cointegration relationship and time varying co-movements among indian and asian developed stock...

International Review of Financial Analysis 21 (2012) 10–22

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International Review of Financial Analysis

Cointegration relationship and time varying co-movements among Indian and Asiandeveloped stock markets

Rakesh Gupta a,⁎, Francesco Guidi b,1

a Griffith Business School, Griffith University, 170 Kessels Road, Nathan, Brisbane, Queensland 4111, Australiab Department of International Business and Economics, University of Greenwich, London SE10 9LS, United Kingdom

⁎ Corresponding author. Tel.: +61 737357593; fax: +E-mail addresses: [email protected] (R. Gupta)

1 Tel.: +44 20 8331 9167.

1057-5219/$ – see front matter © 2011 Elsevier Inc. Alldoi:10.1016/j.irfa.2011.09.001

a b s t r a c t
a r t i c l e i n f o
Article history:Received 24 February 2011Received in revised form 13 April 2011Accepted 5 September 2011Available online 16 September 2011

JEL classification:C32G15

Keywords:Stock marketsCointegrationTime-varying correlationsIndiaAsian stock markets

This paper aims to explore links between the Indian stock market and three developed Asian markets (i.e.Hong Kong, Japan and Singapore) using cointegration methodologies in order to explore interdependence.We further estimate the time-varying conditional correlation relationships among these markets. We findthat correlations rose dramatically during periods of crisis and return to their initial levels after the crisis. Fi-nally, we investigated the presence of different volatility regime across stock markets. International investorsmay find useful to model their portfolio by also considering how volatile stock markets are. Results show thatestimated probability of being in the low volatility state is the highest for all stock markets considered, as wellas the probability to switch from a medium- to high-volatility state. Results suggest a short-run relationshipand absence of a strong long-run relationship among these markets. Absence of long-run linkages amongthese markets may provide potential benefits for the investors that look at emerging markets to enhancetheir risk adjusted returns by including emerging markets in their portfolios.

61 7 37357760., [email protected] (F. Guidi).

rights reserved.

© 2011 Elsevier Inc. All rights reserved.

1. Introduction

Increased financial integration among stock markets in the worldmotivates international investors to look for new investment oppor-tunities in order to improve risk adjusted returns for their portfolios.Stocks in different countries are exposed to different factors and assuch by diversifying investments into international stocks investorsget access to the factors that may not be represented in their domesticmarket. In the context of modern portfolio theory diversification bene-fits arise from lower correlations between the assets included in theportfolio by an investor. Incentives for investing into international mar-kets arise from lower correlations between asset returns as comparedwith that of the domestic assets (Grubel, 1968; Levy & Sarnat, 1970).As world markets integrated and the correlations between the returnsof the developed markets increased investors looked at the emergingmarkets for exploiting benefits of international diversification in thebelief that correlations between developed markets and emergingmarkets will be lower. Investments into emergingmarkets for an inves-tor from the developedmarket have been supported by research earlierby Solnik (1991), Divecha, Drach, and Stefak (1992),Wilcox (1992) andrecently by Driessen and Laeven (2007), Chang, Chen, and Lee (2008)

and Gupta and Donleavy (2009). Recent research including Gupta andDonleavy (2009) has demonstrated that correlations are changingover time and may be increasing. If correlations increase the apparentbenefits of diversification into emergingmarkets potentially diminishes(Kearney & Lucey, 2004). Interdependence (in diversification literaturemeasured as correlations) among these markets and developed mar-kets may affect the scope for diversification possibilities (Pretorious,2002). This issue has been broadly investigated by the empirical litera-ture seeking to identify relationship among developed and emergingequity markets. For example Huang, Yang, and Hu (2000) analysedshort and long-run relationships among two leading internationalstock markets (i.e. the USA and Japan) and several Asian emergingmar-kets (China, Hong Kong and Taiwan) for the period 1992–1997.Although some evidence of short-run relationship has been foundamong those markets, cointegration analysis did not find any long-term equilibrium among these markets.

Other authors have focused on the interdependence amongdeveloped equity markets and Eastern Europe emerging markets.For example Syriopoulos (2007) examined both short- and longrun relationships among Central Europe (CE) emerging markets(Poland, the Czech Republic, Hungary, and Slovakia) and severaldeveloped stock markets (Germany and US) during the period1999–2003. Using Johansen Cointegration test, results show thepresence of a long-run relationship among these markets. Economicreforms, the impact of European Monetary Union (EMU) and

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3 Objective of this study is not to estimate the diversification benefits for developedmarkets to invest in India but to test the interdependence of Indian market with that ofthe developed emerging markets. Presence (or absence) of integration may influencethe potential for using these markets for likely diversification benefits.

11R. Gupta, F. Guidi / International Review of Financial Analysis 21 (2012) 10–22

consistent foreign direct investment inflows in the CE economies canbe considered relevant factors explaining the presence of a cointegrat-ing relationship among CE and developed stock markets.2

In another paper, Syriopoulos and Roumpis (2009) examinedinterdependence between several South Eastern European countries'equity markets and two mature equity markets the US and Germany.Results show the existence of a long-run relationship although in theshort term, investment opportunities may arise for investors interestedin diversifying their portfolios in the South East Europe. Through the useof Dynamic Conditional Correlation models, it is shown that stock mar-ket returns of each group of countries are highly correlated, while corre-lations among the groups are lower.

In a study of Sri Lanka and Asian developed markets for the period1989 to 1994 (Elyasiani, Perera, & Puri, 1998) found that there was nointerdependence between the Sri Lankan and the other stock mar-kets. Qiao, Chang, andWong (2008) examined the issue of integrationamong the Chinese stock markets and the Hong Kong stock market,finding bi-directional volatility spill over between the Chinese B-share and Hong Kong markets. Ratanapakorn and Sharma (2002) in-vestigated how short- and long-run relationships changed across fiveregional stock markets for the pre and post 1997 Asian crisis. Resultsshow that no long-run relationships existed before the Asian crisis,whereas some evidence of integration was observed after the crisis.The main conclusion of this study is that the Asian crisis increased in-tegration among these markets. Raj and Dhal (2008) investigated thedegree of integration of India's stock markets with two Asian regionalequity markets (Hong Kong and Singapore) and three leading inter-national markets (Japan, UK, and US). Authors show existence ofcointegration relationship among these markets using multivariatecointegration tests, whereas pair-wise cointegration tests betweenIndia and each of these markets rejected the hypothesis of cointegra-tion. Also the work of Jang and Wonsik (2002) explored whether co-movements among a sample of Asian stock markets (Hong KongIndonesia, Japan, Korea, Singapore, Taiwan and Thailand) changedas a consequence of the 1997 financial crisis. By using the Engle–Grangercointegration test, these authors found that cointegration characterisedonly a small number of countries, while after the crisis the number ofcointegrated stock markets increased dramatically. Authors do notexplain why the financial crisis should have increased integrationamong these markets. Interdependence among Latin American equitymarkets has been investigated only recently. For example, Chen, Firth,and Rui (2002) investigated the interdependence among six LatinAmerican stock markets during the period 1995–2000. Dividing thesample period in several sub-periods based on a number of global andregional financial crises (i.e. the 1997 Asian crisis and the 1998 Russianand 1999 Brazilian crises) these authors showed that Latin Americanstock markets shared a long-term relationship up until 1999. Bivariateand multivariate cointegration tests did not find evidence of a long-run equilibrium relationship after 1999. Other studies have consideredboth Asian and Pacific-Basin stock market relationships in order toanalyse their degree of integration aswell as the effect of 1997 financialcrisis on their equity markets. For instance Chelley-Steeley (2004)explored the speed of market integration among developed andemerging Asia-Pacific equity markets. Results show that integrationamong emerging Asia-Pacific countries tends to be faster than the inte-gration between emerging and developed markets. In another study,Chi, Li, and Young (2006) examined whether the level of integrationof several Asian emerging equity markets with both the Japanese andthe US equity markets changed as a consequence of the 1997 financialcrisis results confirm that the integration increased immediately after

2 It must also pointed out that these CE economies have joined to the EU in 2004after a process characterised by relaxing trade rules and alignment of legal infrastruc-tures. As pointed out by Aggarwal and Kyaw (2005), countries that are part of a com-mon market may have their stock markets characterised by a higher level of financialintegration.

the crisis. Singh, Kumar, and Pandey (2010) look at the price and vola-tility transmission across North American and Asian stock markets andfind evidence of regional influence in the linkages.

