Global crises have created unprecedented challenges for communities and economies across the world, triggering turmoil in global finance and economy. This study adopts the dynamic conditional correlation multiple generalized autoregressive conditional heteroskedasticity (DCC–MGARCH) model to explore contagion effects across financial markets in crisis. The main findings are as follows: (
Keywords: global turmoil; DCC–MGARCH model; correlation; Granger causality test
International stock markets are closely connected, along with the deep integration of the global economy and finance. Global turmoil, such financial crises and the COVID-19 pandemic, causes strong external shocks to stock markets, thereby accelerating risk spillover. Distinguishing cross-market independence from contagion effect is necessary to measure contagion across stock markets. A timeline of turmoil is divided into a stable period and a period of a crisis, and correlations in different periods are compared. If a moderate correlation exists between two stock markets during a period of stability, then the moderate correlation will experience a significant rise during a period of turmoil. This pair of cross-market correlations before and after a crisis are also referred to as a pair-wise correlation. A significant rise in pair-wise correlations among stock markets before and after a crisis is defined as a contagion. The absence of a significant rise in pair-wise cross-market correlations during a crisis period is defined as interdependence [[
Several channels allow risk spillover to transmit across stock markets. The potential contagion effects are explained by herd behavior, exposure to financial liberalization, as well as changes in macroeconomic fundamentals. The tight integration of the global economy and finance leads to the increasing shared factors between the world economy and Chinese economy, which causes the Chinese economy to be easily affected by strong external shocks. Such an effect can be reflected by the stock markets' performance. In addition, shocks, such as trade and policy coordination, to one market probably change macroeconomic fundamentals in other markets. International trade effectively contributes to sustainable economic growth in China [[
Macroeconomic fundamentals, capital market liquidity, and investor psychology can explain the co-movement of stock markets. Unexpected shock, panic, and fear caused by turmoil can change investors' risk tolerance and trigger panic selling in response to external shocks [[
Global crises have caused economic disruption, economic losses, and fluctuations in financial markets. Recently, the COVID-19 pandemic has threatened the market's equilibrium. Many countries implemented partial or full lockdown as well as social-distancing measures, resulting in the disruption of economic activities [[
The novelty of our analysis is that it conducts a comparison of DCCs during the COVID-19 pandemic and 2008 global financial crisis, and our study focuses on the co-movement between developed markets and emerging markets. Compared with the correlations during the financial crisis, the linkages during the COVID-19 pandemic across markets may be larger. In addition, the dynamic increase in the pair-wise cross-market correlations proves the existence of contagion. Therefore, our analysis determines the dynamic nature of the correlations. Based on the DCC–MGARCH model, we observe that the calculated dynamic correlations and parameter estimations are unbiased despite the heteroskedasticity in the data. This study expands investigations on the effect of unexpected events and catastrophes on financial markets.
This study aims to investigate the existence of contagion effects between the stock markets of China and the United States during global-crisis periods and determine the direction of the contagion when the external catastrophic shock affects the development of the economy of the Chinese entity and changes its macroeconomic fundamentals. The research findings can provide useful suggestions to authorities on market regulations as well as to investors on risk diversification. This paper is organized as follows. Section 2 presents the literature review, including a brief introduction of the research area. Section 3 provides the DCC–MGARCH methodology conducted in this work, and Section 4 introduces the data sources and sample used in this research. Section 5, Section 6 and Section 7 present the main results, robustness test and conclusions.
