Stock Market Linkages: Evidence from US, China, India During Crisis

This case study examines the stock market linkages between the US, China, and India during the subprime crisis of 2007-2009. It employs techniques like Tri-Variate Vector Autoregression, Spillover Index, and Threshold Generalized Autoregressive Conditional Heteroskedastic [TGARCH (1,1)] model to analyze the relationships and volatility spillovers during this period. The study finds a uni-directional causality from the US market to the Indian and Chinese markets, and from the Chinese market to the Indian market, in terms of stock market returns. A volatility spillover is also observed from the US to India and from India to China. The research highlights the diminishing cross-market impact on volatility over time due to the increased impact of past volatility and the 'leverage effect'. Efficient tests reveal an indirect impact of US market volatility on the Chinese market via India, suggesting that portfolio managers should consider these linkages to maintain portfolio values. The study contributes by modeling return and volatility linkages during the actual crisis period, capturing cross-market spillovers, and employing the VAR model along with efficient tests.

Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137–162
STOCK MARKET LINKAGES: EVIDENCE
FROM THE US, CHINA AND INDIA DURING THE SUBPRIME
Amanjot SINGH1
Parneet KAUR2
DOI: 10.1515/tjeb-2015-0012
The Subprime crisis spillovered the returns and volatility from
the US stock market to the other integrated economies. The
present study attempts to analyze the stock market linkages
between the US, India and China, especially during the US
subprime Crisis. The techniqueof Tri-VariateVector
Autoregression and the Spillover Index has been employed so
as to analyze the relations during the time period 2007 to
2009. To estimate the time varying risk parameters, the
technique of Threshold Generalized Autoregressive
Conditional Heteroskedastic [TGARCH (1,1)] model has been
used. A uni-directional causality has been observed from the
US marketto the Indian and Chinesemarket,whereas
anotherunidirectionalcausalityhas also been spotted
running from the Chinese market to the Indian market in the
context of stock market returns during the crisis period. A uni-
directional volatility spillover from the US to the Indian market
and from the Indian to the Chinese market has been found to
be significant. As per the volatility Spillover Index, the cross
market impact on the volatility reduces over a time period
2007-2009, due to the increased impact of the past volatility
and the presence of 'leverage effect'. The falling returns
added to the volatility in the respective markets. The efficient
tests of causality inspired by Hill (2007) reported an indirect
impact of the US market volatility on the Chinese market via
Indian. The portfolio managersshould discount this
information well ahead of time to maintain the portfolio
values by taking positions in futures and options market.
Keywords: Financial Crisis; Spillover; Variance Decomposition; Vector Autoregression Model;
Volatility.
JEL Classification:G01, G15, F00, F36.
1 Research Scholar, Punjabi University, India.
2 Assistant Professor, Punjabi University, India.
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OPEN
DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162138
1. Introduction
The bursting of the housing sector bubble triggered the subprime crisis in the US, which was not
limited only to the banking sector, but also had an impact on the overall financial sector in the
US. Moreover, being the dominant economy and increased integration in the context of trade
and financial channels with the other different countries, the crisis started in the US gets
transferred to the other countries as well, (Angkinand et al., 2009). Even emerging markets like
the BRIC nations felt the heat of the crisis due to their increasing exposure to the developed as
well as other nations (Beirne et al., 2009). The globalization and the increased integration of the
financial system have made the world economies into 'one single market' under which th
macroeconomic challenges in one country have an impact on the other countries as well,
making way for the stock markets in the recipient economies to witness an uneasy phase. When
there are fundamental challenges like twin deficit crisis, lower GDP growth rate, unemployment,
lower consumer confidence, lesser productivity etc., then that do affect the other integrat
economies with which the source country is having the trade and financial relations. However,
most of the times it has been observed that the herding behavior of the investors put the stock
markets in a tizzy phase especially in developing nations (Laih & Liau, 2013). So, both th
fundamental changes and behavioral finance (investment) catalyse as the spillover agents.
