Volatility Spillovers between South Asian Stock Markets: Evidence from Sri Lanka, India and Pakistan

This study examines the existence, magnitude and direction of volatility spillovers between the Sri Lankan stock market and two other major stock markets in the South Asian region: India and Pakistan. Main stock indices of Sri Lanka, India, and Pakistan are employed as proxies to represent stock markets of each country. Daily data over the period 2nd January 2004 to 23rd September 2014 is used for estimations. Volatility spillovers are modeled through a trivariate BEKK – GARCH (1, 1) model to capture the cross-market effects. There exist bilateral intraday volatility spillovers between Sri Lanka and both markets. It is evident that the intraday effect from Pakistan to Sri Lanka is stronger than the same effect from India to Sri Lanka. However, with respect to overnight volatility spillovers, there is only a unilateral spillover effect from Sri Lanka to India. Evidence for the presence of volatility spillovers between these three South Asian economies makes the tasks of monetary policy makers, investors and fund managers more complicated than they would otherwise have been.

INTRODUCTION "Volatility appears to be a meteor shower ['which rains down on the earth as it turns'] rather than a heat wave" -Engle, Ito and Lin (1990) The increasing globalisation and regionalisation of economic activities and financial liberalisation of nations have resulted in the integration of economies and equity markets around the globe (Mukherjee and Mishra, 2010). The integration of stock markets makes trading counterparts highly interdependent on each other's trading activities, thus giving rise to volatility linkages. However, evidence on market interactions and information transmissions in South Asian capital markets is hard to find (Wang, Gunasekarage and Power, 2005). In such a context, it is a sensible and timely attempt to examine whether Sri Lanka as a small emerging market is sensitive to the innovations originating from other markets in the region and/or whether innovations in the Sri Lankan market have any impact on other markets in the region. Hence, the primary focus of this study is on volatility linkages, one of the significant aspects of international financial relations, between Sri Lanka and two other major markets in the South Asian region: namely India and Pakistan. The reason for the selection of these three markets is their prominence in the South Asian region. More specifically, the objective of this study is to uncover whether there are volatility spillovers among the three countries and to find the directions and magnitudes of such spillovers in case of their being present.
Understanding and exploring the nature of volatility transmission between Sri Lanka and other regional markets will be helpful to policy makers in addressing financial stability issues. From the investors' point of view, it will also provide important insights on implications for market efficiency, profitable investment opportunities and risk diversification.
The rest of this study can be outlined as follows. Section 2 will provide the theoretical background for volatility transmissions between markets. Section 3 contains a brief survey of relevant literature. Information on the data and the sample are described in Section 4. Section 5 outlines the proposed econometric model employed to explore the presence, magnitude and direction of volatility spillovers. In section 6, empirical results are reported and discussed. Section 7 contains concluding remarks.

