“Return and volatility spillover between India, UK, USA and European stock markets: The Brexit impact”

The 2016 Brexit referendum created potential turmoil in financial markets. The pur- pose of this study is to examine the impact of the Brexit referendum on the return and volatility spillover between the EU, the UK, and the USA stock markets and the Indian stock market during the pre- and post-Brexit referendum period. The VAR and bivariate GARCH BEKK models were employed. The study results suggest that before the Brexit referendum, Indian stock market returns made no significant return spillover on the other markets. On the contrary, following the referendum, Indian stock returns significantly spilled over to France, Germany, the UK, and the USA stock market returns. The study results also identified a substantial increase in the bidirectional volatil- ity spillover between India-France, India-UK, and India-USA during the post-Brexit referendum period. Therefore, the investors’ opportunity to invest simultaneously in India, UK, EU, and US stock markets for portfolio diversification is limited. India was affected mainly by its own past shocks before the Brexit referendum. However, after the Brexit referendum, Indian markets are getting more and more integrated with other markets. In order to reap the diversification benefits, a prudent investment strategy will need to be developed in the future, especially during times of economic and political uncertainty and market crisis. against it (Alvarez-Diez et al., 2019). Leave campaign had won the majority of votes. The United Kingdom’s decision to exit (Brexit) the European Union has raised many questions of what would be the future trading relationship of the UK with that of the EU and the rest of the world and how this will impact the availability of migrant labor, their future access to the Single Market, and product regulations (Driffield & Karoglou, 2019). Brexit has been a major source of uncertainty for around 40% of the UK’s business. In the next two trading days following the referendum, global stock markets tumbled. For instance, the leading European stock indices for blue-chip companies like the French CAC 40 and the German DAX decreased by 10%. The UK and US equities did not do well too. FTSE 100 crumbled over 5.8%, and S&P 500 decreased by 5.5%. Brexit had an adverse impact on the Indian market too. Nifty 50 fell by 181.85 points. The week following the referendum, the pound/euro exchange rate fell by more than 7% (Guedes et al., 2019). Since then, the future of the UK economy has remained uncertain.


INTRODUCTION
In 2016, UK's summer was marked by significant political and economic turbulence. On June 23, 2016, the United Kingdom's European Union membership referendum, also known as the Brexit referendum, was held. On this day, the United Kingdom voted 51.9 percent in favor of leaving the European Union, while 48.1 percent voted against it (Alvarez-Diez et al., 2019). Leave campaign had won the majority of votes. The United Kingdom's decision to exit (Brexit) the European Union has raised many questions of what would be the future trading relationship of the UK with that of the EU and the rest of the world and how this will impact the availability of migrant labor, their future access to the Single Market, and product regulations (Driffield & Karoglou, 2019). Brexit has been a major source of uncertainty for around 40% of the UK's business. In the next two trading days following the referendum, global stock markets tumbled. For instance, the leading European stock indices for blue-chip companies like the French CAC 40 and the German DAX decreased by 10%. The UK and US equities did not do well too. FTSE 100 crumbled over 5.8%, and S&P 500 decreased by 5.5%. Brexit had an adverse impact on the Indian market too. Nifty 50 fell by 181.85 points. The week following the referendum, the pound/euro exchange rate fell by more than 7% (Guedes et al., 2019). Since then, the future of the UK economy has remained uncertain.

LITERATURE REVIEW
The past few decades witnessed massive turbulence in financial markets resulting in substantial global crises like Black Monday (1987), Asian financial crisis (1997), Subprime mortgage crises (2008), Eurozone crises (2010), and Chinese stock market crash (2015) (BenSaïda et al., 2018). After these significant global crises, numerous researchers have investigated the concept of volatility spillover across the international stock markets. The volatility spillover concept was first discussed in the pioneering work of Engle et al. (1990). In volatility spillover there are two hypothesis tests: The first one is the "Heatwave Hypothesis," which represents own spillover. According to this hypothesis, a particular market's current volatility results from the same market's previous volatility. The heatwave hypothesis suggests that volatility has a country-specific autocorrelation. This event is known as volatility clustering. The second is the "Meteor shower hypothesis," representing cross-spillovers. According to this hypothesis, a particular market's current volatility results from the same market's previous volatility and other markets' previous volatility. Here, the volatility spillover includes both own spillover and cross spillover. This event is known as volatility transmission. Volatility spillover represents shock transmission that cannot be understood by fundamentals (Bekaert et al., 2014).