Many studies have been conducted on the significant economic impacts of previous catastrophes and crises. Siu and Wong (2004) claimed that the SARS outbreak, as an unexpected negative shock in 2003, severely affected short-term consumer spending and services concerning tourism and air travel in the export sector in Hong Kong [[
Stock markets are interdependent and have volatility-spillover effects. Morales and Andreosso-O' Callaghan (2012) found that the US and Asian stock markets are highly interdependent, and shocks from the US stock markets strongly affect Asian markets via the underlying fundamentals that make such economies vulnerable [[
Scholars have applied different empirical models to investigate the contagion effects across markets. Engle (2002) proposed dynamic-conditional-correlation (DCC) models, through which sensible and effective results can be obtained to explore contagion effects [[
Engle (2002) proposed the multivariate autoregressive conditional heteroskedasticity model to estimate the DCC, which relies on the DCC decomposition of the conditional variance–covariance matrix,
(
where
In the DCC model,
(
where
For a GARCH (p, q) process, DCC matrix
(
where
The off-diagonal elements in matrix
(
On the basis of the multivariate distribution assumption, Boffelli and Urga (2016) gave different log-likelihood functions of the estimator [[
(
(
If the two-step estimation is chosen, then the Gaussian log-likelihood function and Student's log-likelihood function can be decomposed into the univariate part, including mean and variance equations, as well as the dynamic correlation part. Under the assumption of estimator of
To explore the contagion effect between Chinese and American stock markets, Standard & Poor's 500 Index (S&P 500), Hang Seng Index (HKHIS), and Shanghai Composite Index (SSEC) were selected as sample data. The daily closing prices of these markets were collected from the website portal, https://
Figure 1 shows a substantial increase of volatility in the time sequences of stock returns on S&P 500, HKHIS, and SSEI indices in correspondence to the outbreak of a crisis. All return series that presented volatility clustering experienced the highest volatility during the period of crisis. For the subprime crisis in 2008, HKHIS and S&P 500 Index experienced a larger fluctuation range after the crisis than before the crisis. However, large changes were observed in SSEC for the pre-crisis and post-crisis periods. HKHIS and SSEC significantly fluctuated before and after the COVID-19 pandemic, whereas S&P 500 Index experienced more volatility in the post-pandemic period than in the pre-pandemic period. Overall, return volatility caused by financial crisis was higher than that caused by the COVID-19 pandemic.
Table 2 displays the statistically significant values of Jarque–Bera, which may be indicative of non-normal distribution. Skewness is more than zero, whereas kurtosis is more than three. The standard deviations of all return series are larger in the periods of both financial crisis and COVID-19 crisis than in the pre-crisis period; thus, return volatility is intensified by crisis events. Therefore, the descriptive statistics before and after the crisis suggest leptokurtosis, fat tail, volatility clustering, as well as non-normal distribution.
The conditional distribution of the financial time series displays characteristics of time-variation, skewness, kurtosis, volatility clustering, and fat tails. The GARCH-t model can effectively catch the volatility of return series because t distribution can accurately describe features of fat-tail distribution, whereas the GARCH model properly shows qualities of financial time series. Estimating the univariate GARCH model is the first step. The fitted GARCH (
Table 3 and Table 4 provide important information about the DCC–MGARCH (
The time-variant conditional correlation for all stock indexes constantly fluctuates before and after the financial crisis, but it tends to be larger during the period of crisis than the pre-crisis period (see Figure 2). The 2008 financial crisis significantly intensified the correlation estimates between HKHIS and SSEC, rising from 0.26 before the crisis to 0.56 after the crisis (see Table 3). These results indicate that stock markets were significantly affected by the financial crisis. Moreover, Figure 2 shows that the conditional correlation between HKHIS and S&P 500 2 heightened after the crisis. Although the value of pre-crisis correlation is only 0.03, post-crisis correlation reaches 0.38 (see Table 3). This result means that the shocks intensified stepwise with the worsening subprime crisis. The DCC estimates between S&P 500 and SSEC approximate to zero, as shown in Figure 2. However, after the outbreak of the financial crisis, these estimates increase above 0.106. All DCC estimates are significant at the 1% level (see Table 3). A statistically significant contagion effect exists between HKHIS and S&P 500 and between HKHIS and SSEC. Therefore, to some extent, the shock caused by the subprime crisis may be partly transmitted from the Hong Kong stock market to the inland stock market, thus increasing the fluctuations in the inland stock market.
Compared with the DCCs for the financial crisis, all time-varying conditional correlations for the COVID-19 pandemic are large (see Figure 2). Although correlations between HKHIS and SSEC preserve the value of more than 0.62 during the whole period, correlations between SSEC and S&P 500 as well as correlations between HKHIS and S&P 500 rise from 0.159 and 0.307 to 0.278 and 0.499, respectively. All DCC estimates are statistically significant at the 1% level, implying that the paired correlation is strong (see Table 4). The results in Figure 2 and Table 3 and Table 4 accurately imply the existence of contagion effects across stock markets, whereas HKHIS and SSEC return indices are interdependent. Volatility caused by crisis events leads to more fluctuation in the inland stock market via the Hong Kong stock market.
