The interactions between COVID-19 cases in the USA, the VIX index and major stock markets

Grima, Simon; Özdemir, Letife; Özen, Ercan; Romānova, Inna Article The interactions between COVID-19 cases in the USA, the VIX index and major stock markets International Journal of Financial Studies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Grima, Simon; Özdemir, Letife; Özen, Ercan; Romānova, Inna (2021) : The interactions between COVID-19 cases in the USA, the VIX index and major stock markets, International Journal of Financial Studies, ISSN 2227-7072, MDPI, Basel, Vol. 9, Iss. 2, pp. 1-19, https://doi.org/10.3390/ijfs9020026 This Version is available at: https://hdl.handle.net/10419/257771 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ International Journal of Financial Studies Article The Interactions between COVID-19 Cases in the USA, the VIX Index and Major Stock Markets Simon Grima 1,* , Letife Özdemir 2, Ercan Özen 3and Inna Rom¯ anova 4   Citation: Grima, Simon, Letife Özdemir, Ercan Özen, and Inna Rom¯ anova. 2021. The Interactions between COVID-19 Cases in the USA, the VIX Index and Major Stock Markets. International Journal of Financial Studies 9: 26. https:// doi.org/10.3390/ijfs9020026 Academic Editor: Kuan Min Wang Received: 27 March 2021 Accepted: 13 May 2021 Published: 20 May 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). 1Department of Insurance, Faculty of Economics, Management and Accountancy, University of Malta, MSD 2080 Msida, Malta 2Department of Logistics Management, School of Applied Sciences, University of Afyonkocatepe, Afyonkarahisar 03200, Turkey; [email protected] 3Department of Finance and Banking, Faculty of Applied Sciences, University of Usak, U¸sak 64200, Turkey; [email protected] 4Faculty of Business, Management and Economics, University of Latvia, LV-1586 Riga, Latvia; [email protected] *Correspondence: [email protected] Abstract: With this study, we aimed to determine (1) the effect of the daily new cases and deaths due to the COVID-19 pandemic in the United States on the CBOE volatility index (VIX index) and (2) the effect of the VIX index on the major stock markets during the early stage of the pandemic period. To do this, we collected and analysed the daily new cases and death numbers during the COVID-19 pandemic period in the United States and the country indexes of the USA (DJI), Germany (DAX), France (CAC40), England (FTSE100), Italy (MIB), China (SSEC) and Japan (Nikkei225) to determine the impact of the VIX index on the major stock markets. We then subjected this data to the Johansen co-integration test and the fully modified least-squares (FMOLS) method. The results indicated that there was co-integration between the VIX and the COVID-19 pandemic and that there was co-integration between the VIX index and major indexes, except for the CAC 40 and MIB. Moreover, the results showed that the new COVID-19 cases in the USA had a higher impact on the VIX than cases of deaths during the same period. Keywords: COVID-19 pandemic; fear index; co-integration test; fully modified least squares method; stock markets 1. Introduction In December 2019, the coronavirus disease 2019 (COVID-19) outbreak began in the city of Wuhan, Hubei region, China. As of 20 March 2020, the virus had already affected more than 500,000 people in more than 60 countries, with around 16% deaths due to this virus. Around 5% of the infected patients were in a critical or serious condition, while there seemed to be a recovery rate of 84% (Worldometer 2020). On 3 February 2020, the Shanghai stock market plunged 8% following the general distress over COVID-19 in China. This shocking disruption rapidly spread to international financial markets. For example, the United States (U.S.) stock prices logged their lowest level in February and the S&P 500 plummeted 4.4% on 28 February 2020. Initially ignored by many countries, the COVID-19 effect was raising serious concerns due to its rapid propagation outside China (Albulescu 2020a,2020b). Can this be the “worst financial crisis the world has ever seen since 1929?” This is what some analysts, such as Elliot (2020), believe. He noted in his article that Stephen Isaccs (2020) of Alvine Capital highlighted that COVID-19 is “unprecedented”, with record levels of leverage and overbought stocks. Moreover, he highlights that both Goldman Sachs and Int. J. Financial Stud. 2021,9, 26. https://doi.org/10.3390/ijfs9020026 https://www.mdpi.com/journal/ijfs Int. J. Financial Stud. 2021,9, 26 2 of 19 HIS Markit revised their forecasts downwards for the world’s real GDP growth in 2020 to 1.25% and 0.7% respectively1. Herron and Hajric (2020) highlighted the panic mode in the markets and noted that stock markets plunged 12% amid COVID-19 fears. However, Desjardins (2020) showed that some markets (of holdings, such as Zoom Video Communications (ZM), Domino Pizza (DPZ), Campbell Soup Company (CPB), Teladoc Health, Inc. (TDOC), The Clorox Company (CLX), Everbridge, Inc. (EVBG) and Virtu Financial, Inc. (VIRT)) were thriving from this situation by creating a vortex to suck up the alternate market universe, which he called “the pandemic economy”. He said that, on average, these companies saw an upward bump of 12.7%. As we note, during a pandemic period, such as the COVID-19 pandemic, the factors affecting portfolios change; therefore, to achieve a well-designed portfolio, we need to understand the impact of cases and deaths on market risk and the stock markets. 