Volatility spillover is the result of financial events and market integration (He, 2001). The connection between the markets is the consequences of crises and the effects of various political, economic, and financial events. Stock markets are extremely responsive to the occurrence of domestic and global events. In the past, numerous studies have empirically investigated the spillover of volatility across worldwide stock markets during the crisis period and various financial, political, and economic events (Ahmad et  . In a nutshell, it can be said that major political and economic events have a significant impact on stock price volatility. The stock market serves as the best indicator of the health of the economy. This study mainly focuses on the political event Brexit, which created significant disruption in the financial markets after the global financial crisis of 2008. The twenty-first century's most remarkable economic and political event is Brexit (Kara et al., 2021). The economic stability of the United Kingdom is at risk due to Brexit, which could have long-term implications. Brexit is likely to generate a significant amount of economic and political uncertainty. The significant political and economic uncertainty increases stock market volatility and affects the financial market by creating financial instability and difficulties (Forbes & Rigobon, 2002;Diebold & Yilmaz, 2009;Bloom, 2009;Diebold & Yilmaz, 2012). Brexit negatively impacted the global equity market (Burdekin et al., 2018). The Brexit referendum adversely affected the travel, leisure, and banking sectors of the British econo-my (Ramiah et al., 2017). Brexit instigated policy uncertainty, leading to financial instability in critical markets and damaging the EU and UK's real economy (Belke et al., 2018;Hosoe, 2018;Samitas et al., 2018). Previous studies confirmed that Brexit outcome caused financial contagion as a result of shock and spillover of volatility among European markets would continue to persist (Aristeidis & Elias, 2018;Li, 2020). Apart from equity markets, currency markets, government bonds, and commodity markets were also affected by the political risk in a Brexit Leave vote (Breinlich et al., 2018). The global economy will be affected by a devalued British pound (Cumming & Zahra, 2016). The uncertainty of Brexit is seen higher in those industries of the UK that are having trade relations with the European Union and on those industries of the UK dependent on migrant labor of the European Union (Bloom et al., 2018). Brexit is likely to create policy dilemmas for the UK government (Teague & Donaghey, 2018).
This study analyzes how a political uncertainty like Brexit can change the correlation among these stock markets. As discussed earlier, major stock indices like the French (CAC 40), German (DAX), UK (FTSE 100), and US (S&P 500) had a significant drop immediately after the Brexit referendum. The reason for choosing these indices is discussed here. The French CAC40 and the German DAX are the leading stock indices for European blue-chip companies. London has substantial economic connections all over the world. India, China, Singapore, Hongkong, and other major Asian economies have a significant economic linkage with London (Lai & Pan, 2018). The US economy plays a dominant market leader role, and the USA has a significant dynamic information spillover effect on all Asian pacific markets due to significant portfolio investment inflows received by the Asian markets from the USA (Kim, 2005). When analyzing the returns and volatility spillover among Asian, European, and North American stock markets, it is observed that a specific index is affected mainly by those indices that open or close before it (Singh et al., 2010). Hence, Asian indices are affected by lagged returns of European and US indices. Immediately following the Brexit referendum, the global stock markets like the French CAC40, the German DAX, UK FTSE 100, India NIFTY 50, and US S&P 500 crumbled (Gu & Hibbert, 2021).
