Returns and volatility spilloverbetween stock prices and

exchange ratesEmpirical evidence from IBSA countries

Manish KumarGlobal Research and Analytics, CRISIL, Chennai, India

Abstract

Purpose – The purpose of this paper is to analyze the nature of returns and volatility spilloversbetween exchange rates and stock price in the IBSA nations (India, Brazil, South Africa).

Design/methodology/approach – The study uses VAR framework and the recently proposedSpillover measure of Diebold and Yilmaz to examine the returns and volatility spillover betweenexchange rates and stock prices of IBSA nations. In addition, multivariate GARCH with time varyingvariance-covariance BEKK model is used as a benchmark against the spillover methodology proposedby Diebold and Yilmaz.

Findings – The results of multivariate GARCH model suggests the integration between stock andforeign exchange markets and indicates the existence of bi-directional volatility spillover betweenstock and foreign exchange markets in the IBSA countries. Spillover results using the Diebold Yilmazmodel suggest the bi-directional contribution between stock and foreign exchange market, in terms ofboth returns and volatility spillovers. Overall, results confirm the presence of returns and volatilityspillovers within the IBSA nations and, in particular, the stock markets play a relatively moreimportant role than foreign exchange markets in the first and second moment interactions andspillovers.

Practical implications – The market participants may consider the relationship between theexchange rate and stock index to predict the future movement of each other effectively. Multinationalcompanies interested in exchange rate forecasting may consider the stock market as an importantattribute. There is an interesting implication for portfolio managers too because of the spillover stockand foreign exchange markets. This knowledge would help to create a fund which performs well.Moreover, the paper can help regulators and policy makers in IBSA nations to understand thestructure of the market in a better way and then design their policies.

Originality/value – The study contributes to the literature by extending the existing studies on thespillover between stock price and exchange rate by investigating the issue for three emergingeconomies, India, Brazil and South Africa. Unlike most studies in the literature which focus onmultivariate GARCH model, this is the first study which explores the issue of returns and volatilityspillover between the stock prices and the exchange rates using spillover measure of Diebold andYilmaz and much longer and recent daily data. Moreover, multivariate GARCH with time varyingvariance-covariance BEKK model is used as a benchmark against the spillover methodology proposedby Diebold and Yilmaz.

Keywords Stock prices, Exchange rates, Returns, Emerging markets, Spill over, Time series analysis,Multivariate GARCH, Variance decomposition, India, Brazil, South Africa

Paper type Research paper

The current issue and full text archive of this journal is available at

www.emeraldinsight.com/1746-8809.htm

The author would like to thank the anonymous reviewers and Editor of the Journal for goingthrough the manuscript patiently and critically and sharing their views in improving the article.

International Journal of EmergingMarketsVol. 8 No. 2, 2013pp. 108-128q Emerald Group Publishing Limited1746-8809DOI 10.1108/17468801311306984

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1. IntroductionStudying the dynamic relationship between forex and stock market has attracted theattention from policy makers, market participants and the academicians for a longtime and offers meaningful insights to them (Tabak, 2006; Aydemir and Demirhan, 2009;Kutty, 2010; Kumar, 2010; Zhao, 2010). For policymakers, analyzing the dynamicrelationship between stock price and exchange rates is important because relationshipbetween two markets may affect their decisions about monetary and fiscal policy.A booming stock market has a positive effect on aggregate demand. If this is largeenough, expansionary monetary or contractionary fiscal policies that target the interestrate and the real exchange rate will be neutralized. Sometimes, policy makers advocateless expensive currency in order to boost export sector. They should be aware whethersuch a policy might depress the stock market (Dimitrova, 2005; Gavin, 1989).

It would also be useful for regulator, as understanding of the stock price-exchangerate relationship may prove helpful to foresee a crisis. Until the 1980s, financial criseswere seen as events that happened in individual markets, without a systemic nature.Nonetheless, the incidence of numerous financial crises such as the crisis of theEuropean Mechanism of Exchange Rates (1992), the Mexican crisis (1994), the Asiancrisis (1997), the Russian crisis (1998) and the Brazilian crisis (1999) were not restrictedto the countries of origin, but they quickly spread all over the world to a number ofinternational markets. These crisis gripped various economies due to significantdepreciation of exchange rates (in terms of US dollar) as well as drastic decline in thestock prices. Thus, it is important to study the transmission of shocks between exchangerates and stock price (Kumar, 2010; Dimitrova, 2005).

Huge volume and value of currencies and stocks traded around the world have alsoled to speculation in these markets. Thus, for the market participants and investmentcommunity, who deal either or both in stock or foreign exchange markets, the dependencebetween the two markets may be used to profitably exploit the relationship. Moreover,diversification in the portfolio (at financial product, asset class, and country level) hasmade exchange rates an integral part of the portfolio held by mutual funds, foreignintuitional investors, hedge funds and other professionally managed funds. Themean-variance approach to portfolio analysis suggests that the expected return isimplied by the variance of the portfolio. This requires an estimate of the correlationbetween stock prices and exchange rates (Kumar, 2010; Dimitrova, 2005). Thus,understanding of the relationship between exchange rates and stock prices may help thefund manager to manage and hedge the risk proficiently.

Multinational companies (MNCs) thrive on most of their sales coming fromoverseas. They have to dabble with many tasks such as decisions on hedging,short-term financing, short-term investment, capital budgeting, earning assessment,and long-term financing. This makes MNCs vulnerable to exchange rate movements.Thus, understanding the exchange rate movements can help MNCs take betterdecisions. This would also benefit MNC’s, in managing their short-term financing, andinvestment, capital budgeting, earning assessment, exposure to foreign contractsand exchange rate risk stabilizing their earnings. Last but not the least, the empiricalfindings helps strengthening the theoretical framework of the determinants of exchangerates or stock market movement, from the perspective of developing economies suchas India, Brazil, South Africa (IBSA) countries, which may be useful for the academiccommunity.

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Thus, the discussion on the dynamic relationship between exchange rate and stockmarket has been the subject of various studies (Mundell, 1963; Dornbusch and Fisher,1980; Bahmani-Oskooee and Sohrabian, 1992; Mok, 1993; Ajayi and Mougoue, 1996;Abdalla and Murinde, 1997; Granger et al., 2000; Phylaktis and Ravazzolo, 2005; Yau andNieh, 2006; Pan et al., 2001; Aydemir and Demirhan, 2009; Kumar, 2010; Zhao, 2010).Existing literature suggests two approaches to study this dynamic relationship.