2. Literature Review Most studies carried out by authors, such as Haacker (2004), Lee and McKibbin (2004), Loh (2006), Kauffman and Weerapana (2006), McKibbin and Fernando (2020), Fernandes (2020), Albulescu (2020a), Albulescu (2020b), Ramelli and Wagner (2020b), Zeren and HIZARCI (2020), on pandemics and their effect on the economies and financial markets relate mainly to HIV/AIDS and SARS. However, there is a small but growing literature emerging on the impact of COVID-19 on the stock markets. In his research, Fernandes (2020) highlights that this pandemic (COVID-19) differs from other global crises since it is a global pandemic, which does not focus only on the low-to-middle-income countries, the interest rates are at historical lows, the world is much more integrated than before and there are spillover effects throughout the supply chains that disrupt the demand and supply. Haacker (2004) showed that HIV/AIDS affected economic units, such as businesses, households, governments, labour supply decisions, labour efficiency and household income. He noted that business costs, public expenditure on healthcare and support of disabled and children orphaned by AIDS increased, causing budget deficits in certain countries. Kauffman and Weerapana (2006) revealed that bad news about HIV/AIDS in the Republic of South Africa had a negative effect on the value of the South African rand against the U.S. dollar. The SARS epidemic had significant effects on various economies that were caused by the reductions in total demand for various goods and services, increases in business operating costs and increases in each country’s risks, which in turn increased the risk premiums. Although the number of infected persons and deaths due to this epidemic was not the same in all countries, the impact on a global scale, which resulted in a cost of 54 billion USD in 2003, was significant (Lee and McKibbin 2004). The capital outflow in Hong Kong and China rose to 1.4% and 0.8% of GDP, respectively, and their risk premium was increased by 200 basis points (Lee and McKibbin 2004). On the other hand, Loh (2006) showed that the SARS pandemic increased airline stocks’ volatility with lower mean returns in certain countries. However, it had a negligible impact on the mean stock market returns and had no significant long-run implications. The author highlighted that airline stocks tended to take on an “aggressive” characteristic in the presence of any pandemic outbreak. McKibbin and Fernando (2020) used the G-Cubed multi-country model to calculate the effect of COVID-19 on the global economy in the early stages of the pandemic while the outbreak was still only in China. They explored seven different scenarios of how COVID-19 might develop and influence macroeconomic outcomes and financial markets using global hybrid dynamic stochastic general equilibrium (DSGE) and computable general equilibrium (CGE) models developed by McKibbin and Wilcoxen (1999,2013). 1Growth below 2% is classified as a global recession. Int. J. Financial Stud. 2021,9, 26 3 of 19 They found that the impact of the spread of COVID-19 on the financial risk in the United States was high relative to the G-20 and OECD countries and that England and several developing countries, such as Argentina, South Africa and Turkey, had a higher degree of relative financial risk resulting from the spreading of COVID-19 than the United States. Therefore, they note that the spreading of COVID-19 to these countries would deeply affect the financial markets. Using these scenarios, they demonstrated that even a controlled outbreak could have a significant impact on the global economy in the short run and that the costs may be avoided by greater investment in public health systems. Fernandes (2020) analysed the economic effects of the COVID-19 outbreak on the world economy as of 22 March 2020. The author noted that most stock markets on that date collapsed and registered their largest recorded one-day falls on record; some well-known companies saw their stock prices fall by more than 80% in a few days. He noted that in the United States, stock markets saw their worst performance with a fall of over 25% and British markets had the largest hit of all developed markets with a decline of more than 35%. He further highlighted that the impact of the outbreak of this pandemic (COVID-19) was being underestimated and could not be compared to other pandemics, such as SARS and the 2008/2009 financial crisis. His findings demonstrated that in a mild scenario, GDP would take a hit ranging from 3–5% depending on the country and that specifically service-oriented and tourism-reliant economies would be negatively affected, with the largest job losses. In the first 40 days of international monitoring of the COVID-19 outbreak, Albulescu (2020a) found in his study that the death ratio positively influenced the VIX and that this influencing effect was stronger outside China. In another study, Albulescu (2020b) found that following the outbreak of the virus infections resulted in a marginally negative impact on crude oil prices in the long run. Moreover, COVID-19 also has an indirect effect on crude oil prices when the volatility of the financial markets was amplified. Ramelli and Wagner (2020b) noted that after the outbreak of COVID-19 in China and the United States, industry stock returns faced disruptions. Stock returns in some sectors, such as telecom services, healthcare and software services, were on the increase in China and the United States. However, stock returns in other sectors, such as energy, transportation, insurance, real estate, retailing and automobiles, were on the decrease. Ramelli and Wagner (2020a,2020b) stated that the Chinese and the U.S. stock markets were quick to