Thesis I.J. Furda

Volatility Spillovers Across Stock Indices:

Empirical Evidence from Developed Markets

I.J. Furda

Master’s thesis, MSc. Finance

ABSTRACT

This study aims to investigate volatility spillovers between global equity markets. Five major

equity indices, United States (S&P 500), Canada (Toronto 300 Composite), United Kingdom

(FTSE 100), Germany (DAX 30) and Japan (Nikkei 225) are being investigated over the years

2002 to 2015. Main findings are that during the great financial crisis overall linkages and spillovers

between the five indices intensified. Strong evidence is found that market linkages, and thereby

volatility spillovers, are increasing over time.

JEL codes: C22, F21, F65, G01, G15

Keywords: volatility spillovers, market linkages, contagion, financial crisis, MGARCH-DCC

Date Thesis: 14/01/2016

Author: Ivo Jurriën Furda

Student ID number: s1854356

Student email: [email protected]

Name Supervisor: Marnix Reijenga

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Table of Contents

Introduction ..................................................................................................................................... 3

1. Literature review ...................................................................................................................... 5

Introduction ...................................................................................................................... 5

Information flow .............................................................................................................. 5

Economic fundamentals versus market contagion ........................................................... 5

Financial crises ................................................................................................................. 7

Interlinkages between the foreign exchange market and the stock market ...................... 7

Empirical methods............................................................................................................ 8

2. Hypotheses............................................................................................................................. 10

Introduction .................................................................................................................... 10

Hypotheses ..................................................................................................................... 10

3. Data & Methodology ............................................................................................................. 12

Introduction .................................................................................................................... 12

Sample collection ........................................................................................................... 12

Correlations .................................................................................................................... 13

Intraday volatilities ......................................................................................................... 13

Overnight and daytime rate of return ............................................................................. 14

Descriptive statistics ....................................................................................................... 14

ARCH family of statistical models ................................................................................ 16

Volatility spillover effects .............................................................................................. 17

Multivariate Dynamic Conditional Correlation Model .................................................. 19

4. Results ................................................................................................................................... 21

4.1 Introduction .................................................................................................................... 21

4.2 Correlations .................................................................................................................... 21

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4.3 Intraday volatilities ......................................................................................................... 24

4.4 Volatility spillover effects .............................................................................................. 25

4.5 Multivariate Dynamic Conditional Correlation Model .................................................. 27

4.6 Conclusion ...................................................................................................................... 30

5 Discussion & Conclusion ...................................................................................................... 32

5.1 Introduction .................................................................................................................... 32

5.2 Discussion ...................................................................................................................... 32

5.3 Limitations ..................................................................................................................... 33

5.4 Future research ............................................................................................................... 33

5.5 Conclusion ...................................................................................................................... 34

Appendix ....................................................................................................................................... 35

References ..................................................................................................................................... 43

Acknowledgments: I would like to sincerely thank my supervisor Marnix Reijenga for all of the

help and guidance given throughout the course of producing this dissertation.

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Introduction

The last decades have shown an increased globalization of financial markets. It can be argued that

globalization makes the overall system more efficient and leads to lower prices for consumers,

however it definitely causes difficulties as well. As within a globalized system market movements

become more intertwined, creating a well-diversified portfolio suddenly seems a lot more

complex. As an example, if volatility easily transmits from one market to another, there is no real

reason for investors to include both markets within the same portfolio.

Not only does higher integration among capital markets make it harder for investors to

diversify risks, it also makes the system more vulnerable to a financial crisis (Büttner, 2011). As

global trade among countries, nowadays, is expanding at a rapid pace, better knowledge about

volatility spillovers between markets seems rather important. It directly affects the private and

professional investors of this world but also yields important implications for politicians and

multinational firms. According to one source “the importance of investigating volatility spillovers

is, therefore, self-evident” (Mozumder, 2015, p. 44).

This study employs daily open and close data of five stock indices, for the years 2002 to 2015,

chosen from the G-7 countries. The five stock markets used for this research are the S&P 500

(United States), Toronto 300 Composite (Canada), FTSE 100 (United Kingdom), DAX 30

(Germany) and Nikkei 225 (Japan). For a more detailed picture about the data and criteria being

used, see Chapter 3. The main research question of this thesis yields:

“Is volatility of a stock market leading the volatility of other stock markets?”

Besides addressing this question the thesis constitutes three sub questions (derived and related to

the main research question). The sub questions being addressed are:

(1) Do volatility spillovers between stock indices increase during a financial crisis?

(2) Are volatility spillovers between stock indices increasing within the long-run?

(3) Is geography still a determinant factor for co-movements between equity markets?

More detailed explanations on why these questions have been chosen can be found in Chapter 2.

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The thesis is structured as follows. Chapter 1 provides the reader a literature overview on

where and how volatility spillovers do originate. Chapter 2 outlines the hypotheses. Chapter 3

describes the process of data collection and the methodology being used for the research of

volatility spillovers between the five stock indices. Chapter 4 depicts and reflects on the results of

the analyses. Chapter 5 discusses and concludes on the results of this study.

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1. Literature review

Introduction

In this chapter the conceptual framework of this research is being developed. First we take a look

at what explains volatility. Secondly we analyze how it evolves, during crises for instance and over

time. The chapter concludes with a brief literature coverage of how volatility spillovers between

financial markets can be researched.

Information flow

Volatility and risk are interrelated. When an asset or index shows greater movements, stability of

returns becomes more uncertain and thereby risk of the initial investment increases. According to

Ross (1989) price volatility equals information volatility. “Volatility is often related to the rate of

information flow” (Ross, 1989, p. 16). As information often comes in clusters, e.g. central bank

announcements or earnings figures, these are the moments when volatility should be greatest. In

other words, it implies that volatility is greatest when most information is released within the

system. Investigating volatility spillovers among global equity indices therefore not only depicts

the overall vulnerability of the system to new information, it also reveals the speed of market

adjustments to this new information. If there would not be volatility spillovers between equity

markets, it implies that the information is only important to that specific market, market-specific

fundamentals might explain the local shock (Hong, 2001). An example of this can be a change in

legislation which only applies to the local economy.

Economic fundamentals versus market contagion

Previous research has shown that there exist two main theories explaining market linkages and

spillovers between stock indices. The first theory is related to fundamentals (e.g. Solnik, 1974).

Common fundamental variables; such as an overlap in business cycles, central bank policies,

exchange rates and the overall inflation environment, might affect stock markets on a global level

(Dumas et al, 2003). In 1974 Solnik published a research in which an equilibrium model was

derived consistent with a single world market concept. The general idea of Solnik’s research is

that in an international capital market many consumption preferences are not restricted to national

output (Solnik, 1974). Grauer et al. (1976) support this theory and argue that multiplicative utility

functions are often affected by the same economic fundamentals. One should keep in mind

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however that the theory of a single world market concept depends upon restrictive assumptions

about homogenous expectations, perfect capital markets and consumption preferences.