Any slowdown or uncertainty in major economies like the USA, UK, and Europe will first affect its own stock market before it affects the stock market of other countries. The stock markets may be affected by their own spillovers (Heatwave hypothesis) and cross-market spillover (Meteor shower hypothesis). These phenomena can be studied using the BEKK GARCH model. Globalization and financial liberalization are the main reason for increased integration among the financial markets (Vo & Ellis, 2018). There is a need to understand this interconnection among the markets of different countries, especially for portfolio managers, international investors, and policymakers, to reap the diversification benefits (Zhou et al., 2012). However, changes in market linkages happen constantly. Capturing the correlation that varies with During the sub-prime mortgage crisis, Indian stock markets remained unaffected by the volatility spillover of US stock markets among all other countries (Chiang et al., 2013). Indian stock markets were found to be the most efficient market compared to all other markets. Studies suggest that Indian markets are the least risky in terms of market risk (Chiang et al., 2013). India has a negative correlation with that of the Asia Pacific region, which indicates that the impact of the South Asian crisis on India is minimal (Bhar & Nikolova, 2009). Therefore, this negative correlation suggests diversification opportunities to investors. However, Brexit has created uncertainty among the global business community. India's most important trading partners are the EU and the UK. As a result of Brexit, it will increase the bilateral trade cost between the EU and the UK, which in turn will affect their trade flows. Due to this, their trading partners will be affected indirectly (Roy & Mathur, 2016). As a result of Brexit, restrictions are imposed on labor movement, which restricts EU citizens to enter and work in the UK. It has led to labor shortage in the UK. Brexit will adversely impact Indian companies that have heavily invested in the UK and having operations in the UK because barriers might make the migration of laborers and professionals to the UK more difficult. Those Indian companies like TATA that have a UK subsidiary that does business in the Eurozone will suffer (Chaudhuri, 2020). Companies will consider relocating their plant to other EU countries to enjoy the tariff benefits. United Kingdom used to be India's export market and investment destination within the EU (Tripathi, 2021). Britain was India's gateway to Europe for many Indian firms. Brexit has affected this too. Studies confirm that India and EU would have gained more had UK continued its membership with EU than quitting them (Roy & Mathur, 2016). Thus, the uncertainty of Brexit has an adverse impact on Indian investments. Therefore, this study will examine whether the uncertainty of Brexit has affected Indian markets and whether it has changed the market linkage of the Indian market with other considered markets.
To the authors' knowledge, the earlier research has not examined the impact of the Brexit referendum on the volatilities of European stock markets like Germany and France, UK, and US stock markets on the Indian stock market using the GARCH BEKK model. Therefore, this study will add to the existing body of knowledge by exploring the impact of Brexit and investigating the linkage between the above-mentioned countries' stock indices on the Indian primary stock index (NIFTY 50) by investigating both return and volatility spillover during the pre-and post-Brexit referendum period. The motivation for this study is that there are many risks associated with Brexit and its impact on the European Union, USA, and UK markets. Understanding its repercussions on the Indian market will help portfolio managers, financial institutions, government, and investors adapt their investment strategies accordingly.

METHOD
In this study, the daily closing values of the India, France, Germany, the United Kingdom, and the United States indices abbreviated as Nifty The data sample for this paper is split into two categories. The first group includes the period before the Brexit referendum (from January 1, 2012 to June 22, 2016), and the second group comprises the period after the Brexit referendum (from June 23, 2016 to December 31, 2020). The whole study is grouped into pre-and post-Brexit referendum periods. In comparison to monthly or weekly price data, daily stock returns data provides accurate information on stock price fluctuations. While estimating the BEKK GARCH model, the indices mentioned above were grouped into pairs. This way, four pairs were made: India -France, India -Germany, India -United Kingdom, and Indiathe United States of America.
This study used the Vector autoregressive model to investigate the likeliness of return spillover over a period and among different markets. This model evaluates the sign and the strength of the cross-correlation among the returns of different markets (Hung, 2019). The VAR model with one and five lags are estimated during the pre-and post-Brexit referendum period, respectively, to study the linkage among the stock indices returns. The VAR model equations used in this study are as follows: where r India,t , r France,t , r Germany,t , r UK,t , and r USA,t are the stock index returns of India, France, Germany, the UK and the USA, respectively.
To investigate the spillover of volatility or interdependence between India-France, India-Germany, India-UK, and India-USA, this paper uses the (Baba Engle Kraft Kroner) BEKK GARCH model introduced by Engle and Kroner (1995). One of the crucial features of this model is that conditional covariances matrices are allowed to be positive definite by the construction itself (Majdoub & Mansour, 2014). This model lets interaction among the conditional covariance and variances.
While estimating, this model provides substantial parameter reduction (Hung, 2019). A bivariate BEKK-GARCH model is being used in this study.
where R t = [R 1,t , R 2,t ] represents returns for the stock market variables and α refers to constant. u t = [ε 1,t , ε 2,t ] denotes residual vector. H t refers to conditional covariance matrix. Ω t-1 represents the set of market information accessible at time t-1.
The covariance matrix for the bivariate GARCH BEKK model can be presented as follows: where θ refers to vector of parameters to be estimated, n denotes number of markets, and T represents the number of observations. This study mainly focuses on α and β parameters to assess the characteristics of volatility spillover between markets.