respond to concerns about the possible economic consequences of the COVID19 pandemic and explain that this resulted because the investors became increasingly worried about corporate debt and liquidity, which mutated into an economic crisis that was augmented through financial channels. Zeren and HIZARCI (2020) investigated the co-integration relationship between COVID-19 cases and some selected stock markets. They used data between 23 January 2020 and 13 March 2020. Their findings showed that there was a co-integration relationship between the COVID-19 cases and the SSE, KOSPI and IBEX35, and no relationship with the FTSE MIB, CAC40 or DAX30 was found. This result showed the geographical effect of COVID-19 on stock markets as the virus spread to the European countries at the beginning of March. Cheng (2020) highlighted that stock investors underpriced the risk of the COVID-19 pandemic and showed that trading in the VIX futures market was a step behind in relating the risks. He noted that although the cases of COVID-19 were increasing rapidly in Europe starting in March and there were reports of community spreading and deaths in the United States, the S&P 500 had declined slightly, while the price of the VIX had risen by 42%. Onali (2020) investigated the impact of the COVID-19 cases and deaths on the U.S. stock market, specifically the Dow Jones and the S&P500 indices. He allowed for changes in trading volume and volatility expectations, as well as day-of-the-week effects. Using a GARCH(1,1) model on the data collected during the period from 8 to 9 April 2020, he found that, except for China (where reported cases had an effect), changes in the number of cases and deaths in the United States and six other countries strongly affected by the Int. J. Financial Stud. 2021,9, 26 4 of 19 COVID-19 crisis did not have an impact on the U.S. stock market returns. However, he further noted that his findings evidenced a positive impact for some countries on the conditional heteroscedasticity of the Dow Jones and S&P500 returns, that the VAR models indicated that reported deaths in Italy and France had a negative impact on stock market returns, a positive impact on the VIX returns and that the magnitude of the negative impact of the VIX on stock market returns spiked threefold. In their study, Baker et al. (2020) used textual analysis to quantify the impact of news on COVID-19 cases on the volatility in the stock market, specifically the Dow Jones index, using data up to 9 April 2020 for cases and deaths in the United States, China, France, Iran, Italy, Spain and the United Kingdom. They found that the volatility impact was much larger during this pandemic than during similar disease outbreaks and that the COVID-19 crisis had caused a change in the relationship between volatility expectations and stock market returns. In a further study, Yilmazkuday (2020) investigated the impact of the number of deaths related to COVID-19 on the S&P500 index. He used daily data collected during the period between 31 December 2019 and 1 May 2020 and used a structural vector autoregression model, using a measure for the global economic activity, the spread between 10-year treasury maturity and the federal funds rate. The results showed that a 1% increase in the U.S. cumulative daily COVID-19 cases resulted in around a 0.01% cumulative reduction in the S&P 500 Index after one day and around a 0.03% reduction after one month, with the largest observations during March 2020. Using data up to June 2020 from the aggregated stock market and the dividend futures, Gormsen and Koijen (2020a,2020b) measured the investors’ expectations on economic growth as a response to the COVID-19 outbreak and the subsequent policy responses until June 2020. They showed that the growth expectations across maturities evolved and provided a simple model for understanding the joint dynamics of short-term dividend futures, stock markets and bond markets. As noted from the literature, there are a limited number of papers that study the impact of COVID-19 cases on the VIX index and the impact of the VIX index on the major stock markets during the COVID-19 pandemic, especially using U.S. data. 3. Aim and Data Therefore, given the above discussion and the uncertainties during this COVID-19 “pandemic economy”, we aimed to answer the following research questions: (1) What was the impact of COVID-19 data on the VIX index in the United States? We hypothesised that: Hypothesis 1 (H1). Bad news on COVID cases and deaths in the United States did not influence the VIX index. Hypothesis 2 (H2). Bad news on COVID cases and deaths in the United States influenced the VIX index. (2) What was the impact of the VIX on the major world stock exchanges during the same period? We hypothesised that: Hypothesis 3 (H3). As the VIX index increased, the major world stock exchange prices would also increase. Hypothesis 4 (H4). As the VIX index increased, the major world stock exchange prices would decrease. To address the first research question, we used daily new case and death numbers during the COVID-19 pandemic in the United States. Since the cases started to increase as Int. J. Financial Stud. 2021,9, 26 5 of 19 of 27 January 2020 in the USA, we collected data for the period of 27 January 2020 to 29 May 2020 (the analysis period). Then, to determine the VIX effect on the major stock exchanges during the COVID-19 pandemic period, we collected and analysed daily closing price data for the USA (DJIA), Germany (DAX), France (CAC40), England (FTSE100), China (SSEC), Japan (Nikkei225) and Italy (MIB) for the period between 2 January 2020 