The second theory is market contagion. Grubel and Fadner (1971) were among the first to

embark on the theoretical explanation of contagion. In their paper it is hypothesized that correlation

between equity markets is merely a function of the share of an industries’ domestic consumption.

More recently King and Wadhwani (1990) came up with a theory called the Market Contagion

Hypothesis. Foreign market price changes might reveal important information for the domestic

market as well as it shows the willingness of foreign investors to pay for certain assets. “An

individual trading in London may feel that information is revealed by the price changes in the New

York and Tokyo stock exchanges” (King and Wadhwani, 1990, p. 7). According to King and

Wadhani the rather complex structure of mapping signals leads to a ‘non-fully revealing

equilibrium’ in which price changes in a domestic market are depended upon the price changes in

foreign markets through ‘structural contagion coefficients’. Engle, Ito and Lin in 1990 conducted

a research in which informational effects on the yen/dollar exchange rate are examined. Market

dexterity, a form of market efficiency, which requires stock prices in different markets to react

simultaneously to new information, was tested throughout their research. According to Engle, Ito

and Lin (1990) if a market is dexterous and no new news comes out there will be no price

movement within this market. If this is not the case volatility spillovers are evidence against the

market dexterity hypothesis. Their empirical results reflect that the yen/dollar foreign exchange

market is not dexterous and is affected by volatility spillovers.

In 2000 Allen and Gale published a paper dedicated to financial contagion. It was found

that, due to banks holding interregional claims on other banks, a small liquidity preference shock

in a single region can lead to contagion to an arbitrarily number of n regions. More recently Forbes

and Rigobon (2002, p. 2) classified contagion as “a significant increase in cross-market linkages

after a shock to one country or group of countries”. Forbes and Rigobon state that co-movements

can only be considered as contagion if cross-market co-movements between markets increase

significantly, if this is not the case then any continued strong linkages between the two markets

exist in all states. The latter is dubbed for by the authors as mere “interdependence” between the

two markets, instead of contagion.

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Financial crises

While each financial crisis is different in its’ very nature, crises often do reflect similarities

(Reinhart and Rogoff, 2008). Typical to almost every crisis is that generally market volatility

increases sharply and spills over between and across markets. During extremely bad events, read

crises, people often act irrational and tend to ignore economic fundamentals, resulting in excess

volatility (Bae et al., 2003). The key presumption made by Bae, Karolyi and Stulz is that small

shocks propagate fundamentally different from large-return shocks. The definite onset of a

financial crisis in terms of contagion effects, however, is heavily debated for over the last decades.

It can be argued that if trade is mainly regional so should the contagion be (Glick and Rose,

1999). Another reasoning yields that even though a crisis initially has local origins and

characteristics it can eventually have a substantial effect on global trade as a whole. Due to direct

or even indirect trade linkages to global markets, a local crisis can evolve into a global instability.

After the 1997 South East Asian crisis the OECD estimated that “a slowdown in trade with Asia

could result in a fall of nearly 1 percent in the level of GDP over two years in the OECD area as a

whole” (Caporale et al, 2006, p. 376). The origin of contagion however still remains hard to

identify as it might be caused by similarities in fundamentals between markets or can simple be a

result of spillovers across markets (Alba et al., 1998).

Interlinkages between the foreign exchange market and the stock market

In order to diversify a portfolio well knowledge about volatility transmissions between stock and

foreign exchange rates is essential. Some even argue that the “efficiency of the market can also be

known through the volatility spillover across the markets” (Panda & Deo, 2014, p. 70).

Generally, there exist two theories on the relationship between stock and foreign exchange

markets. Flow-oriented models (Dornbusch and Fischer, 1980) emphasize the relationship

between the behavior of the exchange rate and the current account. Underlying thought of these

models is that exchange rate movements work through within the ability for firms to generate

profits and are thereby affecting the overall firms’ competitiveness. When the domestic currency

is becoming cheaper compared to a foreign currency exports of the domestic firms should increase.

As an effect stock prices should increase due to these increased exports. Contrary, as an exchange

rate appreciates stock prices should decrease. These models therefore assume a positive correlation

between exchange rates and stock prices.

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The second theory is called ‘stock-oriented models’. These models imply that it is capital

mobilization, not trade flows, which drives exchange rate movements (Branson, 1983). Demand

and supply for domestic assets here determine the domestic exchange rate. The lead variable here

is the stock price and a negative relation with respect to exchange rates is assumed within these

models (Mozumder, 2015). Implying that an increase in stock prices, due to an increased demand

function for these domestic assets, should make the domestic currency more expensive. If stock

prices would deteriorate however the domestic exchange rate would depreciate also. The results

of empirical research, to what extent both theories match up to reality, are mixed.

Empirical methods

Several methodologies have been derived on how to measure volatility transmissions. This section

will briefly cover two of the most applied methods. The methodology of cross-market correlation

coefficients compares the correlation between markets prior to a shock and during the shock. As

during shocks volatility within the overall system increases substantially most studies find that

volatility spillovers increase across markets during a shock (e.g. Agenor et al., 2006). King and

Wadhwani (1990) test for an increase in stock market correlations between the United States, the

United Kingdom, and Japan after the United States market crash in 1987: contagion effects

between these markets are found. Another study by Lee and Kim (1993) confirms this finding and

states that that national stock markets became more interrelated after the crash. Not only did co-

movements among stock markets increased substantially, Lee and Kim also found that when

United States stock market volatility was high, overall correlations between markets intensified.

This finding testifies that volatility can, in part, be self-sustaining.

Another, probably most known, method for analyzing the transmission mechanism

between markets is the ARCH, and related GARCH, model. A more detailed explanation of what

these models entail can be found in Chapter 3, section 3.7. Hamao et al (1990) were among the

first to find out that daily close-to-open and open-to-close returns can be deployed in the GARCH

model and its’ extensions to measure volatility transmissions. Hamao et al (1990) compared three

major stock indices (London, Tokyo and United States) and found evidence of volatility spillovers

from London to Tokyo and New York to London over the years 1985 to 1988.

Two additional techniques, which might be applied by researchers to examine spillovers,

make use of co-integrating vectors and firm-level data (see Forbes and Rigobon, 2002; Dungey et

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al., 2005). For this research is chosen to make use of correlation analysis, the GARCH (1.1.) model

plus an extension of the standard GARCH model (the MGARCH-DCC model) to analyze volatility

spillovers between five global equity markets, see Chapter 3 for a detailed explanation.