Furthermore, the inter linkages among the markets gets strengthened during a crisis period, as
studied by Yang et al. (2003) while studying the Asian financial crisis. The fund managers
investors should discount the linkages among the markets concerned as this would have
impact on the portfolio diversification strategies especially during an adverse event.
How the linkages among the US, Indian and Chinese stock markets pan out during the subprime
crisis? And does the lagged returns in the US had an impact on the stock markets of the China
and India? Or the other way around. Similarly, does the volatility in the US market had an impact
on the volatility in the Indian and Chinese markets?. The present study attempts to model the
stock market linkages i.e. the first moment (returns) as well as the second moment (volatility)
between the US, India and China during the Subprime crisis and answers the questions that has
been raised, by employing Vector Autoregression (VAR) Model. To estimate the conditional
variance, Threshold Generalized Autoregressive Conditional Hetroskedastic Model [TGARCH
(1,1)] model has been used. The period considered for the purpose of study ranges from 2007
to 2009. A case of two promising emerging markets (India and China) and one developed
market (United States; eventually the source of Global Financial Crisis) has been taken.
Moreover, there are differences in the timings of stock markets of the countries concerned: a
VAR model with lags as endogenous variables would solve this problem in accounting for
spillovers. There are numerous studies that have tried to capture the stock market linkag
between the US, Indian and Chinese markets during the subprime crisis (see for details l
Nikkinen et al., 2013; Bianconi et al., 2013; and many more.). But most of the studies have
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162139
taken a very long period ranging from six to eight years to capture the linkages. However, the
present study has tried to account for the linkages during the period 2007-2009, when th
major events took place in the US market in relation to the subprime crisis embodying Lehman
Brother Crisis, etc. As per the Business Cycle Dating Committee of the National Bureau o
Economic Research (2010), the recovery from the US crisis started from June 2009 so the
period up till December 2009 has been considered thereby taking the time period comprising of
a trough. Apart from the stock market linkages, the study also made an attempt to capture the
return and volatility spillovers in an index among the countries concerned; inspired by the
methodology adopted by Diebold and Yilmaz (2009).
The Global Competitiveness Report 2013-2014 published by World Economic Forum has
recently placed China ahead of the other BRICS nations. China and India are slowly opening up
their financial market and other markets as well for the foreign players. Gupta and Wang (2009)
highlighted the estimates of the other researchers where they are projecting a manifold
increase in the India-China trade numbers compared to the US-China trade relations during the
year 2020. With the increasing trade relations with the other countries and increasing capital
flows from the Chinese economy, Rajwade (2014) in his article titled "China's Global Economic
Power", reported that the day is not that far when we will be having the Yuan as the fu
reserve currency being decided by the monetary authorities. The steps taken in the form
incorporating a BRIC bank are further paving the way for this achievement.
Both the China and India are among the strongest emerging markets having a wide base
middle income strata of the society, thereby providing a protection to the demand side of the
products and services. The trade relations between the China and India are increasing over a
period of time. The increasing trade and financial linkages among the China and India ha
made the stock markets in these respective nations interlinked with each other, as reported by
the results. These linkages further have an impact on the portfolio diversification benefits under
which the correlationbetweenthe asset classes should be lower in order to enjoy the
diversification benefits (Click & Plummer, 2005). Our motive is to study the linkages among the
US, Chinese and Indian stock markets and especially during the subprime crisis. The behavior of
the US, Chineseand Indian stock marketsduring the financialcrisis is a lesson to be
comprehended by the International investors in their efforts to hedge against downside risks in
future. The study would provide an insight to the portfolio diversification strategies to be
followed by the managers during a turbulent period.