and 29 May 2020. The COVID-19 data was collected from www.worldometers.info (accessed on 13 May 2021) (Worldometer 2020), while the index data was collected from www.investing.com (accessed on 13 May 2021) (Investing 2020). We conducted the analysis presented below to determine the effect of the COVID-19 pandemic on the VIX index and the effect of the VIX index on the major stock markets during the pandemic period. This study is especially equally important for those portfolio and fund managers who build their portfolios around the market indexes and academics who study the effects of specific announcements. In addition, this can be of benefit to risk managers, underwriters and actuaries who might need to revise their measurements in line with new data and information and for portfolio diversification and portfolio management decisions. The research period was chosen to eliminate as much as possible any noise that may have been introduced due to pandemic fatigue and the news of vaccines and antiviral medicines since there was no fatigue yet and no news about the vaccines in this period; the concentration of everyone was on the element of uncertainty. We wanted to specifically understand how news of the widespread pandemic affected the so-called fear index and major markets. 4. Methodology and Empirical Results 4.1. Effect of the COVID-19 Pandemic on the VIX Index The VIX index and daily new case and death numbers during the COVID-19 pandemic are provided in Figure 1. Int. J. Financial Stud. 2021, 9, x FOR PEER REVIEW 5 of 19 of 27 January 2020 in the USA, we collected data for the period of 27 January 2020 to 29 May 2020 (the analysis period). Then, to determine the VIX effect on the major stock exchanges during the COVID19 pandemic period, we collected and analysed daily closing price data for the USA (DJIA), Germany (DAX), France (CAC40), England (FTSE100), China (SSEC), Japan (Nikkei225) and Italy (MIB) for the period between 2 January 2020 and 29 May 2020. The COVID-19 data was collected from www.worldometers.info (accessed on 13 May 2021) (Worldometer 2020), while the index data was collected from www.investing.com (accessed on 13 May 2021) (Investing 2020). We conducted the analysis presented below to determine the effect of the COVID-19 pandemic on the VIX index and the effect of the VIX index on the major stock markets during the pandemic period. This study is especially equally important for those portfolio and fund managers who build their portfolios around the market indexes and academics who study the effects of specific announcements. In addition, this can be of benefit to risk managers, underwriters and actuaries who might need to revise their measurements in line with new data and information and for portfolio diversification and portfolio management decisions. The research period was chosen to eliminate as much as possible any noise that may have been introduced due to pandemic fatigue and the news of vaccines and antiviral medicines since there was no fatigue yet and no news about the vaccines in this period; the concentration of everyone was on the element of uncertainty. We wanted to specifically understand how news of the widespread pandemic affected the so-called fear index and major markets. 4. Methodology and Empirical Results 4.1. Effect of the COVID-19 Pandemic on the VIX Index The VIX index and daily new case and death numbers during the COVID-19 pandemic are provided in Figure 1. Figure 1. Natural logarithms of the VIX index and daily new case and death numbers in the USA. It can be noted from Figure 1 that the VIX index increased with the increase in the number of the COVID-19 case and death numbers in the USA. Furthermore, the VIX fear index started to increase with the first pandemic case in the USA. Moreover, the VIX index made a significant leap even when there were no deaths. The VIX index reached the highest level before the pandemic contamination and death figures peaked. This could have been because the COVID-19 case numbers were not always accepted as fact by some people. As the pandemic cases and death numbers became more and more evident, the level Figure 1. Natural logarithms of the VIX index and daily new case and death numbers in the USA. It can be noted from Figure 1that the VIX index increased with the increase in the number of the COVID-19 case and death numbers in the USA. Furthermore, the VIX fear index started to increase with the first pandemic case in the USA. Moreover, the VIX index made a significant leap even when there were no deaths. The VIX index reached the highest level before the pandemic contamination and death figures peaked. This could have been because the COVID-19 case numbers were not always accepted as fact by some people. As the pandemic cases and death numbers became more and more evident, the level of fear began to drop from the peak. The VIX index reached its peak by mid-March 2020, while the number of cases and deaths peaked at the end of March 2020. On the other hand, by Int. J. Financial Stud. 2021,9, 26 6 of 19 the third week of March, one could be witness that the stock markets studied here fell to their lowest levels. To examine the relationship between the VIX index and daily new case and death numbers of the COVID-19 pandemic, we first needed to determine whether the time series was constant. The unit root properties of the time series used in the study were investigated using the unit root tests developed by Dickey and Fuller (1979) (augmented Dickey–Fuller (ADF)) and Phillips and Perron (1988) (PP). The unit root test results are given in Table 1. Table 1. Unit root