MSc dissertation

COINTEGRATION BETWEEN STOCK
MARKETS IN THE PRESENCE OF
FINANCIAL CRISIS
MSc Financial Forecasting and Investment
Student number 2163365
Supervised by Panagiotis Andrikopoulos
August 2015

Cointegration between stock markets in the presence of financial crisis 2015
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Statement of originality
This dissertation is submitted as a partial requirement of the degree of MSc Financial
Forecasting and Investment.
I confirm that this research is my own work, written in accordance with the guidance
on plagiarism in the Student Handbook, that is included in the University of Glasgow
Statement of Plagiarism. Explicit reference is provided in text where ideas and/or words
are taken from the external source. No services of any professional agencies were used to
produce this piece of work.
I give the permission of this dissertation to be used, photocopied, and made available
through the University.
In addition, I understand that any false statement leads to disciplinary actions taken
in accordance with the University of Glasgow regulations.
Word count: 12,860 (excluding cover page, acknowledgement, abstract, table on
contents, list of tables, bibliography, and tables in the body part).
Signed: Date:

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Acknowledgements
First of all, I would like to thank my supervisor Dr Panagiotis Andrikopoulos for his
guidance and help during this research.
I would like to thank my Mum who has always encouraged me and helped me
throughtout my time at the University of Glasgow. Thank you for being a true role model.
A special thanks to my flatmates and Mr McGill. You're precious stars.
Finally, thank you for taking time to read this dissertation.

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Abstract
Stock market linkges are vital when assessing international diversification
opportunities. It is important to understand to what degree stock markets are
interconnected and whether there is a leader and a follower in this relationship. This
dissertation looks at the linkages between the US stock market and stock indices in 5
different countries – the UK, Germany, France, Switzerland, and Japan. Period covers the
financial crisis of 2008, running from January 2002 until December 2014.
The empirical results show that all data sets are non-normal and have a unit root.
This is a typical specification found in time series data. It has been found that cointegration
exists only between one pair – S&P 500 and FTSE 100. Nevertheless, all pairs have been
assessed through the VAR and GARCH methods in order to find evidence of volatility
spillovers. It was concluded that the US stock market indeed transmits information to other
markets, however, it influences them with different strength. The strongest volatility and
shocks spillover effects were found to be between the S&P 500 and SMI indices. This
clearly indicates an interrelation between markets despite the fact that no cointegration is
present in this pair.

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Table of Contents
Statement of originality.......................................................................................................2
Acknowledgements ..............................................................................................................3
Abstract ................................................................................................................................4
Table of Contents.................................................................................................................5
List of tables and figures.....................................................................................................7
1. INTRODUCTION........................................................................................................8
2. LITERATURE REVIEW..........................................................................................11
2.1. The concepts of cointegration, volatility spillovers, and contagion ..................11
2.2. Reasons behind interdependence between stock markets..................................12
2.3. Linkages between stock markets........................................................................15
2.4. Volatility spillovers............................................................................................18
2.5. Stock markets’ relationships during the financial crisis of 2008.......................21
3. COINTEGRATION, CONTAGION, AND PORTFOLIO DIVERSIFICATION
25
4. DATA AND METHODOLOGY...............................................................................28
4.1. Hypothesis of the research .................................................................................29
4.2. Statistical analysis of data..................................................................................29
4.3. Formal methodology..........................................................................................30
5. EMPIRICAL RESULTS ...........................................................................................39
5.1. Statistical features of data sets ...........................................................................40
5.2. Unit root testing .................................................................................................41

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5.3. Testing for cointegration....................................................................................43
5.4. Application of VEC and VAR models...............................................................46
5.5. Application of BEKK-GARCH model ..............................................................54
6. CONCLUSION...........................................................................................................59
6.1. Limitations of the research.................................................................................60
Bibliography.......................................................................................................................62

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List of tables and figures
Graph 1: Patterns of stock indices from 2002 until 2015…………………………39
Table 1: Descriptive statistic of stock index returns……………………………....40
Table 2: Unit root test results for six stock indices………………………………..42
Table 3: Augmented Dickey-Fuller test results…………………………………...43
Table 4: Cointegrating vector test of the whole data set………………………….45
Table 5: Cointegrating vector test for pairs of indices……………………………45
Table 6: Estimation of VAR model……………………………………………….48
Table 7: OLS estimation of VEC model…………………………………………..51
Table 8: VECM estimation during various periods……………………………….53
Table 9: Results of BEKK-GARCH model estimation…………………………...55

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«An investment in knowledge pays the best interest.»
-Benjamin Franklin
1. INTRODUCTION
The topic of volatility spillovers and stock market linkages has always been in the
centre of attention of not only economists and researchers, but also current and potential
investors. Currently, financial markets are experiencing a high degree of linkages due to
increasing international trade, easier flow of capital across the borders, and overall
globalisation. Such procedures have significantly reduced the isolation of individual
markets and increased the possibility of news shocks being transmitted from one market to
another. This, therefore, indicates that linkages between stock markets and economies have
become stronger over the last years. Potentially, it can both benefit and harm the investor,
as it becomes harder to predict how one market might react once the news from outised
economies are received by the home market. At the same time, if it is found that markets
are not linked, it can benefit an investor by reducing the risk one undertakes.
Financial investors are those who are mostly interested in knowing to what extend
stock markets are linked. According to modern portfolio theory, an investor should
diversify a portfolio among assets that are negatively correlated (Markowitz, 1952).
Correlation indeed plays a major role within the topic; however, correlation framework
does not always work for investor, especially, when one wants to build a strategy in a long
run. This is due to correlations being time varying. However, cointegration framework can

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be used in order to examine linkages between stock markets, especially it is useful in long
run since it does not possess same limitations as the correlations framework.
There are different channels of news transmission across the economies and stock
markets; however, the overall topic can be divided in two sections – one that covers short-
term dependences and the one that studies long-term relationships. It is clear that long-
term is more profitable strategy, since it has been found that stock market tends to go up in
the long run (Siegel, 2002). Studying mean returns is a popular way to examine linkages,
however, volatility was found to be a good indicator of interdependances between stock
markets. Volatility spillovers and news shocks are looked at in this research.
Information transmission across markets has always been of interest among
economists and investors, however, this topic became even more essential and highly
studied during the financial instability that was seen worldwide. The most recent financial
crisis of 2008 has shown that there are linkages between markets, since it was found that
the crisis originated in the US, but a decline in prices was experienced in a large number of
markets worldwide. This is the main purpose of this research – to investigate volatility
spillovers and linkages between stock markets during the crisis of 2008.
The main aim of this paper is to investigate linkages between stock markets from
January 2002 until December 2014. The reason for this is to see whether stock markets are
cointegrated and whether this relationship may benefit or harm an investor. The majority
of previous studies have shown that the US market plays a vital role in the worldwide
economy, and therefore, the US has been chosen to represent the “home” market of the
investor in this research. Six different stock markets, including the US S&P 500 were
chosen, with models such as VAR, VECM, and BEKK-GARCH being applied.

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The outline of the dissertation
The structure of the dissertation is as follows:
Chapter 1 is the introduction. It covers the main objectives of the research,
background and motivation, as well as, the importance of the chosen topic within the area
of finance and portfolio management.
Chapter 2 gives the overview of the current literature on the topic of stock market
linkages. It covers such aspects, as the concepts of cointegration and contagion, volatility
spillovers, and explains linkages between various stock indices during the most recent
financial crisis.
Chapter 3 is devoted to the portfolio diversification topic. Essentially, it looks at how
cointegration and diversification interact and interrelate, and how a potential investor can
benefit from those relationships.
Chapter 4 describes the methodology applied within this research. It shows
preliminary steps to test for stationarity, as well as, various models that are used to test for
stock market linkages, and transmission of information across markets.
Chapter 5 represents the findings of the dissertation. Firstly, it describes the data sets
that are being examined, and then unit root and cointegration are tested. Finally, specific
models are applied to test for cointegration and volatility spillovers.
Chapter 6 is the conclusion, that presents the summary of results. It covers the most
vital aspects of the findings and limitation of the research.

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2. LITERATURE REVIEW
Linkages between stock markets are of great interest not only to academics, but also
to potential investors who are looking for opportunities to minimise risk of investment.
Works made in 1970s, for instance, Granger and Morgenstern (1970), Lessard (1974), and
Hilliard (1979) all have found low correlation between national stock markets. Eun and
Shim (1989, p. 241) advise that this might lead to suggestion of international
diversification of portfolio. However, it has been observed during the stock market crash
of 1989, as well as during the financial crash of 2008 that major stock indices around the
world declined more or less simultaneously. This, therefore, indicates that stock indices
are indeed correlated to some degree. Thus, cointegration of markets and volatility
spillovers, or contagion, that occurs when major economic events happen, have to be
investigated in order to improve portfolio diversification, especially at the international
level.
2.1. The concepts of cointegration, volatility spillovers, and
contagion
Firstly, it is important to define all three concepts – cointegration, volatility
spillovers, and contagion. According to Fabozzi, Focardi and Kolm (2006, p. 386), if two
or more series are said to be cointegrated it means they stay close to each other even if
they “drift about” as individual processes. Back in 1990, King and Wadhwani said that
there is no surprise in the fact that stock markets across the world are correlated. This is
due to International Capital Asset Pricing Model that allows such correlation to be present

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(King and Wadhwani, 1990). Therefore, it can be said that nowadays it would be even less
surprising to find such interdependences between stock markets due to ease of information
flow worldwide.
Volatility spillovers are attributed to the fact that some economic events do not only
affect those who participate in them, but also those who seem to be unrelated to the event.
Spillover effect is associated with mentioned above degree of integration and correlation
between markets.
The concept of contagion is clearly connected to volatility spillovers and
cointegration. Forbes and Rigobon (2002, p. 2223) define contagion as “a significant
increase in cross-market linkages after a shock to one country (or a group of countries)”.
One can argue with this definition, as it shows that contagion is present only when there is
a significant increase in cross-market comovement. Thus, when there is no significant
increase in comovement, any degree of correlation between stock markets suggests that
there are linkages between them and a term “interdependence” can be used in this case
(Forbes and Rigobon, 2002). Hence, contagion can be seen as an extreme case of
interdependence when markets are linked to a greater than average degree.
2.2. Reasons behind interdependence between stock markets
Attention of a large number of researchers has been drawn to the topic of
interdependences between stock market even more after the financial crisis of 2008.
However, it is important to understand the background of such linkages between stock
markets and why a high degree of cointegration and contagion is good or bad for the world
economy. Luchtenberg and Vu (2015, p. 179) point out that identification of channels that
transmit contagion is vital for policymakers in order to contribute in effective elimination

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of negative consequences of contagion that can occur during the financial meltdown. “By
understanding the conditions under which contagion may occur, contagion should be able
to be predicted and and policy responses can be enacted in a more timely manner”
(Luchtenberg and Vu, 2015, p. 179).
Caccioli et al (2015, p. 50) point out that there are various types of connections
between financial institutions; they range from common assets held on different
institutions’ balance sheets to specific transactions between these institutions that are
considered to be direct linkages. These linkages are not limited to be just between the
entities of one country, but do also represent international connections. Consequently, this
makes economies of different countries to be linked as well. Caccioli et al (2015, p. 50)
say that such a degree of cointegration can be an advantage in a way of increased
efficiency of these entities, however, “it can also provide channels for contagion, thereby
creating potential sources of systematic risk”.
Moreover, since this particular research focuses on the cointegration between
markets when the financial crisis is present, it is vital to point out whether a stock market
cointegration and contagion is an advantage when economies and financial sector are not
stable. Contagion has obviously been detected earlier than during the most recent financial
crisis. Moser (2003, p. 157) says that international financial contagion is a consequence of
having the “new global economy”. Claessens and Forbes (2004, p. 2) attribute financial
contagion, especially that detected in 1990’s to changes in psychology, behaviour, and
attitude of potential investors. Authors mention that there are two reasons why financial
contagion occurs: fundamental causes and investors’ behaviour (Claessens and Forbes,
2004, p. 5). Jithendranathan (2013, p. 118) explains fundamental linkages as those that
arise from trading activity between countries, as well as movement of funds, i.e. borrowing
and lending that is done by individuals, companies, and countries. Moreover, Moser (2003,