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162140
Figure 1. Market Capitalisation % of GDP
Source: World Bank Data
Figure 1 highlights the market capitalization as a percentage of GDP over a period of time. In the
US, the market capitalization has been very high during the period 1999-2000 whereas in India
and China it has been high during the period 2007-2008. A very high value (generally above 100)
indicates over-valuation of a market. The high market capitalization in China and India du
2007-2008 spotlights the buoyancy in the stock markets before the financial crisis. After t
period, a significant decline in the market capitalization as a percentage of GDP can be observed
due to theemergence of the crisisduring that time period.The decrease in themarket
capitalization signifies a sharp decline in the stock market due to the emergence of the Subprime
crisis. Although most of the countries witnessed this type of a downward rally in their sto
markets yet how the markets pan out in terms of the linkages with each other is a question that
needs to be answered. The results obtained after employing the VAR model along with th
efficiencytests, spotlightthe existenceof unidirectionalspilloversamong the countries
undertaken during the crisis period. The subprime crisis started in the US acted as a spil
agent in the context of stock market returns and volatility; from the US market to the Indian and
Chinese markets.
Our paper contributes to the existing literature in three ways. Firstly, we tried to model
return and volatility linkages among the US, China and India during the actual subprime crisis
period 2007-2009, considering a trough phase as well instead of taking a longer period of time.
Secondly, we have captured the cross market spillovers in the context of stock market returns
and volatility in the form of an index creation. Thirdly, we have employed the VAR model for both
50
70
90
110
130
150
170
190
China Market capitalization of listed companies (% of GDP)
India Market capitalization of listed companies (% of GDP)
United States Market capitalization of listed companies (% of GDP)
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162141
the stock market returns and volatility along with Efficient tests proposed by Hill (2007). Th
results obtained from the TGARCH model have been further modelled into the VAR framework.
The rest of the paper has been divided into five sections. Section 2 relates to the review of the
literature, sections 3 and 4 comprise the Research Methodology part and the Empirical findings
and Interpretation part, respectively. Section 5 concludes the paper.
2. Literature review
Over a period of time, many researchers have tried to capture the linkages among the stock
markets. The studies are not limited to the stock markets alone, yet the other areas like
commodity markets, currency markets and the debt markets have also been taken up by
the researchers in order to account for the linkages among them. A rich literature is
available on the stock market linkages in this context.
Hamao et al. (1990) examined return spillovers and volatility spillovers in the three major
stock markets (New York, Tokyo, and London) by using univariate GARCH models and
reported significant volatility and return spillovers among the concerned countries.
Friedman and Shachmurove (1997) examined the European Community stock markets by
employinga Vector Autoregression(VAR) model. The results showed that the smaller
markets, such as Belgium, Denmark and Italy do not have an impact on other markets. The
impulse responses reported that Britain is a leading market that have an impact on the
France, Netherlands, and Germany. Tabak and lima (2002) examined the causal
relationships among the stock markets of Latin America and the United States. The results
highlighted that there is some short-run relationship between these stock markets. The
Granger causality test detected causality between the Brazilian stock market and other
Latin American stock markets. In order to study the dynamic linkages between crude oil
price shocks and stock market returns in 22 emerging economies Maghyereh (2004) used
Vector Autoregression (VAR) analysis as well. The results supported the evidence that oil
shocks have no significant impact on stock index returns in emerging economies.
Click and Plummer (2005) reported that the stock markets of Indonesia, Malaysia,
Philippines, Singapore, and Thailand are cointegrated and possess a long run relationship
after the Asian financial crisis. The authors also performed certain exclusion tests to see
that whether all the variables are present in the long run relation or not. The results showed
that all the variables contribute in a significant way in the long run.
While studying the linkages between the two stock exchanges in mainland China, Hong
Kong and in the U.S. by employing M-GARCH approach, Li (2007) came out with the finding
that the Chinese mainland stock markets have a linkage with the Hong Kong market but
have no direct interaction with the U.S. stock market. Valadkhani and Chancharat (2008)
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162142
investigated cointegration and causality relations between the stock market price indices of
Thailand and its major trading partners (Australia, Hong Kong, Indonesia, Japan, Korea,
Malaysia, the Philippines, Singapore, Taiwan, the UK and the US). The results of Granger
causality reported unidirectional causalities running from the Hong Kong, the Philippines
and the UK to Thailand. The authors also found bidirectional Granger causality, between
Thailand and three of its neighboring countries (Malaysia, Singapore and Taiwan). Abas
(2009) examined the linkages of the two leading emerging markets, i.e. Chinese and Indian
market with other developed markets by employing Granger causality and cointegration
tests using an error correction model. The author came out with the finding that the Chinese
and Indian markets are correlated with all four developed markets undertaken for the
purpose of study, United States, United Kingdom, Japan and Hong Kong.