test results. Variables Augmented Dickey–Fuller (ADF) Test Phillips–Perron (PP) Test Stationary Level Level Difference Level Difference Intercept Trend and Intercept Intercept Trend and Intercept Intercept Trend and Intercept Intercept Trend and Intercept ln(VIX) −1.43 −1.02 −10.81 *** −11.06 *** −1.45 −1.01 −10.66 *** −10.89 *** I(1) ln(cases) −2.51 −2.24 −7.15 *** −18.24 *** −1.05 −1.19 −16.87 *** −17.38 *** I(1) ln(deaths) −1.47 −1.54 −2.04 −2.21 −1.03 −0.47 −8.50 *** −8.54 *** I(1) *** Indicates statistical significance at the 1% level. In the ADF (augmented Dickey–Fuller) and PP (Philips–Perron) tests, H 1 (the basic hypothesis) was established as the series had a unit root. That is, it was not stationary. Later after Table 1was examined further, it was determined through the results of the ADF test that the level values of the VIX and COVID-19 case and death variables were not statistically significant and contained a unit root. Therefore, H 1 was rejected. A unit root was a stochastic trend in a time series, which was explained as a random walk with drift, and if the time series has a unit root as in this case, it means that there was an unpredictable systematic pattern and, therefore, one cannot regress the data since it had no meaning. The Phillips–Perron test statistics also provided results that supported the ADF test statistics. It can therefore be concluded that the non-stationary variables in the level values did not have a unit root in their first differences, that is, their integration degrees were I(1) (Phillips and Perron 1988). The fact that the series were integrated with the same degree does not mean that they always acted together in the long term. After determining that they were stationary in the first differences of the series, the existence of a long-term equilibrium relationship between the series was investigated according to the co-integration method developed by Johansen (1988) and Johansen and Juselius (1990). The Johansen co-integration test is based on vector autoregression model (VAR) analysis. The VAR model with a lagged k is shown as follows (Brooks 2008): yt=β1yt−1+β2yt−2+· · · +βkyt−k+ut(1) To use the Johansen and Juselius (1990) test, the VAR model must be converted to an error correction model (VECM), as follows: ∆yt=Πyt−k+Γ1∆yt−1+Γ2∆yt−2+· · · +Γk−1∆yt−(k−1)+ut(2) Γ and Π represent coefficient matrices. Coefficient matrix Π contains information about the long-term relationships. In the Johansen and Juselius co-integration method, the trace and maximum eigenvalue statistics are examined to reveal the existence of a co-integration relationship and the number of cointegrated vectors. To perform a co-integration test, it is necessary to determine the appropriate lag length first. The appropriate lag length was determined by estimating an unrestricted VAR model with the variables used in the analysis. In determining the appropriate lag length, the LR (likelihood ratio), FPE (final prediction error), AIC (Akaike information criterion) and SC (Schwarz) and HQ (Hannan–Quinn) criteria were used. The result of the VAR lag length selection criteria is presented in Table 2. Int. J. Financial Stud. 2021,9, 26 7 of 19 Table 2. VAR lag length selection criteria. Lag LR FPE AIC SC HQ 0 NA 0.723416 8.189857 8.279836 8.225905 1 565.1489 0.000485 0.882386 1.242302 1.026580 2 50.95824 0.000301 0.402481 1.032334 * 0.654819 * 3 14.48562 0.000307 0.420392 1.320183 0.780876 4 14.82427 0.000309 0.423630 1.593358 0.892259 5 25.41032 0.000262 0.248140 1.687805 0.824914 6 14.88065 0.000259 * 0.227977 * 1.937579 0.912896 7 4.938314 0.000304 0.369188 2.348727 1.162252 8 17.07307 * 0.000284 0.280869 2.530344 1.182077 * Indicates the appropriate lag length. The appropriate lag length for the estimated VAR model was 6 according to the FPE and AIC criteria and 2 according to the SC and HQ criteria. Inverse roots of the AR characteristic polynomial were investigated regarding whether the estimated VAR model for 2 lag lengths contained a unit root. In Figure 2, we can see that all the inverse roots of the characteristic polynomial of the AR were located within the unit circle. The fact that the inverse roots were located in the unit circle shows that the predicted model displayed a stationary structure. Int. J. Financial Stud. 2021, 9, x FOR PEER REVIEW 7 of 19 length, the LR (likelihood ratio), FPE (final prediction error), AIC (Akaike information criterion) and SC (Schwarz) and HQ (Hannan–Quinn) criteria were used. The result of the VAR lag length selection criteria is presented in Table 2. Table 2. VAR lag length selection criteria. Lag LR FPE AIC SC HQ 0 NA 0.723416 8.189857 8.279836 8.225905 1 565.1489 0.000485 0.882386 1.242302 1.026580 2 50.95824 0.000301 0.402481 1.032334 * 0.654819 * 3 14.48562 0.000307 0.420392 1.320183 0.780876 4 14.82427 0.000309 0.423630 1.593358 0.892259 5 25.41032 0.000262 0.248140 1.687805 0.824914 6 14.88065 0.000259 * 0.227977 * 1.937579 0.912896 7 4.938314 0.000304 0.369188 2.348727 1.162252 8 17.07307 * 0.000284 0.280869 2.530344 1.182077 * Indicates the appropriate lag length. The appropriate lag length for the estimated VAR model was 6 according to the FPE and AIC criteria and 2 according to the SC and HQ criteria. Inverse roots of the AR characteristic polynomial were investigated regarding whether the estimated VAR model for 2 lag lengths contained a unit root. In Figure 2, we can see that all the inverse roots of the characteristic polynomial of the AR were located within the unit circle. The fact that the inverse roots were located in the unit circle shows that the predicted model displayed a