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p. 160) indicates the reason of interdependence among counties in economic fundamentals
being linked together through the balance of payments. Shocks and transmission of news is
also part of economic fundamentals. For instance, Connolly and Wang (2003) in their
research do distinguish between unconditional and conditional news effect on volatility
and their results suggest public information flow impacts volatility only to a small degree.
Financial contagion is linked to stock market efficiency, i.e. the Efficient Market
Hypothesis (EMH) introduced by Fama in 1970. Connolly and Wang (2003) suggest that
economic fundamentals mentioned above are not able to fully explain stock market
contagion, and this is where EMH can help. Jithendranathan (2013, p. 119) says that due to
irrational behaviour of investors and information asymmetry that exists in the market price
movements can be transmitted to other markets resulting in contagion. King and
Wadhwani (1990, p. 6) point out that investors have different information sets available to
them so “they can infer valuable information from price changes in other markets”.
Meanwhile, even when information becomes available it should affect all markets at the
same time, however, not always information is publicly available to all individuals and the
ability to process it quickly and efficiently is not possessed by everyone (King and
Wadhwani, 1990, p. 6).
It is clear that contagion can be an advantage, as it links economies together and
makes information to flow more easily. Yet, during the financial instability high degree of
interconnection between markets may lead to economies that are not directly related to an
event “suffer” as well. For example, Moser (2003, p. 158) says that nowadays a financial
instability in one country may be threatening to the stability of global financial system;
however, not all shock that happen and are transmitted through economies can be
considered as contagion.

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2.3. Linkages between stock markets
Not only it is important to look to the degree of integration between various stock
markets, but also to what extent one can affect the other. There has been a large number of
significant economic event happening over the last 50 years, and there are no doubts they
have affected the stock markets’ behaviour not only in the country where the particular
event took place, but different economies worldwide. Obviously, not every stock index has
the same power and influence on the world economy; therefore, it is possible to say that
there are so-called “leaders” and “followers”.
Granger and Morgenstern (1970), Ripley (1973), and Panto et al (1976) were among
the first to start researching the area of linkages between stock markets and started using
correlation analysis in order to investigate those linkages. For instance, Ripley’s (1973, p.
356) main purpose was to study the systematic covariation between stock prices in
developed countries. He points out that stock markets’ covariances is a vital subject for
individual investors who are willing to allocate funds in such way that it maximises return
for the undertaken level of risk. Though the research by Ripley (1973) did not involve use
of complex econometric models, author still concluded that “more than a half of the
movement in the typical developed country’s stock market index is unique to the country,
but the percentage varies widely between countries” (Riley, 1973, p. 360). The topic of
linkages between stock markets has been substantially improved by Granger (1981) and
subsequently by Granger and Engle (1987) where the relationship between cointegration
and error correction models was firstly introduced (Granger, 1981), and later this
relationship was further extended with development of specific procedures and tests
(Granger and Engle, 1987).

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Cerny (2004) looked at the transmission of information between various stock
markets and indicated such an aspect as “increasing globalisation of the world economy”
has one of the main impacts on stock indices (Cerny, 2004, p. 2). Author also emphasises
on the fact that loosening of economic barriers between countries, as well as, evolution of
information technologies facilitated in stock markets integration as opposed to stock
market fragmentation (Cerny, 2004, p. 2). This has contributed to the tighter linkages
between economies. Recent research by Grobys (2010) looked at four European stock
markets and their cointegration and consequently volatility spillovers. Grobys (2010, p.92)
found that three out of four markets are cointegrated meaning they “follow the same
stochastic trend”. Author also shows that after examining second order moments it was
found that over time volatility spillover effect became more substantial. Mylonidis and
Kollias (2010) point out that there is a vast majority of studies performed on the
cointegration of European stock markets, which do agree on the fact that integration has
generally strengthened in the post-1990 period. However, findings suggest different
degrees of cointegration, especially with the respect to timing.
The linkages between various stock markets have also been examined in the
presence of major economic events. Yang et al (2006, p. 727) point out that although
correlation between stock markets worldwide is higher during the period of volatile
markets, for instance, financial crisis, it is still questionable if these tight linkages between
stock indices exist after the crisis period is over. For instance, Arshanapalli and Doukas
(1993) used the stock market crash of October 1987 as a milestone event while they have
studied relationships between the US stock market and major Western European markets.
Their findings suggest a presence of weak relationship between stock markets before the
financial crash, however, a strong interdependence was found to occur after the crash.
More resent research by Yang and Bessler (2008) have looked at the contagion among

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various stock markets around the period of financial crash of October 1987. Their results
indicate that there has been a drop in all seven stock markets on or following the date of
US stock market crash on October 19. They also point out that the US was the “origin of
the international crash” (Yang and Bessler, 2008, p. 308). Moreover, they found that
Japanese stock market did not participate in the downward pressure to the same extent as
other indices, but instead Japanese market was the one that helped the US to recover.
Yang et al (2006) have studied the interdependence between stock markets in the
USA, Germany, and four Eastern European countries. Russian financial crisis of 1998 was
used as a milestone event, and cointegration before and after have been studied. Their
findings suggest that both short-term dynamic linkages and long-term cointegration
between the US market and those of Europe were strengthened after the financial crisis
took place (Yang et al, 2006). Moreover, authors suggest higher integration regionally and
globally of Eastern European markets after the crisis, comparing to the period before the
crisis happened. Use of regime switching models has helped Yang et al (2006) to find that
stock market cointegration is indeed time varying, i.e. it changes depending on how
volatile stock markets are. Lucey and Voronkova (2008, p. 1320) have looked at whether
the Russian crisis of 1998 has made any impact on linkages between Russian and other
equity markets. After employing traditional multivariate cointegration approach, authors
have not observed any equilibrium relationship in the period of 1995 - 2004. Lucey and
Voronkova’s (2008) study indicates that Russia has been and also remains isolated from
the world equity markets. On the other hand, applying more complex analysis that allows
for time variations and breaks in the cointegration relationship, it has been found that
Russian market still does not show any strong evidence of long-run convergence with both
regional and developed equity markets.

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Nonetheless, there is a number of researches that indicate absence of any level of
cointegration between national stock markets. For instance, Richards (1995, p. 652)
suggests, “there is a little empirical evidence for the proposition that stock returns of
different countries are cointegrated”. However, author says that results may be in
accordance with expectations, addressing them to the standard asset-pricing model that
implies that “return indices should contain random-walk components which would
preclude cointegration” (Richards, 1995, p. 652). Cerny (2004) looked at the degree of
cointegration between seven stock markets around the world and found that only one pair
out of all possesses some cointegration. However, Cerny (2004, p. 16) sees a reason in
such a finding in the lack of number of observations. Therefore, this result has to be treated
with caution and can serve as a proof that the longer the period that is being covered by a
research the more reliable results will be.
Once again, it is important to differentiate between the cointegration and contagion
as it might affect findings of the research. Study made by Forbes and Rigobon (2002) have
found absence of contagion, but claim that interdependence between markets is still
present. They have used the model that accounts for the heteroscedasticity present in the
time series data and found no significance increase in cross market correlations during the
studies periods. Forbes and Rigobon (2002, p. 2250) interpret this result as an absence of
contagion, however, there was a high level of comovement between markets.
2.4. Volatility spillovers
It is clear that due to high level of interconnection between world stock markets
volatility spillovers are present. This is associated with some markets being more powerful
and influential than the others and, therefore, it makes shocks to be transmitted across the

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world more easily. According to the theory of Efficient Market Hypothesis by Fama
(1970), new information that “hits” the market triggers its movements. If markets are
highly related, then new information will be dealt with in a same way and simultaneously
by all investors, however, it has been proved that information “hits” different markets at
different speed (Johansson and Ljungwall, 2009). This, therefore, proves that there are
“pioneer” stock markets and lag stock markets that cannot acquire new information
quickly.
Eun and Shim (1989) and Becker et al (1990) were among first to study spillover
effects of different stock markets. For instance, Eun and Shim (1989) have looked at the
daily stock market returns in nine different countries - the US, the UK, Australia, Japan,
Hong Kong, France, Canada, Germany, and Switzerland. They found that stock markets
are indeed interdependent and the US is being the “leader”, i.e. making the most influence
on the other markets. In addition, markets responded to external shocks sent by the US
with a lag of one day, with most shocks disappearing within two days time.
Introduction of GARCH-family models has made a huge impact on ability to study
volatility spillovers on stock markets. Engle, Ito and Lin (1990) were among the first to
initiate the use of multivariate GARCH models in order to estimate volatility spillover. In
their research, they have looked at the intraday volatility spillover between the US and
Japanese foreign exchange markets. They have particularly focused on the news in Japan
and found that this news do affect the exchange rate, explaining this to be due to existence
of private information (Engle, Ito and Lin, 1990, p. 540). Since then, multivariate GARCH
model became a popular choice among many authors who have been studying volatility
spillovers and volatility clustering (Karolyi (1995), Bekaert and Harvey (1997),
Christiansen (2003)). For instance, Theodossiou et al (1997) used multivariate GARCH to
study spillover effect between stock markets in the US, Japan, and the UK. His conclusion

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refers to the fact the US market affect those in the UK and Japan and triggers statistically
significant spillover effect. Ng (2000, p. 207) emphasises that understanding volatility’s
sources and behaviour is important for pricing domestic securities, as well as,
implementation of hedging strategies worldwide and making asset allocation decisions.
Author looks at the Pacific-Basic region and to what extent volatility in these markets in
affected by shocks happening in other national markets. After constructing a volatility
spillover model, Ng (2000, p. 230) found that both regional and world factors affect
volatility in Pacific-Basin region, with world factors having greater influence.
Nonetheless, findings suggest that in four out of six Pacific-Basin countries “the Japanese
and the US shocks together account for less than 10% of weekly variation in returns” (Ng,
2000, p. 231).
Baele (2002) investigated whether economic, monetary, and financial integration
that have been strengthened in Europe have significantly altered the intensity of
transmission of shocks from the US and aggregate European index to thirteen European
stock indices. Important to note that Baele (2002) allows for switching between different
regimes depending on whether shock spillover intensity is high or low. He finds both
statistical and economic significance in regime switches in volatility spillover intensities
(Baele, 2002, p. 32). The results indicate presence of correlation between markets that is
statistically significant, however, no contagion between European and the US market has
been found.
Zhang and Jaffry (2015, p. 27) point out that studies on volatility spillovers can be
divided in two categories: those that focus on domestic markets, and those that study
international markets spillover effects. Kang and Yoon (2014) have looked at the domestic
markets examining volatility spillover effects between futures and spot markets in Korea.
High-frequency data has been used with application of BEKK-GARCH model. Kang and

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Yoon (2014, p. 203) conclude that bi-directional causality relationship between markets
exists, meaning that both markets respond to the new information simultaneously.
However, study by Zhong, Darrat and Otero (2004) indicate that trading on the futures
market of Mexican stock index has caused instability in the spot market. After applying
various methods, like Vector Error Correction Model (VECM), EGARCH model, and
cointegration technique, their conclusion suggests that the futures market transmits
volatility to the spot market.
When looking at the spillover effects in the international context major
developments in technology and flow of capital across the word has facilitated
globalisation. Li and Giles (2015) have looked at the volatility spillovers between the USA
and Japan and world emerging markets. Authors found spillovers to be robust both over
the short and long term, with spillover effect becoming stronger and more apparent during
the last five years (Li and Giles, 2015, p. 164). Christiansen (2003) has studied the
volatility spillovers in the international bond market and found the effect to be substantial.
Essentially, Christiansen (2003) looked at the volatility transmission in European bond
markets from the bond market in the USA.
2.5. Stock markets’ relationships during the financial crisis
of 2008
The financial crisis of 2008 has made a huge impact on every aspect of countries’
economies worldwide, and it is impossible to identify an economic area that has not been
affected. It is not of a surprise that there have been a large number of studies made
specifically on the financial crash of 2008.