The microeconomic, or the goods market, or traditional, or flow oriented approachconcentrate on the current account of the balance of payment. This approachhypothesizes that exchange rate changes influence international competitiveness andtrade balance, impacting real income and output. Thus, fluctuations in exchange rate cansignificantly affect the firm value. Exchange rate influence the firm’s profits and value,depending on when it faces transaction, translation, and economic exposure. Over purelydomestic ones, firms with foreign operations are more affected (Kumar, 2010). In summary,the microeconomic approach suggests that exchange rates lead the stock price (Dornbuschand Fisher, 1980; Ma and Kao, 1990; Ajayi and Mougoue, 1996; Yau and Nieh, 2006).

The macroeconomic, or the portfolio, or asset market approach focuses on thecapital account as a significant determinant of exchange rate dynamics. This approachsuggests that a rise in stock prices increases the domestic wealth of investors, helpingincrease the demand for money. Consequently, interest rates rise, capital flows intothe domestic economy and the domestic-currency appreciates. This approach assumesthere is a negative relationship between stock prices and exchange rates, with causalityrunning from the stock market to the foreign exchange market (Kumar, 2010).Bahmani-Oskooee and Sohrabian (1992), Granger et al. (2000), Caporale et al. (2002),Vygodina (2006), Pan et al.(2001), Ai-Yee Ooi et al. (2009) and Lee and Lee (2009) stressthe importance of the portfolio approach in analyzing the relationship.

Reviewing the literature suggests that a large number of studies have examined thecontemporaneous as well causal relationship in the returns of the two markets. Results ofmost of the studies support the contemporaneous as well as dynamic relationshipbetween the two markets. Nevertheless, the direction and sign of the relationship betweenthe foreign exchange and stock market relation is not ubiquitous in the developed, Asianas well as other emerging nation. Few studies (Bahmani-Oskooee and Sohrabian, 1992;Doong et al., 2005; Aydemir and Demirhan, 2009; Zhao, 2010; Kumar, 2010) concludedthat there exists bi-directional causal relationship between the two markets. However,results of few studies (Bhattacharya and Mukherjee, 2003; Muhammad and Rasheed,2003; Stavarek, 2005; Rahman and Uddin, 2009) suggests that there is causal relationshipbetween stock price and exchange rates. Moreover, the review also suggests the mixedconsensus about the existence of cointegration between exchange rates and stock prices.The earlier studies have used various linear and non-linear methodologies to examine thedynamic relationship between the two markets, such as, linear Granger causality, vectorautoregression (VAR) and vector error correction model, Engle and Grangercointegration test and Johnson cointegration model, Hiemstra and Jones non-linearGranger causality, noisy Mackey-Glass non-linear causality model, etc. Variation inresults among different economies may be because of the different degree of the capitalmobility, trade volume and economic links; as well as omitted variable bias (for instance,interest rates may influence stock and currency markets).

Much of the available empirical evidence on the linkages between stock marketsand exchange rates has concentrated on the first moment’s, i.e. causal relationship in the

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returns of the two markets; however, various studies have also investigated thevolatility spillover between stock market returns and exchange rates within the sameeconomy over time and across different countries. Kanas (2000), Yang and Doong (2004),Dark et al. (2005) and Francis et al. (2006) studied the volatility spillovers in developedcountries between currency and stock markets. The results suggest that the exchangerate changes influence on the stock market with the less direct impact then the stockmarket on the currency exchange market. Such spillover mechanism on developedeconomies is natural and expected, as there is no such significant change on the foreignexchange markets of advance nations.

There also exist volatility spillover’s studies (Pyun et al., 2000; Choudhry, 2000, 2004;Caporale et al., 2002; Xu and Fung, 2002; Doong et al., 2005; Wu, 2005; Qayyum andKemal, 2006; Morales, 2008; Yang and Chang, 2008; Choi et al., 2009; Lee and Lee, 2009;Zhao, 2010) on various emerging stock and foreign exchange markets as well. Theresults were similar to the results of the studies done on developed markets. Engle et al.(1990) proposed two hypotheses: “heat wave” and “meteor shower” on how volatilitymay manifest itself across trading centers. The “heat wave” hypothesis suggests thatvolatility has only location-specific autocorrelation, so that a volatile day in market“A” is likely to be followed by another such day in A, but not typically in market “B”.The “meteor shower” hypothesis suggests that intraday volatility spills over from onemarket to another, so that a volatile day in market A is likely to be followed by one inmarket B. The two hypotheses were further supported by Baillie and Bollerslev (1991)and Baillie et al. (1993). Forbes and Rigobon (2002) suggest that such spillovers can beseen as a consequence of greater financial integration or contagion effects.

The review suggests that, most of the studies agree that the extent to which themarket evaluates and assimilates new information is reflected in the volatility process.As a result, the investigation of volatility spillover can be of help is studying thefinancial contagion between countries or different asset class. Moreover, examining thedirection of volatility spillover would be important for identifying the nature offinancial contagion (Inagaki, 2007).

Most studies use weekly, daily and intra-day data of the financial time series fromvarious developed nations and emerging markets, to analyze the returns and volatilityspillovers. Empirical research has also documented volatility transmission from developedto emerging markets. In literature, univariate and multivariate GARCH/EGARCHmodels have been used as a standard method for investigating financial spillovers.Literature review also reveals that most studies mainly focus on the investigation of firstand second moment interaction, among assets of developed countries, and the integrationof developing with developed markets as well. However, in the existing literature, littleattention has been paid to examine the nature of returns and volatility spillover betweenstock prices and exchange rates for three south-south nation namely India, Brazil andSouth Africa (IBSA nation).