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2. Hypotheses

Introduction

In this chapter the hypotheses will be outlined. All hypotheses are supported by recent theories or

earlier research conclusions from the field, besides most of the hypotheses build on further to

sections 1.2, 1.3 and 1.4 of Chapter 1. Each hypothesis matches one of the research questions. The

first hypothesis is related to the main research question of this study: Is volatility of a stock market

leading the volatility of other stock markets? The second hypothesis is linked to sub question 1,

the third hypothesis to sub question 2 and the fourth hypothesis to sub question 3.

Hypotheses

The Market Contagion Hypothesis of King and Wadhani (1990, p. 7) states that “individuals

cannot get the full information about the market and therefore they will get information from other

markets”. The Market Contagion Hypothesis, among several other theories, see section 1.3, form

the foundation for the first hypothesis of this thesis.

H1: Volatility of a stock market is leading the volatility of other stock markets.

The second hypothesis builds further onto the literature coverage and theories explained in section

1.4, Chapter 1. During a crisis, volatility generally increases sharply and spills over across markets.

Numerous papers have found evidence of increased contagion effects during crisis times (e.g.

Calvo and Reinhart, 1996; Baig and Goldfajn, 1999). More recently Hon et al. (2007) found that

the dot-com bubble in the United States NASDAQ led to a significant structural break in co-

movements within the technology, media and telecommunication industry. The second hypothesis

of this thesis therefore becomes:

H2: Volatility spillovers between stock indices increase during a financial crisis.

Theoretically, greater bilateral trade flows in goods and financial assets between countries lead to

a synchronization of business cycles. Erb et al. (1994) researched cross-equity correlations

between the G-7 countries for the years 1970 to 1993 and found that the degree of business cycle

synchronization has a significantly positive effect on stock market integration. Another source

stated that “the impact of financial integration on cycle synchronization, in turn, is not

unambiguous” (Imbs, 2004, p. 723). As the last decades have shown increased globalization, trade

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linkages and interrelated synchronization of financial markets, it can be hypothesized that volatility

spillovers between markets over time have intensified.

H3: Volatility spillovers between stock indices increase in the long-run.

Nowadays, where the ease and speed of gathering information is high, one should expect that time

differences become of less importance to stock markets’ co-movements. Besides improved

information access and availability, over the years, digitalization has clearly led to lower

transaction costs for all market participants. Improved information availability and decreasing

transaction costs hint at geographical distances becoming of less importance for stock markets.

In determining trade flows between countries however location still seems of key

importance. Many researchers have developed gravity models in order to explain trade of goods

between countries (e.g. Engel and Rogers, 1996; Brenton et al., 1999). Strong geographic equity

market linkages, among other things, therefore can be due to countries sharing a common border.

Secondly, it is known from “the international portfolio diversification literature that portfolios are

less internationally diversified than asset allocation models would predict” (Flavin et al., 2002,

p.3). As a third argument why location still might be of influence for co-movements one should

think of, and question, overlapping trading hours. Overlapping trading hours between markets

implicitly mean that market participants often focus on the same informational signals. The fourth

and final hypothesis of this thesis therefore yields:

H4: Geographical location is a source of influence on stock markets’ co-movements.

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3. Data & Methodology

Introduction

For this research five major stock indices, S&P 500 (United States), Toronto 300 Composite

(Canada), FTSE 100 (United Kingdom), DAX 30 (Germany) and Nikkei 225 (Japan) are compared

to each other. Section 3.2 covers the collection and criteria of the data. Section 3.3 and 3.4 outline

the importance of correlations and intraday volatility correlations. Section 3.5 explains the

difference between overnight and daytime rates of return of stock exchanges. The following

section, 3.6, outlines the descriptive statistics of the continuously compounded close-to-open and

open-to-close data series. For each index a GARCH (1,1) model is created. Section 3.6 starts off

with a main introduction on the ARCH family of statistical models. Section 3.7 derives the

GARCH (1.1) being tested in this research. The last section 3.8 covers an extension, multivariate

dynamic conditional correlation, of the GARCH (1.1) model.

Sample collection

This study employs daily open and close data of five stock indices, for the years 2002 to 2015,

chosen from the G-7 countries. The five stock markets used for this research are the S&P 500

(United States), Toronto 300 Composite (Canada), FTSE 100 (United Kingdom), DAX 30

(Germany) and Nikkei 225 (Japan). All data are collected from Thomson Reuters Datastream,

Yahoo Finance and Google Finance.

In order to make solid inferences about volatility spillovers, the dataset is sorted. In other

words, only if data on a specific day is available for all five indices this data is used. Approximately

this yields around 200 days, matching for all five indices, on an annual basis. Secondly, to test for

specification under different periods, the dataset is divided into three time periods. The first time

period entails the years prior to the subprime crisis (pre-crisis), the second period covers the crisis

period (crisis) and the third period covers the years after the subprime crisis (post-crisis). The total

period of study is from March 1, 2002 to October 1, 2015 with a total of 2303 observations. The

three periods range from:

1. Pre-crisis period – March 1, 2002 to January 10, 2008 (1024 observations).

2. Crisis period – January 11, 2008 to March 31, 2009 (236 observations).

3. Post-crisis period – April 1, 2009 to October 1, 2015 (1043 observations).

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According to Diebold and Yilmaz (2012, p. 13) one can see four “volatility waves” during

the recent, global financial, crisis: July to August 2007, January to March 2008, September to

December 2008 and in the first half of 2009. There is chosen for January 11, 2008 to March 31,

2009 for the crisis period as from the January to March 2008 episode the volatility index of all

markets surged most substantially. Panda & Deo (2014, p. 72), who investigated spillover effects

between the Indian and American stock market during the recent crisis, used the same crisis period

in their research.

Correlations

Correlation analyses depict how the five stock indices move together over time. Total return index

data is used here. This is rather important as not all indices do reinvest dividends, by using total

return index data, from Thomson Reuters, this problem is accounted for.

How correlations between the five indices move or change over time can be seen as a good

starting point for anyone who wants to know more about, possible, volatility spillovers between

markets. Although correlation and volatility spillovers often are interrelated to each other this does

not need to be the case, as there could be other reasons, apart from spillover effects, which causes

correlations between markets.

Intraday volatilities

The correlation analysis tells us how indices move together over time. In order to get a better view

if intraday volatilities of these five different markets show similarities as well, chosen is to look at

intraday volatilities also. By measuring the difference for each market between the intraday high

index prices and intraday low index prices one could figure out the correlations between intraday

indices movements.

𝑅𝑖,𝑡𝐼𝑁𝑇𝑅𝐴 = ln(𝑝𝑖,𝑡

𝐻 ) − ln(𝑝𝑖,𝑡𝐿 ) (3.1)

Where i represents the country’s stock exchange and 𝑝𝑖,𝑡𝐻 the country’s index price, intraday high

and 𝑝𝑖,𝑡𝐿 the country’s index price, intraday low. Subsequently, the correlations of intraday stock

price movements for all five countries’ (𝑅𝑖,𝑡𝐼𝑁𝑇𝑅𝐴) are compared.