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The failure of the subprime mortgage market triggered the financial system of the
world to become unstable. Luchtenberg and Vu (2015) have identified reasons behind the
level of contagion during the global crisis of 2008. After using the logistic regression,
Luchtenberg and Vu (2015, p. 202) have found that changes in economic indicators, such
as relative levels of export, relative inflation, industrial production, and changes in
investor’s risk aversion have contributed to a level of contagion. Authors agree with
findings of Kenourgios (2014) and claim that there has been an increase in risk aversion of
investors during the beginning phase of the global financial crisis of 2008; this is
potentially associated with changes in investor’s expectations of economics factors, such
as level of inflation, level of production, and levels of import and export (Luchtenberg and
Vu, 2015, p. 202).
Bekaert et al (2014, p. 2597) claim that financial crisis of 2008 is the first major
crisis since the Great Depression of 1929 - 1932 that affected economies globally. Even
though the USA were identified as the origin of the crisis, as well as, the market (subprime
mortgages market) where the bubble developed is relatively small, it spread across all
economies, with some countries facing even worse decline of the equity market than the
United States (Baekert et al, 2014, p. 2598). It made it clear that contagion is playing a
vital and potentially negative role. Baekert’s et al (2014) findings show presence of
contagion when studying a factor model. However, authors found a weak evidence of
contagion between the US and other equity markets during the crisis. They have indicated
that portfolios held in countries with weak economic fundamentals, high fiscal and current
account deficits faced a higher degree of contagion both from national and international
markets and were affected harder overall.
Choudhry and Jayasekera (2014) have studied not only returns, but also volatilities
and leverage spillovers between banking industry and various European stock markets.

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Authors divided data set into pre-crisis and during-crisis samples applying BEKK-
GARCH model throughout their research. Results suggest an increase in volatility
spillover effect between European economies during the financial crisis when comparing
in to the period of pre-crisis. Zhang and Jaffry (2015, p. 27) support finding of Choudhry
and Jayasekera (2014) saying that little evidence of spillover effects was found when
looking at the pre-crisis period, however, during the crisis there is a strong volatility
transmission from smaller European stock markets to the UK and US stock markets.
Since there are different linkages between countries, Ozkan and Unsal (2012) have
developed a framework that looks at both trade and financial linkages to study
interdependence of equity markets during the most recent crisis. Their findings are as one
would expect – low degree of contagion is associated with the low degree of impact of
global economy on domestic economy (Ozkan and Unsal, 2012, p. 29). Having a low
contagion is advantageous for country’s economy since it is able to quickly recover from
the external shock. Moreover, findings suggest that financial interdependence, openness to
trade internationally, and the level of foreign currency denominated debt play the vital role
in determining how global financial shocks are influenced by the monetary policy regimes
(Ozkan and Unsal, 2012, p. 30).
It has been discovered that the majority of studies written on contagion have looked
at the aggregate equity markets of different countries; however, it is possible to measure
contagion of different sectors across various countries and regions. There is evidence that
not only financial sector has been majorly affected by the crash, but also it has transmitted
to different sectors, like healthcare, transportation, and telecommunications. For instance,
Baur (2012) have looked at how the global financial crisis of 2008 has spread from the
financial sector to the real economy. Author studies a large sample of both countries and
sectors, as well as, there are different channels of contagion being tested, such as

24
contagion within the financial sector of one country, contagion within the financial sector
between different countries, and contagion between the financial sector and the real
economy of one country (Baur, 2012, p. 2680). Results are unsurprisingly showing that the
financial sector played the main role during the crisis, additionally it was found that there
is no country or region among those studied that has been unaffected by the crash (Baur,
2012, p. 2691). Contagion of the real economy was found to be weak, especially for such
sectors as healthcare, telecommunications and technology, with Baur (2012, p. 2691)
arguing that it indicates an ability of investors to effectively diversify portfolios by
distinguishing between sectors. Kenourgios and Dimitriou (2015) have taken a similar
approach to Baur (2012) and investigated financial contagion from regional perspective by
using aggregate stock indices and sector stock indices of both developed and emerging
countries. Findings indicate that many real economy sectors in the USA, Europe, and
Pacific were less vulnerable to their financial sectors during the financial crash. Moreover,
most regions and sectors were found to be immune to negative shocks transmitted in the
beginning of the crisis, however, they were more heavily affected during the later stages of
crisis showing a high degree of cointegration (Kenourgios and Dimitriou, 2015, p. 292).
Authors associate it with changes in investor’s behavior and unwillingness to take any risk.

25
3. COINTEGRATION, CONTAGION, AND
PORTFOLIO DIVERSIFICATION
An important topic that arises when studying stock market cointegration and
contagion is whether findings of such research can help a potential investor to maintain a
profitable position on the stock market. This is linked to abilities to diversify portfolio both
within one country or economy, as well as, benefit from the international diversification.
Moser (2003, p. 161) suggests that it is common to diversify internationally. For instance,
investors like banks, mutual, hedge, and pension funds diversity portfolios over different
countries. But this practice is not limited to only institutional investors and is also common
among individual investors. Pesaran and Pick (2003, p. 2) argue that is it important to
distinguish between contagion and interdependence. They say “investors need to take a
different kind of risk into account for their portfolio choices if markets have a higher
correlation after negative shocks” (Pesaran and Pick, 2003, p. 2). If the correlation
between different markets is higher during the period when negative shocks persist
comparing to non-crisis period, diversification benefits can be a lot less substantial than
anticipated before a negative shock.
As it has been mentioned in Chapter 2.2, existence of information asymmetry plays a
vital role in presence of contagion in the world economy. Yet, Schinasi and Smith (1999)
argue that market imperfections are not the only aspect to take into account and the basic
principles of portfolio theory can be applied. As financial crisis takes place, investors find
it optimal to sell many assets that are risky even if the shock occurs only to one asset, with
Schinasi and Smith (1999) claiming that portfolio diversification and leverage is sufficient
to explain such behaviour. Phylaktis and Xia (2009, p. 2) on the other hand, claim that

26
“sector heterogeneity of contagion” implies presence of sectors that can still provide
diversification benefits in spite of the crisis and present market contagion. Moreover, with
increased globalisation domestic risk factors are less important than non-domestic, which
makes international diversification less preferable and diversification across industries
more beneficial (Phylaktis and Xia, 2009, p. 22).
Goldstein and Pauzner (2004, p. 175) have looked at the self-fulfilling crisis and its
relation to contagion. Goldstein and Pauzner (2004) exlain self-fulfilling crisis as the one
caused by agents withdrawing investments as they fear that others will do the same.
Authors say that after the crisis “hits” the economy investor’s wealth is reduced and they
become more willing to withdraw any investments held in other countries since they are
unaware of agents’ behaviuor in that other country. This makes the crisis to potentially
spread to that other country (Goldstein and Pauzner, 2004, p. 151).
Findings of the study by Yang and Bessler (2008) are essential for understanding of
the management process of global equity portfolio. Especially, authors point out
“existence of contagion among developed markets during a crisis period suggests that
potential benefits of international diversification could be substantially reduced when it is
desired most” (Yang and Bessler, 2008, p. 308). Yang and Bessler (2008) are not the only
ones to mention negative effects of cointegration and contagion. Baur and Miyakawa
(2014) investigated such an aspect as macro-financial contagion, which implies “that the
stock market does not only signal future economic performance but also
contemporaneously affect the real economy” (Baur and Miyakawa, 2014, p. 20). Authors
argue that macro-financial contagion is a disadvantage for investors, firms, and households
that are exposed to risks from the stock market and real economy. Looking at the
contagion between sectors, Baur and Miyakawa (2014) argue that in times of financial

27
decline in both stock prices and real economic activity, investors are going to face bigger
losses due to contagion.
Global financial crisis of 2008 has also “contributed” to studies on portfolio
diversification opportunities. Choudhry and Jayasekera (2014) found that mean of the
betas of most banks in European countries (France, Germany, Greece, Ireland, Italy, Spain,
and Portugal) have risen from the pre-crisis period to the during-crisis period. They found
banks to be resilient and efficient throughout the period of financial instability. In spite of
that, investors have been suffering for the instability of banking sector as a whole of the
investigated countries. Choudhry and Jayasekera (2014, p. 19) attribute it to market shocks
that were found to cause a large number of abnormal returns, therefore “reinforcing the
asset mispricing theory as an explanation for the stock price behaviour”. Private investors,
as well as, institutional investors, hedge funds, or investment banks may exploit such
findings, as they indicate that more profitable arbitrage opportunities are present during the
period of financial crisis, where asset mispricing is evident. Despite having those
advantages, it is not possible to exploit such stock market anomalies and generate positive
returns on the constant manner.

28
4. DATA AND METHODOLOGY
Over the years, there has been a change in methods and techniques used in order to
assess the degree of dependence and linkages between various stock indices’ returns. For
instance, early studies have been looking at the correlations and more simple
interdependence structure between two or more information sets. Boswijk et al (2010, p.
159) explain that in the 1950s and 60’s there were developments in econometric models
that looked at simultaneous equations, which mimic cointegration models. Further
advanced development of multiple-equation models that could possibly be used in order to
forecast become possible with arrival of powerful computers.
Previous literature suggests that use of correlation models was popular when
studying contagion. It essentially involved estimation of cross-market correlations during
stable period and comparing it to a crisis period. For instance, King and Wadhwani (1990)
and Lee and Kim (1993) applied cross-market correlation technique in their studies. The
contagion was said to be observed if there is an increase in correlation when comparing
crisis period to a stable period. However, Samarakoon (2011, p. 725) points out that
hetescedasticity that is usually found in time series data and that is caused by an increase
in stock market volatility observed during crisis, may make correlation coefficients biased.
Moreover, as it has been previously mentioned, contagion is observed when there is a
dynamic increase in return correlations (Samarakoon, 2011, p. 725).
Works by Granger (1981) and Engle and Granger (1987) are fundamental in
studying relationship between non-stationary processes that are sharing a common trend.
Even though two or more time series can be seen as random walk processes, i.e. their
future movements are unpredictable (Tsay, 2005, p. 64), there might be a common external
force that moves these time series together, thereby tying them together.