This paper contributes to the empirical literature by analysing theexistence of a long-run relationship between the Indian and severalAsian developed markets; that is Hong Kong, Japan and Singaporemainly through cointegration methodologies.3 Investors using modernportfolio theory use correlations as measure of asset co-movements asinput into portfolio optimisation problem in determining asset alloca-tions. If they are not integrated and have lower correlations there maybe potential benefits in considering these markets for a possible inclu-sion in the portfolio. Studying the integration of India with majorAsian stock markets is an interesting research topic for several reasons.Firstly foreign portfolio investments (FPI) into Indian stock markets in-creased dramatically in the last decade. In 1999–2000 portfolio invest-ment inflow into India was US$ 2.15 billion, by the end of 2008 Indiaattracted more than US$ 32 billion (Reserve Bank of India, 2009). Inthe light of increase in FPI it is worth investigating integration of India'sfinancial markets with the equity markets of other countries. Secondly,the Indian stock market has not been immune, like many other coun-tries, from the recent international financial crisis. For instance the re-cent subprime mortgage crisis which triggered a global financial crisisalso affected the Mumbai Stock Exchange, which lost 11.6% of itsvalue on the ‘Black Friday’ of the October 24, 2008. As a result it seemsto be appropriate to explore the degree of correlation between Indiaand other Asian markets in order to find out whether interdependencebetween Indian and Asian stockmarkets tends to strengthen during pe-riods of financial crisis.4 The US equitymarket forms approximately halfof the global equity market and it may have significant impact on wehypothesise that the relationship between the four Asian stockmarketsmay be driven by a common shock originated in the U.S. stock market.

We select theHongKong, Singapore, Japan andUS stockmarkets be-cause they are themost important in terms of size at Asian level andU.S.at global level. As Table 1 indicates, these stock markets are large incomparison with their national economies as shown by the ratio ofmarket capitalisation to GDP. On average Hong Kong and Singaporehave the largest capital markets relative to their own economy.5

Stock/GDP ratio measures the development of stock markets. ForHong Kong this ratio on average is 211.42%, which is the highestamongst the sample of Asian stock markets. Turnover ratio measuresthe value of stock transactions relative to the size of the market, and isfrequently used as ameasure ofmarket liquidity. Based on this measurethe Indian stock market has been the most liquid with respect to otheremerging stock markets during the period 2000–2008.

Chambet and Gibson (2008), argue that increasing trade opennesspositively contribute to financial market integration among countries.Also Pretorious (2002) argue that strong bilateral relationship in-crease the level of interdependence between stock markets. Studyby Chen and Zhang (1997) shows that countries with strong economicties in terms of trade tend to have financial markets thatmove together.Chinn and Forbes (2004) show that bilateral trade flows are the mostimportant determinant of cross-country linkages in stock markets. Allcountries considered in the present studies, are important trade part-ners in the international trade with India. Since 2000s, trade amongIndia and these countries increased significantly in terms of value

4 Other reasons of selecting Indian market in the analysis are the following are; Indiais a large emerging economy with a well developed and transparent financial system,legal system in India is similar to the western democratic countries and reliable datafor India is available.

5 As pointed out by Freixas, Hartmann, and Mayer (2008) the size of capital marketwith respect to the economy is important given that economies with larger overallcapital markets are able to provide easier financing for real investment.

Table 1Features of sample stock markets.Source: World Development Indicators.

2000 2001 2002 2003 2004 2005 2006 2007 2008 Average

CAP/GDP ratioIndia 32.18 23.10 25.83 46.56 55.33 68.27 89.51 154.57 55.68 61.22Hong Kong 368.61 303.78 282.75 347.63 401.03 390.10 471.35 561.44 217.59 371.58Japan 67.64 54.98 54.26 71.90 79.86 104.05 108.34 101.67 65.58 78.69Singapore 164.83 136.99 115.36 246.04 252.59 261.83 198.55 211.73 98.94 187.42USA 154.68 137.50 106.53 130.79 140.35 137.26 148.10 145.16 83.29 131.51

Stock/GDPIndia 110.78 52.17 38.86 47.51 54.08 53.56 69.79 94.11 90.56 67.93Hong Kong 223.43 117.87 128.62 153.64 169.73 165.44 212.65 442.79 288.66 211.42Japan 57.72 44.59 40.15 53.75 74.48 109.78 143.32 148.32 119.46 87.95Singapore 98.67 74.01 63.54 94.27 74.15 99.07 132.48 230.15 148.89 112.81USA 326.30 288.22 243.54 142.53 166.41 173.97 255.63 310.10 258.76 240.60

TurnoverIndia 133.64 191.40 225.82 138.54 115.47 94.20 93.06 84.00 85.19 129.03Hong Kong 61.30 34.80 43.48 56.32 55.70 49.27 59.98 89.10 81.84 59.08Japan 69.90 67.90 71.00 87.99 103.46 118.78 132.15 141.60 153.23 105.11Singapore 52.10 46.90 39.29 71.14 51.23 63.09 62.19 122.00 101.34 67.69USA 200.80 201.30 202.51 122.81 126.54 129.10 182.81 216.50 232.26 179.40

Notes. CAP/GDP is the market capitalization of listed companies as percentage of GDP. Stock/GDP is the total values of shares traded as percentage of GDP. Turnover ratio is the totalvalue of shares traded divided by the average market capitalization.

Table 2India international trade, 2000–2009.Source: ESDS International.

2000 2001 2002 2003 2004 2005 2006 2007 2008 2009

India's export toHong Kong 2608 2087 2551 3099 3553 4276 4628 5899 6572 6176Japan 1767 2010 1775 1747 1910 2392 2767 3606 3214 3390Singapore 826 1016 1309 1949 3377 5069 5908 7042 7997 5101USA 9083 9335 10,308 11,363 12,839 16,475 18,515 20,285 20,851 20,039

India's import fromIndiaHong Kong 843 1322 911 1362 1656 2087 2414 2645 5482 7425Japan 2015 2133 1913 2459 2921 3854 4461 5891 7285 6964Singapore 1481 3017 1402 1922 2457 3178 4955 7460 7603 10,178USA 3152 4140 4129 4890 5981 8848 11,172 18,708 18,888 18,108

Notes. Both export and import values are in millions of US dollars.

12 R. Gupta, F. Guidi / International Review of Financial Analysis 21 (2012) 10–22

(Table 2). However the trade integration6 among India and countriesconsidered in the present study do not seem to have a clear trend(Fig. 1). This could mean that we may expect a low level of integrationamong the stock markets of the countries considered.7

Our study attempts to identify long-run relationship of India withstock markets Hong Kong, Japan and Singapore from the perspectiveof international investor from these countries seeking to diversifyhis/her portfolio in the closest emerging economy like India. Therest of the paper is organised as follows. Sections 2 and 3 introducemethodologies and data used in this study. Section 4 discusses empiricalresults, Section 5 presents some policy implications while Section 6concludes with some key findings of this study.

2. Methodology

This study uses different techniques to analyse the relationshipsamong the Indian, US and developed Asian stock markets. The first

6 Following Baele and Inghelbrecht (2009) we calculate the Trade Integration Indexas the ratio of imports plus exports over GDP, then we transform those values as indi-ces starting at 100 at the beginning of the sample. GDP values come from World Devel-opment Indicators.