Table 5 shows all the descriptive statistics of the DCCs calculated by the DCC–GARCH (
Based on the DCC-MGRACH (
Pre-financial crisis:
During the financial crisis:
Pre-COVID-19 pandemic:
During the COVID-19 pandemic:
All the eigenvalues are inside the unit circle. Therefore, VAR satisfies the stability condition.
Under the hypothesis of stock-market efficiency, institutional investors are more sensitive to news than individual investors because well-trained institutional investors not only have superior resources but can also benefit from economies of scale in acquiring and processing new information [[
This paper illustrated the contagion effects of global turmoil on the performance of major stock markets. Owing to the high degree of globalization and intensively integrated value chain, investors' pessimistic sentiment caused by strong external shocks and uncertainty in international trade and finance leads to changes in macroeconomic fundamentals. Moreover, such sentiments play important roles in the transmission of fear during global crises. The main results indicate that significant negative shocks have an adverse impact on the performance of stock-market indices. In addition, dynamic conditional correlations between returns on SSEC and S&P 500 as well as between returns on HKHIS and S&P 500 significantly increase from the pre-crisis phrase to directly after the crisis for both the financial crisis and COVID-19 pandemic, implying contagion effects across stock markets. However, a smaller increase in the DCCs between HKHIS and SSEC returns suggests they are interdependent during the period of the COVID-19 pandemic. Finally, the Granger test confirms the existence of contagion effects and their directions.
The results of the DCC–MGARCH model show the existence of contagion between the Chinese and US stock markets owing to the significant increment in the stock-market correlation after the outbreak of a destructive crisis, whereas violent fluctuations are present in the stock-market connection during a period of stability. Our analysis confirms the findings of Yin et al. (2017), who showed that the financial crisis strengthened the connections among the global stock markets, and further shows a stepwise increase in the cross-market correlations [[
The results imply that investors, bankers, and financial analysts may need to set up different trading strategies to avoid losses, such as hedging risk. Overreaction to the pandemic causes investors to sell stocks and reduces possible financial losses before further deterioration of returns on investments. Hence, financial-market regulators could impose limitations on short selling or repurchase their own stock shares. On the basis of our analysis of the performance of stock-market indices, government officials and bank authorities should implement measures to help different sectors survive this difficult time, including fiscal stimulus (i.e., issuing new government bonds and subsidization) and monetary policy (i.e., interest-rate cuts) [[
We encountered limitations in examining the performance of the stock indices. Owing to difficulties in collecting data, we may have overlooked many factors, including investors' preferences and stock-market experiences and firms' specific and individual characteristics, which can affect their returns. In other words, we did not explore the transmission channels in detail. We selected the sample stock indices arbitrarily, and the empirical results may be subject to sample-data-selection bias. In addition, the test results may be affected owing to the 10-month sample data. Finally, we focused only on short-term cross-market contagion effects and conducted our analysis from the perspective of financial crisis contagion.
This study contributes to future research, as we can analyze the transmission path of stock markets from the perspective of the effect of a crisis on a country's actual economy and offer new insights into the impact of a crisis on the co-movement of stock markets. Moreover, studies on long-term cross-market co-movement can be conducted. The causes of financial contagion effects, such as herding behavior, rational expectations, risk aversion, and investors' sentiments, can be further explored in response to disastrous crises.
Graph: Figure 1 Time sequences of stock returns in the periods of the financial crisis in 2008 and the COVID-19pandemic. (a) The period of financial crisis in 2008; (b) The COVID-19 pandemic period.
Graph: Figure 2 Dynamic and constant conditional correlations for return series. The light blue line gives the constant conditional correlation by using the CCC–MGARCH model. (a) The period of financial crisis in 2008; (b) The COVID-19 pandemic period.
Graph: mathematics-10-01819-g002b.tif
Table 1 Unit-root results from Phillips–Perron test and Augmented Dickey–Fuller test.