In light of these developments, in this study, an attempt is made to overcome thedrawbacks identified in the earlier studies by examining the financial spillover betweenstock prices and exchange rates for IBSA economies. The study selects IBSA nationbecause, in 2003, the tri-lateral cooperation of IBSA dialogue forum was launched withmajor objective of cooperation in trade and investment, agriculture, climate, culture,defense, education, energy, health, science, technology, poverty alleviations and socialdevelopment. IBSA countries are emerging economies and in terms of economic power,

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the World Bank ranks Brazil 8th, India 11th and South Africa 31st by traditional grossdomestic product (GDP) (Source: World Development Indicators database). The marketcapitalization in the stock exchanges for year 2010 of IBSA countries are 1,628,673,1,457,790 and 532,890 (in millions of US dollar), respectively, (Source: Seeking Alpha).Moreover, according to Bank of International Settlements report, average daily turnoverin April 2010 for IBSA countries as a percentage of global foreign exchange marketturnover were 0.9, 0.7 and 0.7, respectively. However, their percentage share in 1998 was0.1, 0.2 and 0.4, respectively.

Government policy changes, including abolishment of capital inflow obstructions,flexible exchange rates system, economic restructuring, human and physical capitalformation, foreign institutional and foreign direct investment, accumulation of foreignexchange reserves have contributed greatly to stronger economic fundamentals and thushave played a key role in IBSA countries. Moreover, an important contributor to growthin IBSA markets has been the massive rise in the size of middle class. Another area thatis poised to support economic growth in IBSA markets is investment, particularly ininfrastructure. Moreover, globalization and interdependent stock markets, abolishmentof capital inflow obstructions, have thrived in the past two decades. These factors haveaffected not only the exchange rates, but also stock prices, and thus, the risk of investmentdecisions and portfolio diversification. Thus, the collective size and relevance of IBSAcountries in the global economy have widened the scope of studying the relationshipbetween exchange rates and stock prices. A key issue in IBSA economies therefore refersto the questions, to what extent stock market dynamics would in turn affected byexchange rate developments or stock market dynamics would affect exchange rates.

Given this background, the main objective of the study is to analyze the nature ofreturns and volatility spillovers between exchange rates and stock price in the IBSAnation. In literature, univariate and multivariate GARCH models have been used tomodel financial spillovers. However, this is the first study which uses VAR frameworkand the recently proposed spillover measure of Diebold and Yilmaz (2009) to examinethe returns and volatility spillover between exchange rates and stock prices of IBSAnation. Variance decomposition analysis of the VAR model is used to identify spilloversof return and volatility shocks from the indigenous shocks. This methodology is simpleand intuitive, yet rigorous and replicable to implement and can analyze causation patterndynamics. To measure volatility, exponential GARCH (Nelson, 1991) model is used as it iscapable of explicitly capturing asymmetries. In addition, multivariate GARCH with timevarying variance-covariance BEKK model is used as benchmark against the spillovermethodology proposed by Diebold and Yilmaz (2009). The BEKK-GARCH (1,1) modelhas been utilized to analyze the spillover in a bi-variate fashion. The BEKK-GARCH (1,1)has the attractive property which suggests that the conditional covariance matrices arepositive definite by construction. Moreover, the model has the capability to analyze thereturns and volatility linkages as well as across the market, i.e. returns and volatilityspillover effect. Thus, the present study would complement the emerging body ofliterature by investigating how the behavior of spillover in the IBSA countries are similaror differ from those in the other emerging and developed markets. We believe that theresults of this study’s empirical analysis would enhance the understanding of spilloveractivities in the IBSA nations.

The rest of the paper is set out as follows. In Section 2, we describe the data andbriefly review the unit root tests, cointegration tests and spillover index methodology.

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In Section 3, we present our empirical results. Finally, Section 4 summarizes thefindings and brings out the implications.

2. Data and methodologyThe data set comprises the daily closing price for the benchmark stock market indicesin India (S&P CNX Nifty), Brazil (Bovespa) and South Africa (FTSE/JSE Top 40 Index).Moreover, the study uses the daily exchange rate data of Indian rupee versus US dollar(INR/USD), Brazilian real versus US dollar (BRL/USD) and South African rand versusUS dollar (ZAR/USD). The three stock indices and exchange rates data series spans1 January 2000 to 17 January 2011. All the time series data has been obtained fromBloomberg. To overcome the problem of non-stationarity, the three indices and threeexchange rate series are transformed into continuously compounded returns. Figure 1shows the plots of daily returns of indices and exchange rate for each market.

These plots show a clustering of larger returns volatility around the starting pointsof downward trends, both short-run and long-run downward trends, as in March 2005or mid-2007, when was the start of the current downward trend on both markets.

Table I describes the measure of central tendency (i.e. mean), a measure of statisticaldispersion (i.e. standard deviation), measure of shape of distribution (i.e. skewness andkurtosis) and a goodness-of-fit measure of departure from normality (i.e. Jarque-Bera (JB)).

Figure 1.Daily returns of indicesand exchange rates for

IBSA nation

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A perusal of the standard deviation for the indices of IBSA nation suggests thatBovespa is more volatile than their counter parts. However, among the exchange rates,South African rand seems to be more volatile than Indian rupee and Brazilian real. Themeasure of skewness and kurtosis indicates that Nifty is more skewed and peaked thanthe indices of other IBSA nation. Moreover, all the indices are negatively skewed. TheSouth African rand seems to be more skewed than the Indian rupee and Brazilian real,however, Indian rupee is more peaked than the other two currencies. It is interesting toobserve that all the exchange rate returns are positively skewed. Thus, descriptivestatistics suggests that all the time series exhibit skewness and high kurtosis which iscommon in financial time series. The results of JB statistics indicates that the nullhypothesis of normal distribution is rejected for each differenced series.

2.1 Unit root and cointegration testThis study uses Augmented Dickey-Fuller (ADF) and Kwiatkowski, Philips, Schmidtand Shin (KPSS) tests (Gujarati, 1995; Brooks, 2002) to examine whether the time seriesof exchange rates and stock indices of IBSA nations are stationary or not. Afterwards,we examine the existence of long-run relationship between stock index and exchangerates of the IBSA countries using two steps Engle and Granger (1987) method. Wepreferred to use this method rather than the Johansen Cointegration test is because ofthe simplicity of the Engle and Granger test and moreover, there are two variablesunder investigation, and hence, there could be at most one cointegrating vector.Tables II and III show the result of unit root and cointegration test, respectively, for thestock index and exchange rate series of three IBSA economies.

