP-Gumbel
ω	1.030 (0.361)	−0.220 (0.754)	0.767 (0.342)	0.931 (0.354)	0.295 (0.357)	0.824 (0.748)	1.320 (0.375)	1.003 (0.371)
β¯	−0.147 (0.225)	0.643 (0.351)	−0.079 (0.638)	−0.176 (0.485)	0.277 (0.489)	−0.022 (0.484)	−0.964 (0.542)	−0.269 (0.524)
α¯	−1.134 (0.392)	−0.306 (0.454)	−0.762 (0.321)	−0.835 (0.355)	−0.646 (0.376)	−1.119 (0.569)	1.059 (0.354)	−0.397 (0.375)
AIC	−250.022	−220.256	−151.019	−178.914	−148.239	−259.502	−135.684	−250.058
TVP-Rotated Gumbel
ω	1.123 (0.361)	−0.365 (0.754)	1.935 (0.342)	1.209 (0.354)	−0.384 (0.357)	0.413 (0.748)	1.318 (0.375)	1.048 (0.371)
β¯	−0.246 (0.225)	0.734 (0.351)	−0.939 (0.638)	−0.374 (0.485)	0.746 (0.489)	0.232 (0.484)	−0.912 (0.542)	−0.259 (0.524)
α¯	−1.042 (0.392)	−0.174 (0.454)	−1.186 (0.321)	−1.042 (0.355)	−0.210 (0.376)	−0.689 (0.569)	0.900 (0.354)	−0.522 (0.375)
AIC	−255.821	−265.149	−163.798	−171.605	−189.405	−259.502	−167.902	−302.775
TVP-Clayton
ω	−0.098 (0.138)	−0.023 (0.074)	−0.155 (0.323)	−0.173 (0.191)	−0.046 (0.085)	0.024 (0.043)	−2.449 (0.231)	−1.003 (0.237)
β¯	−1.093 (0.431)	−0.325 (0.132)	−0.567 (0.578)	−1.304 (0.510)	−0.499 (0.218)	−0.386 (0.174)	0.324 (0.290)	−0.493 (0.370)
α¯	0.661 (0.145)	0.897 (0.075)	0.771 (0.333)	0.621 (0.174)	0.857 (0.060)	0.929 (0.064)	−0.762 (0.102)	−0.249 (0.207)
AIC	−223.005	−237.688	−142.767	−154.435	−169.366	−236.985	−148.424	−272.179
TVP-Symmetric Joe–Clayton
ψ_0,U	1.054 (0.719)	0.209 (0.127)	−0.064 (0.462)	−0.024 (0.770)	0.463 (1.066)	0.646 (0.932)	−6.585 (1.631)	0.040 (0.541)
ψ_1,U	−9.118 (3.708)	−1.763 (1.003)	−6.523 (3.125)	−5.700 (4.115)	−9.999 (5.252)	−9.999 (5.703)	7.505 (1.297)	−1.148 (1.587)
ψ_2,U	−0.116 (0.297)	0.869 (0.094)	0.038 (0.264)	−0.075 (0.421)	0.110 (0.368)	0.040 (0.481)	−1.002 (0.002)	0.848 (0.158)
ψ_0,L	−0.654 (0.853)	−0.758 (0.777)	−1.108 (0.978)	−0.763 (1.088)	0.042 (0.163)	−0.207 (0.431)	−2.851 (1.240)	−0.256 (0.963)
ψ_1,L	−3.431 (3.524)	−2.829 (2.882)	−5.131 (3.485)	−5.163 (4.179)	−1.028 (0.622)	−5.005 (1.803)	1.765 (4.646)	−2.616 (3.355)
ψ_2,L	−0.357 (0.230)	−0.948 (0.151)	−0.763 (0.161)	−0.343 (0.192)	0.785 (0.090)	−0.998 (0.003)	−0.837 (0.188)	−0.603 (0.640)
AIC	−266.780	−259.465	−160.410	−179.615	−184.155	−251.493	−165.494	−295.562

Notes: The table displays the ML estimates for the static and time-varying copula models for China and G7 stock markets returns. Standard errors are between brackets and Akaike Information criterion (AIC) values are provided for each copula model. Lower AIC values indicate the better-fit copula model.

The above discussion highlights the importance of understanding how the current pandemic has shaped extreme risk spillovers between financial markets, which could be of great interest to investors in their decision-making process and policy makers in stabilizing financial systems. Our literature review indicates also the need for studies considering the impact of catastrophic event on extreme co-movements among equity sectors (Shahzad et al., 2021). We address this important research gap by focusing specifically on the risk spillovers from China’s stock market to G7 equity sectors before and during the COVID-19 outbreak.

Methodology

Systemic risk measures

In this paper, we investigate the risk spillover from China to G7 stock markets using the CoVaR method proposed by Adrian and Markus (2016). CoVaR can be defined as the value at risk (VaR) of the financial system conditional on one market or sector fall into financial distress. It has the advantage of capturing the extreme risk spillover as well as the general spillover effects (see e.g. Girardi and Ergün, 2013, Reboredo and Ugolini, 2015, Reboredo et al., 2016).

Formally, the downside CoVaR is defined as the -quantile of the conditional distribution of , as follows:

where is the -quantile of China’s stock return distribution, denotes returns for the G7 stock markets and the returns for China’s stock market, all at time . Likewise, we can measure the upside CoVaR as

where now denote the upside VaR of China’s stock returns with a confidence level .

Using copula representation, the conditional probabilities expressed in Eqs. (1), (2) can be re-written in terms of copulas , respectively as

where and are the marginal distributions of and respectively. Following Reboredo and Ugolini (2015), a two step procedure is employed to estimate the CoVaR. First, we determine the value of given that , and are known. Second, the CoVaR can be estimated by inverting the marginal distribution function of ,

To test for the significance of downside–upside risk spillover effects, we compare the difference between CoVaR and its corresponding VaR using the Kolmogorov–Smirnov (K–S) test as proposed by Abadie (2002). Under the null hypothesis of no systemic impact from China’s stock market to G7 stock market, the statistic of the test is defined as follows: where and denote the cumulative CoVaR and VaR distribution functions, respectively, and and are the size of the two samples.

Dynamic Copula models

The CoVaR approach implemented in this paper is based on copula estimation results. We will consider different copula functions having different specifications in terms of generator functions and tail dependence coefficients. Overall, six different copula models are selected: the Gaussian, Student-t, Gumbel, Rotated Gumbel, Clayton and symmetric Joe–Clayton copula. The properties of these copula models are summarized in Table 1.

Table 1

Characteristics of bivariate copula models.

Name	Copula	Parameter range	Kendall’s τ	Tail dependence (λ_L, λ_U)
Gaussian	C_N(u,vρ)=ϕ(ϕ^−1(u),ϕ^−1(v))	ρ∈(−1,1)	2πarcsin(ρ)	(0,0)
Student-t	C_ST(u,v|ρ,v)=T(tv−1(u),tv−1(v))	ρ∈(−1,1), υ>2	π2arcsin(ρ)	λ_L=λ_U=2t_υ+1−υ+11−ρ1+ρ
Gumbel	C_G(u,vθ)=exp(−[(−lnu)^θ+(−lnv)^θ]^1/θ)	θ≥1	1−1θ	0,2−2^−1θ
Rotated Gumbel	C_RG(u,vθ)=u+v−1+C_G(1−u,1−vθ)	θ≥1	1−1θ	2−2^−1θ,0
Clayton	C_C(u,vθ)=(u^−θ+v^−θ−1)^−1/θ	θ∈(0,∞)	θθ+2	(2^−1/θ,0)
Symmetric Joe–Clayton	C_SJC(u,v|λ_U,λ_L)=0.5. (C_JC(u,v|λ_U,λ_L)+C_JC(1−u,1−v|λ_U,λ_L)+u+v−1)	λ_U,λ_L∈(0,1)	no closed form	(2^−1/γ,2−2^−1/κ)

Notes: The table summarizes the properties of bivariate copula families used in this work. and are the gaussian and the Student-t c.d.f with degrees of freedom. denotes the Joe–Clayton (BB7) copula given by with and .

It can be seen that the selected copula models are able to capture symmetric dependence as well as asymmetric dependence between stock markets. The dependence is symmetric in both tails of the distribution for the Gaussian and Student-t copulas. The Gaussian copula has no tail dependence while the Student-t copula can capture dependence in the tail. In contrast to the symmetric copulas, the Gumbel, rotated Gumbel, Clayton and SJC copulas can be used to capture asymmetry between lower and upper tail. The Gumbel copula exhibits strong right tail dependence and weak left tail dependence, whereas the Clayton copula shows greater tail dependency in the lower tail instead of the upper tail. The rotated Gumbel can be viewed as a mirror image of the Gumbel, i.e. it exhibits weak right tail dependence and strong left tail dependence. The SJC copula, introduced in Patton (2006) as a linear combination of Joe–Clayton copula (BB7), allows for asymmetry in the upper and lower tail and by construction, it nests the symmetry as a special case when .

The parameters of the above mentioned copulas are allowed to vary through time using some specified evolution paths. For the selected elliptical copulas, i.e. Gaussian and copulas, the time-varying dependence parameter evolves through time as in the DCC(1,1) model of Engle (2002):

where the parameter constraints and represent non-negative scalars satisfying and is the covariance matrix of standardized residuals .

For Archimedean copulas, the evolution path is specified as in Patton (2006): where is the modified logistic function, intended to keep the dependence parameter in the domain of definition.

We estimate the parameters of the copula using the inference functions for margins (Joe and Xu, 1996). We first determine the margin parameters by maximum likelihood method:

Next, given estimates and , the unknown parameters of the copula  are determined as

This two-step procedure has the advantage to solve the maximization problem in case of high dimensional distributions. Under the usual regularity conditions, the IFM estimator is asymptotically efficient and normal.