THEORETICAL BACKGROUND
Factors underlying contagion such as herding, trade linkages, financial linkages and the wake-up call hypothesis are the best candidates for a theoretical explanation of the existence of volatility spillovers, their magnitudes and directions. Blasco, Corredor and Ferreruela (2012) states that herding is present in a certain market 'when investors opt to imitate the trading decisions of those who they believe to be better informed, rather than acting upon their own beliefs and information'. When investors merely mimic the trading actions of others in this manner, the information content of prices may decrease drastically, making market prices informationally inefficient. Thus, herding behavior makes markets more volatile than if investors would have acted independently (Froot, Scharfstein and Stein, 1992;Choe, Kho and Stulz, 1999;Alper and Yilmaz, 2004;Avramov, Chordia and Goyal, 2006). When markets tend to be informationally inefficient and excessively volatile, foreign as well as local investors are likely to engage in a situation of mass departure of capital from the relevant market. This behavior of market participants may lead to transmission of volatility between asset markets (Van Rijckeghem and Weder, 2001;Pritsker, 2001).
Trade linkages refer to the real association between countries as established by trading physical goods and services. Corsetti et al. (2000) explains how trade linkages, mainly based on competitive devaluation, implicitly contribute to volatility spillovers among trading partners depending on their market conditions. They conclude that competitive devaluation targeted at achieving economic growth through exports can induce sharper currency depreciation than that required by any initial deterioration in fundamentals. Moreover as cited in Kaminsky, Reinhart and Vegh (2003), Nurkese's classic story of competitive devaluations further explain how asset prices in the market of each trading partner get affected by currency devaluations in one country. Thus, if market participants expect a game of competitive devaluation, they are more likely to sell their holdings of securities and to curtail or refuse to extend their lending to those countries.
With financial globalisation, financial institutions have gained access to international financial market transactions. Through these financial linkages, the banking system gets updated about the occurrences of shocks or news events. In addition, the effect of these events may get amplified by the international and the domestic interbank markets through volatility spillover effects between countries. Moreover, according to a model developed in Kodres and Pritsker (2002), volatility transmission can occur when 'informed' investors begin to respond to private information on a certain country-specific factor by optimally rebalancing the exposure of their portfolios to the shared macroeconomic risk factors in markets of other countries. When there is asymmetric information in the countries where rebalancing occurs, 'uninformed' investors are not able to fully identify the source of the change in asset demand and they respond to it as if the rebalancing is relevant to information on their country. As a result, an idiosyncratic shock may generate excess volatility across asset markets of countries (as cited in Kaminsky et al., 2003).
Wake-up call hypothesis also provides a theoretical explanation to volatility spillovers. Kaminsky et al. (2003) defines a 'wake-up call' as a situation in which investors 'wakeup' to the weaknesses that have been revealed in a crisis country and proceed to avoid and move out of countries that share similar characteristics with the crisis country.

A BRIEF SURVEY OF LITERATURE
Volatility of returns provides valuable insights into the flow of information between markets (Ross, 1989;Tanizaki and Hamori, 2009), and the extent to which markets are interlinked will govern the level of volatility spillovers between/among markets (Gonzalo and Olmo, 2005). Hamao, Masulis and Ng (1990), Lin and Ito (1994), Koutmos and Booth (1995), and Karolyi (1995) are among many others who pioneered scholarly work in analysing the presence of volatility spillovers across markets. Both Hamao et al. (1990) and Koutmos and Booth (1995) studied the Tokyo, London, and New York markets using daily data around the 1987 crisis and report contradictory findings with regard to the spillover effect between London and Tokyo. Karolyi (1995) empirically illustrates the possibility of having such contradictory findings due to different conditional variance specifications, and without loss of generality one can also argue that it could be due to different sample periods. More interestingly, Ng (2000) brought empirical evidence to show that volatility spillovers are driven by currency fluctuations, market liberalisation and the size of trades. Kaminsky et al. (2003) later provided theoretical explanations to this in the form of channels of information transmission or contagion. Continuing along the same lines, Connolly, Stivers and Sun, (2005) and Rua and Nunes (2009) examine the co-movements of return and volatility. Tanizaki and Hamori (2009) examines the return and volatility spillovers in the presence of the holiday, asymmetry and day-of-the-week effects as well. Jung & Maderitsch (2014) looks into structural breaks in volatility spillovers between international financial markets and does not find evidence of contagion. Beirne, Caporale, Schulze-Ghattas & Spagnolo (2013) cite evidence for volatility spillovers from mature to emerging stock markets. Alotaibi & Mishra (2015) report significant return spillover effects from global and regional stock markets to Gulf Cooperation Council (GCC) stock markets.
In addition, Wei, Liu, Yang and Chaung (1995), Miyakoshi (2003), Worthington and Higgs (2004) and Li and Giles (2015) study the volatility and return spillovers from developed markets to Asian emerging markets. Cha and Oh (2000) reports that the links between developed markets and Asian emerging markets began to increase after the stock market crash in October 1987 and significantly intensified since the outbreak of the Asian financial crisis in July 1997. Wang et al. (2005) report that evidence on market interactions together with information transmissions in South Asian capital markets is hard to find, despite the increased economic activities and the interest of local and foreign investors in these markets due to recent economic reforms and the liberalisation of capital markets.
There are only a few studies that inquire into the linkages of the Colombo Stock Exchange (CSE) with other markets in the region. Elyasiani, Perera and Puri (1998) examines the interdependence and dynamic linkages between Sri Lanka and the markets of its major trading partners from 1989 to 1994. The study finds no significant interdependence between the Sri Lankan market and other equity markets due to many reasons such as small capitalisation, lack of liquidity, high concentration in blue chips and unilateral investment barriers on Sri Lankan investors at that time. Given that this study was carried out even before the 1997 East Asian Financial Crisis, it can be argued that those findings have little relevance to the present day links between the same markets. Wang et al. (2005) examine the return and volatility spillovers from USA and Japan to India, Pakistan and Sri Lanka during the period 1993 to 2003 and find a significant effect of volatility spillovers from USA to India and Sri Lanka. In addition, Mukherjee and Mishra (2010) also investigate the return and volatility spillovers between Indian stock market and 12 other developed and emerging Asian countries over a period from 1997 to 2008 and report that there is a significant and contemporaneous intraday volatility spillover effect from India to Sri Lanka.