29
The following Chapter emphasises on data that have been studies in course of this
research. It also introduces the formal methodology that has been applied.
4.1. Hypothesis of the research
The null hypothesis of this research and its alternative are as follows:
H0: There are linkages between stock markets in the presence of financial crisis of
2008.
HA: Stock markets are not linked in the presence of financial crisis of 2008.
Therefore, the main objective of the research is to identify to what extent stock
markets are linked and whether this relationship remained constant throughout the studied
period.
4.2. Statistical analysis of data
In order to proceed with the application of econometric models, it is important to
determine the nature of studied data. Descriptive statistic is a valuable tool in this research
as it helps to identify specifications of data sets that leads to a corret decision of what
econometric model has to be used.
This research focuses on studying relationship between the US stock index S&P 500,
the UK stock index FTSE 100, German index DAX, Swiss index SMI, Japanese NIKKEI,
and the French stock index CAC. The closing daily prices of all indices were obtained

30
from the Bloomberg platform. The studied period runs from 1 January 2002 until 31
December 2014. Period is chosen in such a way that whole data set can be divided into
three sections — pre-crisis, crisis, and post-crisis. Formula below was applied to obtain
daily returns on both stock market indices:
!! = ln!(
!!
!!!!
)
where Pt denotes the closing price in time t (t=1,…, n).
4.3. Formal methodology
Since the main purpose of this research is to identify linkages between stock markets
and study volatility spillovers, therefore, the applied methodology is divided into two
sections — firstly, study employs the unit roots test to confirm stationarity of the process,
as well as, Johansen’s cointegration and error correction models and VAR model. This is
done in order to examine long run relationship across stock indices. Secondly, in order to
identify information transmission and spillover effect, GARCH model is applied. As the
GARCH family includes a big variety of models, only multivariate models are used in this
research – the BEKK model.
4.3.1. Long-term and short-term interdependence
When studying stock market linkages, on one hand, there might be a long-run
dependence present in the data, but on the other hand, interdependence can be found
during short periods of time, for instance, during the financial crisis only. Therefore,
different techniques have to be applied. Presence of long-term interdependence can be
(4.1)

31
identified through cointegration techniques proposed by Johansen. Throughout many
researches it has been found that stock prices, due to being time series, are not stationary,
however, stock index returns are stationary (Tsay, 2005, p. 64). It might be possible that
there is no cointegration present when looking at the long run, however, there still might
be a short run dependence. VAR model is used to account for such specification as
whether relationship between markets is positive or negative, as well as, its strength.
4.3.2. Unit root test for stationarity
There are several tests that are used to check for stationarity of data. For instance,
Dickey-Fuller test, Augmented Dickey-Fuller test, test by Kwaitkowski, or Phillips-Perron
test can be used. This research focuses on Augmented Dickey-Fuller (ADF) test proposed
by Dickey and Fuller (1979). Harris (1995, p. 28) claims Dickey-Fuller test to be the most
popular among researchers due to its simplicity and more general nature. ADF test helps
to determine the order of integration. The standard Dickey-Fuller test assumes identical
and independent distribution of standard errors, and since this is not the case in most data
and errors allow for heterogeneity and serial correlations, the Augmented Dickey-Fuller
test is used (Harris, 1995, p. 47). The null and alternative hypotheses under the ADF test
are as following:
H0: Unit root is present in the data set.
HA: There is no unit root in the data set.
Pfaff (2008, p. 55) mentions that random walk process is seen as a prototype for a
unit root process. Many see behaviour of stock market as being a random walk process.

32
Therefore, application of unit root test will help to identify whether stock indices used in
this research are random walk processes.
4.3.3. Test for cointegration, Johansen’s method
After the order of integration in the process in determined, it is possible to build a
model that leads to stationary relations among the variables. Testing for cointegration is
necessary in order to verify whether the studied relationship between stock indices is
empirically meaningful. Engle-Granger cointegration testing technique (1987) is explained
by Brooks (2014, p. 378) as being one of the most popular regardless its drawbacks; it is
being widely used to perform analysis of the cointegration in data. However, as mentioned
by Brooks (2014, p. 379) OLS estimation that is being used in Engle-Granger method
cannot be applied when there are more than two variables in the system. Therefore, it is
proposed to use Johansen’s method for cointegration testing (Johansen, 1988; Johansen
and Juselius, 1990). The following methodology has been obtained from Brooks (2014).
VAR model was found to be more suitable to test for cointegration between stock markets
(Samarakoon 2011, p. 726). Johansen’s test is based on vector autoregressive system,
which has the following representation as VECM model (Brooks, 2014, p. 386):
∆!! = !Π!!!! + Γ!∆!!!! + Γ!∆!!!! + ⋯ + Γ!!!Δ!!! !!! + !!
П represents the long-run coefficient matrix and its properties are used to examine
cointegration between vectors Yt. The test for cointegration between al Yt’s depends on the
rank of the matrix П. So that if П has the value of zero, it indicates no cointegration
between variables, while having a rank with the value greater than zero is associated with
(4.2)

33
some degree of cointegration between variables. There are two test statistics that are used
with Johansen’s cointegration framework (Brooks, 2014, p. 387):
!!"#$% ! = −! ln!(1 − !!)
!
!!!!!
and
!!"# !, ! + 1 = −!"# 1 − !!!! ,
where r stands for the number of cointegrating vectors under the null hypothesis, T
stands for the number of observations, and !! is the estimated value for the ith ordered
eigenvalue from the Π matrix. Trace statistic tests for the maximum amount of r
cointegrating vectors against the alternative of more than r vectors. Maxim eigenvalue
statistic conducts separate tests for each eigenvalue with the null of r amount of
cointegrating vectors against the alternative of r+1.
Econometrics packages, in particular EViews software that is being used in this
research, do provide cointegration tests, and obtained results are presented in Chapter 5.
4.3.4. VECM and VAR models
The Vector Error Correction Model and Vector Autoregressive model are used as
another way of representing the cointegrated vector I(1) process (Hayashi, 2000, p. 633).
Hill et al (2011, p. 499) points out that application of VECM and VAR models is
especially useful in order to account for dynamic properties and interactions of time series
data.
(4.3)
(4.4)

34
Empirical application unit root analysis discussed in Chapter 5.2 gives an indication
of whether the time series data is a stationary or non-stationary process. VAR model can
be easily adjusted to whether the initial data set is stationary or not. Hill et al (2011, p.
500) explain as if two data sets are stationary I(0) then it is possible to apply the VAR
model without making any transformations to the data sets. However, of data is non-
stationary, then the first difference has to be used instead of the level data, for instance,
first differences of daily return series instead of the actual daily returns. So that, in first
case scenario formulae is as follows (Hill et al, 2011, p. 499):
!! = !!" + !!!!!!! + !!"!!!! + !!
!
!! = !!" + !!"!!!! + !!!!!!! + !!
!
Formulae 4.5 and 4.6 describe the case when a variable is function of its own lag and
the lag of the second variable in the system. When these two equations are considered as a
system, it is the VAR model. In case when data sets are non-stationary, the formulae have
the following representation (Hill et al, 2011, p. 499):
∆!! = !!!∆!!!! + !!"∆!!!! + !!
∆!
∆!! = β!"∆!!!! + !!!∆!!!! + !!
∆!
It is seen that not only the lagged values are used, but they are also the values are the
first difference. The tem vt, which is included in all equations, represents the unpredictable
variation in yt, or the innovation in yt that cannot be predicted by the past values of y and x
(that are yt-1 and xt-1). The advantage of VAR model is that it can be used even where there
is no cointegration found among the variables.
(4.5)
(4.6)
(4.7)
(4.8)

35
However, when cointegration is indeed present, it has to be accounted for and the
VAR model has to be modified. Introduction of cointegrating relationships leads to the use
of VEC model. For instance, it is assumed that two non-stationary variable are
cointegrated, then they have the following representation (Hill et al, 2011, p. 500):
!! = !! + !!!! + !!
where it is seen that one variable is dependent on the values of the other variable.
The VECM is the special case of the VAR model for non-stationary cointegrated data and
has the following form:
∆!! = !!" + !!! !!!! − !! − !!!!!! + !!
!
∆!! = !!" + !!" !!!! − !! − !!!!!! + !!
!
Hill et al (2011, p. 500) explains that coefficients α11 and α21 are known as error
correction coefficients; their purpose is to show how much Δyt and Δxt respond to the
cointegrating error (yt-1-β0- β1xt-1=et-1).
4.3.5. GARCH framework to test for volatility spillovers
According to Forbes and Rigobon (2002, p. 2228) there are different methods to test
for linkages between markets, and one of them is to use GARCH framework to “estimate
variance-covariance transmission mechanisms between countries”. Based on the
discussion in chapter 2 it has been observed that GARCH family models are one of the
most appropriate to examine presence of volatility spillovers within the data. Since
(4.9)
(4.10)
(4.11)

36
GARCH family has a wide variety of various extensions and specifications of the basic
model, it is needed to only examine those that are used for testing the spillover effect. The
basic GARCH model was introduced by Bollerslev (1986) as a generalisation of ARCH
model by Engle (1982). The GARCH(p,q) model has the following structure (Hill et al,
2008, p. 372):
!! = !! + !!
!!|!!!!~!(0, !!)
!! = ! + !!!!!!
!
+ !!ℎ!!!
!
!!!
!
!!!
where ht is the variance of the error term, q is the number of lagged error terms in the
model, while p is the number of lagged variance terms.
Multivariate GARCH models discussed by Engle, Ito and Lin (1990) are widely used
in equity, bond, and foreign exchange markets. According to Brooks (2014, p. 467) there
are several different multivariate GARCH formulations, for instance, the VECH, the
diagonal VECH, and the BEKK models. All of those specifications allow for N number of
assets and their returns, variances, and covariances are being modeled.
The VECH model
Specification of VECH model is as follows (Bollerslev, Engle, and Wooldridge,
1988):
!"#$ !! = ! + !"#$% Ξ!!!Ξ!!!
!
+ !"#$%(!!!!)
Ξ!|!!!!~!(0, !!)
(4.12)
(4.13)
(4.14)
(4.15)
(4.16)

37
where Ht is the variance of error term and it represents a NxN conditional variance-
covariance matrix, Ξt is a Nx1 innovation vector, Ψt-1 is the information set that is available
at the time t-1, and the VECH(!) is the column-stacking operator that is applied to the
upper portion of the symmetric matrix (Brooks, 2014, p. 468). Silvennoinen and Terasvirta
(2008, p. 3) explain the model to have every conditional variance and covariance to be the
function of all lagged conditional variance and covariance and also lagged squared returns
and cross products of returns. Brooks (2014) mentions that VECH model requires a lot of
variables to be estimated even when just two assets are used, and the amount of estimated
variables grows rapidly as more assets are added which complicates the whole process of
model estimation. Therefore, it is possible to use the diagonal VECH model that has the
conditional variance-covariance matrix to be restricted to the form developed by
Bollerslev, Engle, and Wooldridge (1988) where A and B estimated in equation 4.15 are
assumed to be diagonal. However, the disadvantage of this model is that there are no direct
volatility spillovers from one time series to another to be present. Even though such a
restriction considerably reduces the number of parameters to be estimated, it is a
disadvantage in this particular research as it specifically looks at the volatility spillovers.
The BEKK model
The model had been developed by Baba, Engle, Kraft, and Krone (Engle and Krone,
1995) and addresses the problem that VECH model faces and ensures that the H matrix is
always positive definite. It has the following specification (Brooks, 2014, p. 470):
!! = !!
! + !!
!!!!! + !!
Ξ!!!Ξ!!!
!
! (4.17)

38
where A and B are NxN matrices of parameters and W is an upper triangle matrix of
parameters. The presence of volatility spillovers is estimated through both matrices A and
B. The diagonal parameters in matrix B show the effect of lagged volatility; the off-
diagonal parameters represent the cross-market effects (Xiao and Dhesi, 2010, p. 153). For
instance, when there are only two assets within the model, matrix A can be represented as
follows:
!!
=
!!! !!"
!!" !!!
In this case, the parameter α12 represents the volatility spillover from market 1 to
market 2, and α21 represents the volatility spillover from market 2 to market 1. Moreover,
Xiao and Dhesi (2010, p. 159) the matrix A represents the ARCH effect, while the matrix
B represents the GARCH effects in the system. It is essential to point out that these
spillover effects might be different, since one market can be a “leader” and having more
influence on the other, the “follower” market. The statistical significance of these
estimated parameters tells about the volatility spillover effect.
(4.18)