Marginal models

For the marginal models, we consider an specification for the conditional mean and the GJR GARCH model of Glosten et al. (1993) for the conditional variance. More specifically, the marginal model for each stock market is given by where the disturbance is a i.i.d random variable with zero mean and unit variance that follows the skewed student-t distribution of Hansen (1994). The parameter captures asymmetric effects and if and otherwise; it implies that when bad news will lead to a greater rise in volatility compared to good news.

Data

We construct our dataset using the MSCI total return indices for China and G7 countries2 on a daily basis from January 2013 to June 2021, thus covering the periods before and during the COVID-19 crisis. The pre-crisis period ran from 1 January, 2013 through 30 December, 2019 and the crisis period from 31 December 2019, when the WHO China Country office reported officially a cluster of cases of pneumonia in Wuhan, to 09 June, 2021.

Because analyzing the risk spillover at the market level only may mask the potential heterogeneous and asymmetric effects of the crisis on various sectors (Forbes, 2002 and Tai, 2004), we also collect regional sector price indices for ten sectors (energy, basic materials, general industrials, cyclical consumer goods, non-cyclical consumer goods, financials, healthcare, technology, telecommunication services and utilities). These sectors have been categorized following the broad distinction of Thomson Reuters Business Classification (TRBC). All data are denominated in USD and sourced from DataStream.

The data, plotted in Fig. 1, Fig. 2, show that all indices exhibited bursts at the end of the first quarter of 2020 as the COVID-19 crisis evolves and spreads to other countries. The return series are obtained by using the logarithmic differences of the consecutive prices expressed in percentage. The Basic characteristics of the data at market and sector levels have been summarized in Table 2 and Table 3, respectively. Panel A of both Tables present the summary statistics on the variables of interest in the pre-crisis period, and Panel B show similar statistics in the crisis period.

Fig. 1

Time series plot of daily stock indices for the G7 (regional and country indices).

Fig. 2

Time series plot of daily sectoral indices for the G7 (regional indices).

Table 2

Summary statistics of stock index returns.

	G7	China	Germany	Canada	USA	Italy	France	Japan	UK
The pre-crisis period
Min	−4.945	−6.606	−8.757	−4.018	−4.136	−15.693	−10.083	−6.330	−11.467
Mean	0.043	0.027	0.022	0.014	0.052	0.019	0.032	0.032	0.016
Max	3.512	5.849	4.816	4.442	4.854	6.806	5.757	6.390	5.742
SD	0.695	1.182	1.060	0.871	0.798	1.391	1.039	1.105	0.973
Skew.	−0.731	−0.171	−0.499	−0.140	−0.526	−0.917	−0.652	−0.274	−0.996
Kurt.	4.277	2.295	4.082	2.428	3.797	10.223	6.787	3.589	13.766
Q(12)	40.772^∗	41.994^∗	29.179^∗	37.864^∗	14.474	32.944^∗	32.990^∗	93.895^∗	53.685^∗
Q^2(12)	326.356^∗	261.602^∗	144.521^∗	679.081^∗	489.611^∗	113.981^∗	184.671^∗	416.230^∗	394.698^∗
JB	1543.09^∗	405.73^∗	1332.98^∗	450.24^∗	1171.64^∗	8150.02^∗	3606.82^∗	994.56^∗	14616.4^∗
ARCH	165.997^∗	154.413^∗	93.426^∗	241.658^∗	216.623^∗	80.466^∗	112.593^∗	222.591^∗	217.295^∗
KPSS	0.051	0.049	0.052	0.043	0.048	0.061	0.055	0.038	0.052
The crisis period
Min	−10.723	−6.091	−15.094	−14.204	−12.917	−20.544	−14.903	−6.517	−14.161
Mean	0.073	0.070	0.063	0.070	0.082	0.046	0.057	0.045	0.009
Max	8.683	4.942	10.243	12.214	8.992	8.623	8.471	7.102	10.995
SD	1.640	1.520	1.826	1.964	1.862	2.009	1.831	1.265	1.828
Skew.	−1.286	−0.457	−1.545	−1.688	−1.037	−3.256	−1.575	0.022	−1.104
Kurt.	13.030	1.379	15.939	19.497	12.171	32.185	14.447	5.289	13.806
Q(12)	147.661^∗	15.793	48.209^∗	102.696^∗	193.259^∗	52.148^∗	49.260^∗	19.365^∗∗∗	42.290^∗
Q^2(12)	431.813^∗	142.241^∗	87.431^∗	398.714^∗	498.924^∗	38.535^∗	114.579^∗	146.926^∗	132.038^∗
JB	2686.07^∗	41.36^∗	4015.8^∗	5965.97^∗	2320.64^∗	16445.2^∗	3331.09^∗	424.10.52^∗	2976.40^∗
ARCH	146.844^∗	81.34^∗	73.288^∗	133.483^∗	157.770^∗	35.498^∗	73.984^∗	84.994^∗	87.835^∗
KPSS	0.068	0.084	0.067	0.056	0.062	0.064	0.060	0.094	0.059

Notes: The table displays summary statistics of log change of stock price indices in G7 (regional), China, Germany, Canada, USA, Italy, France, Japan and the UK (Daily Data). Q(12) and Q(12) are the Ljung–Box statistics for serial correlation. JB is the empirical statistic of the Jarque–Bera test for normality. ARCH is the Lagrange multiplier test for autoregressive conditional heteroskedasticity. KPSS is the Kwiatkowski et al. (1992) test for stationarity with a constant and time trend. *, ** and *** indicate the rejection of the null hypotheses of no autocorrelation, normality, homoscedasticity and stationarity at the 1%, 5% and 10% levels of significance respectively for statistical tests.

Table 3

Summary statistics for sector returns.

	Energy	Bas. mat.	Indust.	Cyc.Gds	Non-Cyc.Gds	Financials	Health.	Techn.	Telecom.	Utilities
The pre-crisis period
Min	−12.244	−4.929	−5.340	−5.413	−3.430	−7.478	−4.022	−4.665	−4.157	−4.006
Mean	−0.001	0.018	0.046	0.045	0.036	0.038	0.052	0.068	0.032	0.035
Max	18.027	3.221	2.933	3.851	3.064	2.815	3.723	5.512	3.587	3.357
SD	1.256	0.870	0.707	0.706	0.601	0.780	0.798	0.955	0.707	0.707
Skew.	0.930	−0.351	−0.659	−0.678	−0.544	−0.957	−0.455	−0.538	−0.300	−0.525
Kurt.	28.985	1.911	3.565	3.927	3.115	6.818	2.332	3.407	2.935	2.254
Q(12)	15.899	63.468^∗	87.730^∗	62.566^∗	28.802^∗	47.757^∗	24.908^∗∗	28.272^∗	23.541^∗∗	16.376
Q^2(12)	260.769^∗	217.523^∗	222.587^∗	297.045^∗	144.685^∗	207.026^∗	256.855^∗	440.777^∗	89.329^∗	82.673^∗
JB	63749.35^∗	312.38^∗	1090.64^∗	1303.19^∗	821.80^∗	3787.75^∗	472.57^∗	963.85^∗	676.81^∗	466.69^∗
ARCH	285.882^∗	120.217^∗	123.809^∗	143.255^∗	99.102^∗	133.340^∗	135.480^∗	188.119^∗	68.903^∗	61.613^∗
KPSS	0.059	0.046	0.046	0.048	0.038	0.054	0.071	0.033	0.048	0.044
The crisis period
Min	−21.229	−10.446	−9.955	−10.145	−9.209	−13.066	−9.165	−13.364	−8.492	−11.804
Mean	−0.002	0.084	0.058	0.096	0.052	0.062	0.059	0.121	0.025	0.021
Max	15.358	10.282	9.003	7.965	6.100	10.655	6.579	9.053	4.933	9.728
SD	2.917	1.675	1.634	1.592	1.240	2.100	1.459	1.998	1.201	1.778
Skew.	−1.282	−0.897	−0.949	−1.346	−0.960	−1.034	−0.700	−0.885	−1.040	−0.580
Kurt.	12.948	10.445	10.184	11.163	13.092	10.250	9.273	9.451	10.048	12.122
Q(12)	51.322^∗	53.943^∗	63.447^∗	76.289^∗	111.625^∗	82.464^∗	141.478^∗	142.873^∗	93.367^∗	102.608^∗
Q^2(12)	189.386^∗	238.099^∗	339.685^∗	269.311^∗	462.496^∗	372.398^∗	519.729^∗	347.929^∗	346.463^∗	620.077^∗
JB	2653.4^∗	1708.9^∗	1633.179^∗	2008.15^∗	2665.6^∗	1664.05^∗	1337.63^∗	1406.58^∗	1602.317^∗	2256.53^∗
ARCH	93.910^∗	93.595^∗	107.755^∗	132.079^∗	164.639^∗	116.599^∗	173.260^∗	126.743^∗	126.583^∗	186.638^∗
KPSS	0.055	0.088	0.083	0.096	0.049	0.065	0.044	0.056	0.054	0.033

Notes: The table displays summary statistics of log change of G7 sectoral indices (Daily Data). Q(12) and Qž(12) are the Ljung–Box statistics for serial correlation. JB is the empirical statistic of the Jarque–Bera test for normality. ARCH is the Lagrange multiplier test for autoregressive conditional heteroskedasticity. KPSS is the Kwiatkowski et al. (1992) test for stationarity with a constant and time trend. *, ** and *** indicate the rejection of the null hypotheses of no autocorrelation, normality, homoscedasticity and stationarity at the 1%, 5% and 10% levels of significance respectively for statistical tests.