DATA AND SUMMARY STATISTICS
The sample includes three stock markets in the South Asian region: the CSE, the Bombay Stock Exchange (BSE) and the Karachi Stock Exchange (KSE). Each country is assumed to be represented by its main market index. Accordingly, volatility of returns on ASPI of Sri Lanka, S&P BSE 500 of India and KSE ASPI of Pakistan have been used to trace the spillovers among these markets. The study uses daily data over the sample period 2 nd January 2004 to 23 rd September 2014, which results in 2,429 observations. The preference for daily data over weekly or monthly data is due to the fact that the interactions between markets associated with volatility spillovers are better captured by daily data.
Since trading sessions in the three markets are asynchronous on a given day as indicated in Figure 1, following Lin and Ito (1994) and Mukherjee and Mishra (2010), the scope of the analysis is divided into two sessions, namely intraday session and overnight session. Intraday and overnight return series have been calculated by using the daily index prices for each country in the following manner: Intraday return for country on day is calculated by taking the difference of natural logarithm of closed and open prices and is denoted as _ _ where i = sl (Sri Lanka), ind (India), pak (Pakistan).
Overnight return for country on day is calculated by taking the difference of natural logarithm of open price of day and closed price of day − 1 and is denoted as _ _ where i = sl (Sri Lanka), ind (India), pak (Pakistan).  indicating that negative returns are more common than positive returns. Moreover, in terms of kurtosis, all indices have higher peaks. This indicates that all three return series have asymmetric and leptokurtic distributions. The p values of the Jarque-Bera (JB) test statistic also suggest that the return series are not normal.
In two respects, descriptive statistics of overnight returns indicated in Table 3 are different from those of intraday returns. First, both India and Pakistan display positive returns. Again, none of these mean returns is significantly different from zero. The second notable difference is that the Sri Lankan return series is highly negatively skewed, thus indicating that negative returns are more common than positive returns. As compared with the Sri Lankan return series, the Indian return series displays a low positively-skewed distribution while the Pakistan return series displays a low negatively-skewed distribution.

MODEL SPECIFICATIONS
It is widely accepted that autoregressive conditional heteroskedasticity models are much capable of handling volatility. Consider a vector stochastic process { } of order 3 × 1.
After conditioning to the past information which has been generated up to and including time t-1 ( ℱ −1 ), the conditional mean equation system with respect to a finite vector of parameters ( ) is constructed for each session (intraday and overnight) as follows.