39
5. EMPIRICAL RESULTS
The following Chapter represents empirical findings of this research. Firstly, all data
has been analysed with application of basic statistics to understand the characteristics and
behaviuor of all equity market returns. Such statistical measures, as skewness, kurtosis,
Jarque-Bera test statistic are applied on all data sets to examine whether the stock market
returns possess normality features.
First of all, it is interesting to examine behaviour of stock market prices over the
studied period of time. Graphs 1 shows “walks” of all six stock markets – S&P 500, FTSE
100, CAC, NIKKEI, DAX, and SMI.
0
4,000
8,000
12,000
16,000
20,000
02 03 04 05 06 07 08 09 10 11 12 13 14
CAC DAX FTSE 100
NIKKEI SMI SP500
Graph 1: Patterns of stock indices from 2002 until 2015

40
Looking at the Graph 1, it is clearly seen that all stock markets have experienced an
overall rise from 2002 until the peak in 2007. However, again all indices faced a dramatic
decline in the period from 2007 to 2008. Since it has been mentioned that the US has been
found to trigger the subprime mortgage crisis, as well as, it is seen that all stock market
exhibit the same pattern it is possible to claim that there is a linkage between the markets.
However, this conclusion is based on examining the graphical representation of data and
has to be supported by the econometric model.
5.1. Statistical features of data sets
Daily closing prices have been transformed into returns and descriptive statistic of
all indices’ returns can be seen below in Table 1.
Table 1 represents the summary of statistical features that help analising daily
returns of six stock indices. It is seen from the Table 1 that mean values of all data sets are
close to zero, with standard deviation values being relatively low. According to Hill et al
Index Mean
Standard
deviation Minimum Maximum Skewness Kurtosis
Jarque-Berra
statistic
12035.72
0
7889.765
0
3351.009
0
4099.657
0
6157.631
0
6852.796
0
9.693566
NIKKEI 0.000148 0.015396 -0.12111 0.132346 -0.486268 10.10283
SMI 0.000104 0.011979 -0.081078 0.107876 0.039055
7.924192
CAC -2.09E-05 0.014979 -0.094715 0.105946 0.064379 8.435831
DAX 0.000193 0.015309 -0.074335 0.107975 0.037809
12.38572
FTSE100 6.79E-05 0.012126 -0.092645 0.093842 -0.0136295 10.47539
S&P500 0.000177 0.012688 -0.094695 0.109572 -0.217887
Table 1: Descriptive statistic of stock index returns

41
(2011, p. 33) mean value is 0 and standard deviation of 1 when financial data is standardly
normally distributed. Minimum and maximum values are in accordance with expectations,
however, under the normal distribution the value of kurtosis is 3 with skewness of
distribution being zero. These two features are violated in all data sets, with high value of
kurtosis indicating non-normal distribution (leptokurtosis), as well as, values of skewness
show that returns are not symmetrically distributed around zero (Hill et al, 2011, p. 148).
Non-zero skewness and leptokurtosis are also associated with fat tails that are found to be
present in financial data sets (Fama, 1965). Jarque-Bera test statistic is associated with
values of skewness and kurtosis of index returns. The null hypothesis claims presence of
normal distribution. Table 1 clearly shows that null hypothesis of normal distribution is
rejected in all cases, since all probability values associated with statistic values (are found
under the Jarque-Bera test values in Table 1) are less than 0.01, the probability value
implied by the significance level of 1%. It can be concluded that results of statistical
analysis of all 6 index returns are in accordance with those described by Fama (1965) and
are consistent with the theory of non-normal stock returns distribution.
5.2. Unit root testing
As mentioned in Chapter 4.3.2 there are various tests that can be applied to examine
presence of unit roots in the data set. EViews econometric package provides different test
and ADF has been chosen in this research. Results of ADF test are shown in Table 2 with
values of probability test associated with it shown in the brackets.
ADF test is performed under the null hypothesis of presence of the unit root in the
data; unit root test is applied on the actual stock market prices. If one if testing for
stationarity, then the null hypothesis implies stationarity and the test is applied on the stock

42
return series rather than prices. ADF test was performed with two specifications –with
inclusion of intercept term and with inclusion of both intercept term and a trend.
According to Table 2, all series have a unit root. This is due to all probability values
shown in brackets being higher than 1% with leads to inability to reject the null hypothesis
of unit root.
As it has been detected that all indices have a unit root, therefore, it is needed to test
whether return series are stationary in order to apply any models in further Chapters. The
same ADF test has been applied on return series and results are presented in Table 3.
Index
ADF
(intercept)
ADF
(intercept and
trend)
S&P500
0.135867
(0.9684)
-1.259256
(0.8970)
FTSE100
-1.509667
(0.5288)
-2.725131
(0.2263)
DAX
-0.474290
(0.8937)
-2.457633
(0.3495)
CAC
-1.996204
(0.2887)
-1.981606
(0.6106)
SMI
-1.198108
(0.6776)
-1.690165
(0.7557)
NIKKEI
-1.210439
(0.6722)
-1.312561
(0.8845)
Level series
Table 2: Unit root test results for six stock indices

43
Table 3 shows that all return series are stationary, since it is possible to reject the
null hypothesis and conclude that there are no unit roots in the data sets. According to
Mahadeva and Robinson (2004, p. 3) it is important to use stationary data in modeling and
forecasting, as the use of non-stationary data may lead to misleading parameter estimates,
as well as, unit root testing can help to examine the process behind the data set and what
model has to be built.
5.3. Testing for cointegration
Johansen’s test is performed directly on stock index prices data sets. Johansen’s test
can only be applied on the time series that are integrated of the same order. The null
hypothesis implies that there is no cointegration between any variables in the models. Test
Index
ADF
(intercept)
ADF
(intercept and
trend)
S&P500
-44.79313
(0.0001)
-44.81320
(0.0000)
FTSE100
-28.14928
(0.0000)
-28.15146
(0.0000)
DAX
-58.72470
(0.0001)
-58.73049
(0.0000)
CAC
-28.94250
(0.0000)
-28.94481
(0.0000)
SMI
-28.08285
(0.0000)
-28.09129
(0.0000)
NIKKEI
-58.40117
(0.0001)
-58.40102
(0.0000)
Return series
Table 3: Augmented Dickey-Fuller test results

44
was applied with the use of EViews package with results having two statistics – the trace
statistic and maximum eigenvalue statistic. Results of estimating all return series are
presented in Table 4, while results of cointegration test between pairs of return series can
be found in Table 5. The overall result in Table 4 indicates that cointegration is indeed
present in the model. Looking at the probability values associated with trace statistic it is
possible to reject both the null hypothesis of no cointegration and the null hypothesis of 1
cointegrating vector with the 99% confidence level. Looking at the probability values
associates with maximum eigenvalue statistic can conclude the same result. Since it is
possible to accept the null hypothesis of “at most 2” cointegrating vectors in the model,
there is no need to look at the remaining rows with higher number possible vectors
(Brooks, 2014, p. 395). However, the Johansen’s test does not give any information
regarding the nature of relationships in the model and to what extent indices are linked to
each other; test only indicates whether cointegration is present or not.
Examining pairs of indices, that is S&P 500 index paired with other indices, is vital
to understand whether there are any benefits from international diversification. Chiou
(2009, p. 94) address the question of whether international diversification is still need in
the presence of high integration between global markets. Author finds that despite high
integration, international diversification is indeed benefits the US investor (Chiou, 2009, p.
108).

45
Table 4: Cointegrating vector test of the whole data set
Since this testing once again indicates just the presence of cointegration between
paired stock indices, it is essential to run further models to investigate whether relationship
between stock markets changed due to financial crisis of 2008 and whether diversification
benefits are affected by much macroeconomic event.
Table 5 shows cointegration test between S&P 500 and other indices. There is no
cointegration found between the US index and other indices discussed with one exception.
Presence of one cointegrating vector was found only in one pair, which is with FTSE 100.
It can be due to the fact that both stock markets are bigger and more influential when
Index Eigenvalue
Trace
statistic
Max-eigen
statistic
Eigenvalue
Trace
statistic
Max-eigen
statistic
Conclusion
FTSE 100 0.006765 22.48173* 21.41723* 0.000337 1.064501 1.064501 Cointegration
DAX 0.004053 12.82332 12.81414 2.91E-06 0.009177 0.009177 No cointegration
CAC 0.001291 4.076747 4.746 6.80E-07 0.002147 0.002147 No cointegration
SMI 0.002699 8.555245 8.527705 8.73E-06 0.027539 0.027539 No cointegration
NIKKEI 0.003465 11.01819 10.95243 2.08E-05 0.06576 3.841466 No cointegration
No cointegrating vector At most 1 cointegrating vector
Table 5: Cointegrating vector test for pairs of indices
Hypothesised
No. of CE(s)
Eigenvalue Trace statistic
Max-Eigen
Statistic
None 0.028507 200.3162* 91.24721*
At most 1 0.019026 109.0690* 60.60549*
At most 2 0.009250 48.46352 29.31819
At most 3 0.005083 19.14533 16.07905
At most 4 0.000843 3.066278 2.659348
At most 5 0.000129 0.406930 0.406930

46
compared to other four indices. Same result was obtained by Cerny (2004), where author
found only one cointegrating relationship among 8 stock indices. On the other hand, Baele
(2002) found no evidence of cointegration among European stock markets. Also as a
conclusion it is possible to say that international diversification will indeed be beneficial,
as markets do not have a long-run relationship. This is an important finding to consider by
any potential investors, since it can make the overall return to be higher.
5.4. Application of VEC and VAR models
It has been found in previous Chapter that not all pairs of stock indices have an
integrating vectors, however, it has been found that all series are indeed non-stationary. It
is assumed that data series become stationary after taking the first differential.
VAR model
There are two types of VAR model – restricted and unrestricted. The use of them
depends on whether there is cointegration present in the model, with unrestricted model
being applied when there in no cointegration and restricted model being applied when
cointegration is indeed present. From the Table 5 it is seen that cointegration is present
only in one pair – that is S&P 500 and FTSE 100, however, FTSE 100 is still included in
VAR estimation.
The model is estimated with EViews statistical package and results are presented
below in Table 6. Since there are six stock indices in the model and it is assumed to use the
first lag (shown as (-1)) and the second lag (shown as (-2)) of each index there are 78
coefficients in the overall VAR system. This is due to the fact that VAR consists of six

47
models, where each stock index is the dependent variable with 13 independent variables.
Table 6 shows the values of every coefficient within the VAR system, while standard
errors are shown in round brackets and probability values are shown in square brackets.
The 99% confidence level has been chosen while analyzing the results of VAR estimation.
The main purpose of this research is to examine whether there are any volatility
transmission mechanisms present between the stock indices, as well as, whether a level of
cointegration between the US stock market changed after the financial crisis comparing to
the period before. Therefore, the first column in Table 6 shows the effect of lagged values
of five stock indices on the S&P 500 index. It is of no surprise to notice that one lag and
two lag values of the S&P 500 index itself have a major influence on the level of index
today. This pattern was found to persist in every column. It is of interest to point out that
both coefficients and account for the effect that CAC makes on S&P 500 were found to be
significant.
Comparing to S&P 500 index, the UK stock index FTSE 100 was found to be
dependent on both, its own lagged values and lagged values of the S&P 500. This indicates
the volatility spillover effect that exists between two markets, however, the US market
being the leader and “sending” information to the FTSE 100, since there was no effect
from FTSE 100 to S&P 500 present.