Ismail and Rahman (2009) analyzed the relationship between the US and four Asian
emerging stock markets, namely Hong Kong, India, South Korea and Malaysia by employing
linear Vector Autoregressive(VAR) model and nonlinear Markov Switching Vector
Autoregressive (MS-VAR) model. The results reported that Hong Kong (HSI) and Indian (BSE)
markets are significantly affected by the previous one month return of the Korean (KOSPI)
market, whereas Malaysia market significantly gets affected by the previous one month
return of Hong Kong (HSI) and Korean (KOSPI) markets. Moon and Yu (2010) found an
evidence of significant volatility spillover from the US market to the Chinese in the post
break period (December 2005) by employing symmetric and asymmetric GARCH-M models.
The results are in contrast with Li (2007) because of the time period undertaken for the
purpose of study. By making use of various statistical measures Gupta (2011) studied the
Co-movementand the direction among the emergingcountries, especially the BRIC
countries during the condition of financial turmoil. The author finds out that the Indian,
Russian and Chinese markets Granger cause Brazilian market. Jeyanthi (2012) examined
both the long - run as well as short - run relationships between the stock prices of the BRIC
countries by employing Granger Causality test. The Granger causality test reveals that there
is bidirectional Granger causality that exists between India and Brazil, India and China for a
full sample period and the pre crisis period. Gangadhar and Yoonus (2012) examined the
financial integrationbetween the US and the Indian stock market by using Vector
Autoregression as well as Cointegration technique. The results found no Co-integration
between the two indices, but the Indian returns gets significantly affected by the US returns,
whereas Reddy and Wadhwa (2012) explored the financial integration of the BRIC emerging
markets and the US market by employing Granger causality test. The results indicate that
there is a unidirectional relationship between the US and other stock markets of the BRIC
nations. Padhi and Lagesh (2012) employedDCC GARCH model to capture the co-
movement in volatility in the India, Asian and US market and came out with the finding that
bilateral shocks and volatilityspillover exists in the India/Malaysia,India/Taiwan and
India/Indonesia markets. Singh and Sharma (2012) studied the inter-linkages between the
stock markets of Brazil, Russia, India, and China by using the Granger causality model,
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162143
Vector Auto Regression (VAR) model and Variance Decomposition Analysis. The results
report that the Russian, Indian and Brazilian stock exchanges affects each other and does
gets affected by their own returns excluding the Chinese markets. By employing asymmetric
BEKK-GARCH and the VAR approach, Zhang and Jaffry (2015) reported strong bi-directional
volatility spillovers during the global financial crisis period between the Mainland China and
Hong Kong stock markets.
3. Research Methodology
In order to explore linkages among the US, China and India, during the US crisis, stock market
indices of the respective countries have been taken into account. The health of an economy
can easily be judged based on the equity market of that country. The equity markets are
considered to be the riskiest markets compared to the other counterparts and every type of
information relating to the economy quickly gets discounted in an equity index (Kumar &
Dhankar, 2009). The indices used are S&P 500 (US), NIFTY (INDIA) and the Shanghai
Composite Index, SSE (CHINA) ranging from January 2007 to December 2009. The daily data
have been collected from the website of respective stock exchanges, Yahoo Finance and Wall
Street Journal. The CNX NIFTY is a well diversified equity index comprising 50 stocks whereas
SSE Composite Index consists of stocks (A shares and B shares) at the Shanghai Stock
Exchange. Similarly S&P 500 contains good quality stocks having strong fundamentals and
liquidity. The daily continuously compounded returns (RSANDP, RNIFTY and RSSE) have been
calculated for the US, India and China respectively by taking the log of the series.ൌ ‘ ‰ ሺȀ–– ൌ ͳሻכͳͲͲ (1)
Where R is the daily return, Pt is the current price and Pt-1 is the previous day price in local
currencies. The gaps in the daily prices have been filled up by taking mean of nearby two
points. The prices have been taken in their local currencies instead of dollar prices because
the local prices would take care of the volatilities in the common currency values.