India Brazil South AfricaNifty INR/USD Bovespa BRL/USD FTSE/JSE ZAR/USD

Mean 0.00046 1.78 £ 10205 0.00052 22.47 £ 10205 0.00046 4.35 £ 10205

SD 0.01733 0.00377 0.01980 0.01115 0.01467 0.01132Skewness 20.34754 0.01030 20.11606 0.04995 20.11899 0.66370Kurtosis 10.3615 15.6814 6.62588 12.2840 6.16252 7.27607Jarque-Bera 6,069.04 17,850.9 1,490.60 9,733.89 1,157.11 2,306.21No of observations 2,664 2,664 2,710 2,710 2,761 2,761

Table I.Returns descriptivestatistics

ADF test KPSS testVariable t-statistics t-statistics

Panel A: IndiaNifty 237.2744 0.20461INR/USD 252.5792 0.10105Panel B: BrazilBovespa 251.5844 0.15098BRL/USD 252.7293 0.37793Panel C: South AfricaFTSE/JSE 250.3820 0.08939ZAR/USD 251.3038 0.14606

Note: The critical values for ADF and KPSS test at 1 percent level are 23.4327 and 0.739, respectivelyTable II.Unit root test

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2.2 BEKK-GARCH (1, 1) modelExtending the univariate GARCH model to a n-dimensional multivariate modelrequires the estimation of n different mean and corresponding variance equationsand (n2-n)/2 covariance equations. As our interest is the time-varying covariancematrix, we define the mean equation in the following way:

rt ¼ mþ 1t; 1tjVt21 , N ð0;HtÞ ð1Þ

where rt is a vector of appropriately defined returns and m a (N*1) vector of parametersthat estimates the mean of returns series. The residuals vector is 1t with thecorresponding conditional covariance matrix Ht given the available information setFt21. The equivalent to a univariate GARCH (1,1) model is given as follows:

vechðHtÞ ¼ Vþ Avechð1t2110t21Þ þ BvechðHt21Þ ð2Þ

where Ht is the time-varying (N*N) covariance matrix, F denotes an (N*N)(N(N þ 1)/2*1)vector and A and B are (N(N þ 1)/2*N(N þ 1)/2) matrices. The VECH operator stacksthe lower portion of an (N*N) symmetric matrix as an (N (N þ 1)/2*1) vector which can bedone since the covariance matrix is symmetric by definitions. In the bi-variate VECHmodel, the matrices are all (3 £ 3) matrices, thus, leading to 27 parameters to be estimated.The disadvantage of this model is that it has large number of parameters and to ensureHt positively, restrictions are required to be imposed.

The BEKK model is an improvement to the VECH model, as the number ofparameters is reduced and the positive definiteness of the covariance matrix isguaranteed. Therefore, in this study, we have used the BEKK-GARCH model suggestedby Engle and Kroner (1995). The covariance matrix of the unrestricted BEKK modelin bi-variate case is represented as:

Ht ¼ B 0Bþ C01t2110t21C þ G 0Ht21G ð3Þ

where Ht is the conditional covariance matrix and B is the 2 £ 2 upper triangularmatrices. It is obvious from the above equation that the covariance matrix is guaranteedto be positive definite as long as B’B is positive definite. The element Cij of the 2 £ 2matrix C indicates the impact of market ivolatility on market j and reflects ARCH effect ofvolatility. The element Gij of the 2 £ 2 matrix G indicates the persistence of volatilitytransmission between market i and market j and reflects GARCH effect of volatility.

Dependent Tau-statistics Probability z-statistics Probability

Panel A: India

Ln Nifty 20.44367 0.96650 20.79149 0.97260

Ln INR/USD 21.95430 0.55190 27.27510 0.55100

Panel B: Brazil

Ln Bovespa 21.99042 0.53310 24.18859 0.79570

Ln BRL/USD 22.249207 0.39860 26.70077 0.59580Panel C: South Africa

Ln FTSE/JSE 20.75603 0.93770 21.21221 0.96090Ln ZAR/USD 22.08764 0.48220 27.61573 0.52510

Table III.Engle and Granger

cointegration test

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The total number of estimated parameter is 11. The bi-variate BEKK-GARCH (1,1) modelcan be written as:

h11;t h12;t

h21;t h22;t

" #¼

b11;t b12;t

b21;t b22;t

" #0

b11;t b12;t

b21;t b22;t

" #

þc11;t c12;t

c21;t c22;t

" #0

121;t21 11;t21; 12;t21

12;t21; 11;t21 122;t21

24

35 c11;t c12;t

c21;t c22;t

" #

þg11;t g12;t

g21;t g22;t

" #0

g11;t21 h12;t21

h21;t21 h22;t21

" #g11;t g12;t

g21;t g22;t

" #ð4Þ

where h11,t denotes the variance of the change rate of stock index returns, h12,t denotes thecovariance of the change rate of exchange rate and stock index returns, h22,t denotes thevariance of exchange rate returns. When we explore the volatility spillovers effect fromstock market to foreign exchange market, we should test whether the coefficients c12 andg12 are statistically significantly different from zero. When we explore the volatilityspillovers effect from foreign exchange market to stock market, we need to test c21 and g21

are significantly different from zero. If there is no volatility spillovers effect betweenforeign exchange and stock markets, the non-diagonal elements c21, g21, c12 and g12 ofmatrices c and g are not statistically significantly different from zero. The study uses theUCSD GARCH Toolbox for MATLAB provided by Kevin Sheppard[1] in order toestimate the BEKK-GARCH (1, 1) model. The results are presented in Table IV.