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Overnight and daytime rate of return

There are two parts of the stock market’s return, the close-to-open and open-to-close returns. The

close-to-open return is often dubbed as the market’s overnight rate of return:

𝑅𝑖,𝑡𝐶𝑂 = ln(𝑝𝑖,𝑡

𝑂 ) − ln(𝑝𝑖,𝑡−1𝐶 ) (3.2)

The continuously compounded close-to-open return, 𝑅𝑖,𝑡𝐶𝑂, denotes the movement of the domestic

stock market after the market closes and opens the next day again. The continuously open-to-close

return or daytime rate of return captures the stock markets daily, difference between close and

open price of the market, movement:

𝑅𝑖,𝑡𝑂𝐶 = ln(𝑝𝑖,𝑡

𝐶 ) − ln(𝑝𝑖,𝑡𝑂 ) (3.3)

Descriptive statistics

The descriptive statistics of the open-to-close and close-to-open data for the five stock indices can

be found in Table 1, descriptive statistics. Overall the series are not normally distributed. The value

of kurtosis is positive in all three sub-periods. This indicates a leptokurtic character of returns. In

other words, the data is asymmetric in nature.

Interesting is that for all markets mean returns are higher during the pre-crisis overnight

market (close-to-open) than during the pre-crisis daytime part of the market (open-to-close). This

points out that, during the pre-crisis period, markets reacted more strongly to news coming out

during after-market hours than during opening hours. One explanation here can be that markets

are rather interrelated to each other. Another reason can be that important domestic news often is

published during the after-market hours (often the case with quarterly earnings calls of companies

for instance). During the crisis (see Table 1.2) however this changed as for most markets

movements during market hours (open-to-close) were greater than during after-market hours

(close-to-open). Post-crisis (see Table 1.3), average after-market moves are again of greater

magnitude than movements during opening hours.

Although skewness only tells us something about the period’s daily, overnight and

daytime, distribution of mean returns with respect to the median returns, several things can be

stated. During the crisis period, skewness, in general, widened. This is implying that during crisis

times, mean and median figures became more distorted from each other. The standard deviations

of the close-to-open and open-to-close returns of the five indices confirm this. During the crisis

period, for close-to-open and open-to-close returns, standard deviations increased significantly.

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Post-crisis we see that all markets are negatively skewed, the mean is less than the median here.

Data of the post-crisis period seems to be more asymmetric in nature than the pre-crisis period. It

can be stated that the distribution of returns therefore is less clustered than prior to the crisis.

Table 1.1, descriptive statistics close-to-open and open-to-close variables (pre-crisis period)

Pre-crisis variable mean median min. max st. dev. skewness kurtosis

S&P 500 𝑅𝑆&𝑃,𝑡𝐶𝑂 0.00024 -0.00002 -0.04495 0.06081 0.00650 0.483 20.627

𝑅𝑆𝑃,𝑡𝑂𝐶 0.0000028 0.00047 -0.03644 0.06025 0.00982 0.179 6.170

Toronto 300 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 0.00082 0.00086 -0.03243 0.03649 0.00640 -0.213 8.100

𝑅𝑇𝑆𝑋,𝑡𝑂𝐶 -0.00026 0.00003 -0.03136 0.05166 0.00708 0.041 5.923

FTSE 100 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 -0.00012 0.00032 -0.05589 0.05904 0.01136 -0.234 7.613

DAX 30 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 0.00053 0.00036 -0.08899 0.10568 0.01116 0.084 21.992

𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.00011 0.00055 -0.05411 0.07399 0.01414 0.113 7.437

NIKKEI 225 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 0.00044 0.00080 -0.06432 0.04152 0.01047 -0.624 7.633

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 -0.00015 -0.00025 -0.04867 0.04535 0.00960 -0.175 4.218

Table 1.2, descriptive statistics close-to-open and open close variables (crisis period)

Crisis variable mean median min. max st. dev. skewness kurtosis

S&P 500 𝑅𝑆&𝑃,𝑡𝐶𝑂 -0.00153 -0.00044 -0.09142 0.11615 0.01632 0.398 22.267

𝑅𝑆𝑃,𝑡𝑂𝐶 -0.00092 0.00103 -0.09127 0.10246 0.02392 -0.121 5.579

Toronto 300 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 -0.00084 -0.00027 -0.08562 0.17261 0.02128 1.689 22.827

𝑅𝑇𝑆𝑋,𝑡𝑂𝐶 -0.00105 0.00026 -0.07891 0.07154 0.02014 -0.389 5.680

FTSE 100 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 -0.00203 -0.00185 -0.09265 0.08469 0.02153 -0.076 5.901

DAX 30 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 -0.00103 0.00015 -0.10405 0.12223 0.01951 0.159 16.455

𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.00166 -0.00209 -0.06486 0.11141 0.02002 0.659 8.113

NIKKEI 225 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 -0.00084 -0.00025 -0.06841 0.05467 0.01640 -0.314 5.964

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 -0.00159 -0.00160 -0.10563 0.11658 0.02344 -0.198 9.240

Table 1.3, descriptive statistics close-to-open and open close variables (post-crisis period)

Post-crisis variable mean median min. max st. dev. skewness kurtosis

S&P 500 𝑅𝑆&𝑃,𝑡𝐶𝑂 0.00018 0.00030 -0.06827 0.04682 0.00774 -0.652 15.782

𝑅𝑆&𝑃,𝑡𝑂𝐶 0.00071 0.00096 -0.04891 0.04563 0.01005 -0.298 5.975

Toronto 300 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 0.00022 0.00026 -0.05065 0.08428 0.00882 -0.064 15.008

𝑅𝑇𝑆𝑋,𝑡𝑂𝐶 0.00018 0.00064 -0.03597 0.03346 0.00768 -0.214 4.920

FTSE 100 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.00029 0.00043 -0.04779 0.04193 0.01075 -0.108 4.531

DAX 30 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 0.00064 0.00102 -0.06707 0.06352 0.01172 -0.429 7.784

𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 0.00017 0.00043 -0.07336 0.05879 0.01182 -0.194 5.781

NIKKEI 225 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 0.00086 0.00131 -0.08258 0.10326 0.01324 -0.067 9.693

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 -0.00011 0.00002 -0.09277 0.05544 0.00999 -1.164 16.232

16

ARCH family of statistical models

In this research the standard GARCH (1.1) and an extension, the multivariate dynamic conditional

correlation model, are used. As there are many extensions to the ARCH and GARCH models, we

begin with a brief review of the ARCH family of statistical models. To capture the effect of

changing volatility in a time series, Engle (1982) developed the autoregressive conditionally

heteroscedastic (ARCH) model where the conditional variance 𝜎𝑡2 is a linear function of past

squared errors. The simplest representation of this model is an ARCH (1) which has the form

𝑦𝑡 = 𝛽1 + ∑ 𝛽𝑖

𝑛

𝑖=2

𝑥𝑖𝑡 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

𝜎𝑡2 = 𝛼0 + 𝛼1 ∈𝑡−1

2

where 𝑦𝑡 denotes the stock return in one market, and 𝑥𝑖𝑡 are the factors that could influence the

stock return. Although the ARCH framework forms the basis for many models it comes along with

some difficulties. First, it is not clear how to decide on the number of lags of squared residuals.