It can be noticed first that all return series showed negative skewness values, except Japan in the second period and the energy sector in the first period. Second, higher kurtosis values are more pronounced especially in the crisis period. This is consistent with the existence of fat tails in the return distributions, asymmetry and departure from the normality assumption. The Jarque Bera test results confirm this conclusion and reject the normality assumption for all return series at the conventional significance level. Furthermore, the Ljung–Box statistics highlight the presence of serial correlation in return and squared return series in almost all cases. Also, the ARCH-Lagrange multiplier (ARCH-LM) statistics are significant for all the series in both periods indicating the presence of ARCH effects. The differences between the maximum and minimum returns show that the range were greater for the crisis period (except for China) compared to the precrisis period. This suggests a greater probability of large decreases during the COVID-19 period. Finally, the results of the KPSS stationarity test confirm that all return series were stationary.

Table 4, Table 5 report the unconditional correlations for return series in both periods. As expected, there is an increase in the level of correlation between China and all G7 stock markets in the aftermath of the pandemic. The same holds true for sectoral indices. The highest correlation in the crisis period is observed for the G7 stock market and the cyclical consumer goods sector and the lowest one is for Japan and the utilities sector.

Table 4

Correlation between stock indices in the precrisis period (lower triangle) and the crisis period (upper triangle)

	G7	China	Germany	Canada	USA	Italy	France	Japan	UK
G7		0.516	0.730	0.896	0.987	0.712	0.737	0.333	0.739
China	0.426		0.497	0.500	0.470	0.423	0.491	0.379	0.500
Germany	0.673	0.376		0.764	0.633	0.903	0.954	0.402	0.889
Canada	0.738	0.331	0.555		0.854	0.752	0.780	0.289	0.802
USA	0.952	0.326	0.499	0.648		0.625	0.638	0.228	0.641
Italy	0.608	0.300	0.809	0.519	0.457		0.917	0.328	0.858
France	0.697	0.382	0.930	0.588	0.519	0.853		0.401	0.920
Japan	0.233	0.320	0.122	0.142	0.034	0.068	0.131		0.415
UK	0.679	0.406	0.805	0.633	0.489	0.740	0.844	0.180

Notes: The table gives the unconditional correlation between daily returns of China and the G7 stock markets in the precrisis and crisis periods.

Table 5

Correlation between the G7 sectoral indices and China in the precrisis period (lower triangle) and the crisis period (upper triangle)

	China	Energy	Bas. mat.	Indust.	Cyc.Gds	Non-Cyc.Gds	Financials	Health.	Techn.	Telecom.	Utilities
China		0.439	0.499	0.503	0.536	0.386	0.437	0.457	0.499	0.433	0.334
Energy	0.250		0.816	0.828	0.734	0.667	0.860	0.634	0.598	0.690	0.603
Bas. mat.	0.435	0.652		0.924	0.872	0.821	0.880	0.784	0.731	0.813	0.769
Indust.	0.451	0.587	0.830		0.910	0.843	0.940	0.812	0.752	0.847	0.797
Cyc.Gds	0.446	0.539	0.747	0.901		0.810	0.852	0.831	0.888	0.800	0.751
Non-Cyc.Gds	0.268	0.412	0.552	0.684	0.703		0.820	0.868	0.762	0.905	0.893
Financials	0.385	0.592	0.747	0.867	0.836	0.633		0.760	0.705	0.833	0.790
Health.	0.306	0.451	0.575	0.722	0.737	0.651	0.709		0.853	0.813	0.816
Techn.	0.388	0.488	0.614	0.769	0.806	0.575	0.711	0.728		0.711	0.694
Telecom.	0.289	0.409	0.532	0.603	0.609	0.672	0.577	0.492	0.437		0.846
Utilities	0.147	0.345	0.414	0.462	0.451	0.693	0.427	0.435	0.347	0.573

Notes: The table gives the unconditional correlation between daily sectoral indices of China and the G7 markets in the precrisis and crisis periods.

Results

Marginal results

In the first step, we estimate by using the maximum likelihood estimation (MLE) method a GJR-GARCH model for the return data. The Akaike Information Criterion (AIC) is used to select the number of parameters and in the autoregressive and moving average specifications in Eq. (3). The results reported in Table 6, Table 7 indicate that conditional volatility is past-dependent and very persistent over time. The Ljunk–Box statistics for serial correlation in the residual and the squared residual models, indicate that the standardized residuals are approximately i.i.d and confirm the absence of ARCH effects. They are thus far more suitable to copula estimation than the raw return series. The parameters of the skewed-t distribution are all significant which clearly show that return series depart from normality and that the probability of extremely negative and positive realizations for our returns is thus higher than that of a normal distribution.

Table 7

Marginal estimation results for sector indices returns.

	Energy	Bas.mat.	Indust.	Cyc.Gds	Non-Cyc. Gds	Financials	Health.	Techn.	Telecom.	Utilities
Mean
ϕ_0	0.008 (0.014)	0.010 (0.018)	0.032^∗∗(0.014)	0.031^∗∗(0.014)	0.035^∗(0.013)	0.023 (0.015)	0.051^∗(0.016)	−0.068^∗(0.019)	0.021 (0.015)	0.036^∗∗(0.016)
ϕ_1	0.021 (0.018)	0.11^∗(0.024)	0.132^∗(0.022)	0.107 (0.022)	0.031 (0.023)	0.079 (0.022)	0.014 (0.023)	−0.020 (0.022)	0.072^∗(0.023)	0.023 (0.023)
ϕ_2	0.011 (0.017)	0.015 (0.022)	−0.008 (0.012)	−0.000 (0.032)	−0.017 (0.021)	0.012 (0.028)	0.013 (0.020)	0.012 (0.024)	0.006 (0.023)	−0.014 (0.019)
ϕ_3					−0.005 (0.026)				0.001 (0.023)	−0.006 (0.023)
Variance
ω	0.019^∗(0.006)	0.015^∗∗(0.007)	0.018^∗(0.005)	0.018^∗(0.005)	0.027^∗(0.007)	0.031^∗(0.008)	0.301^∗(0.006)	0.040^∗(0.010)	0.042^∗(0.016)	0.024^∗∗(0.010)
α	0.028^∗∗(0.012)	0.015 (0.015)	0.017 (0.014)	0.038^∗∗(0.016)	0.032 (0.021)	0.051^∗(0.019)	0.000 (0.015)	0.000 (0.017)	0.030 (0.023)	0.033 (0.030)
β	0.918^∗(0.015)	0.921^∗(0.024)	0.863 (0.024)	0.852^∗(0.023)	0.815^∗(0.037)	0.809^∗(0.030)	0.864^∗(0.019)	0.853^∗(0.025)	0.825^∗(0.052)	0.887^∗(0.041)
λ	0.091^∗(0.019)	0.096^∗(0.023)	0.193^∗(0.037)	0.173^∗(0.035)	0.180^∗(0.039)	0.246^∗(0.050)	0.188^∗(0.031)	0.236 (0.040)	0.135^∗(0.039)	0.077^∗(0.022)
Asym.	−0.071^∗∗(0.028)	−0.131^∗(0.033)	−0.142^∗(0.029)	−0.194^∗(0.0228)	−0.095^∗(0.028)	−0.130^∗(0.027)	−0.119^∗(0.029)	−0.182^∗(0.028)	−0.084^∗(0.029)	−0.169^∗(0.030)
Tail	6.012^∗(0.903)	6.654^∗(0.901)	6.057^∗(0.757)	7.240^∗(1.202)	6.624^∗(0.923)	5.207^∗(0.610)	6.475^∗(0.880)	4.745^∗(0.518)	6.894^∗(1.013)	7.164^∗(0.991)
LogLik	3480.1	2803.5	2302.6	2292.2	1947.8	2542.9	2524.7	2897.4	2316.2	2420.4
Lj	12.697 [0.314]	17.233 [0.101]	13.853 [0.241]	12.469 [0.329]	18.297 [0.075]	8.620 [0.657]	12.084 [0.357]	9.590 [0.568]	8.538 [0.665]	6.681 [0.824]
Lj2	22.877 [0.018]	18.899 [0.063]	10.727 [0.466]	6.198 [0.860]	7.766 [0.734]	9.459 [0.580]	5.041 [0.929]	5.569 [0.900]	8.165 [0.698]	15.803 [0.149]
ARCH	23.407 [0.025]	18.746 [0.095]	10.747 [0.551]	6.025 [0.915]	7.993 [0.786]	9.283 [0.679]	5.027 [0.957]	5.460 [0.941]	8.104 [0.777]	15.956 [0.193]

Notes: see Table 6 notes.

Copula results

We considered the potential impact of COVID-19 pandemic on dependence by fitting copula models to GARCH-filtered log-returns for the precrisis and the crisis period. For each subperiod, we examined the systemic risk of China’s stock market for the G7 stock market as a whole and for each country belonging to this group. We also examined the systemic risk of China’s stock market for the major stock sectors in the G7 group.

Table 8 reports the static (Panel A) and time-varying copula (Panel B) model estimation results for China’s stock market paired with the G7 and with each G7 stock market in the precrisis period. For static copula models, we can observe that the dependence parameters for all pairs are positive and significant. The time-invariant student-t copula provide the best fit for all pairs, except for the China–Italy and China–Japan pairs where the SJC-copula performs better according to the AIC corrected for the small sample bias. China has the highest dependence with UK and the lowest dependence with Japan. Overall, the results for static copula models show that, irrespective of the assumed copula model, China and the G7 stock markets are linked each others during bearish and bullish markets, albeit in different magnitude.