2.3 Measuring returns and volatility spilloversThe study uses the spillover index methodology introduced by Diebold and Yilmaz(2009) to measure the returns and volatility spillovers between foreign exchange andstock market of IBSA nation. Measurement of these spillovers is based on VARmodels. The VAR model helps to analyze the decomposition of forecast error variance

Nifty – INR/USD Bovespa – BRL/USD FTSE/JSE – ZAR/USDParameters Coeff. t-stat. Coeff. t-stat. Coeff. t-stat.

mb11 0.34948 105.903 0.24978 130.774 0.17881 255.442b12 0.02014 118.470 20.04181 2167.240 20.06516 91.7746b22 20.01238 225.7917 0.07811 22,2317.1 0.08653 2786.636c11 0.37823 257.299 0.20180 388.076 0.28843 497.293c12 0.01261 217.413 20.02913 22,913.00 20.00320 22.8571c21 20.05674 226.7642 0.00664 247.4286 20.03056 152.800c22 0.38280 22,392.50 0.33040 21,573.33 0.22687 21,334.53g11 0.90419 2837.213 0.97045 24,043.54 0.94891 23,953.79g12 20.00783 71.1818 0.00861 430.500 0.00744 14.5882g21 20.03911 26.9724 20.00253 2168.667 0.00640 246.153g22 0.92531 213,218.7 0.94261 11,931.7 0.97025 119,784Logliklihood 24,915.417 29,007.836 28,522.799

Table IV.Bivariate BEKK-GARCH(1, 1) parameter estimates

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thereby providing a measure of the overall relative importance of an individualvariable in generating variations in its own and on other variables. That is, the effectthat each variable in the system has on itself and on other variables over different timehorizons (say h-step ahead) can be measured by decomposing this forecast variance.This information is used in measuring interdependence and spillover effects acrossmarkets. Thus, it transforms wealth of information into a single quantitative measurecalled as spillover index (Diebold and Yilmaz, 2009).

To illustrate the creation of a spillover index, consider a co-variance stationary firstorder bi-variate VAR model represented as:

yt ¼ Cyt21 þ 1t ð5Þ

where yt ¼ ð y1t; y2tÞ0 is a 2 £ 1 matrix and Ci is a 2 £ 2 coefficient matrix.

If yt is covariance stationary, then according to Wold decomposition theorem, theabove model can be written as infinite moving average process of its innovationprocess.

Formally:

yt ¼X1i¼0

fimt2i ð6Þ

where fi is coefficient matrix and mt is vector of white noise.The h-step-ahead forecast of yt is given by:

ytþh ¼X1i¼h

fimtþh2i ð7Þ

The forecast error and its variance matrix can be calculated as:

ytþh 2 ytþh ¼Xh21

i¼0

fimtþh2i

varð ytþh 2 ytþhÞ

ð8Þ

Consider y1,t, the first element of yt matrix. Its h-step-ahead forecast error is given by:

y1;tþh 2 y1;tþh ¼ ðf0;11m1;tþh þ f1;11m1;tþh21 þ · · ·fh21;11m1;tþ1Þ

þ ðf0;12m2;tþh þ f1;12m2;tþh21 þ · · ·fh21;12m2;tþ1Þð9Þ

and the variance of its h-step-ahead forecast error is given by:

s 2y1;h

¼

Proportion of variance due to own shock

s 2y1

f20;11 þ f2

1;11 þ · · ·f2h21;11

� �|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}þ

Proportion of variance due to y2 shock

s2y2

f20;12 þ f2

1;12 þ · · ·f2h21;12

� �|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} ð10Þ

Thus, for a two-variable system, the total forecast variance of variable y1,t is equal tothe sum of the variance in y1,t due to shocks in y1,t and the variance in y1,t due to shocksin y2,t. So the total spillover (TS1) is given by:

f20;11 þ f2

1;11 þ · · ·f2h21;11 þ f2

0;12 þ f21;12 þ · · ·f2

h21;12 ð11Þ

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Similarly, the total spillover (TS2) of variable y2,t is given by:

f20;21 þ f2

1;21 þ · · ·f2h21;21 þ f2

0;22 þ f21;22 þ · · ·f2

h21;22 ð12Þ

Hence, the variance decomposition allows us to split the forecast error variance of eachvariable into parts, attributable to the various system shocks.

In the case of two-variable system, the total forecast error variation {trace (fif0i)}

would be given by:

f20;11 þ f2

1;11 þ · · ·f2h21;11 þ f2

0;21 þ f21;21 þ · · ·f2

h21;21þ

f20;12 þ f2

1;12 þ · · ·f2h21;12 þ f2

0;22 þ f21;22 þ · · ·f2

h21;22

ð13Þ

This spillover can be converted into an easily interpretable index, by expressing itrelative to total forecast error variation. The ratio can be expressed in percentage andspillover index can finally be represented as:

S ¼TSi

traceðfif0iÞ

*100 ð14Þ

In summary, by aggregating the variance decomposition into a single value, we getinformation about the degree of spillovers across markets. This study uses bi-variateVAR system, where the lag order is selected based on the Swartz Bayesian InformationCriteria (SBIC).

Following Nelson (1991), we estimate daily conditional variance of exchange ratesand stock market index of IBSA nation represented by the following equation:

logs 2t ¼ f1 þ w1logs

2t21 þ g1

1t21

st21

��������þ c1

1t21

st21þ j ð15Þ

The EGARCH model possess useful properties for estimating volatility dynamics in aunified framework and are consistent with the stylized facts in foreign exchange ratedynamics, such as volatility persistence and clustering.

3. Results3.1 Unit root testTables II shows the results of ADF and KPSS tests performed on the stock index andexchange rate returns of IBSA nations.

Results of ADF test suggest that the absolute value of t-statistics is greater than theabsolute critical value at 1 percent level for the index and exchange rate returns of theIBSA nations. This indicates that all the time series are stationary (i.e. the nullhypothesis of a unit root is rejected for all the series in first difference). Results of KPSStest are also in agreement with ADF results, as the t-statistics is smaller than thecritical values at 1 percent level.

3.2 Cointegration testTable III, reports the results of the Engle and Granger (1987) cointegration test.

The results of Engle and Granger cointegration test suggests that tau-statistics andnormalized autocorrelation coefficient (i.e. z-statistics) both accept the null hypothesis

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of no cointegration (unit root in the residuals) at the 1 percent level. This indicatesthat Nifty and INR/USD, Bovespa and BRL/USD and FTLSE/JSE and ZAR/USD are notcointegrated and thus, there is no long-run relationship between stock indices andexchange rates for India, Brazil and South Africa. Findings of Engle and Grangercointegration tests are consistent with the findings of earlier studies for South African(Ocran, 2010), Brazil (Tabak, 2006), and Indian (Kumar, 2010) market. Moreover,findings of Engle and Granger cointegration tests are consistent with the findingsChoudhry (2000), Yang and Doong (2004), Pan et al. (2001), Yang and Chang (2008),Morales (2008) Lee and Lee (2009), Zhao (2010) and Kutty (2010) for developed marketssuch as the USA, the UK, and Japan as well as for Asian and Latin American markets.