Second, the number of lags of squared errors might be very large if required to capture all

dependences in the conditional variance. Third, non-negativity constraints might be violated. “The

more parameters there are in the conditional variance equation, the more likely it is that one or

more of them will have negative estimated values” (Brooks, 2008, p. 391).

Four years later, in 1986, Bollerslev (1986) and Taylor (1986) independently developed

the GARCH model. The GARCH framework differs from the ARCH framework by the fact that

it allows the conditional variance to be dependent upon its’ previous own lags

𝜎𝑡2 = 𝛼0 + 𝛼1 ∈𝑡−1

2 + 𝛽𝜎𝑡−12

Over the years, several extensions have been made to GARCH models, resulting in more complex

hybrid models. Generally, as it is widely used among practitioners nowadays, it can be stated that

the ARCH model has been outdated by the GARCH model and its’ extensions.

17

Volatility spillover effects

In this research a GARCH (1.1) model is applied, where the domestic continuously compounded

close-to-open (equation 3.2) return is taken as a dependent variable and the continuously open-to-

close return (equation 3.3) of the foreign market is added as an independent variable. Due to time

differences, see Appendix Figure A. 1, lagged open-to-close returns are being used when

necessary.

S&P 500

The GARCH (1,1) model for the American market with respect to spillovers from the British

market therefore becomes:

𝑅𝑆&𝑃,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐹𝑇𝑆𝐸,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

𝜎𝑡2 = 𝛼0 + 𝛼1 ∈𝑡−1

2 + 𝛽𝜎𝑡−12

As the S&P 500 and the Toronto 300 Composite index trade at the same hours, this effect is not

estimated. For sake of simplicity, for the other markets only the mean models are shown.

American market with respect to spillovers from the German market:

𝑅𝑆&𝑃,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

American market with respect to spillovers from the Japanese market:

𝑅𝑆&𝑃,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Toronto 300 Composite index

The GARCH (1,1) model for the Canadian market with respect to spillovers from the British


𝑅𝑇𝑆𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐹𝑇𝑆𝐸,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Canadian market with respect to spillovers from the German market:

𝑅𝑇𝑆𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Canadian market with respect to spillovers from the Japanese market:

𝑅𝑇𝑆𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

18

DAX 30

The GARCH (1,1) model for the German market with respect to spillovers from the American


𝑅𝐷𝐴𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑆&𝑃,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

German market with respect to spillovers from the Canadian market:

𝑅𝐷𝐴𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

German market with respect to spillovers from the British market:

𝑅𝐷𝐴𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐹𝑇𝑆𝐸,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

German market with respect to spillovers from the Japanese market:

𝑅𝐷𝐴𝑋,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

NIKKEI 225

The GARCH (1,1) model for the Japanese market with respect to spillovers from the American


𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑆&𝑃,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Japanese market with respect to spillovers from the Canadian market:

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Japanese market with respect to spillovers from the British market:

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐹𝑇𝑆𝐸,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Japanese market with respect to spillovers from the German market:

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡 𝐶𝑂 = 𝛽1 + 𝛽2 𝑅𝐷𝐴𝑋,𝑡−1

𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

Unfortunately, the FTSE 100 close-to-open return cannot be calculated as notational difficulties

make it impossible to extract the “real” opening prices from historical databases. Often the opening

price depicts the closing price of the former trading day. The New York Times even created a

special index to circumvent this problem, which states the opening price as of 08:03 (GMT). Long-

term daily data, for the years 2002 to 2015, from this index however could not be obtained.

Volatility spillovers from other markets to the FTSE 100 therefore are not calculated. As a result,

the open-to-close return of the FTSE 100 indeed captures the overnight return also, there is chosen

for this as it still provides us with valuable insights.

19

Multivariate Dynamic Conditional Correlation Model

An extensive literature (e.g. Bauwens et al., 2003) on alternative GARCH specifications exists,

here we will look deeper into a specific extension of the GARCH (1.1.) model, the multivariate

GARCH (MGARCH) models. The general MGARCH framework yields

𝑦𝑡 = 𝐶𝑥𝑡 + ∈𝑡

∈𝑡 = 𝐻𝑡1/2

𝑣𝑡

where 𝑦𝑡 is a m-vector of dependent variables, C is a m x k parameter matrix, 𝑥𝑡 is a k-vector of

explanatory variables, 𝐻𝑡1/2

is the Cholesky factor of the time-varying conditional covariance

matrix 𝐻𝑡, and 𝑣𝑡 is a m-vector of zero-mean, unit-variance independent and identically distributed

innovations (Baum, 2014).

Most applied multivariate volatility spillover models are the Constant Conditional

Correlation (CCC) model of Bollerslev (1990) and the Dynamic Conditional Correlation (DCC)

model of Engle (2002). Main criticism on the CCC model is that it does not account well for time-

varying correlations (see Tse, 2000; Savva & Osborn, 2004; Aielli, 2013). Another “desirable

practical feature of the DCC models, is that multivariate and univariate volatility forecasts are

consistent with each other. When new variables are added to the system, the volatility forecasts of

the original assets will be unchanged and correlations may even remain unchanged depending

upon how the model is revised.” (Engle, 2002, p. 29). For this reason, apart from the standard

GARCH (1.1) model, the DCC model is applied within this research. The DCC GARCH model

proposed by Engle (2002) can be written as

𝑦𝑡 = 𝐶𝑥𝑡 + ∈𝑡

∈𝑡 = 𝐻𝑡1/2

𝑣𝑡

𝐻𝑡 = 𝐷𝑡1/2

𝑅𝑡𝐷𝑡1/2

𝑅𝑡 = diag(𝑄𝑡)−1/2𝑄𝑡diag(𝑄𝑡)−1/2

𝑄𝑡 = (1 − 𝜆1 − 𝜆2)𝑅 + 𝜆1 ∈̃𝑡−1∈́̃𝑡−1+ 𝜆2𝑄𝑡−1

where

𝑦𝑡 is an m x 1 vector of dependent variables;

𝐶 is an m x k matrix of parameters;

𝑥𝑡 is k x 1 vector of independent variables, which may contain lags of 𝑦𝑡;

𝐻𝑡1/2

is the Cholesky factor of the time-varying conditional covariance matrix 𝐻𝑡;

𝑣𝑡 is an m x 1 vector of normal, independent, and identically distributed innovations;

and 𝐷𝑡 is a diagonal matrix of conditional variances.

