This paper contributes to the extant literature by several ways. First, as mentioned above, we focus our research on the risk of stock market crashes, which allows us to pay more attention to those asymmetric negative and extreme risks.
Second, we create a fear sentiment by using the Baidu index towards the pandemic to examine if panic for the epidemic will correlate with the market crash.
Finally, we investigate the role of fear sentiment in the impact of COVID-19 on the stock market crash risk. More importantly, our findings carry some policy implications. One of the most important policies is to alleviate the investors' panic to mitigate the equity market crash risk. The second preventive measure could be considered as the way to communicate about the number of infected cases as well as deaths. To recapitulate, our findings might provide the policymakers with the deep understanding of how to response to and cope with the investors' pessimism about the equity markets in a timely and comprehensive manner during such a financial downturn.
The rest of this paper is organized as follows: Section 2 acknowledges the current literature while section 3 describes the data and methodology. Following this, section 4 presents the empirical results of the impacts of COVID-19 on stock market crash risk. Section 5 concludes.
It is essential to construct the solid and sound theoretical framework how the COVID-19 pandemic adversely influence the financial markets. Goodell (2020) compares that the markets are likely to react with the pandemic in the same way with the other forms of disasters such as catastrophic disasters (Gao et al., 2020) or terrorism (Wang and Young, 2020). There is a common trait that investors' risk preferences or their mood towards these events might vary considerably, which means an increase in fear-induced feelings. While the previous events were occurred in specific region or area with the partial disruption, the existence of pandemic locked the travelling status as well as economic transactions in the global 5 / 27 scope. Hence, the effects of pandemic on the total economy will not only enormously influence domestic demands but also completely limit the supply, which is expected to dip the future cash flows of the firms. This phenomenon first manifests itself as the public mood about the future pessimistic feelings.
The COVID-19 pandemic is considered as the unique public health crisis event in terms of its global scope since the influenza pandemic in 1918. Thus, there are many unknown perspectives which need to be examined. One of the biggest concerns is the financial crashes. While Mazur et al. (2020) claimed that the financial market crash in March 2020 was triggered by the government's reactions. Interestingly, the negative effects are more pronounced in some specific industries such as crude petroleum, real estate, entertainment, and hospitality sectors. This paper also confirms what Mishkin and White (2002) found. The equity market crash could results in a drop by 20-25% in the main index during the previous crisis due to the sequence of panic selling. Thus, our motivation is to examine the determinants including the investors' sentiment and the pandemic status could predict the equity market crash risk while Giglio et al. investors' expectations with the short run might correlate with the stock market crash risk. It is noticeable that the previous studies (Giglio et al., 2019; Giglio et al., 2020) also confirm that the probability of equity market crash before the crisis is lower because the investors tend to be more optimistic about stock market returns.
Notwithstanding the evident findings, the further investigation of COVID-19 is still promising since we take no stance on whether the likelihood of market crash risk would significantly change in the two sub-period, including before-and after-the pandemic. Given the foregoing discussion and argument, we accordingly hypothesize the following: H1: The Chinese equity market crash risk in the COVID-19 pandemic is higher than in the previous period.
To examine the first hypothesis, we divide our samples into two sub-periods and employ the statistical test as well as the illustration. The aforementioned literature (such as Giglio et al., 2019; Giglio et al., 2020; Gabaix, 2012; Wachter, 2013) would be the sound and solid framework for our constructions of the first hypothesis.
H2: There is no relationship between investors' sentiment and stock market crash on the onset of COVID-19 pandemic.
Although there are a mounting literature examining how investors overreact or underreact in the COVID-19 pandemic (see more at Schell et al., 2020; Aslam et al., 2020; Yarovaya et al., 2020) , it is still unanswered what drives the Chinese stock market crash risk. It is marginally relevant to consider that the combination of economic uncertainty and behavioral factors positively contributes to financial asset crash risk (for example, Bitcoin (Kalyvas et al., 2020) , Chinese stock market (Jin et al., 2019; Luo and Zhang, 2019) . Noticeably, the concern how the aforementioned factors drive the stock market during the diseases period is still open. In doing so, we use the two proxies such as the fear index for COVID-19 aggregating the data from Baidu Index and the actual figures of pandemic situation to predict the changes in stock market crash risk index, constructed by employing the GARCH-S. The substitution of different proxies would be our alternative approach to check whether our findings and results are robust or not.