3.3 BEKK-GARCH (1, 1) modelIn this study, we attempt to examine the volatility transmission or spillover effect,therefore, using equation (4) we estimate three bi-variate BEKK-GARCH (1, 1)equations which are formed using the stock indices and exchange rates for each IBSAnations. This can be represented by the following univariate model:

h11;t ¼ b211 þ c2

11121;t21 þ 2c11c2111;t2112;t21 þ c2

21122;t21 þ g2

11h11;t21

þ 2g11g21h12;t21 þ g221h22;t21;

h12;t ¼ b11b12 þ c11c12121;t21 þ ðc21c12 þ c11c22Þ11;t2112;t21 þ c21c221

22;t21

þ g11g12h11;t21 þ ðg11g12 þ g11g22Þh12;t21 þ g21g22h22;t21;

h22;t ¼ b221 þ b2

22 þ c2121

21;t21 þ 2c12c2211;t2112;t21 þ c2

22122;t21 þ g2

12h11;t21

þ 2g12g22h12;t21 þ g221h22;t21;

ð16Þ

The equation (16) indicates that the variances and covariance of asset depend onconstants, lagged squared residual (12

1;t21, 122;t21), products of the lagged cross residual

(11,t2112,t21), lagged variances (h11,t21, h22,t21) and lagged covariance (h12,t21) term.Thus, in order to discover volatility transmissions among or between different assetclasses, it is essential to evaluate the impact of lagged squared and cross residuals, orthe effect of the lagged variance and covariance terms. The results of BEKK-GARCH(1, 1) model are presented in Table IV along with respective t-statistics at 5 percentconfidence level.

The results presented in Table IV indicate that the estimates of BEKK-GARCHmodels are consistent with the conditions of positive definite covariance matrices. Inparticular the determinants of the matrices B, C and G are positive, moreover,parameters b11, c11 and g11 are positive as well for the IBSA countries. The coefficientin matrix C represents ARCH effects, i.e. innovations in lagged squared error terms.However, the coefficient in matrix G indicates the GARCH effects, i.e. volatilityspillover effects.

The results suggest that the diagonal parameters (c11 and c22) of ARCH and (g11 andg22) of GARCH term are significant at 5 percent level. The t-statistics are computed fromrobust standard errors. This indicates that in terms of magnitude, the stock indices ofIBSA nations are affected by their own index new shocks and conditional volatility.The same is true for exchange rates too. Moreover, stock index and exchange rates ofIBSA nations have been found to have cross ARCH and GARCH relationship and are

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119

bidirectional in nature, i.e. the off diagonal parameters (c12 and c21) of ARCH and (g12 andg21) of GARCH term are significant at 5 percent level.

The off diagonal elements of matrix C (c12 and c21) capture the cross-market shockeffects. The results suggest that the off diagonal parameters (c12 and c21) of ARCH termare significant at 5 percent level. This indicates the IBSA stock and foreign exchangemarket shows evidence of bidirectional interaction, meaning that news shock originatingfrom the foreign exchange market effectively influence the stock market and in the sameway news shock originating from the stock market effectively influences the currencymarket.

In addition, the off diagonal elements of matrix G (g12 and g21) capture thecross-market volatility spillover among or between asset classes. The coefficient g12 andg21 is statistically significant at 5 percent level for the IBSA nations. Thus, the overallresult suggests the integration between stock and foreign exchange markets andindicates the existence of bi-directional volatility spillover between stock and foreignexchange markets in the IBSA countries. The presence of significant volatility spillovercoefficient indicates that the volatility of stock index returns is a determinant of thevolatility of the exchange rate and that information contained in stock prices effects thebehavior of exchange rates in the IBSA markets and vice-versa. Engle et al. (1990) in theirstudy stated that market react to news originating in that market (the heat wave) and tonews emanating from other markets (the meteor shower). Thus, our results confirm thepresence of heat wave and meteor shower effects in the IBSA countries. The results of thestudy are consistent with the findings of Mishra et al. (2007) for Indian, Morales (2008) forBrazil and Anoruo and Braha (2009) for South African market. Moreover, findings of thestudy are consistent with the findings of Francis et al. (2006), Aloui (2007), Zhao (2010)and Fu et al. (2011). In addition our results partially support the findings of Kanas (2000),Yang and Doong (2004) and Choi et al. (2009) where the results indicates uni-directionalvolatility spillovers from stock returns to exchange rate.

3.4 Returns and volatility spillovers and spillover indexThis study uses bi-variate VAR model with the lag order selected, based on SBIC criteria.Following Diebold and Yilmaz (2009), the ten-step-ahead forecasts error variancedecomposition associated with the two variables are analyzed. Tables V and VI providethe detailed calculation of the returns and volatility spillover, and spillover indices forthe full sample.

The cell (m, n) in Table V (returns spillover) and Table VI (volatility spillover)suggests that the estimated contribution, to the forecast error variance of time series m,originating from innovations of time series n. The sum total of the cells in the contributionto others row or that of the contribution from others column, gives the numerator of thespillover index. Similarly, sum total of cells in the contribution including own row givesthe denominator of the spillover index.

Results presented in panel A of Table V suggest that innovations to nifty returns explain12.51 percent of the forecast error variance of INR/USD at the ten-day horizon. However,innovations to INR/USD returns explain 0.3305 percent of the forecast error variance ofnifty at the ten-day horizon. In case of Brazil (panel B, Table V), innovations to bovespareturns explain 23.99 percent of the forecast error variance of BRL/USD at the ten-dayhorizon. However, innovations to BRL/USD returns explain 0.6436 percent of the forecasterror variance of Bovespa at the ten-day horizon. The results in panel C of Table V suggest

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that innovations to FTSE/JSE returns explain 0.2596 percent of the forecast error varianceof ZAR/USD. However, innovations to ZAR/USD returns explain 0.4411 percent of theforecast error variance of FTSE/JSE at the ten-day horizon. Among the IBSA nations,Brazilian stock market explains the maximum forecast error variance in the exchangerates, followed by India and South Africa. Similarly Brazilian exchange rate explains themaximum forecast error variance in the stock market, followed by India and South Africa.