This finding could be explained notably by the UK–China Commercial and investment Relationship. In fact, according to Cainey and Nouwens (2020) Chinese demand is high in most categories where the UK exports or operates such as technology, high-end consumer products and the services sector, especially education, healthcare and finance. Second, Chinese companies are also increasingly present in the UK through acquisition and greenfield operations. Third, China revives Shanghai–London Stock Connect at a time when as the US threatens to bar Chinese companies from American financial markets. The Shanghai–London Stock Connect will allow global investors to benefit from China‘s growth through London, while London Stock Exchange listed companies will be able to access Chinese investors directly.

Several factors could also explain the weak economic dependence between China and Japan. First, since the 2000s, bilateral political relations have become increasingly conflicted leading to the sharp fall of Japan’s foreign investment in the country. Second, China’s industrial upgrading and economic development has been accompanied with its decreasing economic dependence on Japan (for more details on Contemporary China–Japan Relations, see Chiang (2019)).

Looking at the results of Panel B, it is clear that time varying copulas outperform static copula models in all cases, except Japan. Also, the TV-elliptical copulas (Gaussian and Student-t) offered the best fit in six cases out of eight. This shows that there is symmetric tail dependence between China paired with each G7 country and in two cases (Italy and Japan) asymmetric tail dependence as given by the Rotated Gumbel and SJC copula. This also shows that the considered stock markets comove in both extreme positive and negative returns.

Regarding the crisis period, the copula estimation results reported in Table 9 shows that the dependence characteristics has changed in both level and structure. In fact, the results for static copula models indicate an increase of the dependence between China and the G7 stock market. The static Gaussian copula offers the better fit for all countries except Germany and Italy. The highest dependence is observed for the China–Canada pair and the lowest dependence is for China–Japan pair.

Table 9

Copulas estimation results in the crisis period for China and G7 countries.

	G7	Germany	Canada	USA	Italy	France	Japan	UK
Panel A: static copulas
Gaussian
ρ	0.407 (0.045)	0.383 (0.038)	0.384 (0.043)	0.363 (0.046)	0.320 (0.041)	0.356 (0.04)	0.303 (0.044)	0.344 (0.037)
AIC	−88.353	−69.153	−72.045	−69.759	−45.073	−60.316	−42.497	−60.097
Student-t
ρ	0.407 (0.045)	0.388 (0.042)	0.384 (0.043)	0.363 (0.046)	0.323 (0.046)	0.360 (0.043)	0.303 (0.045)	0.349 (0.039)
v	199.993 (33.289)	20.027 (16.870)	199.999 (8.432)	199.999 (16.067)	18.142 (13.919)	25.609 (30.885)	60.538 (41.663)	24.104 (27.184)
AIC	−85.500	−69.602	−70.242	−67.745	−46.464	−60.193	−42.195	−57.383
Gumbel
θ	1.310 (0.051)	1.318 (0.049)	1.277 (0.044)	1.268 (0.048)	1.241 (0.042)	1.270 (0.044)	1.191 (0.041)	1.248 (0.037)
AIC	−71.558	−63.419	−50.174	−58.424	−37.950	−48.683	−29.024	−42.160
Rotated Gumbel
θ	1.276 (0.085)	1.266 (0.044)	1.271 (0.059)	1.229 (0.06)	1.207 (0.042)	1.246 (0.044)	1.214 (0.041)	1.249 (0.046)
AIC	−61.655	−55.526	−59.425	−47.076	−38.312	−51.838	−41.480	−53.935
Clayton
θ	0.170 (0.022)	0.163 (0.025)	0.177 (0.023)	0.147 (0.021)	0.144 (0.023)	0.164 (0.023)	0.158 (0.025)	0.169 (0.022)
AIC	−55.291	−46.937	−57.035	−43.369	−36.935	−47.973	−39.825	−53.185
Symmetric Joe–Clayton
λ_U	0.223 (0.062)	0.232 (0.063)	0.112 (0.073)	0.198 (0.062)	0.129 (0.071)	0.143 (0.071)	0.044 (0.050)	0.062 (0.066)
λ_L	0.122 (0.054)	0.123 (0.061)	0.189 (0.059)	0.089 (0.048)	0.119 (0.053)	0.156 (0.058)	0.181 (0.057)	0.190 (0.057)
AIC	−71.371	−62.939	−58.254	−58.107	−41.106	−53.335	−40.568	−51.025
Panel B: dynamic copulas
TVP-Gaussian
α	0.022 (0.011)	0.026 (0.011)	0.032 (0.013)	0.020 (0.011)	0.021 (0.010)	0.031 (0.012)	0.001 (0.113)	0.039 (0.019)
β	0.949 (0.019)	0.958 (0.011)	0.947 (0.021)	0.947 (0.022)	0.964 (0.011)	0.951 (0.014)	0.022 (1.385)	0.934 (0.034)
AIC	−88.158	−76.599	−76.973	−69.100	−49.467	−68.293	−40.018	−66.005
TVP-Student-t
α	0.022 (0.011)	0.027 (0.011)	0.032 (0.013)	0.021 (0.012)	0.020 (0.010)	0.032 (0.013)	0.058 (3.782)	0.019 (0.038)
β	0.019 (0.949)	0.957 (0.011)	0.947 (0.021)	0.947 (0.022)	0.965 (0.011)	0.949 (0.014)	0.000 (121.833)	0.935 (0.033)
v	199.964 (55.956)	35.719 (33.730)	198.619 (11.107)	199.773 (6.302)	29.995 (34.787)	34.211 (116.599)	145.505 (1053.41)	42.994 (42.686)
AIC	−85.722	−75.096	−74.755	−66.760	−48.097	−66.895	−39.465	−64.427
TVP-Gumbel
ω	−0.264 (0.000)	−0.191 (0.728)	−0.054 (0.607)	−0.369 (0.545)	−0.183 (0.110)	0.359 (0.564)	−0.660 (0.657)	−0.189 (0.437)
β¯	0.691 (0.000)	0.640 (0.336)	0.602 (0.136)	0.757 (0.001)	0.652 (0.050)	0.379 (0.012)	0.767 (0.015)	−0.659 (0.052)
α¯	−0.018 (−0.367)	−0.394 (0.278)	−0.793 (1.988)	−0.304 (0.366)	−0.544 (0.117)	−1.265 (0.326)	0.624 (0.324)	−0.583 (2.053)
AIC	−80.487	−71.263	−66.674	−65.097	−46.484	−62.289	−40.311	−50.933
TVP-Rotated Gumbel
ω	2.114 (0.000)	−0.078 (0.728)	−0.213 (0.607)	2.217 (0.545)	2.095 (0.110)	0.262 (0.564)	−0.620 (0.657)	−0.190 (0.437)
β¯	−0.889 (0.000)	0.589 (0.336)	0.672 (0.136)	−1.002 (0.001)	−0.875 (0.050)	0.418 (0.012)	0.779 (0.015)	0.652 (0.052)
α¯	−1.713 (−0.367)	−0.652 (0.278)	−0.519 (1.988)	−1.925 (0.366)	−2.090 (0.117)	−1.127 (0.326)	0.460 (0.324)	−0.514 (2.053)
AIC	−69.978	−64.651	−69.674	−54.496	−46.369	−62.711	−47.188	−61.973
TVP-Clayton
ω	−1.996 (0.365)	−1.932 (0.418)	−2.270 (0.329)	−2.308 (0.426)	−2.451 (0.438)	−1.864 (0.362)	−0.784 (0.413)	−1.294 (0.614)
β¯	−0.672 (0.452)	−0.575 (0.661)	0.424 (0.273)	−0.676 (0.447)	−0.849 (0.529)	−1.037 (0.723)	−1.177 (0.921)	−1.445 (0.816)
α¯	−0.806 (0.079)	−0.611 (0.157)	−0.866 (0.060)	−0.826 (0.089)	−0.814 (0.141)	−0.676 (0.096)	0.166 (0.237)	−0.330 (0.333)
AIC	−52.671	−43.830	−55.014	−41.347	−35.493	−46.234	−37.498	−52.736
TVP-Symmetric Joe–Clayton
ψ_0,U	0.170 (4.011)	1.031 (5.181)	−4.735 (5.489)	−0.805 (2.463)	1.505 (1.591)	1.787 (4.442)	−1.169 (0.530)	1.329 (0.715)
ψ_1,U	−9.999 (17.873)	−9.999 (20.641)	7.460 (16.687)	−6.863 (11.090)	−9.995 (8.011)	−9.999 (23.348)	3.079 (1.436)	−7.452 (4.268)
ψ_2,U	−0.985 (0.006)	−0.980 (0.031)	−0.689 (0.167)	−0.986 (0.005)	0.354 (0.189)	0.552 (1.025)	0.866 (0.102)	0.908 (0.040)
ψ_0,L	−0.359 (1.118)	0.545 (0.318)	0.520 (0.294)	0.722 (0.284)	0.443 (2.904)	0.195 (6.726)	−1.138 (0.668)	0.745 (1.847)
ψ_1,L	−3.742 (6.540)	−3.228 (1.902)	−2.749 (1.463)	−3.590 (1.355)	−2.806 (11.354)	−9.999 (22.781)	2.635 (1.897)	−9.999 (6.864)
ψ_2,L	0.176 (1.203)	0.920 (0.039)	0.911 (0.070)	0.941 (0.019)	0.875 (0.019)	−0.849 (0.087)	0.681 (0.154)	−0.804 (0.150)
AIC	−68.019	−66.965	−57.578	−60.401	−40.658	−60.547	−35.943	−54.744

Notes: see Table 8 notes.

Time-varying symmetric tail independence as given by the TVP-Gaussian copula is the best copula fit for Germany, Canada, Italy, France and UK stock markets. Thus, our results point out that the Chinese stock market decoupled from G7 stock markets and show independence at the tails in all cases, except Japan. These findings will have important implications for systemic risk.