7 Masih and Masih (1999) argue that one of the factors affecting the degree of inter-dependence among Asian stock markets is certainly due to the level of trade amongthese countries. However another important factor is that some of these countries tendto have the same monetary policy.

one we used was the Engle–Granger cointegration methodology(Engle & Granger, 1987) which is based on analysing stationarity oferror term series obtained from the equation derived with levelvalues of time series that are not stationary on the level but becomestationary when their difference is taken. If the error term series isstationary, this means that there is a cointegration relationshipbetween the mentioned two time series. In the first step of this proce-dure we estimated the following equation:

yt ¼ β0 þ β1xt þ et ð1Þ

where yt and xt are two different stock market indices. The estimatedresiduals et from the above equation are considered to be temporarydeviation from the long-run equilibrium, then they were investigatedby using the following ADF unit root test:

Δ et ¼ α1et−1 þ∑n

i¼2αiΔ et−i þ εt ð2Þ

where α are the estimated parameters and εt is the error term. Thecointegration test is conducted by a hypothesis test on the coefficientα1. If the t-statistic of the coefficient exceeds a critical value, then theresiduals from Eq. (1) are stationary, and thus the two stock marketsyt and xt are cointegrated. (i.e. they move together in the long-period).

8 Chu (2010) uses Granger causality test cointegration analysis to estimate pricelinkages between Hong Kong mandatory fund and the stock market.

9 Malik and Ewing (2009) use bivariate GARCH model in their test of volatility trans-mission between oil prices and equity sector returns.

60

80

100

120

140

160

180

2000 2002 2004 2006 2008

India & Hong KongIndia & Singapore

India & USAIndia & Japan

Fig. 1. Trade integration index, 2000–2009.


Thenext technique usedwas the Johansen'smethodology (Johansen,1988, 1991) which takes its starting point in the vector autoregression(VAR) of order p given by:

zt ¼ cþ A1zt−1 þ…þ Apzt−p þ μt ð3Þ

where zt is an n×1 vector of variables that are integrated of order one—commonly denoted I(1)— and μt is a zero mean white noise vector pro-cess. This VAR can be re-written as:

Δzt ¼ cþΠzt−1 þ ∑p−1

i¼1ΓiΔzt−i þ μt ð4Þ

whereΠ ¼ ∑i¼1

p

Ai−I and Γi ¼ −∑j¼iþ1

p

Aj. If the coefficient matrix has re-

duced rank rbn, then there exist n×rmatrices α and β eachwith rank rsuch that ¼ αβ′ and β′zt is stationary. r is the number of cointegrationrelationships, the elements of α are known as the adjustment parame-ters in the vector error correction model and each column of β is a coin-tegrating vector. It can be shown that for a given r, the maximumlikelihood estimator of β defines the combination of zt−1 that yieldsthe r largest canonical correlations of zt with zt−1 after correcting forlagged differences and deterministic variables when present. Johansenproposed two different likelihood ratio tests of the significance ofthese canonical correlations and thereby the reduced rank of the matrix,that is the trace (λtrace) andmaximumeigenvalue (λtrace) test, which arecomputed by using the following formulas:

λtrace ¼ −T ∑k

j¼rþ1ln 1−λj

� �ð5Þ

λmax ¼ −T ln 1−λrþ1

� �ð6Þ

where T is the sample size, λj and λrþ1 are the estimated values of thecharacteristic roots obtained from the matrix. The trace test tests thenull hypothesis of r cointegrating vectors against the alternativehypothesis of n cointegrating vectors, while the maximum eigenvaluetests the null hypothesis of r cointegrating vectors against the alterna-tive hypothesis of r+1 cointegrating vectors.

Gregory, Nason, and Watt (1996) through a series of simulationtests showed that the power of the Engle and Granger (1987) cointe-gration test is dramatically reduced if a break in the cointegration re-lationship occurs. In order to overcome this drawback, Gregory andHansen (1996) proposed a new test which allowed for breaks in thecointegration relationship. In particular the Gregory–Hansen testtests the null hypothesis that the series are not cointegrated againstthe alternative of cointegration with a single structural break of un-known timing. The timing of a structural break changes under the al-ternative hypothesis if it is estimated endogenously. Gregory andHansen suggest three alternative models accommodating changes inparameters of the cointegration vector under the alternative. Thefirst one (Eq. (7)) is the so-called level shift model (or C model)

that allows for the change in the intercept only. The second model(Eq. (8)) accommodating a trend in data also restricts a shift only tothe change in level with a trend (C/T model). The last model(Eq. (9)) allows for changes both in the intercept and slope of thecointegration vector (or C/S model).

yt ¼ μ0 þ μ1φτ þ αxt þωt ð7Þ

yt ¼ μ0 þ μ1φt þ βt þαxt þωt ð8Þ

yt ¼ μ0 þ μ1φt þα1xt þα′2φτxt þωt ð9Þ

The dummy variable φt which captures the structural change isdefined as follows:

φt ¼ 10

ifif

t>τt≤τ

�ð10Þ

where τ∈(0,1) is a relative timing of the change point. Eqs. (7)–(9) areestimated sequentially with the break point changing. Non-stationarityof the obtained residuals, is checked by the ADF test. Setting the teststatistics to the smallest value of the ADF statistics in the sequence,we selected the value that constitutes the strongest evidence againstthe null hypothesis of no cointegration.

We also conducted the causality test based on Granger's approach(Granger, 1969)8 in order to see any influence between stock marketshere considered. In order to test for Granger causality, we consideredtwo stock market indices xt and yt, then we estimated the followingequations:

Δxt ¼ β0 þ∑n

i¼1β1iΔxt−1 þ∑

m

i¼1β2iΔyt−1 þ ε1t ð11Þ

Δyt ¼ δ0 þ∑n

i¼1δ1iΔyt−1 þ∑

m

i¼1β2iΔxt−1 þ ε1t ð12Þ

After estimating the Granger-causality we run an F-test for jointinsignificance of the coefficients. Assuming the null hypothesis thatxt does not Granger cause yt and vice versa, a rejection of the null hy-pothesis shows a presence of Granger causality. The Granger causalitytests are performed for each pair of stock indices.

A further issue we are going to investigate is the time varying cor-relations among stock markets. In order to explore the issue we usedthe Dynamic Conditional Correlation specification of the MultivariateGARCHmodel developed by Engle (2002).9 In particular we consideredthe following DCC-GARCHmodel for a 2-dimensional vector process fortwo stock markets stock returns which is given by the following condi-tional mean equation:

yt ¼ E yt=It−1ð Þ þ rt ð13Þ

where It−1 is the information set at time t−1. Each univariate errorprocess has the specification ri, t=hi, t

1/2εi, t, and the conditional varianceE(ri, t2 /It−1)=hi, t follows a univariate GARCH(1,1) process, that is:

hi;t ¼ αi0 þαi1r2i;t−1 þ βi1hi;t−1 ð14Þ

with the non-negativity and stationarity restrictions imposed. The con-ditional correlations are allowed to be time-varying by following theGARCH(1,1) model given by:

qi;j;t ¼ Pρi;j 1−α−βð Þ þ αεi;t−1 þ βqi;j;t−1 ð15Þ

Table 3Summary statistics of daily returns.

BSE 30 Hang Seng Nikkei 225 S&P100 STI

N. obs 2557 2557 2557 2557 2557Mean 0.042 0.011 −0.023 −0.019 0.001Maximum 15.989 13.406 13.234 10.655 7.530Minimum −11.809 −13.582 −12.111 −9.186 −8.695Std. dev. 1.759 1.667 1.589 1.389 1.347Skewness −0.145 −0.022 −0.318 −0.031 −0.232Kurtosis 9.157 11.277 9.955 10.286 7.385Jarque–Bera test 4048.874 7302.785 5197.005 5656.989 2070.953Probability 0.00 0.00 0.00 0.00 0.00

Notes: All daily returns were calculated as log differences using daily closing prices.

11 Roll (1992) argues that the low correlations among international stock markets


where qi, j, t is the time-varying covariance of εt, ρi;j is the unconditionalvariance of εt, while α and β are nonnegative scalar parameters.