RESULTS
The results of the ARCH test, unit root test, and descriptive statistics for before and after the Brexit referendum period, respectively, are presented in The raw series of all five countries' stock markets are plotted in Figure 1 and Figure 2. It can be seen that there has been fluctuation in all five countries before and after the Brexit referendum period. However, the post-Brexit referendum period saw a substantial increase in fluctuations.   The Vector Auto Regression model is used to analyze the return spillover among the selected indices. The lag lengths for pre-and post-Brexit periods are 1 and 5, respectively. The optimum lag lengths were selected based on the suggestions by AIC (Akaike Information Criterion). Table 3 and 4 show the estimated parameters for the VAR mod-  el for the pre-and post-Brexit referendum periods, respectively. In general, it is noticed that during both pre-and post-Brexit referendum periods, the US market made a significant return spillover on the stock markets of other four nations. Before the Brexit referendum, the UK's first lag return substantially impacted itself and the Germany stock market. However, after the Brexit referendum, the UK's second lag return made a significant return spillover on German, France's stock market and itself. Also, the UK's third lag returns made significant return spillover to the German stock market.
Prior to the Brexit referendum, India's first lag had a significant return spillover on itself and not on any other stock market returns. On the contrary, during the post-Brexit referendum period, India's first lag return had significant return spillover on itself and France, Germany, UK, and US stock market returns. India's fifth lag returns had return spillover on itself, and India's second lag had significant return transmission on USA stock market returns during the post period. It was also observed that the German stock market returns made no significant impact on the other markets during the pre-Brexit period. On the contrary, German stock returns significantly spilled over to India and USA stock market returns during the post-Brexit referendum period. Germany's second lag returns impacted India and the USA stock market, and Germany's fifth lag significantly impacted USA stock market returns. However, France's stock market returns made no significant return spillover on the other markets during both pre-and post-Brexit referendum periods.
Volatility spillover between Indian stock index and rest of the above considered nations stock indices is examined. To investigate the spillover of volatility, the GARCH-BEKK model is used. The estimated outcome of the BEKK model is shown in Table 5. Here A(k,k) represents the ARCH parameter and B(k, k) represents GARCH parameters concerning market k. The essential charac-  Note: ** denotes p-values < 1% significance level, * denotes p-values < 5% significance level.  There are significant ARCH effects in India, the USA, the UK, and France before and after the Brexit referendum. German market had a significant ARCH effect before the Brexit referendum. During the study period, the stock markets of India, the UK, the USA, and France depend on their own history B(k, k). In a nutshell, it can be inferred that there was a significant increase in the bidirectional volatility spillover between India and other three countries' stock markets, namely France, USA, and UK, in the post-Brexit referendum period as compared to the pre-Brexit referendum period. It is also observed that there was asymmetry in volatility spillover. That is, the transmission of shocks from one market to another was not uniform. The result suggests an increase in correlation of volatility transmission between India and the other three stock markets, namely the USA, France, and the UK, after the Brexit referendum. This means that India and the other three markets are substantially integrated in the post-Brexit referendum period. This is valuable information for investors who diversify their portfolios in order to minimize risk.

CONCLUSION
This study aims to investigate the spillover of return and volatility between the stock markets of India and four countries, namely France, Germany, the UK, and the USA, and compare market interactions before and after the Brexit referendum using the VAR model and the bivariate GARCH BEKK model. The results suggested that India did not make a significant return spillover to any other country's stock market during the pre-Brexit period except itself. However, during the post-period, India made substantial return spillover to itself and the other four countries. Before the Brexit referendum period, the past shocks of the USA, the UK, France, and Germany had no considerable influence on the Indian stock market volatility. However, after the Brexit referendum, the past shocks of the USA, the UK, France, and Germany had a considerable influence on the Indian market volatility. Overall, the findings reveal strong evidence of bidirectional spillover of volatility between India and the UK, between India and the USA, and between India and France after the Brexit referendum. Thus, to minimize risk, investors must take caution while investing funds in the Indian stock market along with the EU, UK, and US stock markets. India remained unaffected by the volatility spillover from the US stock market since sub-prime crisis. However, after the Brexit referendum, India was affected by the external shocks of the EU, UK, and US markets, and there was bi-directional volatility spillover between them. Hence, an appropriate asset allocation strategy needs to be developed to enjoy the benefits of diversification in these markets, especially in times of political and economic instability and market crises. Thus, there is a possibility that Indian stock markets will be further exposed to these external shocks in the future.