Phillips–Perron Test Augmented Dickey–Fuller Test Conclusion Global financial crisis −0.228 −0.125 I(1) −0.491 −0.745 I(1) −0.941 −0.965 I(1) −26.777 *** 26.659 *** I(0) −32.784 *** −33.154 *** I(0) −30.622 *** −30.647 *** I(0) COVID-19 pandemic −2.437 −2.399 I(1) −1.185 −1.394 I(1) −2.211 −2.213 I(1) −12.523 *** −12.532 *** I(0) −38.412 *** −39.313 *** I(0) 29.826 *** −29.827 *** I(0)
The null hypothesis is that the variable contains a unit root, and the alternative is that the variable was generated by a stationary process. *** indicates statistical significance at the 1% confidence level.
Table 2 Descriptive statistics analysis of return series.
Mean Std. Dev Skewness Kurtosis Jarque–Bera Observation Global financial crisis Before subprime crisis HKHIS −0.0669 1.4343 0.1276 10.4927 significant 814 S&P 500 −0.0164 0.8814 0.1390 5.48888 significant 818 SSEC −0.1329 1.8647 0.5104 6.257352 significant 788 During subprime crisis HKHIS 0.3545 3.2883 −0.2734 7.3298 significant 164 S&P 500 0.2647 2.8712 −0.1216 6.0053 significant 165 SSEC 0.4141 2.9996 −0.4344 3.7893 significant 160 COVID-19 pandemic Before COVID-19 pandemic HKHIS −0.036 1.027 0.529 5.951 significant 728 S&P 500 −0.052 0.823 0.729 8.327 significant 724 SSEC 0.001 1.031 0.428 7.728 significant 724 During COVID-19 pandemic HKHIS 0.029 1.596 0.441 4.939 significant 200 S&P 500 −0.043 2.432 0.759 9.484 significant 200 SSEC −0.051 1.442 0.494 11.043 significant 202
Table 3 Results of the bivariate DCC–GARCH model for financial crisis.
Financial Crisis: All Samples Parameters (Mean) (constant) (ARCH) (GARCH) Stock Index Hong Kong, China −0.112 *** 0.014 0.107 *** 0.891 *** 0.998 (−3.44) (1.52) (4.84) (40.10) Shanghai, China −0.139 *** 0.025 0.067 *** 0.932 *** 0.999 (−2.77) (1.40) (3.81) (58.85) US −0.080 *** 0.007 0.091 *** 0.905 *** 0.996 (−3.42) (1.36) (4.51) (43.39) Conditional correlation in DCC–GARCH(1,1)-t and CCC–GARCH(1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.325 *** 0.227 *** (6.41) (3.4) Shanghai, China 1 0.066 (0.94) US 1 Dynamic conditional correlation parameters Hong Kong, China–US 0.09 0.29 0.38 Hong Kong–Shanghai 0.021 0.935 0.956 Shanghai, China–US 0.09 0.19 0.28 Pre-crisis period: Conditional correlation in DCC–GARCH(1,1)-t and CCC–GARCH(1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.263 *** 0.03 (0.27) *** (0.15) *** Shanghai, China 1 0.066 (0.042) US 1 Pre-crisis period: Dynamic conditional correlation parameters Hong Kong, China–US 0.09 0.29 0.38 Hong Kong–Shanghai 0.013 0.936 0.949 Shanghai, China–US 0.09 0.09 0.18 Financial crisis: Conditional correlation in DCC–GARCH(1,1)-t and CCC–GARCH(1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.56 *** 0.38 *** (0.57) *** (0.331) Shanghai, China 1 0.106 (0.094) US 1 Financial crisis: Dynamic conditional correlation parameters Hong Kong, China–US 0.09 0.29 0.38 Hong Kong–Shanghai 0.09 0.29 0.38 Shanghai, China–US 0.09 0.09 0.18
Table 4 Results of the bivariate DCC–GARCH model for the COVID-19 pandemic period.