In Table 10, Table 11, we report the estimation results for China paired with the G7 sectoral indices in the pre and crisis periods. Looking first at the results of static copula model in the first period, we can conclude that all sectors indices positively comove with China’s stock market. The obtained results indicate also that the student-t copula is the best fitting static copula model, providing evidence of lower and upper tail dependence in all cases, except for the utilities sector. The highest dependence is observed for the cyclical goods sector, followed by the technology sector, and the lowest one is detected for the utilities sector.

Table 10

Copulas estimation results in the precrisis period for China and G7 sector indices.

	Energy	Bas. mat.	Indust.	Cyc.Gds	Non-Cyc.Gds	Financials	Health.	Techn.	Telecom.	Utilities
Panel A: static copulas
Gaussian
ρ	0.246 (0.021)	0.384 (0.019)	0.387 (0.02)	0.399 (0.019)	0.208 (0.022)	0.338 (0.02)	0.263 (0.021)	0.392 (0.019)	0.251 (0.021)	0.095 (0.023)
AIC	−104.101	−272.367	−274.629	−292.166	−72.846	−202.065	−121.367	−280.216	−110.254	−13.259
Student-t
ρ	0.249 (0.023)	0.386 (0.02)	0.387 (0.02)	0.399 (0.02)	0.208 (0.024)	0.339 (0.021)	0.263 (0.023)	0.394 (0.02)	0.253 (0.023)	0.088 (0.026)
v	19.459 (9.546)	22.921 (10.582)	78.257 (24.223)	36.870 (32.925)	16.666 (8.548)	25.455 (12.993)	23.714 (13.631)	22.906 (16.297)	20.472 (9.712)	13.012 (4.887)
AIC	−107.980	−275.556	−274.737	−293.272	−77.465	−204.713	−124.175	−283.225	−113.721	−20.000
Gumbel
θ	1.165 (0.023)	1.293 (0.026)	1.288 (0.026)	1.297 (0.025)	1.131 (0.018)	1.238 (0.022)	1.173 (0.02)	1.306 (0.027)	1.164 (0.019)	1.058 (0.016)
AIC	−86.078	−235.359	−224.892	−234.597	−58.231	−157.490	−96.584	−243.730	−86.879	−12.504
Rotated Gumbel
θ	1.164 (0.02)	1.295 (0.023)	1.292 (0.024)	1.31 (0.025)	1.136 (0.019)	1.249 (0.023)	1.172 (0.021)	1.297 (0.024)	1.17 (0.02)	1.058 (0.016)
AIC	−100.953	−247.410	−246.745	−271.520	−74.150	−192.442	−110.608	−250.446	−106.638	−21.837
Clayton
θ	0.126 (0.013)	0.194 (0.013)	0.194 (0.013)	0.205 (0.012)	0.110 (0.013)	0.174 (0.013)	0.131 (0.012)	0.194 (0.012)	0.129 (0.013)	0.053 (0.013)
AIC	−93.062	−215.763	−217.378	−243.789	−71.432	−175.049	−103.620	−221.278	−97.056	−17.784
Symmetric Joe–Clayton
λ_U	0.059 (0.033)	0.177 (0.036)	0.164 (0.036)	0.153 (0.036)	0.028 (0.026)	0.098 (0.036)	0.069 (0.031)	0.191 (0.036)	0.054 (0.031)	0.000 (0.002)
λ_L	0.108 (0.030)	0.201 (0.033)	0.206 (0.032)	0.236 (0.030)	0.089 (0.028)	0.191 (0.031)	0.109 (0.029)	0.031 (0.198)	0.112 (0.031)	0.019 (0.020)
AIC	−104.646	−260.231	−255.112	−276.152	−76.434	−192.377	−118.409	−266.019	−108.591	−19.053
Panel B: dynamic copulas
TVP-Gaussian
α	0.038 (0.040)	0.041 (0.011)	0.018 (0.013)	0.009 (0.004)	0.025 (0.012)	0.032 (0.016)	0.031 (0.026)	0.006 (0.002)	0.014 (0.014)	0.038 (0.020)
β	0.907 (0.149)	0.919 (0.027)	0.975 (0.024)	0.989 (0.006)	0.896 (0.055)	0.901 (0.069)	0.900 (0.125)	0.992 (0.002)	0.863 (0.137)	0.898 (0.078)
AIC	−124.182	−309.777	−314.313	−320.629	−77.974	−213.101	−131.813	−303.006	−109.731	−30.000
TVP-Student-t
α	0.032 (0.035)	0.040 (0.011)	0.018 (0.012)	0.009 (0.004)	0.023 (0.012)	0.033 (0.017)	0.029 (0.038)	0.008 (0.004)	0.013 (0.016)	0.035 (0.016)
β	0.927 (0.120)	0.920 (0.027)	0.976 (0.021)	0.989 (0.006)	0.901 (0.059)	0.903 (0.072)	0.911 (0.178)	0.990 (0.007)	0.851 (0.219)	0.908 (0.059)
v	25.904 (10.556)	68.265 (41.796)	125.732 (25.691)	50.294 (45.778)	18.484 (9.512)	25.600 (17.664)	29.349 (49.380)	32.683 (28.890)	21.597 (12.346)	16.297 (7.814)
AIC	−124.491	−308.139	−312.441	−319.317	−79.783	−213.928	−132.113	−302.034	−110.733	−32.536
TVP-Gumbel
ω	2.030 (0.604)	0.632 (0.407)	1.050 (0.612)	1.140 (0.011)	0.650 (0.434)	1.158 (0.621)	1.402 (0.038)	0.899 (0.722)	1.572 (0.556)	−0.024 (0.432)
β¯	−1.000 (0.325)	0.093 (0.728)	−0.190 (0.134)	−0.247 (0.323)	−0.181 (0.116)	−0.373 (0.110)	−0.569 (0.178)	−0.112 (0.123)	−1.160 (0.125)	0.341 (0.225)
α¯	−1.626 (0.118)	-0,831 (0.016)	−1.058 (0.118)	−1.093 (0.051)	−0.309 (0.101)	−1.168 (0.276)	−0.806 (0.011)	0.658 (0.324)	−0.327 (0.223)	0.132 (0.011)
AIC	−99.187	−247.978	−234.770	−244.399	−60.710	−162.926	−103.588	−251.673	−91.880	−15.528
TVP-Rotated Gumbel
ω	2.224 (0.601)	0.649 (0.422)	1.238 (0.612)	1.239 (0.611)	1.300 (0.434)	−1.118 (0.641)	1.445 (0.048)	0.973 (0.752)	−0.556 (0.556)	0.668 (0.432)
β¯	−1.165 (0.322)	0.083 (0.702)	−0.308 (0.134)	−0.343 (0.363)	−0.701 (0.116)	−0.347 (0.110)	−0.550 (0.158)	−0.253 (0.123)	0.803 (0.125)	−0.234 (0.222)
α¯	−1.701 (0.118)	-0,843 (0.016)	−1.176 (0.118)	−0.922 (0.051)	−0.483 (0.101)	−0.712 (0.276)	−1.415 (0.011)	−0.409 (0.324)	0.098 (0.223)	−0.606 (0.011)
AIC	−117.810	−260.182	−128.551	−278.798	−76.976	−197.452	−120.483	−253.686	−109.127	−25.508
TVP-Clayton
ω	−0.302 (0.216)	−0.045 (0.174)	−0.070 (0.125)	−0.030 (0.106)	−1.288 (0.621)	−0.257 (0.178)	−0.039 (0.492)	−0.364 (0.204)	−1.509 (0.421)	0.098 (0.089)
β¯	−1.818 (0.649)	−1.150 (0.662)	−1.326 (0.447)	−1.564 (0.436)	−1.771 (0.950)	−0.915 (0.388)	−1.017 (1.161)	−1.088 (0.453)	−0.754 (0.718)	−0.950 (0.396)
α¯	0.515 (0.149)	0.680 (0.290)	0.619 (0.132)	0.574 (0.067)	0.024 (0.286)	0.589 (0.140)	0.800 (0.496)	0.411 (0.197)	−0.089 (0.211)	0.931 (0.027)
AIC	−102.937	−227.433	−228.703	−260.247	−72.962	−177.567	−109.480	−225.121	−94.758	−19.298
TVP-Symmetric Joe–Clayton
ψ_0,U	0.269 (0.163)	0.119 (0.063)	0.216 (0.834)	0.679 (1.410)	−8.959 (7.495)	−0.292 (1.754)	−0.923 (2.187)	0.912 (0.924)	0.170 (1.592)	−6.003 (1.205)
ψ_1,U	−1.373 (0.930)	−0.584 (0.333)	−6.888 (3.607)	−9.999 (10.259)	8.107 (26.391)	−8.057 (6.725)	−8.725 (10.211)	−9.601 (6.561)	−3.377 (5.747)	−1.033 (3.658)
ψ_2,U	0.964 (0.031)	0.980 (0.016)	−0.142 (0.247)	−0.274 (0.863)	−0.894 (0.057)	−0.160 (0.299)	−0.353 (0.279)	−0.263 (0.833)	0.749 (0.558)	4.328 (0.834)
ψ_0,L	−0.426 (1.453)	0.096 (0.764)	0.244 (0.867)	−0.336 (0.585)	−0.526 (1.975)	−0.724 (0.814)	0.386 (1.226)	−2.497 (1.223)	−0.682 (0.784)	−0.236 (1.195)
ψ_1,L	−9.999 (5.357)	−6.157 (2.679)	−6.084 (4.120)	−2.388 (2.816)	−9.712 (8.602)	−2.439 (3.568)	−9.999 (4.951)	2.765 (4.267)	1.253 (1.583)	−9.999 (9.932)
ψ_2,L	−0.822 (0.113)	−0.439 (0.505)	−0.329 (0.370)	−0.197 (0.369)	−0.573 (0.151)	−0.271 (0.300)	−0.326 (0.197)	−0.742 (0.118)	0.805 (0.224)	0.144 (0.480)
AIC	−110.652	−269.017	−255.249	−275.556	−72.042	−187.737	−118.270	−264.040	−102.854	−14.001

Notes: see Table 8 notes.