stationary structure. -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 In v erse Roots o f A R Characteristic Pol y nomial Figure 2. Inverse roots of the AR characteristic polynomial. The Johansen co-integration test was used to determine the existence of a long-term relationship between the VIX index and daily new case and death numbers of the COVID19 pandemic in the United States. The co-integration test results are given in Table 3. Figure 2. Inverse roots of the AR characteristic polynomial. The Johansen co-integration test was used to determine the existence of a long-term relationship between the VIX index and daily new case and death numbers of the COVID-19 pandemic in the United States. The co-integration test results are given in Table 3. Table 3. Co-integration test results. Hypothesis Trace 0.05 Prob. ** Max-Eigen 0.05 Prob. ** Statistic Critical Value Statistic Critical Value r = 0 * 59.58050 35.19275 0.0000 43.58899 22.29962 0.0000 r≤1 15.99150 20.26184 0.1748 9.531600 15.89210 0.3790 r≤2 6.459904 9.164546 0.1581 6.459904 9.164546 0.1581 Trace test indicates one co-integrating equation(s) at the 0.05 level; * denotes rejection of the hypothesis at the 0.05 level; ** (MacKinnon et al. 1999)p-values. According to the maximum eigenvalue and trace statistics obtained as a result of the Johansen co-integration test, the H 1 hypothesis was rejected. In other words, the hypothesis predicted that there was at least one co-integration vector accepted at the Int. J. Financial Stud. 2021,9, 26 8 of 19 1% significance level. According to these results, it is possible to state that a long-term equilibrium relationship was valid between the VIX index and the daily new case and death numbers of the COVID-19 pandemic in the United States during the analysed period. After the long-term relationship between the VIX index and the case and death numbers was determined, the fully modified least-squares (FMOLS) estimator was used to estimate the long-term coefficients of each variable. While there was a co-integration relationship between the variables, there was a problem of correlation and endogeneity between the explanatory variables and the error terms. In this case, the variables lost their asymptotic properties (Berke 2012). The FMOLS method developed by Phillips and Hansen (1990) took into account the autocorrelation and endogeneity problems arising from the co-integration relationship between the variables. FMOLS estimators are asymptotically deviated and have an asymptotically normal distribution (Phillips and Hansen 1990;Shahbaz 2009). The FMOLS model equation is as follows: VIX =α1+α11Case +α12Death +ε(3) In the equation, ε represents the error term of the model. At the end of the test, we checked and examined which variables were effective on the VIX index and the effect size of the variables affecting the VIX index. The results of the analyses are presented in Table 4. Table 4. FMOLS test results. VIX FMOLS Variables Coefficient t-Statistic C 2.721101 38.52418 *** Case 0.325438 10.28894 *** Death −0.330127 −8.205153 *** R2= 0.753883 Adj. R2= 0.747952 *** Indicates statistical significance at the 1% level. When the FMOLS test results in Table 4were examined, it was seen that there was a statistically significant and long-run positive relationship between the cases and the VIX index. A 1% increase in cases affected the VIX index, which increased by 32.54%. On the other hand, a statistically significant and negative relationship was found between the number of deaths and the VIX index in the long term at the 1% significance level. A 1% increase in the death variable affected the VIX index by a decrease of 33.01%. The reason for this different result was that the VIX index was primarily affected by the increase in the COVID-19 case numbers and less by the death numbers. This may have been because the effect of the COVID-19 deaths was registered only after the case was diagnosed, i.e., there was a delay, and the deaths were expected as there was an increasing number of cases. Therefore, deaths had already been reflected in prices. This result complied with the expectation hypothesis and a common expression in the financial markets “Expectations are bought, facts are sold”. The high R 2 value (0.75), which was found for the diagnostic tests of the model, showed that 75% of the changes in the dependent variable could be explained by the changes in the independent variables. This was evidence of the suitability of the models. According to the results shown in Table 4, the H 2 hypothesis was accepted. This showed that bad news about COVID cases and deaths in the USA affected the VIX index. 4.2. The Effect of the VIX Index on the Major Stock Market Indexes during the Pandemic Period The figures of the VIX, DJIA, DAX, CAC40, FTSE 100, SSEC, Nikkei 225 and MIB indexes are given in Appendix A. Int. J. Financial Stud. 2021,9, 26 15 of 19 Int. J. Financial Stud. 2021, 9, x FOR PEER REVIEW 15 of 19 ln(FTSE100) ln(FTSE100) ln(Nikkei225) ln(MIB) Figure A1. Series of VIX and major stock market indexes. Figure A1. Series of VIX and major stock market indexes. Int. J. Financial Stud. 2021,9, 26 16 of 19 Appendix B Table A1. VAR lag length selection criteria. DJI–VIX DAX–VIX Lag LR FPE AIC SC HQ LR FPE AIC SC HQ 0 NA 0.0005 −1.857 −1.803 −1.835 NA 0.0006 −1.617 −1.563 −1.595 1 409.054 6.82 ×10−6−6.219 −6.057 −6.154 423.469 6.71 ×10−6−6.236 −6.073 * −6.170 * 2 17.637 * 6.10 ×10−6*−6.331 * −6.062 * −6.222 * 9.894 6.53 ×10−6*−6.263 * −5.990 −6.153 3 4.604 6.30 ×10−6−6.299 −5.922 −6.147 5.065 6.71 ×10−6−6.236 −5.854 −6.082 4 4.948 6.48 ×10−6−6.272 −5.788 −6.076 