Results reported in panels A-C if Table VI suggests that volatility spillover fromstock market to foreign exchange market is 5.19, 18.61 and 4.09 percent for India, Braziland South Africa, respectively. Moreover, volatility spillover from foreign exchangemarket to stock market is 2.84, 5.68 and 1.25 percent for India, Brazil and South Africa,respectively.

Panel A: IndiaNifty INR/USD Contribution from others

Nifty 99.7694 0.33056 0.33056INR/USD 12.5144 87.4856 12.5144Contribution to others 12.5144 0.33056 12.8449Contribution including own 112.183 87.8162 6.4225 percent spillover index

Panel B: BrazilBovespa BRL/USD Contribution from others

Bovespa 99.3563 0.64363 0.6436BRL/USD 23.9958 76.0042 23.9958Contribution to others 23.9958 0.64360 24.6394Contribution including own 123.352 76.6479 12.3197 percent spillover index

Panel C: South AfricaFTSE/JSE ZAR/USD Contribution from others

FTSE/JSE 99.74033 0.25967 0.25970ZAR/USD 0.441146 99.5588 0.44110Contribution to others 0.441100 0.25970 0.70080Contribution including own 100.1815 99.8185 0.3504 percent spillover index

Table V.Returns spillover

full sample

Panel A IndiaNifty INR/USD Contribution from others

Nifty 97.1572 2.84280 2.84280INR/USD 5.15950 94.8405 5.15950Contribution to others 5.15950 2.84280 8.00230Contribution including own 102.316 97.6833 4.00110 percent spillover index

Panel B: BrazilBovespa BRL/USD Contribution from others

Bovespa 94.3482 5.65180 5.65180BRL/USD 18.6185 81.3815 18.6185Contribution to others 18.6185 5.65180 24.2703Contribution including own 112.966 87.0333 12.135 percent spillover index

Panel C: South AfricaFTSE/JSE ZAR/USD Contribution from others

FTSE/JSE 98.7491 1.25084 1.25080ZAR/USD 4.09472 95.9052 4.09470Contribution to others 4.09470 1.25080 5.34560Contribution including own 102.843 97.1561 2.6728 percent spillover index

Table VI.Volatility spillover

full sample

Returns andvolatilityspillover

121

While analyzing the returns and volatility spillover, we got some very interestingresults. The results of returns spillover suggest that magnitude of innovations originatingfrom stock market and explaining the forecast error variance of foreign exchangemarket is strongest in case of Brazil (23.99 percent) followed by India (12.51 percent) andSouth Africa (0.44 percent). Similarly, the magnitude of innovations originating fromforeign exchange market and explaining the forecast error variance of stock market isstrongest in case of Brazil (0.64 percent) followed by India (0.33 percent) and South Africa(0.25 percent). The results of volatility spillover are again inline with the results of returnsspillover. These results provide the evidence that among the IBSA nations, the volatilityspillover from stock market to foreign exchange market is highest for Brazil (18.61 percent)followed by India (5.19 percent) and South Africa (4.09 percent). Moreover, the volatilityspillover from foreign exchange market to stock market is again highest for Brazil(5.68 percent) followed by India (2.84 percent) and South Africa (1.25 percent).

The result is expected for South Africa. As in year 2000, South Africa changed themonetary policy regime to inflation targeting. Under this regime, monetary policyintends to set interest rates with the aim of keeping inflation at pre-announced goals.This has resulted in interest rates becoming stable by making them more predictable.Moreover, executing this policy requires the regulators to discard pre-commitment to anyexchange rate parity, predominantly using exchange rate interventions. Thus, this haseffectively made the exchange rate regime a free float. The capital flows to South Africahave increased drastically in last one decade. These large capital inflows were directedto purchases South African bonds rather than equities. The interest rate differentialmight be the main driver of these funs flows rather than growth expectations. In 2010,year-to-date foreign inflows into the South African bond and equity markets are arounda total of ZAR 100 billion, with ZAR 70 billion flowing into the bond market. With thelocal bond market outperforming the local equity market, it is therefore no surprise thatvolatility spillover bi-directional volatility spillover between stock and foreign exchangemarket is lowest among the IBSA nation.

On the other hand, Brazil which has adopted an inflation targeting policy since 1999experienced increase in foreign investment in its stock market. Participation of foreignparticipants in initial public offerings rose, from 48 percent of the total in 2005 to76 percent in 2007. Brazilian stocks were one of the most aggressively traded stocks inemerging economies. However, such stock purchases resulted mainly from “carry-trade”processes, in which investors replaced deteriorating-dollar assets for short-termequities, whose real values were increasing in relative terms. In addition, participation offoreign institutional investors in derivatives market concentrated in very short-termmaturities rose significantly since 2000. Moreover, Brazil’s integration with variousdeveloped and developing international financial markets had left it exposed to externalshocks. Couple of months before the sub-prime crisis of 2008, Brazilian economy wasflooded with short-term foreign capital which substantially appreciated its exchangerate. Immediately, after the fall out of Lehman Brothers and the global crisis, Brazil’s hugeexposure to short-term foreign capital led to rapid depreciation of its currency andmassive fund outflow. After the financial crisis, Brazilian real appreciated more than35 percent against the dollar till October 2009, because of the various economic measurestaken by the regulators and increasing investor enthusiasm for Brazilian assets. Learningfrom the past experience, regulators their in Brazil proposed to impose a 2 percent taxon foreign capital inflows toward equities and fixed-income investments. This policy

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measure was introduced in order to slow the ongoing appreciation of the real againstdollar and other measure currencies. Brazil’s stock market ended 2010 with a whimper,despite strong economic growth. Global concerns about European Government financeshave buffeted the Bovespa stock exchange for much of the year. The strength of theBrazilian real against the dollar also played into the tepid performance, as investorshunted for bargain stocks in developed countries. The disappointing performance forBovespa is a clear outlier among emerging markets, which have largely benefitedfrom the confidence among many investors to take more risks, as well as the rally incommodity prices. This corroborates our findings of very high returns and volatilityspillover between the stock and foreign exchange market in Brazil.

