key: cord-0899635-9pk329ap authors: Okorie, David Iheke; Lin, Boqiang title: Stock Markets and the COVID-19 Fractal Contagion Effects date: 2020-06-06 journal: Financ Res Lett DOI: 10.1016/j.frl.2020.101640 sha: a46012152586e2b8ff75c4354cb27f0ef9098733 doc_id: 899635 cord_uid: 9pk329ap This article investigates the fractal contagion effect of the COVID-19 pandemic on the stock markets. The stock market information of the top 32 coronavirus affected economies (as of 31st March 2020) was sampled for ex-ante and ex-post COVID-19 outbreak analysis using the Detrended Moving Cross-Correlation Analysis (DMCA) and Detrended Cross-Correlation Analysis (DCCA) techniques. The results confirm a fractal contagion effect of the COVID-19 pandemic on the stock markets. Furthermore, this fractal contagion effect fizzles out over time (in the middle and long run) for both the stock markets return and volatility. Therefore, this article provides pieces of evidence for the COVID-19 fractal contagion effect on the stock markets. The COVID-19 pandemic has resulted in panics as well as the temporary closure of businesses in most economies with confirmed positive coronavirus cases. These reactions are bound to affect the performance of the businesses in these economies as well as their stock market dynamics. As long as the coronavirus is contagious and migrations exist, this virus is capable of affecting many economies of the world and their stock markets simultaneously. Therefore, this article seeks to establish a substantial contagion effect of the COVID-19 pandemic on the stock market returns and volatilities. The current coronavirus pandemic emanated in a wildlife market in the city of Wuhan, China. Due to its rapid spread and threats to humans, the market was closed. Subsequently, the whole city, country, other countries of the world are locked down to strategically separate and quarantine the infected persons from the uninfected persons. This outbreak has rapidly spread from China to many, if not all, countries of the world, and a great number of deaths and confirmed positive results have been declared concurrently. In the absence of a working vaccine, an effective model for curtailing and controlling the effects of the COVID-19 in an economy involves a total lockdown and stay at home strategy. For sustenance, most investors liquidate their positions, this includes stock market positions and thus affects the stock markets. Contagion effects, as a result of global events that originate from a country or region, have been an interest in economic and financial literature. Park and Shin (2020) investigated the foreign banks' exposure at the regional and national levels during the 2008 global financial crisis and found that the banks in emerging economies are more exposed directly and indirectly, to the global financial crisis and suffered more capital outflow. Even at the local levels of financial institutions (Agosto, et al., 2020) . However, using conditional correlation methods, there is a regional contagion effect of the financial crisis on the stock markets even though some sectors are relatively less affected than other sectors (Kenourgios & Dimitriou, 2015) . Wang et al. (2017) and Jin & An (2016) examined the impact of the global financial crisis on the G7 and BRICS countries and discovered a multifractal contagion which depends on the recipient country and time scale. There is also a significant contagion effect of the global financial crisis on the top 8 largest economies of the world (Dungey & Gajurel, 2014) Eurozone debt crisis, Bashir et al. (2016) and Ang & Bekaert (2002) equity market, Hussain et al. (2017) crude oil market, etc. The nonlinear process has been a very powerful tool in establishing contagion effects among various markets. Within the existing literature, some of these nonlinear processes that have been adopted to study contagion are the Regime Switching models, Smooth Transition Autoregressive (STAR) model (Terasvirta and Anderson, 1992; Terasvirta, 1994) , Nonlinear Error Correction Models (NECMs) (Granger and Terasvirta, 2003) , Threshold Autoregressive (TAR) models (Tong and Lim, 1980; Tsay 1989; Tong, 1990) , Switching Transition Error Correction and Generalized Autoregressive Conditional Heteroscedasticity (STEC-GARCH) process (Arouri, et. al., 2011) , Exogenous Asymmetric BEKK and DCC processes (Okorie, 2019; Okorie and Lin, 2020), etc. However, among other advantages, the Detrended Moving Cross-Correlation Analysis (DMCA) and the Detrended Cross-Correlation Analysis (DCCA) processes do not require the time series processes to be stationary and they directly use the moment properties of the series to establish