20

For our analysis as a dependent is chosen for the domestic close-to-open returns and all,

three or four in our case, foreign market open-to-close returns are added to the mean part of the

model, see Results section 4.5.

21

4. Results

4.1 Introduction

The long-term success of a portfolio or wealth manager crucially depends upon investment

correlations. In order to reduce risks, and diversify a subset of investments accordingly, knowledge

about asset correlations is of key importance. Section 4.2 and 4.3 provide correlation and intraday

volatility correlation analyses of the five indices. Section 4.4 reflects on the results of the GARCH

(1.1) model. Section 4.5 depicts the results of the MGARCH-DCC model. The concluding section

4.6 sums up the results.

4.2 Correlations

Table 2 and 3 depict the correlations and intraday volatility correlations (see Chapter 3, sections

3.3 and 3.4) of the five indices. These correlations are calculated by use of the total return index,

which reinvests dividends, from Thomson Reuters Datastream. Graph 1 shows what would have

happened if you would have invested your money, not corrected for exchange rate effects, at the

beginning of 2002 in each of the five indices.

Graph 1, total return index, period January 2002 – October 2015

0

50

100

150

200

250

300

S&P 500 FTSE 100 DAX 30 TSX NIKKEI 225

22

It is interesting to see that, over the last 13 years, the DAX 30, FTSE 100 and the S&P500 basically

moved along the same pattern. Although the Toronto 300 Composite and Nikkei 225 depict strong

correlations to the DAX 30, FTSE 100 and S&P 500, periodically, movements of both indices

differ. Whereas the decline of Japanese stock markets clearly set off from beginning 2007, the

Toronto 300 Composite index showed its’ first signs of weakness just 1.5 years later, as of the

middle of 2008. The Canadian index also recovered most strongly from the crisis, whereas the

Japanese index struggled to recover. Table 2 shows how the five indices are correlated to each

other in the three different periods. The three periods range from:

1. Pre-crisis period – January 7, 2002 to January 10, 2008

2. Crisis period – January 11, 2008 to March 31, 2009

3. Post-crisis period – April 1, 2009 to October 1, 2015

Table 2, correlations, total return index

INDICES S&P TSX NIKKEI FTSE DAX

S&P (prior)

S&P (crisis)

S&P (after)

1

1

1

TSX (prior)

TSX (crisis)

TSX (after)

0.981***

0.969***

0.948***

1

1

1

NIKKEI (prior)

NIKKEI (crisis)

NIKKEI (after)

0.937***

0.978***

0.928***

0.960***

0.982***

0.854***

1

1

1

FTSE (prior)

FTSE (crisis)

FTSE (after)

0.976***

0.983***

0.970***

0.983***

0.955***

0.945***

0.965***

0.964***

0.862***

1

1

1

DAX (prior)

DAX (crisis)

DAX (after)

0.948***

0.991***

0.972***

0.939***

0.955***

0.946***

0.923***

0.975***

0.938***

0.970***

0.984***

0.956***

1

1

1 t statistics in parentheses

* p < 0.05, ** p < 0.01, *** p < 0.001

As expected, all correlations are significantly different from zero at a 0.001 significance level. All

correlations range from 0.854 (after crisis, Nikkei 225 versus Toronto 300 Composite) to 0.991

(crisis, DAX 30 versus S&P 500). This already depicts that markets are rather interrelated and

thereby can be seen as a first sign for supporting the first hypothesis (H1: Volatility of a stock

market is leading the volatility of other stock markets). During the crisis we see that correlations

between markets intensified. Except for correlations between the Toronto 300 Composite versus

23

FTSE 100 and Toronto 300 Composite versus S&P 500 all markets became more dependent on

each other. Once again this should be seen as a first sign that our second hypothesis holds (H2:

Volatility spillovers between stock indices increase during a financial crisis).

With respect to the third and fourth hypothesis, evidence is mixed. When comparing the

pre-crisis period versus the post-crisis period for some markets we see evidence correlations

between markets, over time, intensified, but not for all (e.g. FTSE 100 versus Nikkei 225). The

other analyses should clarify if volatility spillovers are indeed increasing over time (H3: Volatility

spillovers between stock indices increase in the long-run.). With respect to finding influences of

geography being a factor in determining co-movements (H4: Geographical location is a source of

influence on stock markets’ co-movements.) the results show a mixed picture. Correlations between

close geographical markets tend to be rather strong, e.g. DAX 30 versus FTSE 100 and S&P versus

Toronto 300 Composite, however so are correlations for separate geographical markets (e.g.

Nikkei versus S&P 500). Furthermore, correlations between close geographical markets are not

becoming stronger. So although correlations between close geographical markets remain strong,

and hereby clearly can be a source of influence, geography as a factor is not becoming more

important over time.

To see how these correlations moved in each of the different years (2002 to 2015) see Table

A. IV in the Appendix. The crisis year 2008 clearly shows the strongest correlations between all

markets. The years 2012, 2014 and 2015 (January to October) can be seen as special years in the

sense that overall correlations between markets decreased strongly. The Nikkei 225 is remarkable

by the fact that during the years 2004, 2007 and 2010 to 2012 the correlations with other markets

decreased significantly. Possible explanations for this can be that Japan’s business cycle is not

matching the business cycle of the other countries in those years, has a diverged monetary policy

or that other major internal events happened (e.g. a tsunami in 2011). With respect to a general

weakening of correlations over the years 2012, 2014 and 2015 there are several possible

explanations. Likely a worsening of the Euro crisis in 2012 and 2014, different central bank

policies, interventions in Ukraine in 2014 and the recently collapsed oil price are the main drivers

of this weakening of correlations during these three years.

24

4.3 Intraday volatilities

As correlations show how markets moved different over time it does not really tell us how markets

react to each other on a daily basis. Intraday volatility correlations (see Chapter 3, section 3.4)

already give us a better indication how daily volatility movements are related to each other. Table

3 shows the intraday volatility, daily difference between high and low prices, correlations.

Additionally, Figure A. III within the Appendix graphically depicts these intraday movements of

the five indices over the years 2002 to 2015.