Table 11

Copulas estimation results in the crisis period for China and G7 sector indices.

	Energy	Bas. mat.	Indust.	Cyc.Gds	Non-Cyc.Gds	Financials	Health.	Techn.	Telecom.	Utilities
Panel A: static copulas
Gaussian
ρ	0.288 (0.044)	0.364 (0.036)	0.376 (0.042)	0.420 (0.046)	0.262 (0.04)	0.269 (0.042)	0.321 (0.045)	0.405 (0.046)	0.313 (0.042)	0.147 (0.041)
AIC	−40.388	−66.044	−72.966	−94.382	−32.994	−37.205	−49.626	−88.571	−46.381	−9.289
Student-t
ρ	0.289 (0.046)	0.372 (0.041)	0.376 (0.042)	0.420 (0.046)	0.264 (0.043)	0.274 (0.042)	0.321 (0.045)	0.405 (0.046)	0.313 (0.043)	0.144 (0.05)
v	37.135 (72.473)	15.153 (8.287)	178.832 (937.715)	199.999 (49.865)	39.628 (150.491)	28.730 (29.163)	199.968 (24.489)	199.768 (4.902)	58.460 (1497.609)	12.142 (6.899)
AIC	−39.316	−66.216	−70.916	−92.249	−32.520	−35.784	−48.950	−87.343	−45.444	−12.588
Gumbel
θ	1.174 (0.062)	1.293 (0.041)	1.282 (0.046)	1.33 (0.058)	1.157 (0.037)	1.165 (0.045)	1.208 (0.042)	1.318 (0.058)	1.226 (0.043)	1.075 (0.031)
AIC	−24.082	−58.672	−59.370	−83.345	−19.905	−23.244	−32.222	−82.239	−37.137	−4.815
Rotated Gumbel
θ	1.199 (0.045)	1.267 (0.045)	1.272 (0.041)	1.288 (0.052)	1.171 (0.041)	1.189 (0.042)	1.217 (0.049)	1.274 (0.056)	1.205 (0.041)	1.100 (0.037)
AIC	−40.531	−59.120	−61.993	−66.906	−30.235	−36.039	−43.571	−65.039	−38.704	−16.075
Clayton
θ	0.151 (0.023)	0.172 (0.024)	0.176 0.024()	0.173 (0.022)	0.132 (0.023)	0.144 (0.024)	0.153 (0.023)	0.169 (0.022)	0.142 (0.024)	0.084 (0.026)
AIC	−40.367	−52.852	−54.402	−55.997	−30.247	−34.930	−42.691	−54.229	−35.036	−13.046
Symmetric Joe–Clayton
λ_U	0.019 (0.037)	0.173 (0.078)	0.066 (0.159)	0.262 (0.055)	0.024 (0.039)	0.022 (0.039)	0.057 (0.056)	0.258 (0.054)	0.119 (0.065)	0.000 (0.002)
λ_L	0.171 (0.053)	0.162 (0.060)	0.060 (0.171)	0.119 (0.054)	0.129 (0.054)	0.154 (0.057)	0.164 (0.057)	0.121 (0.053)	0.116 (0.056)	0.077 (0.057)
AIC	−38.588	−61.431	−64.689	−83.539	−29.036	−33.692	−42.542	−83.897	−40.705	−13.046
Panel B: dynamic copulas
TVP-Gaussian
α	0.024 (0.011)	0.022 (0.011)	0.021 (0.011)	0.017 (0.009)	0.025 (0.033)	0.025 (0.011)	0.024 (0.014)	0.023 (0.040)	0.019 (0.014)	0.037 (0.016)
β	0.959 (0.016)	0.959 (0.018)	0.957 (0.014)	0.966 (0.009)	0.874 (0.302)	0.957 (0.015)	0.937 (0.033)	0.905 (0.311)	0.931 (0.037)	0.909 (0.034)
AIC	−43.372	−68.218	−73.908	−94.304	−32.335	−41.087	−50.242	−86.488	−45.785	−14.065
TVP-Student-t
α	0.025 (0.011)	0.024 (0.012)	0.022 (0.010)	0.017 (0.009)	0.022 (0.033)	0.026 (0.012)	0.024 (0.015)	0.022 (0.036)	0.019 (0.014)	0.035 (0.016)
β	0.958 (0.015)	0.954 (0.019)	0.957 (0.017)	0.965 (0.009)	0.915 (0.250)	0.955 (0.015)	0.937 (0.033)	0.909 (0.274)	0.934 (0.033)	0.916 (0.030)
v	35.691 (40.515)	15.536 (9.291)	116.268 (254.666)	196.02 (46.116)	33.98 (80.251)	37.878 (26.711)	199.384 (9.687)	199.014 (10.936)	58.947 (183.011)	14.616 (10.433)
AIC	−41.905	−68.625	−71.946	−91.929	−31.083	−39.595	−48.151	−84.176	−43.930	−14.264
TVP-Gumbel
ω	−0.352 (0.002)	−0.156 (0.625)	−0.235 (0.017)	−0.346 (0.022)	0.030 (0.124)	−0.179 (0.544)	−0.593 (0.042)	−0.171 (0.119)	−0.550 (0.656)	−0.818 (0.053)
β¯	0.756 (0.014)	0.639 (0.236)	0.682 (0.015)	0.728 (0.014)	0.493 (0.528)	0.665 (0.002)	0.905 (0.265)	0.590 (0.040)	0.869 (0.042)	1.132 (0.093)
α¯	−0.448 (0.000)	−0.540 (0.060)	−0.465 (0.345)	−0.207 (0.344)	−0.740 (0.226)	−0.676 (0.344)	−0.176 (1.977)	−0.172 (0.001)	−0.157 (1.003)	−0.420 (0.001)
AIC	−33.361	−68.553	−69.590	−88.536	−23.832	−33.060	−35.442	−84.737	−41.504	−10.811
TVP-Rotated Gumbel
ω	−0.423 (0.002)	−0.182 (0.635)	0.238 (0.027)	1.965 (0.032)	0.065 (0.134)	−0.361 (0.504)	−0.391 (0.002)	−0.444 (0.109)	−0.541 (0.606)	−0.732 (0.053)
β¯	0.790 (0.054)	0.655 (0.226)	0.370 (0.025)	−0.806 (0.014)	0.485 (0.538)	0.761 (0.022)	0.790 (0.285)	0.740 (0.042)	0.868 (0.032)	1.033 (0.093)
α¯	−0.298 (0.000)	−0.547 (0.060)	−0.734 (0.345)	−1.468 (0.344)	−0.779 (0.226)	−0.411 (0.344)	−0.418 (1.977)	0.091 (0.001)	−0.209 (1.003)	−0.289 (0.001)
AIC	−46.844	−68.791	−66.880	−71.541	−36.290	−44.327	−49.661	−67.287	−42.883	−19.784
TVP-Clayton
ω	−2.044 (0.718)	−2.293 (0.659)	−2.262 (0.500)	−0.064 (0.049)	−3.150 (0.510)	−1.561 (0.547)	−1.598 (0.382)	−0.178 (0.157)	−3.024 (0.545)	−2.524 (0.700)
β¯	0.752 (0.590)	0.503 (0.883)	0.015 (0.460)	0.301 (0.258)	0.164 (0.383)	0.694 (0.713)	1.204 (0.721)	−0.211 (0.630)	0.052 (0.287)	2.214 (1.672)
α¯	−0.377 (0.614)	−0.783 (0.573)	−0.889 (0.106)	1.013 (0.008)	−0.953 (0.099)	0.061 (0.377)	0.082 (0.176)	0.813 (0.190)	−0.981 (0.039)	0.167 (0.277)
AIC	−37.807	−50.778	−50.369	−57.531	−27.959	−31.627	−40.451	−50.292	−33.191	−11.408
TVP-Symmetric Joe–Clayton
ψ_0,U	1.803 (0.899)	−3.010 (1.965)	−0.134 (0.243)	−1.847 (1.403)	0.464 (4.087)	−10.00 (365.526)	−7.182 (6307.9)	0.961 (0.208)	−6.300 (11.399)	−9.879 (8.865)
ψ_1,U	−9.999 (5.338)	0.461 (5.865)	0.318 (1.294)	4.382 (4.848)	−10.00 (12.606)	0.816 (299.006)	9.999 (23.42)	−6.536 (4.792)	4.583 (16.850)	−0.855 (0.618)
ψ_2,U	0.836 (0.051)	−0.993 (0.004)	1.068 (0.025)	−0.087 (0.352)	0.382 (0.266)	−0.995 (0.284)	−0.819 (101.5)	−0.972 (0.016)	−0.995 (0.006)	0.404 (0.491)
ψ_0,L	0.146 (0.506)	0.688 (0.462)	0.344 (1.049)	0.645 (1.228)	0.501 (0.809)	0.793 (1.075)	0.555 (73.174)	−3.852 (2.077)	0.203 (0.289)	0.301 (1.715)
ψ_1,L	−1.024 (1.055)	−4.576 (3.172)	−6.424 (3.330)	−8.205 (6.164)	−4.589 (2.540)	−3.898 (5.812)	−6.121 (5.969)	−2.745 (348.7)	3.835 (6.840)	−1.722 (1.116)
ψ_2,L	0.905 (0.262)	0.673 (0.313)	−0.137 (1.354)	0.137 (0.441)	0.482 (0.176)	0.890 (0.045)	0.883 (13.360)	−0.769 (0.080)	0.868 (0.130)	0.329 (0.185)
AIC	−38.445	−61.785	−79.215	−77.378	−23.962	−37.860	−40.112	−78.968	−39.922	−6.039

Notes: see Table 8 notes.