Going with the literature, the technique of Tri-Variate Vector Autoregression has been
employed in order to analyze the dynamic relations between the US, China and Indian
markets. The VARmodel further consist of three branches to empirically analyze the
relations. Out of these three, two branches have been touched, Granger Causality
Test/Wald Test and the Variance Decomposition Analysis. To estimate the time varying
volatility or conditional variance, TGARCH (1,1) model has been employed. In order to study
the return and volatility spillovers among the countries concerned, the technique adopted
by Diebold and Yilmaz (2009) has been usedalong with efficiency tests of causality
proposed by Hill (2007).
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162144
3.1. Vector AutoRegression Model
The methodology of Vector Autoregression has been introduced by Sims (1980). Under
Vector Autoregression,as the name suggests, the model consists of the dependent
variables which are a function of its own lagged values as well as the lagged values of an
another variable plus an error term. Say there are two variables Y1 and Y2, the mean
equations shall be as follows:ܻଵǡ௧ ൌଵ ൅ܣ ଵǡଵܻ ଵǡ௧ିି  ଵିିିିିିିିିିିିି ൅ܣ ଵǡଶܻ ଶǡ௧ିି  ଵିିିିିିିିିିିିି ൅ ଵǡ௧ (2)ܻଶǡ௧ ൌܿ ଶ ൅ܣ ଶǡଵܻ ଵǡ௧ିି  ଵିିିିିିିିିିିିି ൅ܣ ଶǡଶܻ ଶǡ௧ିି  ଵିିିିିିିିିିିିି ൅݁ ଶǡ௧
Where c1 and c2 is a k×1 vector of constants, Ai is a k×k matrix (for every i = 0, ..., p) andt
is a k×1 vector of impulses or shocks. The1 and 2 are the stochastic error terms which
are also termed as impulses or innovations or shocks. The lagged values of the dependent
as well as the independent variable helps in analysing the dynamic impact of the variables.
Under Cholesky Decomposition, the ordering of the variables has been done as per the
results reported by the Wald test.
3.2. TGARCH (1,1) Model
The TGARCH model, also known as GJR model (Glosten et al., 1993) and an extension of
the plain vanilla GARCH (1,1) model, analyses the impact of a negative shock on the
volatility or, in short, the 'leverage effect'. Apart from TGARCH, there are various other
volatility modelling techniques like EGARCH, Component GARCH, PGARCH, etc. But
consideringthe simplicity of the TGARCHmodel coupledwith as efficient asymmetric
results, we have not used the other models. Moreover, the Component GARCH model
demarcates the conditional variances into two parts: transitory component (short run) and
permanentcomponent(long run). The short timespan (2007-2009)has made us to
consider only an asymmetric TGARCH model. The model is specified as:ܴ௧ ൌ ൅ܿߝ ௧
ߝ௧̱݅݅݀ ሺ ǡͲ ௧ሻ (3)݄ ௧ ൌߙ ൅ ൅ߙ ଵ ߝ௧ିି  ଵିିିିିିିିିିିିି
ଶ ൅ߜߝ ௧ିି  ଵିିିିିିିିିିିିି
ଶ ܦ௧ିି  ଵିିିିିିିିିିିିି ൅ߚ ଵ݄ ௧ିି  ଵିିିିିିିିିିିିି
where, Dt-1 is a dummy variable which estimates the leverage effect of a negative shock. If
t-1<0, then the value 1 is assigned and otherwise zero. If is found to be significant and
positive, then a negative shock has a leverage impact on the conditional variance (1 + ) in
comparison to the positive shock, which have an impact equivalent to1 only. 1 and 1
captures the news impact on the conditional variance and the persistency in volatility
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162145
respectively. The parameters have been estimated by assuming a normal distribution of the
error terms coupled with a maximum likelihood approach (Kaur & Singh, 2015).