Table 3, intraday volatility correlations, total return index

INDICES S&P TSX NIKKEI FTSE DAX

S&P (prior) 1

S&P (crisis) 1

S&P (after) 1

TSX (prior) 0.605*** 1

TSX (crisis) 0.834*** 1

TSX (after) 0.774*** 1

NIKKEI (prior) 0.353*** 0.1969*** 1

NIKKEI (crisis) 0.608*** 0.636*** 1

NIKKEI (after) 0.211*** 0.186*** 1

FTSE (prior) 0.720*** 0.491*** 0.374*** 1

FTSE (crisis) 0.709*** 0.738*** 0.631*** 1

FTSE (after) 0.772*** 0.681*** 0.246*** 1

DAX (prior) 0.760*** 0.373*** 0.385*** 0.799*** 1

DAX (crisis) 0.747*** 0.692*** 0.681*** 0.820*** 1

DAX (after) 0.709*** 0.601*** 0.173*** 0.956*** 1 t statistics in parentheses

* p < 0.05, ** p < 0.01, *** p < 0.001

Although intraday volatility correlations are less strong than general correlations all intraday

volatility correlations are significantly different from zero at a 0.001 significance level (H1).

During crisis times all intraday volatility correlations increased significantly (H2). Except for the

Japanese Nikkei 225 index, pre-crisis versus post-crisis, intraday volatility correlations increased

over time (H3). Furthermore, it is remarkable to note that intraday volatility movements between

geographic close areas are rather strong (Toronto 300 Composite versus S&P500 and the DAX 30

versus FTSE 100) but also intensified over the years. Geography thereby clearly seems of influence

(H4) with respect to intraday volatility movements.

25

4.4 Volatility spillover effects

Table A. V to A. XV within Appendix show the individual GARCH (1,1) models derived in

Chapter 3, section 3.8. As the output of all the models is rather extensive, for sake of simplicity,

only the betas of the open-to-close series are depicted in Table 4.

Table 4, betas of open-to-close series of GARCH (1.1) models.

S&P 500 𝑅𝑆&𝑃,𝑡𝐶𝑂 𝛽2 𝑅𝑆&𝑃,𝑡

𝐶𝑂 𝛽2 𝑅𝑆&𝑃,𝑡𝐶𝑂 𝛽2

pre-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.0610*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.0472*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.0239***

crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.340*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) -0.239*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.207***

post-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.0982*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.0399** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.117***

TORONTO 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂 𝛽2 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝛽2

pre-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.164*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.0961*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.102***

crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.181*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.161*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.360***

post-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.295*** (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.198*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.170***

DAX 30 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡

𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡

𝐶𝑂 𝛽2

pre-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.235*** (𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 ) 0.174*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0137 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.152***

crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.156*** (𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 ) 0.127*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0501 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.313***

post-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.140*** (𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 ) 0.149*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0778** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.330***

NIKKEI 225 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂 𝛽2

pre-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.483*** (𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 ) 0.404*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.315*** (𝑅𝐷𝐴𝑋,𝑡−1

𝑂𝐶 ) 0.311***

crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.317*** (𝑅𝑇𝑆𝑋,𝑡−1


𝑂𝐶 ) 0.233***

post-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.616*** (𝑅𝑇𝑆𝑋,𝑡−1


𝑂𝐶 ) 0.448***

*** p<0.01, ** p<0.05, * p<0.1

As almost all betas are significantly positive: H1 is confirmed. Earlier we saw that indices and

intraday volatilities are strongly correlated to each other, now we see that foreign daytime (open-

to-close) movements are able to explain overnight (close-to-open) movements of stock indices.

Volatility spillovers therefore are real. During the crisis, spillovers increased significantly from

the FTSE 100, DAX 30 and Nikkei 225 (open-to-close) towards the S&P 500. The same is the

case for spillovers towards the Canadian Toronto 300 Composite index. For the DAX 30 (except

for spillovers from the Nikkei 225) and the Nikkei 225 spillovers during the crisis did not intensify.

The fact that America opens later than Tokyo, Berlin and London might explain why the

S&P 500 overnight’s return was so heavily influenced by other the markets’ daytime rate of return

during the crisis. Subsequently, overlapping trading hours of markets likely result in the fact that

most spillovers to the DAX 30 happen during opening hours. Japan’s different picture might be

26

explained by the fact that Japan is following a somewhat different route in terms of economic

sentiment, business cycle and domestic central bank policy. As a general conclusion to the second

hypothesis, during a crisis close-to-open returns are more affected to volatility spillovers from

foreign open-to-close returns, but not necessarily in all cases (H2).

Comparing the pre-crisis period to the post-crisis period we see that, generally, volatility

spillovers between markets over time intensified. This can be interpreted as that domestic markets

are becoming more sensitive to what happens on foreign exchange markets, which is pointing at

an increased globalization of financial markets (H3).

27

4.5 Multivariate Dynamic Conditional Correlation Model

In this section we cover the multivariate dynamic conditional correlation model. Table 5.1 depicts

the pre-crisis period, Table 5.2 the crisis period and Table 5.3 the post-crisis period.

Table 5.1, pre-crisis, multivariate dynamic conditional correlation model

𝑅𝑆&𝑃,𝑡𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂

VARIABLES VARIABLES

VARIABLES

VARIABLES

𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.156*** 𝑅𝐹𝑇𝑆𝐸,𝑡

𝑂𝐶 0.151*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.228*** 𝑅𝑆&𝑃,𝑡−1

𝑂𝐶 0.379***

(0.0283) (0.0247) (0.0377) (0.042)

𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.0588** 𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 0.0025 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 -0.0194 𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 -0.0199

(0.0245) (0.0194) (0.0451) (0.0489)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 -0.021 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 0.0717*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.130*** 𝑅𝐹𝑇𝑆𝐸,𝑡−1

𝑂𝐶 0.0861**

(0.0188) (0.0199) (0.0268) (0.0372)

𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 0.102***

(0.0353)

MGARCH (1,1) MGARCH (1,1) MGARCH (1,1) MGARCH (1,1)

Constant 1.41e-07*** Constant 3.4e-05*** Constant 3.40e-07*** Constant 6.76e-07***

(5.04E-08) (3.91E-06) (1.24E-07) (2.48E-07)

α 0.0236*** α 0.119*** α 0.0286*** α 0.0192***

(0.00443) (0.0331) (0.00521) (0.00437)

β 0.973*** β -0.0108 β 0.968*** β 0.973***

(0.00437) (0.0951) (0.00511) (0.00598)

Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

During the pre-crisis period the S&P 500 overnight return is most affected by the daytime rate of

return of the FTSE 100 (0.156), interestingly daytime movements of the Japanese Nikkei 225 are

not affecting the S&P 500 (-0.021). The Nikkei 225 (open-to-close) however is influencing the

Toronto 300 Composite close-to-open return (0.0717).

Not unsurprisingly the DAX 30 and Nikkei overnight’s return are most affected by the

S&P 500 daytime rate of return (0.228 and 0.379). The Nikkei’s overnight return is more

influenced by the DAX 30 daytime rate of return than by the FTSE 100 daytime rate of return

(0.102 versus 0.0861). One explanation for this can be time differences, as the DAX 30 compared

to Japan closes one hour later than the FTSE 100 index. Another, more likely, reason can be that

Germany is a more important trade partner to Japan than the United Kingdom. Supported by the

theoretical explanation that trade linkages, see section 1.3 in Chapter 1, might explain contagion

effects this would make sense. More research is needed however in order to proof this.