the cross-correlation (contagion effects) in both regimes. In other words, no sample reduction (which can be the case when a series is differenced stationary) and the original observations are used. Generally, the cross-correlation techniques and the nonlinear process approach are both capable of identifying a significant switch or periodic switch in a time series over time. The linkage between the nonlinear processes and the cross-correlation techniques is their ability to specify and identify, at least, two different regimes and allow them to depend on the regime's moments & the smooth transition modalities. The Detrended Moving Cross-Correlation Analysis (DMCA) proposed by Vandewalle & Ausloos (1998) and modified by Kristoufek (2014) (1998) . These approaches have been vastly applied in various areas (Mohti, et al., 2019; Kristoufek, 2014; Zebende, 2011) , including economics and finance (Zhang, Lin, & Yang, 2020; Wang, Wei, & Wu, 2010) . (1) Given a set of time series and of size , we define the profiles in equation (1) where ̅ and ̅ are the mean of the time series and = 1,2, . . . , . Next, each profile is divided into = ⌊ ⁄ ⌋ non-overlapping number of segments, , of length ( ) for DCCA (DMCA). For each segment, , we compute ̃ and ̃ which are the moving averages (local trends) for the DMCA (DCCA) fluctuation functions. Equations (2) and (3) are the fluctuation functions for DMCA and DCCA respectively. where = ( − 1) and is the type of moving average employed. is set to 0 or 0.5 or 1 for forward or centered or backward moving averages respectively. Empirically, the centered moving averages outperforms the rest. Hence, = 0.5 (Zhang, et al., 2020; Mohti, et al., 2019; Kristoufek, 2014) in this analysis. The cross-correlation is defined in equation (4) which ranges from zero to 1 in absolute terms proposed by Podobnik et al. (2009 Podobnik et al. ( , 2010 Podobnik et al. ( , 2011 and respectively are also applied on the (differenced) cross-correlation coefficients in this study of COVID-19 contagion effect. ( / ) = 2 ( / ) ∆ ( / ) > 0 confirms that there is a significant contagion or cross-correlation effect in the stock markets during the COVID-19 pandemic while ∆ ( / ) < 0 suggests that the crosscorrelation or system dependence within the stock markets declined during the COVID-19 period. The stock market returns and unconditional volatility as defined in equations (6) and (7) respectively. is the markets return and is the asset's price at time . is the market volatility at time . The normalized market properties differences , , and are defined as the differences between normalized high, close, and low prices from the normalized open price respectively. Unlike conditional volatility measures of the autoregressive conditional heteroscedastic models (Bollerslev, 1986; Engle & Shepard, 2002; Baba, Engle, Kraft, & Kroner, 1995; Okorie, 2019; Okorie & Lin, 2020), the unconditional measures of a market's volatility have taken different forms, for instance, the squared return, the squared conditional mean return residual, even more, sophisticated approaches, etc. This paper adopts the best analytic scale-invariant unconditional volatility estimator model proposed by Garman and Klass (1980) . The unconditional volatility equation of each asset market is specified in equation (7). is a 3 × 3 − matrix 1 . and and are symmetric matrices of normalized differences. Major stock market index information from the top 32 countries that have recorded over 1500 platforms. We select a relatively short periods before and after the outbreak of the COVID-19 virus to minimize the occurrences of other exogenous shocks or factors that might affect the stock markets and thus bias the findings of this study. In line with this, MacKinlay (1997) stated in his article entitled, Event studies in Economics and Finance, " .. thus, a measure of the event's economic impact can be constructed using security prices observed over a relatively short-time period...". The idea hinges on the fact that there might be other events which may have occurred after the event being studied. As such, the effect of the particular event under study is best captured using a relatively small window around the event's announcement date. Indeed, this is often the case. For instance, after the ICO ban in China, few other economies have proceeded to consider banning ICOs, Okorie (2019) used a piece of relatively small window information around the ICO ban event in China to investigate its effect in the Bitcoin market. (Insert Table 1 ) Table 1 shows the basic summary statistic distribution of the stock market return series from the sampled economies. The average, standardized