= ( ) + (3)
where ( ) is the conditional mean vector and where 1 2 ⁄ ( ) is a 3 × 3 positive definite matrix. Additionally, we assume 3 × 1 random vector to have the following properties: where 3 is the identity matrix of order 3.
Thus, the conditional variance of matrix of can be defined as follows: and, |ℱ −1~( 0, ) The variance-covariance matrix ( ) has been parameterised as a trivariate BEKK GARCH process. For parsimony and computational ease, a restricted version of full BEKK model -more specifically, BEKK GARCH (1, 1) with lower triangular parameter matrices -is used. Bollerslev et al. (1992) state that the GARCH (1, 1) model is sufficient enough for modeling the variance dynamics over very long sample periods. The proposed specification is given by equation (7).
Ω in equation (7) is a 3 × 3 lower triangular matrix of constants. Α and Β are 3 × 3 lower triangular parameter matrices. Matrix Α, elements of which measure the effects of shocks or short-run impact on the conditional variances, shows how the conditional variances are correlated with past squared errors. Matrix Β shows how persistent the conditional variances among the markets are and its elements measure the lagged own GARCH effect on a certain market as well as such effects from other markets. As such, a more elaborative form of the model represented by equation (7) is as follows: ] is a symmetric matrix.
( . . ℎ 12, = ℎ 21, , ℎ 13, = ℎ 31, , ℎ 23, = ℎ 32, ) The diagonal parameters of matrices Α and Β measure the effects of own past shocks or 'news' and own past volatility respectively. The off diagonal elements of matrix Α (i.e. 21 , 31 and 32 ) measure the cross-market impact of lagged squared innovations while the off diagonal elements of B (i.e. 21 , 31 and 32 ) measure the impact of crossmarket lagged volatility on conditional variance (or volatility spillovers). With the proposed restricted version of BEKK model, the results of volatility spillovers 'from other markets to Sri Lanka' and 'from Sri Lanka to other markets' are obtained separately 1 .
However, the results are synthesised in Tables 3 and 4 2 .
The specified model can be estimated efficiently and consistently by using the full information maximum likelihood method (Engle and Kroner, 1995;Kroner and Ng, 1998) under the auxiliary assumption of an iid. normal distribution for the standardised innovations. Given a sample of observations of the returns vector, , the parameters of the trivariate system are estimated by optimising the following conditional loglikelihood function with respect to : where represents the parameter vector to be estimated. Marquardt optimisation algorithm has been employed to obtain the estimate for parameters.