3.3. Cross Market Spillover Index
Diebold and Yilmaz (2009) came out with a spillover index to calculate the total contribution
of the shocks on an asset market arising from the contribution of all other markets. The
index is calculated on the basis of N - variable Vector Autoregression model (Srnic, 2014).
The forecasted error variance calculated under the variance decomposition analysis plays a
central role in calculating the index values. The variance decomposition analysis reports the
contribution of a shock in one variable to the variation in the forecasted error variance of
the other variable. The forecasted error variances are splitted into two parts so as to
demarcate the own variance shocks and cross market variance shocks. Suppose there are
two variables, and the possible spillover shock impacts from the first variable to the second
and vice versa areܽ ൅ǡଵଶ
ଶ andܽ ൅ǡଶଵ
ଶ , respectively. The total of the latter can be regarded as
the total spillover impact, whereas the average of the same represents as an Index value,
calculated N step ahead forecasted variances.
3.4. Efficient Tests Of Causality
Hill (2007) came out with an recursive parametric representation test procedure for the
investigation of multi-steps ahead causation in a trivariate VAR framework (say, X, Y and an
auxiliary variable Z), placing a strong reliance on causality chains (Salamaliki & Venetis,
2013). The tests help in figuring out the impact of one variable on another as 'Direct' or
'Indirect through an auxiliary variable' and long run versus short run impact. We are trying to
model the direct and indirect impact only as the time period under consideration is of
shorter duration. The indirect part of the causality states that there might not be a direc
impact of Y on X yet there can be an indirect impact through an auxiliary variable 'Z'; Y
causes Z and further Z causes X. We have conducted efficient, non-causality tests to check
the impact of Indian, Chinese and the US markets on each other during the crisis period
inspired by Hill (2007) strategy.
The causality chain is based on three sequential steps. At the very outset, we test for two
null hypothesis: Y does not cause (X and Z) at one step ahead and similarly (Y and Z) does
not cause X at one step ahead.
ܪ ൅
ሺஶሻ ൌܻଵ ե ሺ  ǡ ሻ ܶ݁ݏݐͲǤͳ (4)
ܪ ൅
ሺஶሻ ൌሺܻܻܻܻܻܻܻܻܻܻܻܻܻ ǡܼ ሻଵ եݐܶ݁ݏͲǤʹ
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162146
If both the hypothesis are rejected then the test is performed at specific horizons in the
second step:
ܪ ൅
ሺଵሻ ൌܻଵ եݐܶ݁ݏͳǤͲ (5)
If we observe a non-causality (Test 1.0), then we proceed to the following tests as a subpart
of the second step.
ܪ ൅
ሺଵǤଵሻ ൌܻଵ եݐܼܶ݁ݏͳǤͳ (6)
ܪ ൅
ሺଵǤଶሻ ൌܼଵ եݐܶ݁ݏͳǤʹ
If there is a break in the hypothesis (Test 1.1 and Test 1.2), then we assume that Y does not
cause X. If both are rejected then we proceed to step three. In the third and last step the
tests are performed at multiple horizons. For the purpose of calculations, we have taken a
fixed rolling window of 'n' days in the context of stock market returns and volatility in such a
way that initially there are at least 21 trading days left till the sample closing date.
4. Data Analysis and Interpretation
First of all, an attempt has been made to understand the characteristics/properties of the
return series and graphical presentation of the return series. The Table 1 below spotlights
the Mean, Median, Standard deviation, etc. of the return series over a period of time.
Figure 2 exhibits that the logged returns are volatile throughout the period undertaken into
consideration.