48
Table 6: Estimation of VAR model
Both CAC and DAX indices were found to depend on the lagged values of bigger
index – S&P 500, however, FTSE 100 only influences the level of CAC. Also is observed
that smaller European indices can be “grouped” together in terms of them transmitting
S&P 500 FTSE 100 CAC DAX SMI NIKKEI
S&P 500 (-1)
0.893507
(0.017883)
[0.0000]
0.212906
(0.076182)
[0.0052]
0.310620
(0.068948)
[0.0000]
0.0341759
(0.095371)
[0.0003]
0.166001
(0.091880)
[0.0708]
0.483990
(0.221137)
[0.0286]
S&P 500 (-2)
0.098341
(0.01792)
[0.0000]
-0.208335
(0.076341
[0.0064]
-0.335961
(0.069091)
[0.0000]
-0.338828
(0.095569)
[0.0004]
-0.170407
(0.092071)
[0.0642]
-0.352939
(0.221597)
[0.1112]
FTSE 100 (-1)
-0.005281
(0.004261)
[0.2152]
0.941121
(0.018152)
[0.0000]
0.081718
(0.016428)
[0.0000]
-0.013880
(0.022724)
[0.5413]
-0.008170
(0.021892)
[0.7090]
0.056727
(0.052689)
[0.2817]
FTSE 100 (-2)
0.007700
(0.004313)
[0.0743]
0.054811
(0.018375)
[0.0029]
-0.048555
(0.016630)
[0.0035]
0.040828
(0.023004)
[0.0759]
0.024857
(0.022162)
[0.2620]
-0.072502
(0.053338)
[0.1741]
CAC (-1)
0.014449
(0.004698)
[0.0021]
0.030901
(0.020013)
[0.1226]
0.919417
(0.018113)
[0.0000]
0.0561172
(0.025054)
[0.0000]
0.319062
(0.024137)
[0.0000]
0.139512
(0.058093)
[0.0163]
CAC (-2)
-0.016392
(0.004667)
[0.0004]
-0.036637
(0.019882
[0.0654]
0.056479
(0.017994)
[0.0017]
-0.561575
(0.024890)
[0.0000]
-0.303304
(0.023979)
[0.0000]
-0.132289
(0.057713)
[0.0219]
DAX (-1)
0.001816
(0.003364)
[0.5893]
-0.010905
(0.014330)
[0.4467]
-0.044959
(0.012969)
[0.0005]
0.918225
(0.017939)
[0.0000]
0.057242
(0.017283)
[0.0009]
0.114819
(0.041596)
[0.0058]
DAX (-2)
-0.002215
(0.003371)
[0.5112]
0.008871
(0.014362)
[0.5368]
0.033160
(0.012998)
[0.0107]
0.0073052
(0.0017979)
[0.0000]
-0.053063
(0.017321)
[0.0022]
-0.137059
(0.041689)
[0.0010]
SMI (-1)
0.001963
(0.003595)
[0.5850]
-0.018616
(0.015317)
[0.2242]
-0.015055
(0.013862)
[0.2775]
-0.056387
(0.019174)
[0.0033]
0.944883
(0.018473)
[0.0000]
0.042702
(0.044460)
[0.3368]
SMI (-2)
0.000562
(0.003594)
[0.8758]
0.025506
(0.015310)
[0.0957]
0.019722
(0.013856)
[0.1547]
0.050804
(0.019166)
[0.0080]
0.027736
(0.018465)
[0.1331]
0.006388
(0.04441)
[0.8857]
NIKKEI (-1)
0.002326
(0.001441)
[0.1066]
-0.009224
(0.006141)
[0.1331]
0.006602
(0.005558)
[0.2349]
0.004577
(0.007687)
[0.5516]
0.002957
(0.007406)
[0.6897]
0.942882
(0.017825)
[0.0000]
NIKKEI (-2)
-0.002727
(0.001432
[0.0568]
0.008642
(0.006100)
[0.1565]
-0.003742
(0.005520)
[0.4979]
-0.004830
(0.007636)
[0.5271]
-0.000665
(0.007356)
[0.9280]
0.0037311
(0.017705)
[0.0351]
CONSTANT
-4.4300432
(2.22562)
[0.0465]
12.86580
(9.48119)
[0.1748]
-46.02192
(8.580790)
[0.0000]
-54.22370
(11.86923)
[0.0000]
-16.02752
(11.43481)
[0.1610]
-68.88597
(27.52125)
[0.0123]
Index
Coefficient

49
information to and from each other. For instance, price level of DAX is affected by the
lagged values of DAX itself, as well as by the lagged values of CAC and SMI.
Interestingly, SMI was found to receive no information “hit” from the US stock market at
99% confidence level compared to other smaller European indices.
Finally, Japanese NIKKEI follows the same pattern as stock markets mentioned
above and is affected by the lagged values of the index itself. However, it is also affected
by the European CAC and DAX indices.
In can be concluded that S&P 500 is one of the most influential stock indices, since
it affects the values of other indices through information transmission channels. With SMI
and NIKKEI being the least affected by the US stock market’s movements, other indices
are clearly experiencing volatility spillover effect from the US stock market.
VEC model
VEC model can only be applied on one pair of stock indices, the S&P 500 and FTSE
100, because cointegration has been found only between these two markets. VECM is run
using EViews econometric package, and FTSE 100 stock index is assumed to be the
dependent variable in the model, also only one lag is being used. The estimated equation
has the following representation taken from the EViews:
D(FTSE_100) = C(1)*( FTSE_100(-1) - 2.41155622707*SP_500(-1) -
2362.67869152 ) + C(2)*D(FTSE_100(-1)) + C(3)*D(FTSE_100(-2)) +
C(4)*D(SP_500(-1)) + C(5)*D(SP_500(-2)) + C(6)
Coefficient C1 represents the error correction coefficient, with other coefficient up
until C6 representing the short-term causality. Coefficient C6 is the intercept term. After
(4.19)

50
obtaining the above equation it has been run with OLS to check for significance of the
error correction term in order to determine whether long run causality is present within the
model. Results are shown in Table 6.
It can be seen that the error correction coefficient c1 has negative value and is not
significant at 99% confidence level; however, it is indeed significant at 95% confidence
level. If it is assumed that 95% confidence level is considered in this case, result from
Table 6 indicates a presence of long run association between FTSE 100 and S&P 500. It
means that S&P 500 has long run causality on FTSE 100. However, this particular
regression shows relationship over the whole period that is being examined. It is of interest
to divide data set into two subsets and run the same sequence of models to see whether
there has been any difference in long run causality before, during, and after the stock
market crash of 2008.
After examining the graphical representation of the pattern that has been followed by
both S&P 500 and FTSE 100 over the whole period from January 2002 until December
2014, the data set has been divided into three subsamples:
• Pre-crisis period from January 2002 until December 2007;
• Crisis period from January 2008 until December 2009;
• Post-crisis period from January 2010 until December 2014.

51
Table 7: OLS estimation of VEC model
During the pre-crisis period both stock indices exhibited a significant growth, with
each of two having a concave function. Crisis period is starting approximately at the peak
that both indices reached, that has been followed by a dramatic decline. Post-crisis period
is seen as the one when a period of growth in markets started, however, one has to keep in
mind that such a division in data set does not mean that the financial crisis has actually
ended in January 2010.
Results have been obtained from running VEC model in three subsamples and
applying the OLS regression. They are presented in Table 8.
As it is seen from the Table 8, the error correction term’s significance has been
changing from period to period. This is supported by findings of Yang et al (2006) where
different levels of integration between markets was found when studying different periods
of time, especially with the presence of financial crisis. As C1 is the error correction term
that one is interested in it is of interest to point out that C1 has not been statistically
significant neither during the pre-crisis period (only significant at 90% confidence level),
nor during the process of stock indices downturn. Especially, C1 lost any significance
during the crisis. However, post-crisis period shows that S&P 500 has long run causality
Coefficient Value
Standard
errors
Probability
C(1) -0.004920 0.002505 0.0496
C(2) -0.057641 0.017966 0.0013
C(3) -0.023733 0.017936 0.1859
C(4) 0.203750 0.075777 0.0072
C(5) 0.080744 0.075854 0.2872
C(6) 0.725255 0.675714 0.4993

52
on FTSE 100 since the error correction term is significant even at 99% confidence level.
Similar result was obtained by Lee (2012), where the author states that the level of
contagion between the US and UK markets after the crisis is higher than before the crisis.
Coefficients C2 to C6 both from Table 8 and equation 4.19 are representing the
effects that lagged terms of both FTSE 100 and S&P 500 indices make on the value of
FTSE 100 today. It has been found that during the first two periods, i.e. up until January
2010, coefficient C2 was the only term to be significant at 5% level. Looking at equation
4.19, it is seen that coefficient C2 shows that partial effect of lagged value of the FTSE 100
index on the value of FTSE 100 today. This result indicates that there is no information
transmission from American stock market to the UK, and the price level on the UK market
depends heavily on information that hit the UK market yesterday. This, therefore, suggests
presence of volatility clustering and long memory of shocks.

53
Value
Standard
errors
ProbabilityValue
Standard
errors
ProbabilityValue
Standard
errors
Probability
C(1)-0.0073900.0040830.07050.0030600.0094660.7466-0.0261840.0074690.0005
C(2)-0.1055380.0268370.0001-0.1039960.0449610.02110.0268690.0291170.3563
C(3)0.0083430.0267970.7556-0.0635010.0448300.1572-0.0130960.0289500.6511
C(4)0.0085380.1203870.94350.0002930.1824430.99870.5141280.1190730.0000
C(5)0.0315350.1204110.7934-0.0107870.1823510.95290.1635020.1198890.1729
C(6)1.7701221.2864430.1690-2.3473243.9517870.55280.3639451.6094070.8211
Pre-crisisCrisisPost-crisis
Coefficient
Table8:VECMestimationduringvariousperiods

54
5.5. Application of BEKK-GARCH model
It has been shown in the previous Chapter that cointegration only exists between
S&P 500 and FTSE 100 indices. Chapter 4.2 shows that volatility clustering exists in the
data sets and, moreover, it is known that bad news and good news have a different impact
on stock market volatility (Black, 1976), and a simple GARCH model cannot account for
such specifications. It means that multivariate specification of GARCH model suits this
research since not only because a system of equations has to be estimates, but also due to
data sets covering less volatile periods, as well as, highly volatile periods, like the financial
crisis. Therefore, multivariate GARCH model was chosen in order to examine whether
pairs of stock indices possess cointegration. Multivariate GARCH model that is being used
is GARCH (1,1), which assumes that there is one lagged value of variance term and one
lagged value of error term. One has to note that it was shown in Chapter 4.3.5 that VECH
model is a base of BEKK model. In this research it has been decided to estimate BEKK
model since it deals with shortcomings that VECH model exhibits. Since the main purpose
is to see whether there are volatility spillover effects between stock indices, especially if
S&P 500 has transmitted any shocks to the five chosen indices, the BEKK model is the
appropriate model. This is due to VECH model not allowing for volatility spillover effects,
and Ferreira (2005, p. 771) explaining it as the conditional variance not being a function of
other variable shocks and past variance. Nevertheless, Bollerslev, Engle, and Wooldridge
(1988) were among the first to apply VECH model to study the potential tradeoffs in
variances of three different assets – stock market, a bond, and a T-bill. A study by Ferreira
and Lopez (2004) concludes that VECH model is the best option to estimate multivariate
relationships and provides best covariance forecasts when examining out-of-sample data
sets.