The evidence provided by the TVP-copula models shows that time-varying dependence offers a better alternative and outperforms static dependence specification for all pairs, with the exception of the telecommunication sector. According to the AIC, the TVP-Student-t copula offered the best fit for the energy, non cyclical goods, financials, health and utilities sectors, displaying lower and upper tail dependence with China.

Regarding the pandemic period, the reported results in Table 11 indicate that China comove more strongly with all G7 sectors, except the basic materials, industrials and Financials sectors. The TVP-Rotated Gumbel copula provides the best fit for the energy, basic materials, non cyclical goods and financials sectors, showing strong dependence in the left tail only. The China’s stock market did not comove with the industrial, cyclical goods, health, technology and telecommunication sectors during extreme market conditions, as shown by the Gaussian copula.

Spillover analysis

To gain further insights into the systemic impact of the COVID-19 pandemic and its contagion effects across the G7 stock markets on the one hand and, on the other hand, across the G7 stock sectors, we compute the CoVaR for each stock markets and sectoral indices at the 95% confidence level conditional on the VaR of the Chinese stock market at the 95% confidence level .

Fig. 3, Fig. 4 display the trajectory of the calculated upside–downside VaR and CoVaR over time. It can be seen that CoVaR values are unstable over all the considered sample period with sharply movements changes during the period of 2015–2016 Chinese stock market turbulence and also during the US–China trade-war period that starts in July 2018. A more pronounced sudden change is noticed after the onset of the COVID-19 crisis, when contagion effects of the pandemic spread from China to other countries.

Fig. 3

Time series plots of downside and upside VaR and CoVaR for G7 stock market returns.

Fig. 4

Time series plots of downside and upside VaR and CoVaR for G7 stock market returns.

Table 12 present the summary statistics of the upside–downside VaR and CoVaR for G7 stock returns. Considering downside risk, the reported results in the left panel confirm the graphical evidence, that is, CoVaR values are significantly smaller than the VaR values in all cases. This finding is corroborated by the smaller -values associated with the Kolmogorov–Smirnov test, suggesting existence of downside risk spillover effects from China’s stock market to G7 stock markets. Empirical evidence for the pre-crisis period revealed that Canada and Italy have the highest and smallest mean downside CoVaR, respectively. This indicates that Italy’s stock market received the highest systemic impact from China’s stock markets. The result was expected since Italy’s economic and trade relations with China have grown more dynamic in recent years. Moreover, by looking at the G7 average value of downside CoVaR, we can conclude that the systemic impact of China’s stock market on each G7 stock market taken individually, is greater than its impact on the whole stock market. Regarding the crisis-period, we observe an increase in all the CoVaR values which confirm the fact that the systemic risk of China’s stock market becomes on average higher for all G7 stock markets and also for the whole market. Italy still has the smallest mean of downside CoVaR, followed by Germany, France and UK stock markets. This indicates that during the COVID-19 crisis, these stock markets suffer more severely when China’s stock market is in distress.

Table 12

Downside and upside VaR and CoVaR estimation results in the precrisis and crisis periods for G7 stock returns.

		Downside							Upside
		VaR		CoVaR		KS test	VaR		CoVaR		KS test
		Mean	Sd	Mean	Sd	H0:CoVaR = VaR	Mean	Sd	Mean	Sd	H_0:CoVaR = VaR
						H1:CoVaR < VaR					H1:CoVaR > VaR
G7	Pre.	−1.131	0.541	−1.965	1.022	0.566 [0.00]	1.094	0.484	1.680	0.822	0.496 [0.00]
	Crisis	−1.990	1.969	−3.407	3.340	0.421 [0.00]	1.863	1.762	2.859	2.727	0.360 [0.00]
Germany	Pre.	−1.783	0.536	−3.151	1.096	0.692 [0.00]	1.665	0.490	2.680	0.904	0.624 [0.00]
	Crisis	−2.557	1.590	−4.620	3.510	0.534 [0.00]	2.372	1.452	3.904	2.887	0.479 [0.00]
Canada	Pre.	−1.418	0.527	−2.082	0.786	0.397 [0.00]	1.287	0.462	1.748	0.638	0.333 [0.00]
	Crisis	−2.379	2.435	−4.170	4.821	0.434 [0.00]	2.129	2.135	3.373	3.791	0.384 [0.00]
USA	Pre.	−1.297	0.683	−2.139	1.236	0.497 [0.00]	1.256	0.607	1.826	0.982	0.424 [0.00]
	Crisis	−2.256	2.217	−3.712	3.615	0.368 [0.00]	2.108	1.970	3.096	2.918	0.307 [0.00]
Italy	Pre.	−2.246	0.843	−4.512	1.702	0.819 [0.00]	2.111	0.767	2.615	0.966	0.325 [0.00]
	Crisis	−2.806	2.045	−4.662	4.023	0.460 [0.00]	2.620	1.861	4.002	3.343	0.384 [0.00]
France	Pre.	−1.725	0.669	−2.935	1.339	0.572 [0.00]	1.588	0.596	2.429	1.061	0.484 [0.00]
	Crisis	−2.519	1.868	−4.457	4.011	0.455 [0.00]	2.295	1.663	3.645	3.164	0.386 [0.00]
Japan	Pre.	−1.768	0.652	−3.366	1.233	0.772 [0.00]	1.651	0.592	2.536	0.914	0.602 [0.00]
	Crisis	−1.944	0.881	−3.757	1.705	0.770 [0.00]	1.811	0.800	2.198	0.977	0.373 [0.00]
UK	Pre.	−1.588	0.724	−2.901	1.455	0.723 [0.00]	1.457	0.658	2.423	1.197	0.652 [0.00]
	Crisis	−2.474	1.727	−4.371	3.766	0.479 [0.00]	2.263	1.570	3.655	3.077	0.421 [0.00]

Notes: The table displays summary statistics of the VaR and CoVaR for the G7 stock markets in the pre- and crisis period. KS test is the Kolmogorov–Smirnov bootstrapping test proposed by Abadie (2002) to test the null hypothesis of no systemic impact from China to G7 stock markets. -values are reported in square brackets.

These findings can be explained by the strong economic ties these countries have with China and the potential role of trade as a spreader of shocks through Global Value Chains. Indeed, Germany is the top exporter and second-biggest importer of Chinese goods within the EU region in 2019. It is also the second largest European investor in China with continued investment across a range of different industries including automotive, and basic materials. Moreover, Germany is a major European hub for many large multinational corporations owing, among other factors, to its stable economy, strategic location and highly educated workforce. Given the importance of value chains in spreading shocks, Germany can act as a “choke points” through which a shock is likely to propagate and amplify across Europe. Italy is the Chinese fifth largest trading partner in the European region in 2019 and the first member of the G7 group to join the Belt and Road initiative. The signed accords covered a wide range of domains, including cooperation between banks and cooperation on the topics of innovation, science and technology. Although the steady development of China–Italy relations during the last years, Italian companies are lagging far behind Germany in exploiting the advantages offered by the Chinese market. The main reason for this is that the Italian economy is largely dominated by small and medium-sized firms, whose capacity to fully exploit the Chinese market is limited (Prodi, 2014). France has recently more consolidated its position as a driving economic force in the eurozone, especially after the unprecedented exit of the UK. It continues to work closely with China to enhance economic cooperation through trade and investment. The UK–China trade has also increased considerably during the last few years, with close cooperation in infrastructure development, education and technology. Since April 2019, the country imports of goods from Germany, the largest EU trading partners of UK, have declined coinciding with the increased uncertainty surrounding the impact EU exit had on UK’s international trade. The Brexit will present an opportunity to enhance the current cooperation between British and Chinese partners by offering more freedom and flexibility in negotiating terms and deals with China.

Overall, we argue that the magnitude of market risk exposure could depends on the country’s degree of openness to international trade and its capability to diversify the sources of demand and supply across countries (Caselli et al., 2020).

Considering upside risk, the test results presented in the right panel show also that the CoVaR values are significantly greater than the VaR for each stock market. This is an apparent evidence of upside risk spillover effects from China’s stock market. During the pre-crisis period, we observe that the risk spillover effects is higher in the case of Germany and Italy, but lower in the case of Canada stock market. Thus, we can conclude that when China’s stock market shows a bullish trend, this will generate a more positive effect on Germany and Italy than in Canada stock market. The same conclusion of a positive impact on Italy and Germany stock markets is confirmed in the crisis period.

In Table 13, we report the summary statistics of the upside–downside VaR and CoVaR for G7 stock sector returns. Once again, we found clear evidence of downside and upside risk spillover effects from China’s stock market, as confirmed by the KS test results.

Table 13

Downside–upside VaR and CoVaR estimation results in the precrisis and crisis periods for G7 sector indices.