-15
-10
-5
0
5
10
15
20
100 200 300 400 500 600 700
RNIFTY RSANDP RSSE
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DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162147
Figure 2. Graphical presentation of the Stock market returns
Source: Computed by Authors
As one could notice, small changes are followed by smaller changes and the large changes
are followed by larger changes, making a case for the application of the GARCH-type models
to account for the heteroskedasticity in the error terms. During the crisis period, the
average daily returns for the US market are found to be negative, whereas positive returns
have been witnessed by both the Indian and Chinese markets coupled with a higher
standard deviation as compared to the US. The Jarque-Bera test indicates that the return
series are not normally distributed perhaps leptokurtic as the Kurtosis values are greater
than three, with respect to each country. Whereas a positive skewness value of NIFTY return
series indicates a higher probability of positive returns in comparison to the negative returns.
Table 1. Descriptive statistics: Market Returns
Year RNIFTY RSANDP RSSE
Mean 0.03 -0.03 0.02
Median 0.09 0.08 0.29
Maximum 16.33 10.96 9.03
Minimum -13.01 -9.47 -9.26
Standard Deviation 2.14 1.84 2.27
Skewness 0.08 -0.15 -0.34
Kurtosis 9.56 9.55 4.67
Jarque-Bera 1406.26 1403.16 105.84
Probability 0.00 0.00 0.00
Source: Authors’ calculations
The skewness values are negative for the US and Chinese markets, indicating a higher
probability of negative returns. Overall by looking at the average numbers, we can say that,
due to the crisis, US returns have been negativeand the flight of capital towards
profitable opportunitiesentailed to higher averagereturns for the Indian and Chinese
markets.
Figure 3 exhibits a 30 days rolling correlation between the S&P 500 & NIFTY and S&P 500
& SSE; calculated using the computed logged returns. A rolling correlation provides greater
information as the time varying coefficients highlight the relationship between the stock
market returns of the concerned countries. To calculate the correlation coefficients, the
lagged one day return of the US market has been taken instead of the same day return
(contemporaneous)because of the differences that exist in the time horizons. The
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N
DOI: 10.1515/tjeb-2015-0012
Singh, A. & Kaur, P. (2015).
Stock Market Linkages: Evidence From the US, China and India During the Subprime Crisis
Timisoara Journal of Economics and Business | ISSN: 2286-0991 | www.tjeb.ro
Year 2015 | Volume 8 | Issue 1 | Pages: 137 – 162148
correlation coefficients remain volatile throughout the period undertaken for the study.
During the Lehman Brother crisis, correlation coefficients for both the NIFTY and SSE are
very high and positive, thereby depicting a financial integration among the stock markets
during that period. Soon after the event, the coefficients headed southward, making the
clear case of independency reverting back to the Chinese and Indian stock market returns.
Figure 3. 30 Days Rolling Correlation with the US
Source: Computed by the Authors
The negative correlation provides an opportunity to the global investors to diversify, but the
periods of negative or low correlation are followed by the positive correlation that reduces
the diversification benefits in the short run.
4.1. Unit Root Test
The financial time series data suffers from the problem of the presence of a unit root (see
Gujarati et al., 2013). The presence of the unit root can lead to spurious results. The
Augmented Dicky-Fuller test has been used in the study to check the presence of a unit root
in the series. The AugmentedDickey Fuller test augmentsthe lagged values of the
dependent variable in the series:
οܻݐൌߚ൅ͳݐߚʹ൅ݐܻߜߜߜߜߜߜߜߜߜߜߜߜߜൌ ͳ ൅ ൅ߙ݅݅݅݅݅݅݅݅݅݅݅݅݅݅οܻݐ൅൅ൌݐߝ൅൅൅ି  ଵ
(7)
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0.8
2007.01.02
2007.03.02
2007.05.02
2007.07.02
2007.09.02
2007.11.02
2008.01.02
2008.03.02
2008.05.02
2008.07.02
2008.09.02
2008.11.02
2009.01.02
2009.03.02
2009.05.02
2009.07.02
2009.09.02
2009.11.02
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