Eventually, in this work we also focus on the volatility of stockmarkets. The main reason is that volatility is a measure of the riskof the expected returns. Assuming that there are two state of highand low volatility and that low returns are associated with low vola-tility and high returns with high volatility, as well as the hypothesisthat volatility is not constant in the two regimes, we use SWARCHmodels developed by Hamilton and Susmel (1994) in order to esti-mate the probability of switching from low volatility to high volatilityregimes In order to obtain such results, we considered the followingset of equations:

rt ¼ cþ ut ð16Þ

ut ¼ffiffiffiffiffiffigst

pεt ð17Þ

εt ¼ffiffiffiffiffiht

qvt ð18Þ

ht ¼ α0 þ∑q

i¼1αiε

2t−i ð19Þ

where gst is a switching factor with value g1 when the process is in theregime represented by state 1 and g2 when the process is in the state 2and so on. Our main difference with the Hamilton and Susmel (1994)work, is that we considered three states of stock index: a low volatilitystate (that is g1) a medium volatility state (g2) and a high volatilitystate (g3). In this perspective the subscript st in Eq. (17), denotes a latentstate variable which can take on the values 1,2,…, or K: given that weconsidered three states of the stock markets we have that K=3. By sodoing, we can say that structural shifts are indicated as changes in therange of the conditional variance process. We note that εt is a standardARCH (q) setting. Further when st=1(st=2), we obtain ut throughmultiplying εt by

ffiffiffiffiffig1

p ffiffiffiffiffig2

p� �. By setting g1=1, we can say that the vola-

tility of state 2 (3) is g2(g3) times state 1. Following Hamilton andSusmel (1994), st is assumed to follow a first-order Markov process.For the two state (K=2) case, the Markov transition probabilities are:

p½st ¼ 1 st−1 ¼ 1j � ¼ p11; p½st ¼ 2 st−1 ¼ 1j � ¼ p12p st ¼ 2 st−1 ¼ 2j � ¼ p22; p st ¼ 1 st−1 ¼ 2j � ¼ p21½½

Extensions to KN2 are simple. Hamilton and Susmel (1994) demon-strate that the process for st is strictly stationary and can be representedas an AR(1) process. We will call this model for ut as a K-state, q-orderMarkov switching model or SWARCH (k,q), where q is the number oflags in the ARCH process.

3. Data

The sample consists of daily closing stock index prices of India(BSE 30), Hong Kong (Hang Seng), Japan (Nikkei 225), U.S. (S&P100) and Singapore (STI) from August 31, 1999 to June 17, 2009. Allindices have been obtained from Thomson Financial Datastream andthey are in domestic currency in order to avoid problems associatedwith transformation due to fluctuations in exchange rates.10 Table 3shows that during the sample period, the BSE index had the highestaverage rate of returns followed by the Hang Seng index. The stan-dard deviation of returns on BSE is higher than the standard deviationof returns on Hang Seng, Nikkei, S&P100 or STI. All returns have nega-tive skewness implying that the distribution has a long right tail,while the kurtosis values are high in all cases implying that the distribu-tion are peaked relative to normal. The Jarque–Bera test indicates that

10 It must also be pointed out that Thomson Financial Datastream database treats pub-lic holidays as missing data, replacing them by figures calculated by linearinterpolation.

returns of the stockmarkets are not normally distributed for the sampleperiod used here.

Fig. 2 plots both the index values and returns for India, Hong Kong,Japan, Singapore and US. The Nikkei index observed a steep fall duringthe period 2000–2003. From 2003 to 2007 an upward trend is commonacross all markets. From the second half of 2007 we observe a dramaticdecline of stock prices across all markets, whereas some increases seemto characterise the second quarter of 2009. Asian as well as US stockmarket returns show evidence of volatility clustering, that is, as pointedout by Campbell, Lo, and MacKinlay (1997), small returns are followedbymore small returns (low volatility periods) and large returns tend tobe followed by more large returns (high volatility periods). The 2007–2009 financial crisis seem to be the longer and more intense period ofhigh volatility during 2000s reflecting large uncertainty and loss of con-fidence among market participants. As we can see in Fig. 1, almost allstock markets returns reached the highest level of volatility in Septem-ber 2008 when the US government, decided to put two government-sponsored enterprises (GSE), i.e. Fannie Mae and Fannie Mac, into thecontrol of Federal Housing Finance Agency (FHFA).

Table 4 reports the unconditional correlation of the returns of thefour Asian markets. We can observe that the highest correlation is be-tween the STI and Nikkei (over 68%) while surprisingly the lowest isbetween S&P and Nikkei (about 11%).11 Partitioning the period intotwo sub-periods we observe that correlations among stock marketschange over time. An increased level of correlation among India andAsian stock markets is evident during the second half of 2000s(Table 4, panel A).

4. Empirical results

A necessary condition to perform a cointegration test is that theorder of integration of variables has to be the same. In order to detectthe order of integration we employed two unit root test, that is theAugmented Dickey–Fuller (ADF) test (Dickey & Fuller, 1979) andPhillips–Perron (PP) test (Phillips & Perron, 1988). Unit root tests re-sults are shown in Table 5. The null hypothesis of a unit root is notrejected for all indices in log levels, whereas it is rejected when theyare taken in their log first differences.

4.1. Engle Granger cointegration test

If stock markets have a cointegration relationship, the residualerror series of each of the equations estimated in the first step, shouldhave stationarity.12 We check whether residuals of the above equa-tion satisfy these requirements. Results (Table 6) show that there isno long run relationship between BSE and other Asian equity

may be due to reasons like indices construction, differences in the industrial structureas well as in the conduct of national monetary policies.12 First step of Engle Granger method requires estimation of long-run equation usingordinary least squares. Results of this step are omitted here for brevity.

0

5000

10000

15000

20000

25000

-.2

-.1

.0

.1

.2

00 01 02 03 04 05 06 07 08

BSE DLBSE

8000

12000

16000

20000

24000

28000

32000

-.2

-.1

.0

.1

.2

00 01 02 03 04 05 06 07 08HANG SENG DLHANGSENG

Prices ReturnsPrices Returns

Prices Returns

Prices Returns

Prices Returns

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NIKKEI DLNIKKEY

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STI DLSTI

Fig. 2. Daily prices and returns of sample stock indices.

13 Theoretical rational for differing lag length is the different weight assigned to thepenalty term for the number of parameters (Lütkepohl, 2005).14 SC indicated a VAR(1) but residuals were correlated.


markets. This is done by using the specification of the ADF withouttrend. While there is weak evidence of a cointegration relationshipbetween BSE and other Asian stock markets when the ADF test withtrend and intercept is used, no evidence of long-run relationship be-tween Indian and US stock market was found. Because the visual in-spection of the residuals of Engle–Granger equations showsevidence of trend we consider the results of ADF test with trendand intercept more reliable. We infer that there is a long-run relation-ship between BSE and Asian stock markets, while no relationship ex-ists among BSE and the U.S. stock markets.

4.2. Johansen cointegration test

In order to further investigate cointegration results, we employJohansen cointegration test. Johansen's procedure requires estimatinga VAR(p). In order to estimate the optimal number of lag p of the VARwe used both the Akaike Information Criterion (AIC) and the SchwarzCriterion (SC). When we estimated the VAR with BSE and Nikkei in

log form, the AIC selects a VAR model with 7 lags, while the SC selectsa model with 2 lags.13 We estimated the VAR(2) model selected bythe SC given that it is the more parsimonious in terms of coefficientsto estimate. However checking for the serial correlation of the resid-ual series through the autocorrelation LM test, we rejected the nullhypothesis of no serial correlation. In order to eliminate serial corre-lation, we estimated a VAR(4). Checking for the serial correlationwe were not able to reject the null hypothesis of no serial correlationof the residual series. We also find that BSE and HangSeng indicesseem to be best represented by a VAR of order 5. Further a VARwith 2 lag lengths was estimated for BSE and STI equity market indi-ces. For BSE and S&P100, VAR(5) did not reject null hypothesis of nocorrelation in the residual series using LM test.14 After estimating theVARmodels with the optimal number of lags we were able to conduct

Table 4Correlations of stock index returns August 31, 1999 through June 17, 2009.

BSE 30 Hang Seng Nikkei 225 STI S&P 100

Panel A: 1999–2009BSE 30 1Hang Seng 0.448 1Nikkei 225 0.318 0.577 1STI 0.465 0.688 0.520 1S&P 100 0.176 0.188 0.110 0.206 1

Panel B: 1999–2004BSE 30 1Hang seng 0.276 1Nikkei 225 0.224 0.486 1STI 0.303 0.596 0.424 1S&P100 0.057 0.123 0.119 0.163 1

Panel C: 2004–2009BSE 30 1Hang seng 0.565 1Nikkei 225 0.389 0.642 1STI 0.592 0.757 0.597 1S&P100 0.274 0.238 0.103 0.243 1

Table 5Results of the unit root tests.