55
ValueProbabilityValueProbabilityValueProbabilityValueProbabilityValueProbability
C11301.86560.00001281.09210.00001126.86440.00001175.41220.00001134.64130.0000
C25713.71180.00005954.09220.00003728.48900.00006244.45780.000010485.86580.0000
C3-7.71720.00007.68210.0000-8.71470.0000-1.81280.00769.46270.0000
C4-2.08230.41719.48130.05171.33810.497418.92050.0000-18.55760.0007
C540.50540.000066.77290.000035.39190.0000-0.01620.9999-121.65580.0000
A(1,1)0.85650.0000-0.86070.00000.85710.00000.64060.0000-0.86550.0000
A(1,2)0.01010.4620-0.07150.0013-0.00280.53423.55440.00000.03430.0757
A(2,1)0.00010.9603-0.00060.23860.00110.1096-0.07430.0000-0.00030.0715
A(2,2)0.85630.0000-0.85330.00000.86640.0000-0.72400.0000-0.87190.0000
B(1,1)0.56450.00000.53560.00000.55290.00001.38460.0000-0.51870.0000
B(1,2)0.03690.0264-0.01770.55350.00490.43967.11530.00000.00500.8450
B(2,1)-0.00380.0200-0.00150.0055-0.00250.0160-0.14790.00000.00020.4588
B(2,2)0.53580.00000.52790.00000.53790.0000-1.34760.0000-0.51640.0000
FTSE100DAXCACSMINIKKEI
Coefficient
Table9:ResultsofBEKK-GARCHmodelestimation

56
It was found that EViews package estimates diagonal BEKK-GARCH models and
does not provide the full BEKK-GARCH estimation. However, it is essential to obtain the
full estimation, since it will provide both diagonal and non-diagonal coefficients.
Therefore, full BEKK-GARCH model has been estimated with RATS software. Results
are shown in Table 9.
Table 9 shows that not all parameters that are estimated under the BEKK-GARCH
framework are significant at 1% level. Coefficients C1 and C2 are those included in the
mean equation, C3, C4, and C5 are coefficients of constant matrix. Matrices A and B helps
explaining the volatility patterns between stock markets, such as A(1,1), A(1,2), A(2,1),
and A(2,2) are coefficients of ARCH terms, and B(1,1), B(1,2), B(2,1), and B(2,2) are
coefficients of GARCH term (IHS Global Inc., 2013, p. 536). It has been observed that all
diagonal elements, i.e. A(1,1), A(2,2), B(1,1), and B(2,2) corresponding to different pairs
of indices are significant at 1% level. Joshi (2011) has observed the same results when
applying BEKK-GARCH model on the UK, USA and Asian indices. High significance of
A(1,1) and A(2,2) coefficients indicate strong ARCH effects within the model, while high
significance of B(1,1) and B(2,2) implies presence of GARCH(1,1) process driving the
conditional variance of all indices. Values of those coefficients are close, however, some
have a negative effect, whereas SMI (Swiss stock index) possesses the lowest values of
GARCH effect, meaning that markets own volatility affects conditional variance
negatively and to a big extent.
Non-diagonal coefficients A(2,1), A(1,2), B(1,2), and B(2,1) are of more interest
since they represent the shock spillover and volatility spillover effects respectively. Here
results are not as uniform as among the diagonal coefficients. It is seen that the majority of
non-diagonal elements are not significant at 1% level, with only one index having both A

57
and B non-diagonal coefficinets significant. However, if significane level is dropped to
10%, results are indicating linkages between markets. Results show absence of shock
spillover effects between S&P 500 and FTSE 100, and between S&P 500 and CAC. There
is a bidirectional shock spillover effect between S&P 500 and SMI and NIKKEI (at 10%
level), and it is seen that only shock of S&P 500 affect DAX index, but not the other way
round. The strongest effect is obtained between S&P 500 and SMI where news in the US
market transmit instability to the Swiss market.
When looking at the non-diagonal coefficients within B matrix it is seen that there is
volatility spillover effect between that US market and the Japanese market. Also the US
market does not affect the DAX and CAC markets, however, all markets except of
NIKKEI do affect the volatility of the S&P 500. For instance, there is a bidirectional
volatility spillover effect between the UK and the US markets, which indicates that
conditional variance of one index is affected by the past volatility of the other index. These
results are diiferent from Veiga and McAleer (2004) where they have indicated presence
of volatility spillovers between the US and Japanese markets. The strongest effect is again
observed between S&P 500 and SMI, the same as in case of shock spillovers. Findings are
interesting also from the point that cointegration has been detected only between the S&P
500 and FTSE 100, but not among any other pair of indices, however, shock and volatility
spillovers are still found to be present. In comaprison, study made by Sakthivel et al
(2012) has found volatility spillovers among all markets – S&P 500, FTSE 100, and
NIKKEI. This is different from results of this study, since there was no volatility spillover
effect found between the US and Japanese markets.
Addressing the topic of portfolio diversification to the results from the BEKK-
GARCH model it is clear that in some cases there are possibilities of significant risk
reduction. For instance, there are no shock and volatility spillovers between S&P 500 and

58
NIKKEI observed at 1% significance level, as well as, there is no cointegration between
markets. This can benefit a potential investor who is willing to diversify internationally,
since information that hits the US market or the Japanese market is not being transmitted
to the other market, making potential losses limited. Therefore, overall it can be concluded
that econometric models like VECM, VAR, and BEKK-GARCH are suitable to be used in
order to identify better asset allocation possibilities.

59
6. CONCLUSION
The main aim of this dissertation was to investigate whether there are linkages
between the S&P 500 stock index and five other markets – FTSE 100, DAX, CAC, SMI,
and NIKKEI. Data sets consist of closing prices of each index, covering the period from
January 2002 until December 2014. Multivariate GARCH models were applied to study
volatility spillovers from the US market to other markets, with prior data analysis
justifying the use of such models.
Firstly, it was found that all data sets are non-normal, meaning that prices exhibit fat
tails, and generally non-normal distribution. The findings are in accordance with Fama
(1965). Moreover, all sets were found to have a unit root present but returns being
stationary, therefore, in accordance with Mahadeva and Robinson (2004) data was used for
further cointegration analysis. Secondly, cointegration analysis results showed that only
one pair of stock indices have a long run association between each other, that is S&P 500
and FTSE 100. It was showed that cointegration between stock markets is indeed time
varying, the same results was obtained by Mylonidis and Kollias (2010), where authors
show that cointegration between markets clearly depends on the economic conditions.
Volatility and news spillover effects were tested through multivariate GARCH
model – the BEKK-GARCH. Results have shown that even though there was no
cointegration found between some pairs of stock indices, there is still volatility spillover
present. This is the case of a pair of the US S&P 500 and the Swiss SMI. However, this
result should not be considered to be unusual since Forbes and Rigobon (2002) have
shown that markets can be unintegrated and still be affected by each other through
volatility transmission mechanisms. Results indicate presence of volatility spillover effect
from the US to European and Japanese markets, however, they are not as strong as those

60
found by Christiansen (2003), where author shows significant volatility transmission from
the US bond market to other markets.
Finally, results of this research are beneficial for the investor since they show
whether stock markets are interdependent. When it comes to asset allocation in the
portfolio, one wants to lower the risk to a minimum and results of cointegration test can
help to diversify better. Floros (2005) says that the fact that stock markets move together
over the long term cannot provide any long-term benefits to investor. This is clearly
implies to the pair of S&P 500 and FTSE 100, where both cointegration and volatility
transmission were detected. Since there is no cointegration detected between the other
pairs, it can be concluded that they can serve as a good base for diversification; however,
volatility transmission can lower benefits. This means that investors and portfolio
managers have to look for the other options of diversification, like asset class
diversification. It has to be noted that this research is limited, therefore, considering
bigger range of assets, as well as, more stock markets, i.e. both developed and emerging,
can make investor’s decisions more diverse.
6.1. Limitations of the research
It is clear that there are limitations present within the research and one has to be
aware of them when assessing results presented in this paper. It is assumed that domestic
investor is based in the USA and looks for the opportunities to reduce risk in other stock
markets. This is the reason of studying paired values of indices, i.e. the US index being
paired with other five indices. However, a broader picture can be drawn by looking at
paired values between every stock market. Moreover, findings of Christiansen (2003)
show a significant linkage between the US bond market and European markets; therefore,
this essentially raises the question of whether linkages between economies can be assessed

61
only through one asset category, i.e. stocks. Current research can be improved by
including more asset classes.
For instance, Driessen and Laeven (2007) have not only looked at the diversification
benefits of the domestic investor, they have covered a large sample of 52 countries and
have identified how the risk of each individual country may affect the asset allocation
decision. This specification has not been covered within this research and might improve
results. It means that when making an investment decision not only the international
diversification would have been taken into account, but also whether there is any risk
coming from political, economic, or social instability that can affect the portfolio. Existing
research could benefit from inclusion of stock markets in emerging countries alongside
with developed countries, similarly to Li and Majerowska (2008) who have applies
BEKK-GARCH model on emerging economies. This can potentially enlarge the
diversification possibilities.
The other limitation that is present considers data. There can be a larger data set
applied, both in terms of the number of observations, as well as, the number of stock
indices used. For instance, Munteanu et al (2014) have looked at the volatility transmission
from the US to emerging European countries and found them to be statistically significant.
Also there are more models to be considered since multivariate GARCH family is
potentially unlimited. For instance, Silvennoinen and Terasvirta (2008) say that VECH and
BEKK models have already matured enough and there are no improvements to be made.
However, authors point out that Conditional Correlations model may be more suitable
since it has not been developed as much (Silvennoinen and Terasvirta, 2008, p. 21).
Moreover, there are models like VAR-GARCH that can be applied to detect volatility
spillovers. These limitations mentioned above can serve as a good base for the further
developments of the topic.

62
Bibliography
Arshanapalli, B. and Doukas, J., 1993. International stock market linkages: Evidence
from the pre- and post-October 1987 period. Journal of Banking and Finance, 17, pp. 193-
208.
Baele, L., 2002. Volatility Spillover effects in European Equity Markets: Evidence
from a Regime Switching Model, mimeo Ghent University.
Baur, D. and Miyakawa, I., 2014. The stock market, the real economy and contagion.
Working Paper Series 179, Finance Discipline Group, UTS Business School, University of
Technology, Sydney.
Baur, D., 2012. Financial contagion and the real economy. Journal of Banking and
Finance, 36, pp. 2680-2692.
Becker, K.G., Finnerty, J.E. and Gupta, M., 1990. The intertemporal relation
between the US and Japanese stock markets. Journal of Finance, 45, pp. 1297-1306.
Bekaert, G. and Harvey, C., 1997. Emerging equity market volatility. Journal of
Financial Economics, 43, pp. 29-77.
Bekaert, G., Ehrmann, M., Fratzscher, M. and Mehl, A., 2014. The global crisis and
equity market contagion. The Journal of Finance, 69(6), pp. 2597-2649.
Black, F., 1976. Studies of stock price volatility changes. Proceeding of the Business
and Economics Section of the American Statistical Association, pp. 177-181.
Bollerslev, T., 1986. Generalised autoregressive heteroscedasticity. Journal of
Econometrics, 31, pp. 307-327.
Bollerslev, T., Engle, R. and Wooldridge, J., 1988. A capital asset pricing model
with time-varying covariances. Journal of Political Economy, 96(1), pp. 116-131.