average deviations, minimum, and maximum return values are reported for each economy during the calm period and COVID-19 period. Generally, these distributions are higher in magnitude during the COVID-19 period relative to the calm period. It can also be seen that the Iranian stock market experienced the largest maximum return in both periods followed by the Israeli stock market. Moreover, other stock markets have moderate fluctuations in both periods. (Insert Table 2) In Table 2 other stock market volatility has moderate fluctuations in both periods. The periodic changes in all these stock markets suggest a contagion effect of the COVID-19 pandemic. The DMCA and DCCA techniques are applied to the return series from all the sampled stock markets for both the calm period and the COID-19 period. Afterward, the periodic differences where computed. These results are presented in Figure 1 and Figure 2 . (Insert Figure 1) In Figure 1 , the DMCA results for the sampled stock markets are presented. The first-row plots represent the comovement of the sampled stock markets return during the calm periods (exante COVID-19 pandemic). The second-row plots represent the comovement of the sampled stock markets return during the COVID-19 periods (ex-post COVID-19). The third-row plots represent the differences in the sampled stock markets return comovements, thus, the fractal contagion effect of the COVID-19 pandemic in the Stock markets. The total number of confirmed COVID-19 infected persons, , is used to group these economies to observe unique patterns and similarities. The first-column plots present the comovement of the stock markets wherein confirmed COVID-19 cases are above 16,000 persons; between 5,000 to 16,000 infected persons in column two; between 2,700 to 5,000 infected persons in column three; and between 1,600 to 2,700 infected persons in column four (as of 31st March 2020). Based on these results, it is pertinent to conclude that the COVID-19 pandemic has a contagion effect on the stock markets. This effect is stronger for economies with a relatively higher number of confined virus-infected persons. This is practically intuitive given that the outbreak and presence of the COVID-19 cases in an economy make the populace to panic, businesses are closed down as well as other gatherings like churches, meetings, conferences, etc. Every economy does this because they want to strategically group the populace into virus-infected and uninfected persons by asking (and enforcing) that people stay at their homes. This will help to isolate and quarantine infected persons while the rest of the people can return to their normal lives. However, this panic (coupled with the fear of future market performance and possibly global downturns) makes the stock markets investors to take early non-market based actions. In other words, their decision to take short or long positions was not informed by the traditional alpha rule but mostly to have enough resources to afford staying at home until it is necessary to resume their businesses as usual or due to the rapid fall in the asset prices. This is likely the observed and similar patterns for these sampled economies, hence, the contagion effect of the COVID-19 pandemic on the stock markets. The DMCA and DCCA techniques are applied to the stock markets volatility series from the sampled stock markets for both the calm period and the COID-19 period. Afterward, the periodic differences where computed. These results are presented in Figure 3 and Figure 4 . (Insert Figure 2) The first row plots show that there are, more or less, strong comovements among these market volatilities before the COVID-19 pandemic. This is mostly true for economies with higher confirmed cases of the virus infection. However, for those with lesser confirmed cases, the association appears to be stronger too. Therefore, the stock market volatilities associate greatly for all these economies during the calm period. After the outbreak of COVID-19, the DMCA results in the second row confirms a significant comovement among these sampled stock market volatilities for all these groups. Besides, it can be observed that this comovement (Insert Figure 4) This article provides empirical pieces of evidence on the fractal contagion effect of the COVID- Tree networks to assess financial contagion International asset allocation with regime shifts Asymmetric correlations of equity portfolios Nonlinear Shift Contagion Modeling: Further Evidence from High-Frequency Stock Data Multivariate Simultaneous Generalized Arch Do foreign exchange and equity markets co-move in Latin American region? 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