Lag length p ADF P-valuea Bandwidth PP P-valuea

Variables in log levelBSE 30 0 −0.228 0.932 10 −0.262 0.927Hang Seng 0 −1.423 0.572 5 −1.375 0.596Nikkei 225 0 −1.689 0.436 8 −1.588 0.488STI 0 −1.235 0.660 5 −1.292 0.635S&P 100 0 −1.345 0.610 8 −1.382 0.592

Variables in first log differenceBSE 30 0 −47.805 0.001 13 −47.768 0.00Hang Seng 0 −51.542 0.00 4 −51.558 0.00Nikkei 225 1 −38.051 0.00 9 −51.468 0.00STI 0 −49.178 0.00 3 −49.183 0.00S&P 100 1 −40.682 0.00 9 −56.484 0.00

Notes. The critical value for both the ADF and PP t-statistics are−3.43,−2.86, and−2.56at 1%, 5% and 10% levels of significance respectively. For both tests, a constant term wasincluded. For the ADF test the optimal lag lengths are determined by using the AIC witha maximum lag of 26. For the PP test the spectral estimation method is the Bartlettkernel, while the Bandwidth is the Newey-West.

a MacKinnon (1996) one-sided P-values.


the Johansen cointegration test at both bivariate andmultivariate levels.Empirical findings (Panel A of Table 7) do not support the presence ofthe cointegrating vector in the BSE and Nikkei stock markets. The nullhypothesis that BSE and Nikkei market are not cointegrated (r=0)against the alternative of one cointegrating vector (r≤1) is not rejected,since both the λtrace and λmax statistics do not exceed the critical valueswith 5% level of significance.

We found no evidence of cointegration on a bivariate basis be-tween the Indian and other developed markets; we also test if thesemarkets, as group, could be cointegrated. A multivariate Johansentest was carried out15 to test if these markets as group are cointe-grated. The results (Panel B of Table 7) indicate that there is nolong-term relationship among the five stock markets. The absence oflong-run relationship shows an evidence of limitedfinancial integrationamong these markets. As pointed out by Chinn and Forbes (2004)where economic and industrial structures in countries differ then thedegree of financial integration between markets can also be different.

4.3. Gregory and Hansen cointegration test

Structural changes can manifest themselves through changes inthe long-run relationship either in the form of a change in the inter-cept, or a change in the cointegrating vector. So the power of standardtests for the null hypothesis of no-cointegration can be substantiallyreduced (Gregory & Hansen, 1996; Gregory et al., 1996). In order toovercome this problem we applied the methodology of Gregory andHansen (1996) to identify structural changes whichmay affect the re-sults of the cointegration test. The Gregory–Hansen test results(Table 8) show that null hypothesis of no cointegration is rejectedunder all the models (C/S, C/T, and C) considered when we analysedthe pairwise relationship between India and each of the other Asianstock markets. On the other side, the null hypothesis is not rejectedwhen we consider India and US stock markets. From the Gregoryand Hansen results wemay conclude that there is a long-run relation-ship among India and developed Asian markets, this also means thatalthough these markets may have a different path from each other inthe short run, they will stay close to each other in the long-run. Otherstudies have also found these methods to provide conflicting results.

15 We used a VAR(9) for the multivariate cointegration test. Initially we used a parsi-monious VAR(5) selected using AIC against a VAR(7) indicated by SC; however bothmodels show existence of serial correlation among residuals. After several trials weopted for a VAR(9) where there is no evidence among residuals as indicated by auto-correlation LM test.

For instance, Fernandez-Serrano and Sosvilla-Rivero (2001) studyingthe long-run relationship between Japan and several emerging Asianstock markets, found that the Johansen test found no cointegrationwhile the Gregory and Hansen test showed evidence of long-run rela-tionship between Japanese andTaiwanese aswell as Japanese andKore-an equity markets. The results from the cointegration tests areconflicting; to identify true nature of relationship among these marketswe use other techniques in the following sections.

4.4. Granger-causality test

Given that the indices are difference stationary and the cointegra-tion results do not show clear evidence of robust cointegration be-tween them we use a further methodology. Égert and Kočenda(2007) argue that given the lack of cointegration among markets, avalid tool remains the well known Granger causality test in order toidentify the relationship among these markets. Results (Table 9)show that there is bilateral or feedback causality between BSE andHang Seng stock market. Direction of causality is from BSE to Nikkei;however, there is no reverse causation from Nikkei to the BSE stockindex. We found that the STI causes the BSE market returns and viceversa. Finallywe also found that S&P100Granger cause BSE stockmarket.

Granger-causality test16 reported in Table 9 does not consider thepossible structural breaks implied by the Gregory and Hansen cointe-gration test reported in Table 8. The main reason is that structuralbreak dates seem to be quite heterogeneous. However we test howthe recent global financial crisis has affected causality between theIndia's stock market return and those of other Asian stock market.As pointed out by Kenc and Dibooglu (2010), the 2007–2009 globalfinancial crisis started in US on July 2007 as a consequence of the col-lapse of two Bear Sterns hedge funds. The financial crisis caused aslowing of the growth in large emerging economies in Asia (likeChina and India) in early 2008 (Fidrmuc & Korhonen, 2010). Howeveras indicated by Bartram and Bodnar (2009), the global equity marketcrisis can be dated around September 15, 2008, the day of LehamnBrothers bankruptcy. In order to test how the global financial crisishas affected causality between India's stock market return and thoseof other Asian stock market and the US market we divide our samplein two sub-samples. The first one from the August 31, 1999 to September

16 Granger-causality test may sound misleading in the sense that it if a variable some-how causes another to change. However, test does not identify true causality but re-sults merely indicate lead-lag relationship between the variables thus a leadingvariable is assumed to cause change. In this section for simplicity we will use “cause”to mean Granger-cause.

Table 8Test for structural breaks — Gregory and Hansen (1996) cointegration test.

Modelspecification

Breakpoint GH teststatistic

5% Criticalvalue

Ho: Nocointegration

BSE 30 and Hang Seng stock markets returnsFullbreak (C/S) 2000:08:15 −21.826 −4.95 RejectTrend (C/T) 2003:5:20 −21.612 −4.99 RejectConstant (C) 2002:11:05 −21.557 −4.61 Reject

BSE 30 and Nikkei 225 stock markets returnsFullbreak (C/S) 2003:05:06 −23.258 −4.95 RejectTrend (C/T) 2007:11:12 −23.325 −4.99 RejectConstant (C) 2003:05:06 −23.255 −4.61 Reject

BSE 30 and STI stock markets returnsFullbreak (C/S) 2001:09:06 −21.378 −4.95 RejectTrend (C/T) 2007:12:31 −21.350 −4.99 RejectConstant (C) 2002:11:04 −21.295 −4.61 Reject

BSE30 and S&P100 stock market returnsFullbreak (C/S) 2006:05:19 −2.754 −4.95 Do not rejectTrend (C/T) 2003:06:25 −3.569 −4.99 Do not rejectConstant (C) 2005:10:20 −2.976 −4.61 Do not reject

Notes: The critical values for the Gregory–Hansen tests are drawn from Gregory andHansen (1996).

Table 6ADF test results on Engle–Granger cointegration test residuals.

Stockmarkets

ADF test statisticwithout trend

ADF test statistic withtrend and intercept

BSE and HangSeng −1.7 −3.224*BSE and Nikkei 0.129 −3.474**BSE and STI −1.617 −3.210*BSE and S&P −0.039 −2.674

Notes. In the ADF test, critical values are −3.432, −2.862, and −2.567 on modelswithout trend, and −3.961, −3.411, and −3.1247 on models with trend for 1%, 5%,10% levels. Three/two/one stars rejections of the null hypothesis of a unit root at the1%, 5%, and 10% levels.

Table 9Granger-causality test for returns, 1999–2009.