The results presented in Tables V and VI also indicate that returns and volatilityspillover effect from stock market to foreign exchange market is larger than returns andvolatility spillover from foreign exchange market to stock market for IBSA nation. Thismay be due to positive exchange rate volatility on stock returns for some firms offsettingnegative exchange rate volatility on stock returns for other firms to give a weak effectoverall (Morales, 2008). In addition to this, domestic-currency invoicing and hedgingwith exchange rate derivatives may reduce the impact of exchange rate volatility onstock markets. Grant and Marshall (1997) and Bodnar et al. (1995) in their study alsostated that the use of various financial instruments to manage exchange rate risk ispopular among larger and internationally active firm which are the main components ofnational stock market indices to reduce their exposure to exchange rate variations.

A single spillover index is calculated for the returns and volatility separately for eachIBSA nation. These indices are constructed using the information of the stock and foreignexchange rates spillovers for the full sample. The index in Tables V and VI suggests thatapproximately 5.21 percent of forecast variance comes from returns (6.42 percent) andvolatility (4.00 percent) for India, 12.27 percent of forecast variance comes from returns(12.31 percent) and volatility (12.13 percent) for Brazil and 1.51 percent of forecastvariance comes from returns (0.35 percent) and volatility (2.67 percent) for South Africa.This result confirms the findings of Diebold and Yilmaz (2009). The overall resultssuggest the spillovers seem to be important in both returns and volatilities.

4. ConclusionThis study examined the returns and volatility spillover between stock market andexchange rates for the IBSA countries. In order to explore the spillover between twoimportant factors of an economy, first, we applied unit root test to find the stationarityof stock indices and exchange rates for the IBSA nation. The results show that all the dataseries of the variables are non stationary and integrated of order one. Next, we appliedEngle and Granger (1987) methodology to test for the possibility of a cointegratingrelationship. Result shows that there is no cointegrating relationship between stockprices and exchange rates. Then we employed multivariate BEKK GARCH to capture thevolatility transmission between the stock and foreign exchange market for the periodJanuary 2001 to January 2011. In addition, we also used a new methodology known as“spillover index” developed by Diebold and Yilmaz (2009) to examine the returns andvolatility spillover in the two markets for IBSA nations.

The results of multivariate GARCH model suggests the integration between stockand foreign exchange markets and indicates the existence of bi-directional volatilityspillover between stock and foreign exchange markets in the IBSA countries. The results

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123

of the study are consistent with the findings of Mishra et al. (2007) for Indian, Morales(2008) for Brazil and Anoruo and Braha (2009) for South African market. Spilloverresults using the Diebold and Yilmaz (2009) model suggest the bi-directional contributionbetween stock and foreign exchange market, in terms of both returns and volatilityspillovers. This finding corroborates the two hypothesis namely “heat wave” and “meteorwave” proposed by Engle et al. (1990). Overall, our results confirm the presence of returnsand volatility spillovers within the IBSA nations and, in particular the stock markets playa relatively more important role than foreign exchange markets in the first and secondmoment interactions and spillovers.

The study contributes to the literature by extending the existing studies onthe spillover between stock price and exchange rate by investigating the issue for threeemerging economy, India, Brazil and South Africa. Unlike most studies in the literaturewhich focus on multivariate GARCH model, this is the first study which exploresthe issue of returns and volatility spillover between the stock prices and the exchangerates using spillover measure of Diebold and Yilmaz (2009) and much longer and recentdaily data. Moreover, multivariate GARCH with time varying variance-covariance BEKKmodel is used as benchmark against the spillover methodology proposed by Diebold andYilmaz (2009). Thus, we believe that reinvestigating the returns and volatility spilloverbetween the two variables using powerful econometrics methodologies and recent dataset, would contribute to the literature to the emergence of a consensus view on theunderlying issue.

Analysis of returns and volatility spillover is a key research area and so, has seriousimplications for market participants and policymakers. Understanding spilloversources and transmission mechanisms would help in pricing, optimal investment anddecision making. The presence of returns and volatility spillover between stock pricesand exchange rates implies the market inefficiency and lends support to the technicalanalysis. The market participants may consider the relationship between the exchangerate and stock index to predict the future movement of each other effectively. MNCsinterested in exchange rate forecasting may consider the stock market as an importantattribute. There is an interesting implication for portfolio managers too because of thespillover stock and foreign exchange markets. This knowledge would help to create afund which performs well.

Moreover, the results of the two-way returns and volatility spillover between stockand foreign exchange market can also help the regulators and policy makers in IBSAnation to understand the structure of the market in a better way and then design thepolicy, because it may have impact on the development of the financial markets.As rising (falling) stock market would attract capital flows from foreign investors,who sell the foreign (local) currency in substitute for local (foreign) currency. Thus, a rise(fall) in stock prices will appreciate (depreciate) the exchange rates. Moreover, anincrease (decrease) in stock index causes an increment (reduction) in wealth of domesticinvestors thereby increasing (reducing) the demand for local currency and subsequentlypushing up (pulling down) the local interest rates. The raising (lowering) of interest rateswill encourage capital inflows (outflows), resulting in the appreciation (depreciation) ofexchange rates. So, monetary fiscal policies that target the interest rates and exchangerates may get affected because of the booming (falling) stock market. Thus, regulatorsand policy makers can take cognizance of this fact while formulating and implementingthe exchange rates and capital market policies as it can improve the effectiveness of

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monetary policy in achieving its objective. In addition, any policies affecting foreignexchange markets should also account for the impact of shocks from stock market.

Future research can be done by examining the cointegration between exchange ratesand stock market index by including variables like US market data and interest rates.Additionally, we can compare the results on spillover in returns and volatility whenglobal shocks from developed markets are controlled. As a robustness check, we can alsoanalyze whether spillover in returns and in variance is present in different sub-samples.

Note

1. UCSD GARCH Toolbox by Kevin Sheppard can be downloaded from www.kevinsheppard.com/wiki/UCSD_GARCH

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Further reading

Caporale, G.M., Pittis, N. and Spagnolo, N. (2002), “Testing for causality-invariance: anapplication to the East Asian markets”, International Journal of Finance and Economics,Vol. 7 No. 3, pp. 235-45.

About the authorManish Kumar received his BE degree in Mechanical Engineering from Pandit Ravi ShankarShukla University Raipur, India and MS by Research and PhD in Finance from Indian Instituteof Technology Madras, India. Currently, he is working at CRISIL Global Research andAnalytics, Chennai, India. His areas of interest are financial modelling, forecasting, financialtime series analysis and artificial intelligence. Manish Kumar can be contacted at:manishkumar_iitm@yahoo.co.in

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