Overall, the existing literature still has a gap for us to fulfill with two main folds. First, answering the research question 'How is the equity market crash risk before and after the COVID-19 pandemic?' would benefit to not only the practitioners to be cautious about the extreme shocks in the market but also the understandings of empirical evidence for academia. The second question needs to be answered is "What drives the 
The proxy we used in this paper to measure the severity of the COVID-19 epidemic is the logarithmic growth rate of daily confirmed cases (rCases). We also construct an alternative variable using the logarithmic growth rate of daily deaths (rDths) to run the robustness check. The data is retrieved from the CSMAR database.
We create a COVID-19 induced fear sentiment index (fearSent) utilizing the data from the Baidu index following the idea of Da, Engelberg and Gao (2011) . If the searching volume of COVID-19 related keywords is high, it means people are fear or even panic about the epidemic. Specifically, we define the fear index as the log of searching volume plus one. Figure 1 displays the trend of the daily confirmed cases and fear sentiment. Moreover, we set a dummy variable D_fear for fear index: if the searching volume is greater than the median of the 2020 sample, the value of this dummy is one, and zero otherwise. 2020)). To measure the crash risk of stock market, we follow the work of Chen, Hong and Stein (2001) , which associate it solely with the conditional skewness of the market return. They calculate the six-month horizon skewness from the daily returns, however, we use the GARCH-S (GARCH with skewness) model to estimate the daily skewness.
Where t r is the value-weighted market return of Shanghai A shares, t  is the residual and t  is the standardized residual.
period t. t h is the conditional heteroscedasticity with a classical GARCH(1,1) structure. t s represents the conditional skewness process, and we specify it as both autoregressive and dependent on lagged return shocks. To estimate the GARCH-S model, following Leon, Rubio and Serna (2005), we use a Gram-Charlier series expansion and truncate at the third moment. And it should be noted that, due to the high non-linearity of the likelihood function, we use the starting values of parameters estimated from the simple GARCH (1,1) model.
The market data we used is also from the CSMAR database and the sample period in our paper is from January 1, 2017 to March 31, 2020. Table 1 When looking at the statistical evidence, we do not reject the mean difference between two sub-samples including before (0.0002) -after (-0.0016) in Table 1 (t-stat = 1.25, = 0.211). It implies that there is no difference in market return when the COVID-19 pandemic happened. However, with regard to the skewness index,
representing the market crash risk, we observe the significant difference in mean between two periods. To be more precise, the level of market crash in 2020 is significantly higher than the previous period (t-stat = 2.50, = 0.01). Therefore, we do not reject the first hypothesis, implying the higher extreme volatility in the Chinese equity market when having the COVID-19 pandemic. Table 2 further reports the estimation results of GARCH-S model. As expected,
the results indicate a significant presence of conditional skewness. Specifically, the coefficient of lagged skewness is positive and significant (0.148 with a t-statistic 58.079), indicating that the skewness is persistent and high conditional skewness is followed by high conditional skewness. We also find the coefficient of the shock to skewness is positive and significant (0.036 with a t-statistic 15.373), which is similar with that in the variance case. In general, the majority of coefficients are significant, implying the appropriateness of our models when using GARCH-S to estimate the skewness of the market return. 
We conduct a simple time series model to examine the relationship between COVID-19 outbreak and stock market crash risk. Our dependent variable is the crash risk, i.e., conditional skewness calculated from the estimation results of GARCH-S model. Due to the persistence of skewness, we add the lagged skewness term in our model. The benchmark specification of the regression model is specified as:
where t Skew is the conditional skewness derived from the GARCH-S model, and 12 / 27 rCases is the logarithmic growth rate of daily confirmed cases. In addition, c is constant term, and are the coefficients of the one-period lagged term and the logarithmic growth rate of infected cases, respectively. Finally, is the error term in the estimation.
In our paper, we also consider whether the COVID-19 induced fear sentiment index (fearSent) affects the crash risk. And thus, we estimate the following model:
In which, Equation 3 also has similar denotations, which are presented above.