F-statistic Probability

BSE 30 does not cause Hang Seng market 10.990 0.00Hang Seng does not cause BSE 30 market 2.645 0.071BSE30 does not cause Nikkei 225 market 37.906 0.00Nikkei 225 does not cause BSE 30 market 1.2 0.301BSE 30 does not cause STI market 4.179 0.015STI does not cause BSE 30 market 6.273 0.001BSE30 does not cause S&P100 market 0.093 0.910S&P100 does not cause does not BSE30 50.936 0.00


14, 2008, while the second one is from September 15, 2008 to June 17,2009. Granger-causality tests for both samples (see Tables 10 and 11)show that before the crisis BSE market did not cause Hang Seng, whileafter the crisis BSE did cause Hang Seng, while Hang Seng affected BSEstock market before and after the above mentioned crisis. We alsofound that before crisis S&P100 cause BSE30 stock index while afterthe crisis S&P100 index do not cause BSE30. Overall during the currentfinancial crisis Granger results indicate that the influence of Asian aswell as US stock markets on the Indian stock index has totally disap-peared. These stock markets do not cause BSE after September 2008.Analysing the interdependence among Indian and international stockmarkets during the period 2000–2007, Dicle, Beyhan, and Yao (2010)apply the Granger-causality test and find that Indian stock marketshave strong causal dependence with international stock markets con-firming our results coming from the whole sample as well as for thefirst-subsample we considered. To conclude after recent worldwide fi-nancial crisis the stock market in India remains isolated from shockscoming from developed stockmarkets considered in this study. This re-sultmay be surprising given the importance of the Indian economybothat regional and global levels.

4.5. Dynamic Conditional Correlation results

Recognising that constant correlation coefficients are notable to show the dynamic market conditions in response to

Table 7Tests for the number of cointegrating vectors.

Panel A: Bivariate Johansen cointegration results

λtrace Critical value 5% λmax Critical value 5%

BSE 30 and Nikkei 225 market indicesr=0 2.697 15.494 2.687 14.264r≤1 0.009 3.841 0.009 3.841

BSE 30 and Hang Seng market indicesr=0 7.042 15.494 6.852 14.264r≤1 0.189 3.841 0.189 3.841

BSE 30 and STI market indicesr=0 4.4 15.494 4.354 14.264r≤1 0.046 3.841 0.046 3.841

BSE30 and S&P100r=0 3.121 15.494 2.968 14.264r≤1 0.152 3.841 0.152 3.841

Panel B: Multivariate Johansen cointegration results

λtrace Critical value 5% λmax Critical value 5%

BSE 30, Hang Seng, Nikkei 225, STI and S&P 100r=0 57.698 69.818 23.795 33.876r≤1 33.903 47.856 17.288 27.584r≤2 16.615 29.797 12.768 21.131r≤3 3.846 15.494 3.686 14.264r≤4 0.160 3.841 0.160 3.841

Notes: The 5% critical values provided by MacKinnon, Haug, and Michelis (1999)indicate no cointegration.

innovations,17 we estimate DCC-GARCH model proposed by Engle(2002). The parameter estimates of the DCC-GARCH model arereported in Table 12. From the table we can see that the estimatesof the mean equations and variance equations are statisticallysignificant which are consistent with the time varying volatilityhypothesis. In addition the sum of estimated coefficients in thevolatility equations is close to unity, this means that volatility exhibitsa highly persistent behaviour for each pair-wise correlation amongstock markets. The estimated coefficients on the persistence (qi, j, t−1)of the time varying correlation are quite similar in each of the bivariateDCCmodels estimated aswell as the coefficients that show the effects ofthe most recent co-movements (εi, t−1εj, t−1).

The dynamic time varying correlations obtained from the aboveDCC-GARCH models are plotted in Fig. 3. All graphs show evidenceof varying patterns in the correlation dynamic path, which is the rea-son for using the DCC-GARCH modelling strategies. Considering theBSE and Hang Seng stock market returns, the plotted DCC correlationshave a lowest value of 0.083 in November 1999 and the highest of0.955 in October 2009, correlations among BSE and STI range be-tween 0.119 and 1.00, correlations between BSE and S&P100 rangebetween the lowest value of 0.092 in July 2004 and the highest of0.43 in July 2008. BSE correlations with Nikkei vary between 0.071and 0.570. We note that correlations between BSE and Nikkei returnshave remained the lowest of the four sets of correlations. From Fig. 3,during the period of the Twin Tower attacks (September 11, 2001),the correlation between BSE and Asian developed equity markets

17 Longin and Solnik (1995) indicate several reasons why correlations among stockmarkets are not constant over time. They are the presence of a time trend, as well asthe presence of threshold and asymmetry. The first reason is associated to the progres-sive removal of impediments to international investments. The second is due to com-mon factors that affect international markets at the same time.

Table 12Results of bivariate DCC-GARCH (1,1) models on daily return indices.

Panel A — BSE 30 and Hang Seng markets

BSE 30 Hang Seng

I. Returns equations E(yi, t/It−1)=yi, t−ri, tConstant 0.001***(2.24e−04) 6.77e−04***(2.11e−04)

II. Volatility equations E(ri, t2 /It−1)=hi, tConstant 5.83e−06***(7.97e−04) 1.11***(2.970)ri, t−12 0.117***(0.007) 0.061***(0.005)hi, t−1 0.870***(0.007) 0.936***(0.005)

III. Correlation equation E(εi, tεj, t/It−1)=qi, j, tεi, t−1εj, t−1 0.02***(0.004)qi, j, t−1 0.961***(0.007)

Panel B — BSE 30 and Nikkei 225 markets

BSE 30 Nikkei 225

I. Returns equations E(yi, t/It−1)=yi, t−ri, t








rose dramatically when most of the markets all over the worldresponded simultaneously to the attacks in the USA.18 After that periodwe can observe a sharp decline in the intensity of the co-movements.Another increase, in time-varying correlation is observed from 2006to 2008, when the US sub-prime mortgage crisis triggered a global fi-nancial crisis; the highest level of correlation was on October 23rd and24th, 2008 when all stock markets considered here reported heavylosses. On October 24th, returns fell by −11.6% in the BSE index,−10.1% in the Nikkei,−8.66% in both Hang Seng and STI stockmarketsin line with many of the world's stock exchanges with negative returnsof around 10% inmost indices. Our results show that correlations amongstockmarkets are generally low before global crises (like those triggeredby either Twin tower attacks or US subprime crisis) but they increasedramatically when these crises take place. These results suggest thatbenefits coming from international diversifications are available beforeand after these crises however after each crisis these benefits arelower because of correlations do not return to the pre-crisis levels.19

These results are also consistent with recent research dealing with inte-gration among Asian stock markets (Bowman, Chan, & Comer, 2010).

Constant 0.001***(2.24e−04) 5.09e−04***(2.3e−04)

II. Volatility equations E(ri, t2 /It−1)=hi, tConstant 6.70e−06***(8.9e−07) 2.87e−06***(6.3e−07)ri, t−12 0.127***(0.008) 0. 086***(0.007)hi, t−1 0.857***(0.008) 0.904***(0.008)


Panel C — BSE 30 and STI markets

BSE 30 STI

I. Returns equations E(yi, t/It−1)=yi, t−ri, tConstant 0.001***(2.47e−04) 5.503e−04***(1.986)

II. Volatility equations E(ri, t2 /It−1)=hi, tConstant 6.507e−06***(9.02e−07) 1.41e−06***(0.003)ri, t−12 0.128***(0.008) 0.086***(0.007)hi, t−1 0.857***(0.008) 0.910***(0.006)