COVID-19 Pandemic: All Samples Parameters (Mean) (constant) (ARCH) (GARCH) Stock Index Hong Kong, China −0.080 *** 0.027 ** 0.044 *** 0.935 *** 0.979 (−2.57) (1.48) (3.23) (40.10) Shanghai, China −0.050 ** 0.008 0.063 *** 0.935 *** 0.998 (−2.01) (1.56) (3.81) (62.03) US −0.140 *** 0.020 ** 0.083 *** 0.897 *** 0.98 (−6.28) (2.64) (4.62) (47.14) Conditional correlation in DCC–GARCH(1,1)-t and CCC–GARCH(1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.618 *** 0.326 *** (0.664) *** (0.32) *** Shanghai, China 1 0.258 *** (0.274) ** US 1 Dynamic conditional correlation parameters Hong Kong, China–US 0.09 0.45 0.54 Hong Kong–Shanghai 0.023 0.653 0.675 Shanghai, China–US 0.09 0.09 0.18 Pre-COVID-19: Conditional correlation in DCC–GARCH (1,1)-t and CCC–GARCH (1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.623 *** 0.307 *** (0.62 ***) (0.27) *** Shanghai, China 1 0.159 *** (0.159) *** US 1 Pre-COVID-19 pandemic: Dynamic conditional correlation parameters in DCC–GARCH(1,1)-t model Hong Kong, China–US 0.09 0.09 0.28 Hong Kong–Shanghai 0.050 0.552 0.602 Shanghai, China–US 0.058 0.362 0.42 COVID-19 pandemic: Conditional correlation in DCC–GARCH (1,1)-t and CCC–GARCH (1,1)-t model Hong Kong, China Shanghai, China US Hong Kong, China 1 0.67 *** 0.499 *** (0.61) *** (0.526) *** Shanghai, China 1 0.278 *** (0.383) ** US 1 COVID-19 pandemic: Dynamic conditional correlation parameters Hong Kong, China–US 0.09 0.09 0.28 Hong Kong–Shanghai 0.23 0.33 0.56 Shanghai, China–US 0.07 0.64 0.71
Table 5 Descriptive statistics of conditional correlations calculated by using the DCC–GARCH (
Financial Crisis Sample Crisis Period Mean Std. Dev. Min Max S&P500/HKHIS Pre 0.100 0.053 0.0006 0.190 Post 0.357 0.064 0.124 0.618 S&P500/SSEC Pre 0.029 0.001 0.029 0.0295 Post 0.094 0.067 −0.133 0.397 HKHIS/SSEC Pre 0.319 0.053 0.028 0.504 Post 0.524 0.526 0.242 0.759 COVID-19 pandemic Sample Crisis period Mean Std. Dev. Min Max S&P500/HKHIS Pre 0.271 0.048 0.570 0.753 Post 0.509 0.055 0.113 0.758 S&P500/SSEC Pre 0.159 0.066 −0.231 0.942 Post 0.662 0.134 −0.140 0.485 HKHIS/SSEC Pre 0.654 0.035 0.419 0.552 Post 0.672 0.058 0.169 0.848
Table 6 Results of Granger causality Wald tests.
Null Hypothesis Conclusions Pre-financial crisis RS&F500 fail to cause Rssec 14.595 *** Reject Rssec fail to cause Rs&p500 0.0076 Fail to Reject During the financial crisis RS&P500 fail to cause Rssec 19.635 ** Reject Rssec fail to cause RS&P500 1.347 Fail to Reject Pre-COVID-19 pandemic RS&P500 fail to cause Rssec 0.022 Fail to Reject Rssec fail to cause RS&P500 53.858 *** Reject During the COVID-19 pandemic RS&P500 fail to cause Rssec 8.950 Fail to Reject Rssec fail to cause RS&P500 17.635 ** Reject
Data curation, X.L.; Formal analysis, X.J.; Investigation, S.W., H.X. and X.L.; Project administration, S.W. and N.B.; Resources, S.W., H.X. and N.B.; Supervision, S.W. and N.B.; Writing—original draft, X.J.; Writing—review & editing, S.W. and N.B. All authors have read and agreed to the published version of the manuscript.
Not applicable.
Not applicable.
Not applicable.
The authors declare no conflict of interest.
We would like to thank the editor, Zhiping Zhang, and Kangping Wang for their helpful comments on the early versions of this manuscript.
By Xiuping Ji; Sujuan Wang; Honggen Xiao; Naipeng Bu and Xiaonan Lin
Reported by Author; Author; Author; Author; Author