We only substitute the rCase by fearSent to consider how investors' sentiment could predict the stock market crash risk. In order to further investigate the interaction effect between the daily confirmed cases and the fear sentiment, we also add the interaction term in our model. Similarly, we choose that , represent the coefficients for fear sentiment and interaction term while the other components in equation 4 are the same as the previous equations. Our model specification is as follows:
We also employ the Granger causality test to detect the causal relationship between the crash risk of the stock market and the fear sentiment. The model for
Granger causality test is specified as follows:
where p is the largest lag order which is determined through the VAR model and the Bayesian information criterion. The hypotheses tests for Granger causality are presented in Table 6 . Finally, in our robustness section, we use the alternative proxy for the growth rate of confirmed cases as well as death cases to predict the equity market crash risk. In addition, due to the integration of the financial markets, we also run the further estimations to predict the equity market crash risk with the number of infected cases and deaths in the global scope. Our justification is that the Chinese investors do not only react with the local information but also the worldwide news, which might drive their behaviors to the market crash risk.
The equation (2) and (4) are changed into equation (7) and (8) respectively. By doing that, we could examine how our determinants are robust. Our findings will be illustrated and summarized in the following sections.
The estimation results of model (2) are reported in Table 3 . In column (1), we can see that the coefficient of 1 t rCases  is negative and significant. It is consistent with our exception that the COVID-19 outbreak has a negative impact on stock market crash risk. This result also reflects the reality well. With the rapid spread of the epidemic, the value of listed companies has generally been affected, and the stock market has entered a period of obvious downturn, accompanied by large declines or even crashes. Surprisingly, there is no predictive power of the other lagged terms including rCases(t-2) and rCases(t-3) for the changes in market crash risk. Thus, this finding emphasizes the role of information, particularly the number of cases, in the previous trading day on the market shocks. In terms of explanatory power, the R-squared in these markets are around 7 per cent indicating that the lagged variables of logarithmic growth rate of daily confirmed cases can be explained by changes in market skewness, representing the stock market crash risk.
(1) Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. Our findings also confirm the extant literature that the stock markets are likely to be sensitive to the information about the growth in number of confirmed cases as compared to the growth in number of deaths (Ashraf, 2020; Albulescu, 2020) . Thus, apart from the United States market, the new infection cases reported at Chinese level amplify the Chinese market crash risk.
We consider the role of COVID-19 induced fear sentiment in this section. The motivation is that people's panic about the epidemic may remain at a high level, although the number of confirmed cases at this time is not very large. For example, as early as January 20, 2020, Academician Zhong Nanshan publicly confirmed the human-to-human transmission of COVID-19 on TV. A few days later, on January 23, the central government of China announced the lockdown of Wuhan. Although the number of confirmed cases publicly disclosed at that time was still at a low level, people quickly fell into panic. That is to say, the fear sentiment may have an impact on the stock market ahead of the impact from the confirmed cases.
The results of model (3) are shown in Table 4 . We use the variable fearSent in the results of the first two columns. In addition, we also use the dummy variable, d_fear, to re-estimate model (3), and the results are displayed in the last two columns.
We can see that all the coefficients about fear sentiment are negative and significant,
indicating that COVID-19 induced fear sentiment will cause a significant crash in stock market. Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. Table 3 summarizes the estimated results for the Equation 3 .
While Duan et al. (2020) employed the textual analysis of 6.3 million messages on social media to conclude that the Chinese stock market is likely to overact with the growth sentiments, our findings are also consistent with the aforementioned study by using the construction methods of Da, Engelberg and Gao (2011) 
The above results show that both daily confirm cases and fear sentiment can increase the risk of stock market crashes. In this section, we try to further explore the inner links between these impacts to the underlying mechanisms. Table 5 gives the results about the interaction effect between daily cases and fear sentiment. The coefficients of the interaction terms are negative and show their significance. It means that fear sentiment will further amplify the negative impact of confirmed cases on stock market crash risk. In other words, because of fear, the negative impact of COVID has been exacerbated. It shows the importance of preventing investors from falling into panic and maintaining optimism during the epidemic.