4.6. Testing evidence of contagion

Thus the DCC analysis suggests that short-term interdependenciesbetween the BSE and Asian developed markets rose dramaticallythrough the crisis period and after the crisis they returned to approx-imately initial levels. An important consideration is the increase incorrelations during a particular period. Pretorious (2002) argued co-movements among stock markets might be attributed to three fac-tors; the contagion effect, economic integration and stock marketcharacteristics.20 Our objective in this study is to identify if the in-crease in correlations is a result of contagion.21 Following Chiang,Jeon, and Li (2007) we hypothesise that correlation coefficients acrossstock markets are likely to increase during period of high volatility. Ifa crisis hits country A with increasing volatility in its stock market, itwill be transmitted to country B with a rise in volatility and, in turn,the correlation of stock returns in both country A and country B. Inorder to check the validity of the previous assumption, we use the het-eroskedasticity-adjusted correlation coefficients proposed by Forbesand Rigobon (2002), then we use the standard Z-test for statistical in-ferences. As pointed out by Chiang et al. (2007), the main problem of

18 As pointed out by Charles and Darnè (2006), the Twin Tower attacks affectedheavily the world stock markets. The US stock markets closed on the subsequent fourdays after 11/9, while Europeans as well as the Japanese stock markets which experi-enced negative shocks immediately in the days subsequent to the attacks.19 Lin and Swanson (2008) points out that the reduction of diversification benefits isa phenomenon also due to the increasing capital markets integration among developedand emerging stock markets.20 Contagion occurs when co-movements of equity markets are not explained by eco-nomic fundamentals. Economic integration among countries is based on trade relation-ships, as well as economic indicators which can affect directly stock markets, like,interest rates and inflation, while stock market characteristics are based on the compo-sition of whole economies as well as the size of equity markets (Pretorious, 2002).21 Increase in correlations can be because of any of the three factors cited here. Scope ofthis study is to identify if the change in correlations is based on underlying economic factors(economic integration and/or stock market characteristics) or because of contagion.

Panel D — BSE 30 and S&P100 markets

BSE 30 S&P100

I. Returns equations E(yi, t/It−1)=yi, t−ri, tConstant 0.001***(2.59e−04) 2.58e−04(1.70e−04)

II. Volatility equations E(ri, t2 /It−1)=hi, tConstant 6.721e−06***(1.672e−06) 8.547e−07***(2.97e−07)ri, t−12 0.130***(0.016) 0.066***(0.009)hi, t−1 0.854***(0.017) 0.929***(0.008)

III. Correlation equation E(εi, tεj, t/It−1)=qi, j, tεi, t−1εj, t−1 0.005*(0.003)qi, j, t−1 0.993***(0.004)

Notes: Standard errors are in parenthesis. Three/two/one stars indicate the significancelevel at 1%, 5% and 10%.

Correlations of BSE with HANGSENG

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 20090.00

0.25

0.50

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Correlations of BSE with Nikkei

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 20090.0

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0.6Q21

Correlations of BSE with STI

2000 2001 2002 2003 2004 2005 2006 2007 2008 20090.00

0.16

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0.48

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Correlations of BSE with S&P100

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 20090.05

0.10

0.15

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0.45Q21

Fig. 3. Time varying correlations for pair wise stock markets returns.


this analysis is that the source of contagion must be identified in ad-vance. Because of the recent financial crisis started in US and the spreadall over the world, we consider the US as the source of contagion in ourstudy. Our methodology is based on two steps. Firstly, following Forbesand Rigobon (2002), we calculated the adjusted correlation coefficient(ρ*). The second step involves calculating the T-statistic test suggestedby Morrison (1983) in order to calculate the null hypothesis of no in-crease in correlation.22

Results (Table 13) show firstly, that the magnitude of adjustedcorrelations is lower than the unadjusted correlation coefficients.

22 The two steps model can be explained as follows. In the first step the adjusted cor-

relation coefficient (ρ*) is calculated as follows:

ρ� ¼ ρ=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ δ 1− ρð Þ2� q

where δ=[Var(r2)h/Var(r2)l]−1 and ρ is the unadjusted correlation coefficients (vary-

ing with the high- or low-volatility period) which is calculated as follows:

ρ ¼ Corr r1; r2ð Þ ¼ Cov r1; r2ð ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiVar r1ð ÞVar r2ð Þp ¼ β1Var r2ð Þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

β21Var r2ð Þ þ Var v1ð Þ�

Var r2ð Þq

¼ 1þ Var v1ð Þβ21Var r2ð Þ

" #−1=2

where r1, t and r2, t are stock returns in markets 1 and 2 at time t, respectively, in the

equation r1, t=β0+β1r2, t+ν1, t and ν1, t is a stochastic noise independent of r2, t; δ is

the relative increase in the variance of r2; Var(r2)h and Var(r2)h are the variance of r2in a high-volatility period and a low-volatility period, respectively. In the second step

we calculate the T-statistic test as follows:

T ¼ Z0−Z1ð Þ=ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1N0−3ð Þ þ

1N1−3ð Þ

�s

where Z0=1/2 ln[(1+ρ0)/(1−ρ0)] and Z1=1/2 ln[(1+ρ1)/(1−ρ1)] are Fisher trans-

formations of correlation coefficients before and after the crisis. We assume that the

crisis started to have worldwide effect since the 15th of September 2008, that is imme-

diately after the Lehmann brothers' bankruptcy. N0=2356 and N1=195 are the num-

ber of observations before and after the crisis erupted. The test statistic is fairly robust

to the non-normality of correlations coefficients. That statistic has been also employed

by Basu (2002) and Corsetti, Pericoli, and Sbracia (2005).

Secondly the contagion effect based on adjusted correlation coeffi-cient is less wide given that the number of significant adjusted corre-lation coefficients after the crisis is lower than the number ofunadjusted correlation coefficients considered in the same period.Thirdly, relevant contagion effects occurred especially from US to In-dian stock market. By changing the source of contagion we found thatsome effect of the crisis also spread from both Hong Kong and Singa-pore stock markets to India.

Kuper and Lestano (2007) argue that linkages between financialmarkets can be affected by crisis events. Our results show that thetime varying correlations among the Indian and Asian as well as USstock rose in correspondence of unexpected international crisis. Over-all the correlations among these markets are generally positive, thisimplies a certain degree of positive interdependence during the peri-od considered.

4.7. Results of volatility switch

Table 14 shows the estimates of SWARCH models for various dailystock index returns. We estimate models with K=3 state and q=2ARCH terms. From these results, we can see that the medium volatil-ity state (g2) is 6.3 times that of the low volatility state for India, 5.9for Hong Kong, 6.5 for Singapore, 4.3 for Japan and 8.57 for US. Onthe other hand, we may see that the high volatility state is 83 timesmore volatile than the low-volatility-state in India, more than 88times in Hong Kong, 39 times in Singapore, 28 times in Japan and57 times more volatile than the low volatility state in US. The proba-bility of a switch from the low-volatility state to the medium volatilitystate (p12) is quite low for all markets, while the probability to switchfrom low to high volatility is the lowest for all countries (p13). Wemay note that the probability of switching from the medium to thehigh volatility state (p23) is generally higher. For each market thelength of stay in a given state can be calculated as (1−pii)−1 fori=1, 2 or 3. The low volatility state (p11) can be expected, on average,to last 6.71 days in India, 6.13 days in Hong Kong, 6.57 days in Singa-pore, and 5.88 days in Japan; whereas the medium volatility stateseems to last 3.64 days in India, 3.87 days in Hong Kong, 4.38 daysin Singapore and 4.24 days in Japan and 6.49 days in US. These results

Table 13Test of significant increases in correlation.