1.768 7.17 ×10−6−6.171 −5.680 −5.973 5 6.426 6.53 ×10−6−6.264 −5.673 −6.025 4.009 7.45 ×10−6−6.134 −5.534 −5.892 6 1.119 7.02 ×10−6−6.194 −5.495 −5.911 3.098 7.82 ×10−6−6.086 −5.378 −5.800 7 7.432 6.97 ×10−6−6.202 −5.396 −5.877 13.231 * 7.21 ×10−6−6.170 −5.353 −5.840 8 6.418 7.00 ×10−6−6.201 −5.286 −5.831 2.932 7.58 ×10−6−6.122 −5.197 −5.749 CAC40–VIX FTSE100–VIX Lag LR FPE AIC SC HQ LR FPE AIC SC HQ 0 NA 0.001450 −0.860 −0.806 −0.838 NA 0.000725 −1.553 −1.499 −1.531 1 485.286 7.19 ×10−6−6.166 −6.003 * −6.100 * 442.02 5.82 ×10−6−6.378 −6.215 * −6.312 * 2 9.335 7.05 ×10−6*−6.186 * −5.914 −6.076 8.499 5.76 ×10−6*−6.389 * −6.117 −6.279 3 4.692 7.28 ×10−6−6.155 −5.774 −6.001 4.723 5.94 ×10−6−6.358 −5.977 −6.204 4 1.781 7.77 ×10−6−6.090 −5.600 −5.892 2.267 6.31 ×10−6−6.299 −5.809 −6.101 5 3.544 8.12 ×10−6−6.047 −5.448 −5.805 1.701 6.74 ×10−6−6.233 −5.634 −5.992 6 4.018 8.43 ×10−6−6.011 −5.303 −5.726 2.550 7.12 ×10−6−6.179 −5.471 −5.893 7 12.204 * 7.87 ×10−6−6.082 −5.265 −5.752 15.302 * 6.39 ×10−6−6.290 −5.473 −5.960 8 3.062 8.26 ×10−6−6.036 −5.110 −5.662 2.843 6.73 ×10−6−6.241 −5.315 −5.867 SSEC–VIX Nikkei225–VIX Lag LR FPE AIC SC HQ LR FPE AIC SC HQ 0 NA 0.000237 −2.670 −2.613 −2.647 NA 0.000387 −2.182 −2.125 −2.159 1 378.70 * 2.72 ×10−6−7.140 −6.968 * −7.071 * 356.73 * 6.07 ×10−6−6.337 −6.166 * −6.268 * 2 9.253 2.66 ×10−6*−7.161 * −6.875 −7.046 9.472 5.93 ×10−6*−6.360 * −6.077 −6.246 3 1.132 2.88 ×10−6−7.082 −6.683 −6.921 3.392 6.23 ×10−6−6.311 −5.914 −6.151 4 3.812 3.01 ×10−6−7.039 −6.525 −6.832 2.839 6.59 ×10−6−6.255 −5.745 −6.050 5 1.283 3.25 ×10−6−6.963 −6.335 −6.710 6.848 6.61 ×10−6−6.253 −5.630 −6.002 6 2.744 3.44 ×10−6−6.907 −6.165 −6.609 2.599 7.01 ×10−6−6.196 −5.459 −5.900 7 5.993 3.48 ×10−6−6.899 −6.042 −6.554 4.440 7.24 ×10−6−6.166 −5.316 −5.824 8 0.606 3.80 ×10−6−6.814 −5.844 −6.424 8.771 7.03 ×10−6−6.199 −5.236 −5.811 MIB–VIX Lag LR FPE AIC SC HQ 0 NA 0.002137 −0.472 −0.417 −0.450 1 489.63 8.95 ×10−6−5.948 −5.783 * −5.881 2 12.488 8.45 ×10−6−6.005 −5.730 −5.894 * 3 8.284 8.36 ×10−6*−6.016 * −5.630 −5.860 4 1.979 8.92 ×10−6−5.952 −5.456 −5.752 5 2.507 9.45 ×10−6−5.896 −5.289 −5.651 6 2.008 1.01 ×10−5−5.834 −5.116 −5.544 7 11.415 * 9.48 ×10−6−5.896 −5.068 −5.562 8 2.473 1.00 ×10−5−5.842 −4.903 −5.463 * Indicates the appropriate lag length. Int. J. Financial Stud. 2021,9, 26 17 of 19 Appendix C Int. J. Financial Stud. 2021, 9, x FOR PEER REVIEW 17 of 19 Appendix C -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 DJI-VIX -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 DA X -VI X -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 C A C40-VIX -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 FTSE100-VIX -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 SSEC-VI X -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 Nikkei225-VI X -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1. 5 M IB-VI X Figure A2. Inverse roots of the AR characteristic polynomials. Figure A2. Inverse roots of the AR characteristic polynomials. Int. J. Financial Stud. 2021,9, 26 18 of 19 References Albulescu, Claudiu. 2020a. Coronavirus and Financial Volatility: 40 Days of Fasting and Fear. Available online: https://ssrn.com/ abstract=3550630 (accessed on 13 May 2021). Albulescu, Claudiu. 2020b. Coronavirus and oil price crash: A note. arXiv arXiv:2003.06184. Baker, Scott R., Nicholas Bloom, Steven J. Davis, Kyle Kost, Marco Sammon, and Tasaneeya Viratyosin. 2020. The Unprecedented Stock Market Reaction to COVID-19. White Paper. Chicago: Becker Friedman Institute for economics at Chicago. Berke, B. 2012. Exchange Rate and IMKB100 Index Relationship: A New Test. Maliye Dergisi 163: 243–57. (In Turkish) Bird, Ron, and Danny Yeung. 2010. How Do Investors React Under Uncertainty? Working Paper Series 8; Sydney: The Paul Woolley Centre for Capital Market Dysfunctionality, University of Technology, Available online: https://www.uts.edu.au/sites/default/ files/PaperBirdRon.pdf (accessed on 13 May 2021). Brooks, Chris. 2008. Introductory Econometrics For Finance, 2nd ed. Cambridge: Cambridge University Press. Cheng, Ing-Haw. 2020. VIX Clues Show How Stock Investors Underpriced the Risk of the Coronavirus Pandemic. April 4. Available online: https://www.marketwatch.com/story/how-stock-investors-underpriced-the-risk-of-the-coronavirus-pandemic-2020 -04-03 (accessed on 13 May 2021). Desjardins, J. 2020. The Pandemic Economy: Which Stocks Are Weathering the Storm? Visual Capitalist. Available online: https: //www.visualcapitalist.com/the-pandemic-economy-which-stocks-are-weathering-the-storm/ (accessed on 13 May 2021). Dickey, David A., and Wayne A. Fuller. 1979. Distribution of the Estimators for Autoregressive Time Series with a Unit Root. Journal of the American Statistical Association 74: 427–31. Elliot, S. 2020. Analyst Anticipates ‘Worst’ Financial Crisis Since 1929 amid Fears of a Global Recession. Available online: https: //www.cnbc.com/2020/03/20/analyst-anticipates-worst-crisis-since-1929-amid-recession-fears.html (accessed on 13 May 2021). Epstein, Larry G., and Martin Schneider. 2003. Recursive multiple-priors. Journal of Economic Theory 113: 1–31. [CrossRef] Fernandes, Nuno. 2020. Economic Effects of Coronavirus Outbreak (COVID-19) on the World Economy. Available online: https: //ssrn.com/abstract=3557504 (accessed on 13 May 2021). Gilboa, Itzhak, and David Schmeidler. 1989. Maxmin Expected Utility with Non-Unique Prior. Journal of Mathematical Economics 18: 141–53. [CrossRef] Gormsen, Niels Joachim, and Ralph S.J. Koijen. 2020a. Coronavirus: Impact on Stock Prices and Growth Expectations. Edited by M. Haacker. Washington, DC: The Macroeconomics of HIV/AIDS IMF. Gormsen, Niels Joachim, and Ralph S. J. Koijen. 