EMPIRICAL RESULTS AND DISCUSSION
The intraday session involves only contemporaneous volatility spillovers under the assumption that information generated in one market during a day is fully transmitted to the other market on the same day. The results of intraday spillovers reported in the left panel of Table 3 confirm the presence of significant volatility spillover effects from both India and Pakistan towards Sri Lanka. With respect to overall shock spillovers, the estimated results indicate that the shock in Indian market will be significantly transmitted to the Sri Lankan market while the overall shock spillovers from Pakistan to Sri Lanka are marginally significant at 10% level. As indicated in the right panel of Table 3, volatility spillovers from Sri Lanka to India are more significant than spillovers to Pakistan. With respect to the overall shock spillovers, estimated results conclude that the transmission of shocks from Sri Lanka to India is not significant whereas their transmission to Pakistan is highly significant.
According to the left panel of Table 4, there is no evidence to claim that overnight volatility spillovers exist from both India and Pakistan towards Sri Lanka. However, with respect to overall shock spillovers, the estimated results indicate that the transmission of shocks from India is highly significant though there is no evidence to say that overall shocks get spilled over from Pakistan to Sri Lanka.  The figures in the right panel of Table 4 suggest that the volatility spillovers from Sri Lanka to India are highly significant. However, there is no evidence to claim that volatility spillovers do exist towards Pakistan. With respect to overall shock spillovers, the estimated results conclude that there are significant spillover effects from Sri Lanka to both India and Pakistan.
The Ljung-Box Q statistic for residuals and squared residuals are used to test for the presence of unfiltered linear and non-linear dependencies in residuals, , of the estimated BEKK model. Results are reported in Table 5, which indicates that Ljung-Box Q statistic is not statistically significant for lags 14 and 20 in both regressions intraday and overnight except in one case, where the statistic is marginally significant at 10% level. This confirms that the proposed model to estimate volatility spillover effects among the three markets has been correctly specified. Note. *** Significant at 1%; ** Significant at 5%; * Significant at 10%; LB -Q (14) and (20) and LB -Q 2 (14) and (20) denote the Ljung-Box Q statistics for residuals for 14 lags and 20 lags and squared residuals for 14 and 20 lags, respectively.
In this context, based on the model of cross-border daily equity returns by Griffin, Nadari and Stulz (2004), a few reasons can be pointed out to explain why capital has been pushed towards Sri Lanka from India. First, CSE was able to make huge gains for investors even during the 2008/09 post global financial crisis period and was not subject to many major drops in prices as the other larger markets. Second, CSE was the sixth best performing equity market within the region by 2013 while outperforming BSE. In fact, to counter the negative fallout of the global meltdown on the Indian and Pakistan equity markets, the governments of both countries implemented some macroeconomic and policy level measures. For instance, the Indian central bank took a number of monetary easing and liquidity enhancing measures to facilitate flow of funds (Bajpai, 2011). Pakistani authorities declared an unusual amnesty in January 2012 to facilitate stock market growth by allowing investors to buy shares with no questions raised about where their money had come from. With the introduction of this remission, the daily volume traded on KSE has doubled; which lasted until June 2014. Based on the same model, it can be argued that capital might have been pulled from Sri Lanka to Pakistan because of it being top performer within the region, ahead of Sri Lanka and India. In addition, Sri Lanka's status of being the relatively smallest market with less liquidity, more predictability and higher returns (Padhi and Lagesh, 2012), might have had an impact on pushing capital from other markets towards it.
Moreover, most of the emerging markets have thin trading, lack of transparency coupled with informational inefficiency and speculative trading by few market makers which make those markets vulnerable to financial bubbles followed by a market crash (Chan, Lee and Woo, 2003). Because of these shared characteristics among the three markets, the behavior of market participants around the crisis period and resulting transmission of capital flows across the markets can be explained by the wake-up call hypothesis (Kaminsky et al., 2003) as well as the flight to quality argument (Baur and Lucey, 2009;Johansson, 2010).

CONCLUDING REMARKS
This study set out to explore the existence, size and the direction of volatility spillovers between Sri Lankan stock market and two major South Asian regional equity markets, viz., India and Pakistan. The empirical literature in this area, especially in the context of Sri Lanka, is inconclusive and not common compared to studies on the equity markets in other countries. Findings show the existence of bilateral intraday volatility spillovers between Sri Lanka and India as well as Sri Lanka and Pakistan. It has been evident that, with respect to the intraday session, the effect from Pakistan to Sri Lanka is stronger than the effect from India to Sri Lanka. However, with respect to the overnight session, we found only a unilateral spillover effect from Sri Lanka to India.
In terms of the cross-market lagged squared innovations, estimated results indicate highly significant spillovers from Sri Lanka to Pakistan and from India to Sri Lanka in both intraday and overnight sessions. In addition, there are significant spillovers from Sri Lanka to India only in the overnight session.
The exploration and close examination of the nature of volatility spillovers between Sri Lanka and other markets have important implications for policy makers in addressing financial stability issues especially with regard to monetary policy. Monetary policy can simply rely on controlling market fundamentals only if there is no adverse impact from existing volatility spillovers. Furthermore, as Giannellis, Kanas, & Papadopoulos (2010) point out, monetary authorities have to be cautious about volatility in asset markets if it is caused by non-fundamental factors such as irrational investing behavior in such markets. The existence of volatility spillovers from other South Asian markets to the local market also implies that policy makers have to be watchful during turbulent times such as financial crises. Moreover, investors and other fund managers benefit from the new research insights on shock and volatility spillover effects between Sri Lanka and other markets in the region. The findings also provide important insights on implications for market efficiency, profitable investment opportunities and risk diversification. Nevertheless, findings based on past data may be of limited use in investments in stock markets where returns depend largely on current events and news.