Unadjusted correlation before crisis Unadjusted correlation after crisis Adjusted correlation after crisis T-statistica (unadjusted) T-statisticsb (adjusted)

US as the sourceUS–IN 0.064 0.449 0.189 −5.630*** −2.269***US–HK 0.086 0.359 0.145 −3.926*** −1.460*US–JP 0.102 0.121 0.046 1.353 3.043US–SG 0.142 0.344 0.151 −2.927*** −1.318*

Hong Kong as the sourceHK–IN 0.378 0.579 0.286 −3.573*** −1.684**HK–JP 0.522 0.671 0.356 −3.165*** −1.603HK–SG 0.649 0.783 0.584 −0.461 −4.293***

Singapore as the sourceSG IN 0.401 0.653 0.374 −4.836*** −2.581***SG HK 0.649 0.783 0.508 −3.804*** −2.323***SG JP 0.494 0.584 0.319 −1.725** −0.923

Japan as the sourceJP IN 0.293 0.345 0.158 −0.788 −0.366JP HK 0.522 0.671 0.367 −3.165*** 1.073JP SG 0.494 0.584 0.299 −1.725** −0.869

Notes. The null hypothesis is no increase in correlation. The 1%, 5% and 10% critical values for a one-sided test of the null are −2.32, −1.64 and −1.28 respectively. ***, ** and *indicate statistical significance at the 1%, 5% and 10% levels, respectively.

a This statistic has been calculated on the unadjusted correlation coefficients after the crisis.b This statistic has been calculated on the adjusted correlation coefficients after the crisis.


seem to be quite unusual if compared to other works. For instanceCanarella and Pollard (2007), using daily observation relatively toseveral Latin America stock markets from January 1994 to April2005, found that the low volatility state in these markets can beexpected, on average, to last from 113 to 476 days.23

5. Policy implications

We studied potential cointegration between stock prices amongIndia and developed stock markets over a period of 10 years. Resultsof our study show the absence of a stable cointegration relationshipamong these markets. The absence of a stable relationship has a num-ber of implications. First, the absence of a stable relationship shouldbe recognised and incorporated by investors, researchers and analystswho wish to formulate models of stock price behaviour.24 Absence oflong-run relationship between stock market of India with other mar-kets sued in this study should be interpreted with caution because thesample data has presence of extreme events such as twin towers col-lapse and financial crisis of 2008. Third, international investors maywish to consider that India stock markets are partially immune to ex-ternal shocks, this makes stock market of India particularly suitablefor portfolio diversification strategies. Analysts and researchersought to give due consideration to the finding that stock market ofIndia is not completely immune to the global events such as financialcrisis. This study finds that a long-run relationship between thesemarkets does not exist however; periods of extreme events do cause In-dianmarket to co-move with the developedmarkets considered in thisstudy. The length of low volatility periods is longer in India than theother stockmarkets considered in the study, whichmeans that adverseevents may not cause an abrupt outflow of capital from India. Higherlevel of transparency in the stock market in India and the clarity ofrules governing foreign investments in India may have helped deepen-ing and stability of themarket in India.25 This provides further incentive

23 It must be pointed out that Canarella and Pollard (2007) only considered aSWARCH model with just two states (that is low and high volatility states), so wemay suppose that using one more volatility state may reduce the number of dayswhich characterise the low volatility state.24 Investors, researchers and analysts commonly use correlations as measure ofcomovements of the stock returns in their portfolio allocation models.25 Test of stability and market deepening is beyond the scope of this study.

to investors for considering stock market of India as a potential marketfor inclusion in their diversified portfolios. These findings are of rele-vance for theflowof foreign direct investments into India. For the policymakers this provides evidence that the monetary and fiscal policies asimplemented during the recent past have worked well.

6. Conclusions

This paper investigated the relationship between Indian and Asiandeveloped equity markets over the 1999–2009 period. By applyingthe unit root test we find that all stock prices are nonstationary.Engle and Granger cointegration tests found no evidence of cointe-gration among these markets, also using the sophisticated Johansencointegration test, no long-run relationship between India and anyof the Asian developed markets was discovered. Further examinationusing the Gregory–Hansen approach identifies no cointegration withstructural breaks among these markets. From the last results we mayinfer that there is no stable long-run relationship among these stockmarkets. This means that there are potential benefits for portfolio di-versification of international investors aiming to diversify into Indianstock market. The presence of a cointegration relationship, albeit notstable over time, may be a result of strengthening of trade relationsamong countries considered in this study. We further estimated thetime varying correlation between the Indian and Asian stock marketsusing bivariate DCC-GARCH models. Results show that the assump-tion of constant conditional correlation does not hold, we find evi-dence of time varying correlations between stock markets. Furtherthe DCC analysis suggests that the conditional correlations betweenIndia and these other markets rose dramatically through the periodsof international crisis (i.e. the September 11, 2001 attacks as well asthe recent financial crisis). However we also found that after both cri-ses correlations returned to their initial levels. These findings are sim-ilar to that of Chiang et al. (2007) who found that correlations amongAsian stock market indices increased sharply during the 1997 finan-cial crisis. There are theoretical reasons for these findings. An externalshock may cause a change in the conditional variances of one or moremarkets and this change in conditional variances at market levels canresult in a change in correlations between the expected returns ofthe markets. If the influence of the external shock is the same onboth themarkets, the external shock is not expected to have any impact

Table 14Estimates of SWARCH (3,2) model for stock indexes returns.

BSE Hang Seng STI Nikkey S&P100

c0 0.058**(0.024)

0.025(0.023)

0.005(0.011)

−0.012(0.025)

−0.018(0.016)

α0 0.780***(0.065)

0.628***(0.051)

0.420***(0.036)

0.838***(0.098)

0.264***(0.021)

α1 0.045*(0.024)

0.036(0.022)

0.026(0.022)

0.044**(0.023)

0.008(0.016)

α2 0.0407**(0.018)

0.052***(0.017)

0.039**(0.018)

0.048*(0.021)

0.056***(0.016)

p11 0.851***(0.026)

0.837***(0.012)

0.848***(0.026)

0.830***(0.046)

0.846***(0.023)

p21 0.151***(0.028)

0.167***(0.013)

0.150***(0.0273)

0.171***(0.046)

0.146***(0.025)

p12 0.254***(0.044)

0.242***(0.023)

0.219***(0.037)

0.213***(0.061)

0.224***(0.032)

p22 0.726***(0.047)

0.742***(0.023)

0.772***(0.038)

0.774***(0.061)

0.741***(0.038)

p13 −0.01(0.295)

−0.005(0.265)

−0.010(0.286)

−0.01(0.304)

−0.00(0.177)

p23 0.403(0.340)

0.403(0.289)

0.409(0.312)

0.315(0.318)

0.463**(0.208)

g2 6.309***(0.598)

5.933***(0.483)

6.596***(0.634)

4.345***(0.472)

8.57***(0.870)

g3 83.855***(0.007)

88.893*(49.548)

39.525**(16.978)

28.221***(2.820)

57.608***(0.001)

Notes. Standard errors are in brackets. ***/**/* denotes statistical significance at 1%, 5%,and 10% levels. The values of the parameter g2 and g3 denote the volatility of state 2and state 3 respectively.


on the correlations between the expected returns of the twomarkets. Ifthe external shock is asymmetrical on the conditional variances, it willcause a change in correlations. Further, an increase in the volatility inthe random variables can cause the sample correlations betweenthese variables to increase even if the principle processes that generatethe variables remain unchanged (Gupta & Mollik, 2008). In our study itappears that the increase in correlations between India and Asian stockmarkets immediately after the 2008 financial crisis is a result of somecontagion effects. In order to investigate the issue, we split our samplein two sub-period. Taking the US as the source of contagion, we showthat a contagion effect spreads from US to India. Another issue we ex-plored was the presence of different volatility regimes across all mar-kets. International investors usually model their portfolios by takinginto consideration the volatility of emerging markets. Using SWARCHmodel we studied the shift in volatility between low, medium and highvolatility regimes. Results indicate that the variance in high volatility re-gime is 83 times more volatile than the low-volatility-state in India andmore than 88 times in Hong Kong. Alternatively a developed stock mar-ket like Hong Kong seems to be more volatile than an emerging stockmarket when it is in a high volatility state. On the other hand, we findthat estimated probability of being in the low volatility state is the high-est for all stock markets considered, while considering the probability toswitch from a state to another we find that the probability of movingfrom the medium- to high volatility state is the highest for all marketsconsidered. We note that this approach exhibits some limitations,given that the model is not able to detect the probability of each stockmarket to stay in a particular volatility regime.

This study finds that Indian stock market has a weak interdepen-dence with other developed Asianmarkets and the USmarket. Findingsof the study also suggest that India's stock market is largely insulatedfrom global events (it is not strongly affected by global events). Further-more volatility in the stock market of India is more stable as comparedwith the developed Asian stockmarkets. These characteristics of a stockmarket may be attractive for international investors who seek to investin foreign markets to improve their risk adjusted returns and/or wantexposure to the factors that are not represented in their domesticeconomy.

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