2020b. Coronavirus: Impact on Stock Prices and Growth Expectations. Working Paper No. 2020–22. Chicago: University of Chicago, Becker Friedman Institute for Economics. [CrossRef] Haacker, Markus. 2004. HIV/AIDS: The Impact on the Social Fabric and the Economy. Washington, DC: International Monetary Fund, chp. 2. pp. 41–95. Herron, J., and V. Hajric. 2020. The Market’s in Panic Mode.’ Stock Markets Plunge 12% Amid Coronavirus Fears. Time. Business Stocks. Coronavirus Brief. Bloomberg. Available online: https://time.com/5803847/coronavirus-stocks-fall/ (accessed on 13 May 2021). Investing. 2020. Available online: https://www.investing.com/indices/major-indices (accessed on 13 May 2021). Isaccs, S. 2020. Deutsche Bank: Coronavirus May Impact Financial Targets. Breaking News. Alvine Capital Management, Chairman Investment Committee. Virus Outbreak. On the Phone. Available online: https://www.cnbc.com/video/2020/03/20/coronavirusworst-market-crisis-since-great-depression-strategist.html (accessed on 13 May 2021). Johansen, Søren. 1988. Statistical analysis of co-integrating vectors. Journal of Economic Dynamics and Control 12: 231–54. [CrossRef] Johansen, Soren, and Katarina Juselius. 1990. Maximum Likelihood Estimation And Inference On Co-integration: With Application To The Demand For Money. Oxford Bulletin of Economics and Statistics 52: 169–210. [CrossRef] Kauffman, Kyle, and Akila Weerapana. 2006. The Impact of AIDS-related news on exchange rates in South Africa. Economic Development and Cultural Change 54: 349–68. [CrossRef] Lee, Jong-Wha, and Warwick J. McKibbin. 2004. Estimating the Global Economic Costs of SARS. In Learning from SARS: Preparing for the Next Disease Outbreak: Workshop Summary, Institute of Medicine, Board on Global Health, Forum on Microbial Threats. Washington, DC: National Academies Press, pp. 92–109. Li, Y. 2019. The Market and Its Fear Gauge That Tracks Volatility Are Moving Together. That Could Be a Bad Sign. CNBC. Available online: https://www.cnbc.com/2019/11/22/the-stock-market-and-its-fear-gauge-vix-are-moving-in-unison.html (accessed on 13 May 2021). Loh, Elaine. 2006. The impact of SARS on the performance and risk profile of airline stocks. International Journal of Transport Economics/Rivista Internazionale di Economia dei Trasporti 33: 401–22. MacKinnon, James G., Alfred A. Haug, and Leo Michelis. 1999. Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration. Journal of Applied Econometrics 14: 563–77. [CrossRef] McKibbin, Warwick, and Roshen Fernando. 2020. The Global Macroeconomic Impacts of COVID-19: Seven Scenarios. Working Paper 19/2020. Rochester: Centre for Applied Macroeconomic Analysis, Centre for Applied Macroeconomic Analysis (CAMA). McKibbin, Warwick J., and Peter J. Wilcoxen. 1999. The Theoretical and Empirical Structure of the GCubed Model. Economic Modelling 16: 123–48. [CrossRef] McKibbin, Warwick J., and Peter J. Wilcoxen. 2013. A Global Approach to Energy and the Environment: The G-cubed Model. In Handbook of CGE Modeling, Chapter 17. Amsterdam: Elsevier, pp. 995–1068. Int. J. Financial Stud. 2021,9, 26 19 of 19 Onali, Enrico. 2020. COVID-19 and Stock Market Volatility. Available online: https://ssrn.com/abstract=3571453 (accessed on 13 May 2021). Özen, Ercan, and Metin Tetik. 2019. Did Developed and Developing Stock Markets React Similarly to Dow Jones in Process 2008 Crisis? Frontiers in Applied Mathematics and Statistics 5: 49. [CrossRef] Phillips, Peter C. B., and Bruce E. Hansen. 1990. Statistical inference in instrumental variables regression with I(1) processes. The Review of Economic Studies 57: 99–125. [CrossRef] Phillips, Peter C. B., and Pierre Perron. 1988. Testing for a Unit Root in Time Series Regression. Biometrika 75: 335–46. [CrossRef] Ramelli, Stefano, and Alexander F. Wagner. 2020a. Feverish Stock Price Reactions to COVID-19. Swiss Finance Institute Research Paper 20: 12. Available online: https://papers.ssrn.com/sol3/Papers.cfm?abstract_id=3550274 (accessed on 13 May 2021). Ramelli, Stefano, and Alexander F. Wagner. 2020b. What the Stock Market Tells Us about the Consequences of COVID-19. In Mitigating the COVID Economic Crisis: Act Fast and Do Whatever It Takes. Edited by Baldwin di Mauro. London: CEPR Press, Centre for Economic Policy Research, ISBN 978-1-912179-29-9. Available online: https://voxeu.org/article/what-stock-market-tells-usabout-consequences-COVID-19 (accessed on 24 March 2020). Ritholtz, Barry. 2020. As Bad as 2008? The Market’s Fear Index Is Starting to Think So. Bloomberg Opinion. Markets. Available online: https://www.bloomberg.com/opinion/articles/2020-03-12/coronavirus-worse-than-2008-market-s-vix-fear-indexthinks-so (accessed on 13 May 2021). Shahbaz, Mohammad. 2009. A Reassessment of Finance-Growth Nexus for Pakistan: Under the Investigation of FMOLS and DOLS Techniques. The IUP Journal of Applied Economics 8: 65–80. Williams, Christopher D. 2009. Asymmetric Responses to Earnings News: A case od Ambiguity. Working Paper. Chapel Hill: University of North Carolina. Worldometer. 2020. COVID-19 Coronavirus Pandemic. Available online: https://www.worldometers.info/coronavirus/#countries (accessed on 13 May 2021). Yilmazkuday, Hakan. 2020. COVID-19 Effects on the S&P 500 Index. Available online: https://ssrn.com/abstract=3555433 (accessed on 13 May 2021). Zeren, Feyyaz, and Atike HIZARCI. 2020. The Impact of COVID-19 Coronavirus on Stock Markets: Evidence from Selected Countrıes. Muhasebe ve Finans ˙ Incelemeleri Dergisi Bulletin of Accounting and Finance Review 3: 78–84. [CrossRef]