		Downside							Upside
		VaR		CoVaR		KS test	VaR		CoVaR		KS test
		Mean	Sd	Mean	Sd	H0:CoVaR = VaR	Mean	Sd	Mean	Sd	H_0:CoVaR = VaR
						H1:CoVaR < VaR					H1:CoVaR > VaR
Energy	Pre.	−1.952	0.860	−2.849	1.252	0.393 [0.00]	1.866	0.815	2.623	1.142	0.360 [0.00]
	Crisis	−3.929	2.818	−7.657	6.012	0.646 [0.00]	3.739	2.671	4.774	3.865	0.265 [0.00]
Bas.mat.	Pre.	−1.469	0.404	−2.380	0.828	0.564 [0.00]	1.350	0.366	2.028	0.681	0.491 [0.00]
	Crisis	−2.297	1.477	−4.628	3.252	0.690 [0.00]	2.100	1.338	2.785	2.073	0.391 [0.00]
Indust.	Pre.	−1.169	0.455	−1.939	0.921	0.538 [0.00]	1.112	0.409	1.664	0.743	0.467 [0.00]
	Crisis	−2.079	1.761	−4.106	3.695	0.585 [0.00]	1.929	1.582	3.004	3.373	0.246 [0.00]
Cyc.Gds	Pre.	−1.176	0.473	−1.941	0.894	0.545 [0.00]	1.075	0.409	1.573	0.683	0.460 [0.00]
	Crisis	−2.121	1.703	−3.593	2.867	0.429 [0.00]	1.892	1.472	2.853	2.233	0.357 [0.00]
NonCyc.Gds	Pre.	−0.976	0.322	−1.421	0.544	0.572 [0.00]	0.976	0.300	1.334	0.478	0.521 [0.00]
	Crisis	−1.410	1.182	−2.647	2.424	0.643 [0.00]	1.380	1.101	1.677	1.478	0.278 [0.00]
Financials	Pre.	−1.324	0.602	−2.215	1.164	0.564 [0.00]	1.244	0.546	1.889	0.955	0.489 [0.00]
	Crisis	−2.643	2.438	−5.361	5.500	0.505 [0.00]	2.440	2.211	3.071	3.188	0.145 [0.00]
Health	Pre.	−1.295	0.453	−1.961	0.800	0.491 [0.00]	1.282	0.414	1.788	0.679	0.430 [0.00]
	Crisis	−1.781	1.325	−2.946	2.501	0.437 [0.00]	1.725	1.211	2.615	2.111	0.376 [0.00]
Techn.	Pre.	−1.743	0.696	−2.898	1.352	0.564 [0.00]	1.393	0.607	2.110	1.017	0.472 [0.00]
	Crisis	−2.767	1.991	−4.780	3.476	0.450 [0.00]	2.286	1.737	3.542	2.663	0.352 [0.00]
Telecom.	Pre.	−1.161	0.277	−1.740	0.413	0.815 [0.00]	1.130	0.261	1.611	0.373	0.778 [0.00]
	Crisis	−1.491	0.939	−2.226	1.395	0.608 [0.00]	1.440	0.881	2.049	1.259	0.566 [0.00]
Utilities	Pre.	−1.207	0.272	−1.573	0.518	0.436 [0.00]	1.131	0.240	1.378	0.408	0.359 [0.00]
	Crisis	−2.001	1.651	−3.431	3.156	0.540 [0.00]	1.830	1.454	2.053	1.742	0.175 [0.00]

Notes: The table displays summary statistics of the VaR and CoVaR for the G7 sector indices in the pre- and crisis period. KS test is the Kolmogorov–Smirnov bootstrapping test proposed by Abadie (2002) to test the null hypothesis of no systemic impact from China to G7 sector returns. -values are reported in square brackets.

Results in the precrisis period provide evidence that the technology sector has the smallest mean downside CoVaR followed by the energy and basic material sectors. The non-Cyclical goods sector has the highest mean downside CoVaR among all stock sectors followed by the utilities and telecommunication sectors. This is the evidence that the market risk exposure to China’s stock market was of most intensity in case of the energy sector and of least intensity in case of the non-Cyclical goods sector. As with stock markets, our results for the crisis period show that mean downside CoVaR increases during the pandemic and this is highlighted for all sectors albeit in different magnitudes. Particularly, the downside risk spillover effect becomes more intense in case of the energy sector, followed by the financials, technology and basic materials sectors.

In terms of upside risk, our analysis indicates that extreme upwards movements in China’s stock market generate positive impact on energy and technology sectors in both precrisis and crisis periods. The positive impact is more pronounced in the onset of the COVID-19 pandemic.

To test for asymmetry in risk spillover, we apply the KS test to compare the upside and downside values of CoVaR normalized by its corresponding VaR. This potential asymmetry may be due to the fact that investors react differently to bad news and good news. Moreover, it may be also due to the flight to quality or flight to safety effect. Indeed, in times of higher uncertainty and crisis, investors interest move from riskier investments to purchase the safest possible assets. The estimated results of the KS test, reported in Table 14, Table 15 show an asymmetric behavior of the upside and downside CoVaR risk spillovers to the G7 stock markets, i.e. the downside spillovers measured by the normalized CoVaR values were greater than the upside spillovers. A similar result is found for the G7 stock sector returns. Thus, we can conclude that investors and portfolio managers should design asymmetric hedging strategies to protect their portfolio against extreme downward movements in China’s stock market.

Table 14

Asymmetric downside–upside risk spillover effects from China to G7 stock markets returns in the precrisis and crisis periods.

	G7		Germany		Canada		USA
	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis
H0:CoVaRDownNorm. = CoVaRUpNorm.	0.471 [0.00]	1.00 [0.00]	0.372 [0.00]	0.328 [0.00]	0.410 [0.00]	0.511 [0.00]	0.440 [0.00]	1.00 [0.00]
H1:CoVaRDownNorm.> CoVaRUpNorm.
	Italy		France		Japan		UK
	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis
H0:CoVaRDownNorm. = CoVaRUpNorm.	1.00 [0.00]	0.331 [0.00]	0.402 [0.00]	0.378 [0.00]	1.00 [0.00]	1.00 [0.00]	0.720 [0.00]	0.291 [0.00]
H1:CoVaRDownNorm.> CoVaRUpNorm.

Notes: The table displays the results of the Kolmogorov–Smirnov bootstrapping test to investigate the existence of asymmetric downside–upside risk spillover effect from China to G7 stock markets. -values are reported in square brackets.

Table 15

Asymmetric downside–upside risk spillover effects from China to G7 sector returns in the precrisis and crisis periods.

	Energy		Bas.mat.		Indust.		Cyc.Gds		NonCyc.Gds
	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis
H0:CoVaRDownNorm. = CoVaRUpNorm.	0.153 [0.00]	0.997 [0.00]	0.330 [0.00]	0.998 [0.00]	0.322 [0.00]	0.717 [0.00]	0.440 [0.00]	0.996 [0.00]	0.432 [0.00]	0.971 [0.00]
H1:CoVaRDownNorm.>CoVaRUpNorm.
	Financials		Health.		Techn.		Telecom.		Utilities
	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis	Pre.	Crisis
H0:CoVaRDownNorm. = CoVaRUpNorm.	0.457 [0.00]	0.992 [0.00]	0.430 [0.00]	0.574 [0.00]	0.341 [0.00]	0.998 [0.00]	0.997 [0.00]	0.999 [0.00]	0.258 [0.00]	0.998 [0.00]
H1:CoVaRDownNorm.> CoVaRUpNorm.

Notes: The table displays the results of the Kolmogorov–Smirnov bootstrapping test to investigate the existence of asymmetric downside–upside risk spillover effect from China to G7 sector returns. -values are reported in square brackets.

Conclusion

In this paper, we examine the interdependence and risk spillover effects from China to G7 stock markets during the COVID-19 period at both market and sector levels. The results for this study point to several conclusions that can be summarized as follows. Firstly, we found evidence of positive dependence between China and G7 stock markets that became more pronounced in the pandemic period. Moreover, the G7 stock markets exhibited symmetric upper and lower tail dependence in the pre-crisis period and zero tail dependence in the crisis period, with the exception of Japan. Secondly, we reported evidence of downside and upside spillover effects from China to G7 stock markets, although with different magnitudes across subperiods. Indeed, the magnitude of upside–downside spillovers was higher from China to Italy’s and Germany’s stock markets, particularly throughout the COVID-19 period.

Similarly, we found that sectors indices positively comove with China’s stock market in both subperiods. The dependence in the tails differs across G7 stock sectors as these exhibit different levels and structures of bivariate dependence. As for stock markets, the results for the stock sectors corroborate the observation that suggest downside CoVaR increases throughout the pandemic, and this is illustrated for all industry sectors. Particularly, we provided evidence of higher upside–downside risk spillover from China to the energy and technology sectors in both sub periods. In contrast, the telecommunication and non-cyclical goods sectors were less exposed to the downside tail risk during the COVID-19 period. Overall, our results indicated the existence of an asymmetric behavior of the upside and downside CoVaR risk spillovers to the G7 stock and sector returns.

In light of these findings, some important theoretical and practical implications for policymakers are given as follow. First, examining the sensitivity of G7 stock market returns during the COVID-19 period may provide investors with valuable information about the magnitude and dynamics of downside market movements. Second, it is strategically important for investors to consider how risks spillovers propagate through sectors and determine which are the less exposed sectors to the information transmission. Third, it may also provide investors, policy makers and regulators with a valuable objective analysis to carry out portfolio investment choices, risk control actions and take sound policy steps. This kind of analysis is useful for determining co-movement of G7 stock returns throughout a variety of time periods spanning from short to long-run investment horizons and intensities. Based on the extent of returns co-movement, such research may help investors place their investments across multiple investment periods. Finally, an effective framework of global regulation should be established to prevent financial risk from spreading across borders and to ensure financial stability within and between countries.

CRediT authorship contribution statement

Riadh Aloui: Conceptualization, Methodology, Investigation, Writing. Sami Ben Jabeur: Writing, Investigation, Editing, Resources. Salma Mefteh-Wali: Writing, Investigation, Writing & supervision.