63
Boswijk, H.P., Franses, P.H. and van Dijk D., 2010. Cointegration in a historical
perspective. Journal of Econometrics, 158, pp. 156-159.
Brooks, C., 2014. Introductory Econometrics for Finance, 3rd
ed. Cambridge:
Cambridge University Press.
Caccioli, F., Farmer, D., Foti, N. and Rockmore, D., 2015. Overlapping portfolios,
contagion, and financial stability. Journal of Economic Dynamics and Control, 51, pp. 50-
63.
Cerny, A., 2004. Stock market integration and the speed of information transmission.
Working paper series, ISSN 1211-3298.
Chiou, W.P., 2009. Benefits of international diversification with investment
constraints: An over-time perspective. Journal of Multinational Financial Management,
19, pp. 93-110.
Choudhry, T. and Jayasekera, R., 2014. Market efficiency during the global financial
crisis: Empirical evidence from European banks. Journal of International Money and
Finance, pp.1-20.
Christiansen, C., 2003. Volatility-spillover effects in European bond markets, mimeo
Aarhus School of Business.
Claessens, S. and Forbes, K., 2004. International financial contagion: The theory,
evidence and policy implications. International Monetary Fund conference.
Connolly, R.A. and Wang, F.A., 2003. International equity market comovements:
Economic fundamentals or contagion? Pacific-Basin Financial Journal, 11, pp. 23-43.
Dickey, D.A. and Fuller, W.A., 1979. Distribution of the estimators for
autoregressive time series with a unit root. Journal of the American Statistical Association,
74, pp. 427-431.

64
Driessen, J. and Laeven, L., 2007. International portfolio diversification benefits:
Cross-country evidence from a local perspective. Journal of Banking and Finance, 31, pp.
1693-1712.
Engle, R. and Granger, C., 1987. Co-integration and error-correction:
Representation, estimation and testing. Econometrica, 55, pp. 251-276.
Engle, R. and Krone, K., 1995. Multivariate simultaneous generalized ARCH.
Economic Theory, 11(1), pp. 122-150.
Engle, R., 1982. Autoregressive conditional heteroscedasticity with estimates of the
variance of United Kingdom inflation, Econometrica, 50, pp. 987-1007.
Engle, R., Ito, T. and Lin, W., 1990. Meteor showers or heat waves? Heteroscedastic
intra-daily volatility in the foreign exchange market. Econometrica, 58, 525-542.
Eun, C. and Shim, S., 1989. International transmission of stock market movements.
The Journal of Financial and Quantitative Analysis, 24(2), pp. 241-256.
Fabozzi, F., Focardi, S. and Kolm, P., 2006. Financial Modeling of the Equity
Market. Hoboken: John Wiley & Sons Inc.
Fama, E., 1965. The behaviour of stock-market prices. Journal of Business, 38, pp.
34-105.
Fama, E., 1970. Efficient capital markets: a review of theory and empirical work.
The Journal of Finance, 25(2), pp. 383-417.
Ferreira, M. and Lopez, J., 2004. Evaluating interest rate covariance models within a
value-at-risk framework. Working Paper Series 2004-03, Federal Reserve Bank of San
Francisco.
Ferreira, M., 2005. Forecasting the comovements of spot interest. Journal of
International Money and Finance, 24, pp. 766-792.

65
Floros, C., 2005. Price linkages between the US, Japan and UK stock markets.
Financial Markets and Portfolio Management, 19(2), pp. 169-178.
Forbes, K. and Rigobon, R., 2002. No contagion, only interdependence: Measuring
stock market comovements. The Journal of Finance, 57(5), pp. 2223-2261.
Goldstein, I. and Pauzner, A., 2004. Contagion of self-fulfilling financial crises due
to diversification of investment portfolios. Journal of Economic Theory, 119, pp. 151-183.
Granger, C. and Morgenstern, O., 1970. Predictability of stock market prices.
Lexington: Heath Lexington.
Granger, C., 1981. Some properties of time series data and their use in econometric
model specification. Journal of Econometrics, 16, pp. 121-130.
Grobys, K., 2010. Have volatility spillover effects of cointegrated European stock
markets increased over time? The Review of Finance and Banking, 2(2), pp. 83-94.
Harris, R., 1995. Using cointegration analysis in econometric modeling. London:
Prentice Hall.
Hayashi, F., 2000. Econometrics. Princeton University Press.
Hill, C., Griffiths, W. and Lim, G., 2008. Principles of Econometrics, 3rd
ed.
Hoboken: John Wiley & Sons Inc.
Hill, C., Griffiths, W. and Lim, G., 2011. Principles of Econometrics, 4th
ed.
Hoboken: John Wiley & Sons Inc.
Hilliard, J., 1979. The relationship between equity indices on world exchanges. The
Journal of Finance, 34(1), pp. 103-114.
Jithendranathan, T., 2013. Financial market contagion. In: Baker, K. and Kiymaz, H.
2013. Market Microstructure in Emerging and Developed Markets. Hoboken: John Wiley
& Sons, Inc.

66
Johansen, S. and Juselius, K., 1990. Maximum likelihood estimation and inference
on cointegration with application to the demand of money. Oxford Bulletin of Economics
and Statistics, 52, pp. 169-210.
Johansen, S., 1988. Statistical analysis of cointegration vectors. Journal of Economic
and Dynamic Control, 12, pp. 231-254.
Johansson, A.C. and Ljungwall, C., 2009. Spillover effects among the Greater China
stock market. World Development, 37, pp. 839-851.
Kang, S.H. and Yoon, S., 2014. Intraday price and volatility spillovers between
Japanese and Korean stock markets. Korea and the World Economy, 15(2), pp. 185-207.
Karolyi, A., 1995. A multivariate GARCH model of international transmissions of
stock returns and volatility: The case of the United States and Canada. Journal of Business
and Economic Statistics, 13(1), pp. 11-25.
Kenourgios, D. and Dimitriou, D., 2015. Contagion of the global financial crisis and
the real economy: a regional analysis. Economic Modeling, 44, pp. 283-293.
Kenourgios, D., 2014. On financial contagion and implied market volatility.
International Review of Financial Analysis, 34, pp. 21-30.
King, M.A. and Wadhwani, S., 1990. Transmission of volatility between stock
markets. The Review of Financial Studies, 3, pp. 5-33.
Lee, H., 2012. Contagion in international stock markets during the sub prime
mortgage crisis. International Journal of Economic and Financial Issues, 2(1), pp. 41-53.
Lee, S.B. and Kim, K.J., 1993. Does the October 1987 crash strengthen the
comovements among national markets? Review of Financial Economics, 3, pp. 89-102.
Lessard, D., 1974. World, national and industrial factors in equity returns. The
Journal of Finance, 24, pp. 379-391.

67
Li, H. and Majerowska, E., 2008. Testing stock market linkages for Poland and
Hungary: A multivariate GARCH approach. Research in International Business and
Finance, 22(3), pp. 247-266.
Li, Y. and Giles, D., 2015. Modeling volatility spillover effects between developed
stock markets and Asian emerging stock markets. International Journal of Finance and
Economics, 20(2), pp. 155-177.
Lucey, B. and Voronkova, S., 2008. Russian equity market linkages before and after
the 1998 crisis: Evidence from stochastic and regime-switching cointegration tests.
Journal of International Money and Finance, 27, pp. 1303-1324.
Luchtenberg, K.F. and Vu, Q.V., 2015. The 2008 financial crisis: stock market
contagion and its determinants. Research in International Business and Finance, 33, pp.
178-203.
Mahadeva, L. and Robinson, P., 2004. Unit root testing in a central bank. Centre for
Central Banking Studies, Bank of England, number 22.
Markowitz, H., 1952. Portfolio selection. The Journal of Finance, 7, pp. 77-91.
Moser, T., 2003. What is international financial contagion? International Finance,
6(2), pp. 157-178.
Munteanu, A., Filip, A. and Pece, A., 2014. Stock market globalization: The case of
emerging European countries and the US. Procedia Economics and Finance, 15, pp. 91-
99.
Mylonidis, N. and Kollias, C., 2010. Dynamic European stock market convergence:
Evidence from cointegration analysis in the first euro-decade. Journal of Banking and
Finance, 34, pp. 2056-2064.
Ng, A., 2000. Volatility spillover effects from Japan and the US to the Pacisif-Basin.
Journal of International Money and Finance, 19, pp. 207-233.

68
Ozkan, G. and Unsal, F., 2012. Global financial crisis, financial contagion and
emerging markets. IMF Working Paper 12-293.
Panto, D.B., Lessig, V.P. and Joy, M., 1976. Comovement in international equity
markets: A taxonomic approach. Journal of Financial and Quantitative Analysis, 11, pp.
415-432.
Pessaran, M.H. and Pick, A., 2003. Econometric issues in the analysis of contagion.
Unpublished manuscript, University of Cambridge.
Pfaff, B., 2008. Analysis of Integrated and Cointegrated Time Series with R. 2nd
ed.
New York: Springer.
Phylaktis, K. and Xia, L., 2009. Equity market comovement and contagion: A
sectoral perspective. Financial Management, 38(2), pp. 381-409.
Richards, A., 1995. Comovements in national stock market returns: Evidence of
predictability, but not cointegration. Journal of Monetary Economics, 36, pp. 631-654.
Ripley, D.M., 1973. Systematic elements in the linkage of national stock market
indices. Review of Economics and Statistics, 55, pp. 356-361.
Sakthivel, P., Bodkhe, N. and Kamaiah, B., 2012. Correlation and volatility
transmisson across international stock markets: A bivariate GARCH analysis.
International Journal of Economics and Finance, 4(3), pp. 253-264
Samarakoon, L.P., 2011. Stock market interdependence, contagion, and the US
financial crisis: The case of emerging and frontier markets. Journal of International
Financial Markets, Institutions and Money, 21, pp. 724-742.
Schinasi , G. and Smith, T., 1999. Portfolio diversification, leverage, and financial
contagion. IMF Working Papers 99-136.
Siegel, J., 2002. Stocks for the Long Run: The Definitive Guide to Financial Market
Returns and Long-term Investment Strategies, 3rd
ed. New York: McGraw-Hill

69
Silvennoinen, A. and Terasvirta, T., 2008. Multivariate GARCH models. To appear
in Handbook of Financial Time Series. New York: Springer.
Theodossiou, P., Kahya, E., Koutmos, G. and Christofi, A., 1997. Volatility
reversion and correlation structure of returns in major international stock markets.
Financial Review, 32(2), pp. 205-224.
Tsay, R.S., 2005. Analysis of Financial Time Series, 2nd
ed. Hoboken: John Wiley &
Sons Inc.
Veiga, B. and McAleer, M., 2004. Testing the sensitivity of spillover effects across
finncial markets, mimeo University of Western Australia.
Xiao, L. and Dhesi, G., 2010. Volatility spillover and time-varying conditional
correlation between the European and US stock markets. Global Economy and Finance
Journal, 3(2), pp. 148-164.
Yang, J. and Bessler, D., 2008. Contagion around the October 1987 stock market
crash. European Journal of Operational Research, 184, pp. 291-310.
Yang, J., Hsiao, C., Li, Q. and Wang, Z., 2006. The emerging market crisis and stock
market linkages: Further evidence. Journal of Applied Econometrics, 21, pp. 727-744.
Zhang, Q. and Jaffry, S., 2015. Global financial crisis effects on volatility spillover
between Mainland China and Hong Kong stock markets. Investment Management and
Financial Innovations, 12(1), pp. 26-34.
Zhong, M., Darrat, A.F. and Otero, R., 2004. Price discovery and volatility spillovers
in index futures markets: Some evidence from Mexico. Journal of Banking and Finance,
28, pp. 3037-3054.

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