(1) Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. Table 3 summarizes the estimated results for the Equation 5. In the first column, we use the variable, Fear Sentiment, and in column (2), the dummy variable, D_Fear Sentiment, is used. The total observations are 787 over our research period.
It is important to consider the existence of interaction term in our regression due to two main reasons. First, the investors' fear exhibit the dynamics pattern with the fatality ratio. It means that when the number of infected cases increase, the investors' sentiments might be induced by the fears. Second, the feelings of fear would mitigate the risky behaviors on the onset of pandemic. This might lead to the decrease in infected cases. Therefore, looking at the interaction variable constructed by the aforementioned components would offer some insights, especially how this factor increases or decreases the equity market crash risk.
There are three main conclusion which could be drawn from the regression in Table 5 . First, the interaction variable increases the likelihood of market crash risk at 1% significance level. This can be exemplified that both factors amplify the negative impact on the equity market shocks. Second, our results are robust although we substitute the fear emotion with continuous or binary variable. It does not only emphasize the dynamics pattern but also confirms the existing role of investors' emotion on the systematic risk. Third, to compare the previous regression in Table 3 and 4, the explanatory level, captured by R 2 , is substantially improved. It implies that the interaction variable could positively contribute to the explanatory feature of the changes in the equity market crash risk.
One of the worth noting points is that our existing findings mainly stem from the correlation. We are cautious about confirming the sound tone for causal relationship before obtaining any statistical evidence. In doing so, we perform the Granger causal test to examine whether the fear emotion could cause the market risk crash or not. Of course, the opposite direction is also examined. Interestingly, we only observe the mono-direction in the Granger causality between fear sentiments and the market crash risk.
To be more precise, the fear sentiment is the factor which causes the changes in the market crash risk while we do not have any evidence in the opposite direction. In doing so, we come into conclusion that the investors' attitudes towards the uncertainties in terms of fear, macroeconomics and microeconomics will be stimulus to the risk of market crash risk. Our findings also confirm the extant literature of fear and stock market dynamics (such as Bitcoin market, Chen et al. (2020) ; the financial markets, Sharif et al. (2020) ; energy market, Salisu et al. (2020) ). By examining the causal relationship, our policy implication would be focused on how to alleviate the investors' panic to maintain the stability of the market. This is important, indeed.
An alternative proxy to measure the severity of the COVID-19 epidemic is the growth rate of daily deaths (rDeaths). We use it to redo our empirical analysis and the results are shown in Table 6 . In general, the results are consistent with the previous.
Furthermore, we substitute the number of global cases for that of the cases of China for another robustness checks since the people in China does not just pay attention to the progress of COVID-19 in China but also to the global progress. Table 7 and Table   8 show the results of the corresponding regressions, which illustrates that our conclusions remain robust. Thus, we could draw the policy implications from what we Notes: ***, **, * represent statistical significance at 1%, 5%, and 10% levels, respectively. The t-statistics are presented in the brackets. Model (1), (2),
(3), (4), and (5) represent the differences of the set of Fear Sentiment proxy including none of use, Fear Sentiment, dummy for Fear Sentiment, Fear Sentiment and dummy for Fear Sentiment, respectively. The total observations are 787 over our research period.
This paper has examined the relationship between the COVID-19 and the stock market crash risk. First, we confirm that COVID-19 will increase the likelihood of the stock market crash risk. It not only means that it will bring about a decline in stock market returns, but also means aggravating the negative symmetry of stock market returns and increasing the possibility of extreme downturns in stock prices. Second, we find that even when the number of confirmed cases is not very large, people's fear about the virus will increase the crash risk of the stock market.
It reminds us that preventing the spread of panic during the epidemic is helpful in reducing the crash risk. Finally, we also find that fear sentiment can not only directly increase the crash risk, it will also boost the negative impact of COVID-19 on the stock market crash risk. Thus, our study also draws two main policy implications.
First, the closer observation from lawmakers on the financial markets with the dynamics of fear and the number of cases is necessary. It is due to the fact that the governor could manage how to immediately support the market when the shake of fear is overwhelming. By doing this, the market crash risk might be managed in some urgent cases. Second, investors are likely to be sensitive with not only the local information (Chinese domestic infected cases or deaths) but also the global news. 