28

Table 5.2 depicts the crisis period. As this period is more volatile we expect greater

volatility spillovers between all markets and subsequently the signs to increase in magnitude.

Table 5.2, crisis, multivariate conditional correlation model



𝐶𝑂

VARIABLES VARIABLES

VARIABLES

VARIABLES


𝑂𝐶 0.389*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 -0.0745* 𝑅𝑆&𝑃,𝑡−1

𝑂𝐶 0.375***

(0.0587) (0.117) (0.0404) (0.0527)

𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.207*** 𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 -0.272** 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 0.0277 𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 -0.0566

(0.0706) (0.12) (0.0405) (0.0526)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.141*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 0.358*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.481*** 𝑅𝐹𝑇𝑆𝐸,𝑡−1

𝑂𝐶 0.093

(0.0412) (0.0703) (0.038) (0.0587)

𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 -0.0253

(0.0762)


Constant 6.32E-07 Constant 2.66E-06 Constant 0.000109*** Constant 0.000504***

(5.52E-07) (2.3E-06) (2.14E-05) (4.31E-05)

α 0.129*** α 0.113*** α 1.614*** α -0.0238***

(0.0247) (0.0324) (0.472) (0.00222)

β 0.903*** β 0.892*** β -0.00118 β -0.993***

(0.0125) (0.0263) (0.00715) (0.00155)


With respect to the S&P 500 overnight’s return we see that all signs indeed increased in magnitude

during the crisis, FTSE 100 (pre-crisis 0.156 versus crisis 0.284), DAX 30 (pre-crisis -0.0588

versus crisis -0.207), Nikkei 225 (pre-crisis -0.021 versus 0.141). The same is the case for the

Toronto 300 Composite overnight’s return, FTSE 100 (pre-crisis 0.151 versus crisis 0.389), DAX

30 (pre-crisis 0.00225 versus crisis -0.272), Nikkei 225 (pre-crisis 0.0717 versus crisis 0.358).

The DAX 30 overnight’s return during the crisis significantly increased w.r.t. the Nikkei’s

daytime rate of return (pre-crisis 0.130 versus 0.481). Rationally this makes sense as the Nikkei,

of the five indices, is the market closest to the opening hours of the DAX 30, see Appendix, Graph

A. 1. Once again the Nikkei 225 behaves differently from the rest, as Nikkei’s overnight rate of

return is not per se more heavily influenced, by the foreign daytime rate of returns, during the

crisis. Overall H2 is confirmed, volatility spillovers do increase during crisis times.

29

Table 5.3 depicts the post-crisis period. As this period is less volatile than the crisis period we

expect smaller volatility spillovers between all markets, besides we are interested how this period

compares to the pre-crisis period (H3).

Table 5.3, post-crisis, multivariate conditional correlation model



𝐶𝑂

VARIABLES VARIABLES

VARIABLES

VARIABLES


𝑂𝐶 0.231*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.121*** 𝑅𝑆&𝑃,𝑡−1

𝑂𝐶 0.432***

(0.023) (0.0315) (0.0438) (0.0503)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.0876*** 𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 0.0521* 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 0.0713 𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 0.0169

(0.0242) (0.0282) (0.0557) (0.0513)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.106*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 0.334*** 𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 0.0257

(0.0238) (0.03) (0.0422)

𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 0.208***

(0.0384)


Constant 0.000101*** Constant 1.5e-06*** Constant 3.04e-06*** Constant 3.53e-06***

(6.92E-06) (4.1E-07) (1.04E-06) (8.87E-07)

α -0.00997*** α 0.0662*** α 0.0450*** α 0.0497***

(0.00152) (0.0131) (0.00989) (0.0102)

β -0.799*** β 0.914*** β 0.929*** β 0.921***

(0.105) (0.0142) (0.0158) (0.0145)

Due to computational issues the statistical program (Stata) had with calculating the original DCC for the American market (close-to-open) DAX

returns (open-to-close) are not included within the model. Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

For the Toronto 300 Composite overnight’s return we observe that post-crisis volatility spillovers

are of greater magnitude than the prior-crisis volatility spillovers, FTSE 100 (pre-crisis 0.151

versus crisis 0.389 versus post-crisis 0.231), DAX 30 (pre-crisis 0.00225 versus crisis -0.272

versus post-crisis 0.0521), Nikkei 225 (pre-crisis 0.0717 versus crisis 0.358 versus post-crisis

0.106). Volatility spillovers to the Canadian market are increasing over time (H3).

For the DAX 30 index we find mixed evidence for H3, S&P 500 (pre-crisis 0.228 versus

crisis -0.0745 versus post-crisis 0.121), Nikkei 225 (pre-crisis 0.130 versus crisis 0.481 versus

post-crisis 0.334). Volatility spillovers from the Japanese market to the German market are

increasing over time but not from the American market to the German market. A possible

explanation for this is that most spillovers between the S&P 500 and the DAX 30 happen during

opening hours. For the Japanese market we find evidence for H3 for the spillovers from the S&P

500 (pre-crisis 0.379 versus crisis 0.375 versus post-crisis 0.432) and the DAX 30 (pre-crisis 0.102

versus crisis -0.0253 versus post-crisis 0.208).

30

For the American market, post-crisis spillover effects to the S&P 500 are smaller than pre-crisis

spillover effects, e.g. FTSE 100 (pre-crisis 0.156 versus crisis 0.284 versus post-crisis 0.0986).

Therefore, H3 cannot be confirmed for the American market. The fact that spillovers to America

are not increasing over time might be due to the relative size of the American equity market, see

Appendix Figure A. II.

4.6 Conclusion

In conclusion, this thesis tried to answer the main research question:

“Is volatility of a stock market leading the volatility of other stock markets?”

Basically all results depict this to be the case. Correlations and intraday volatility correlations

between all markets are rather strong (see Table 2 and 3). Besides, foreign open-to-close returns

significantly explain domestic close-to-open returns (see Table 4, 5.1, 5.2 and 5.3). Both GARCH

(1.1.) and MGARCH-DCC models confirm that volatility spillovers between the five indices do

exist: H1 is confirmed.

The first sub question and hypothesis 2 of this thesis are related to spillover effects during

a financial crisis. During crisis times, January 2008 to March 2009, overall correlations between

the five indices intensified. Intraday volatility correlations confirm this finding, a significant

increase during the crisis was found with respect to intraday volatility movements among the five

indices. Spillovers from foreign markets’ daytime rate of return on the S&P 500 and Toronto 300

Composite overnight’s rate of return did increase during the crisis. Germany’s DAX 30 overnight’s

rate of return, during the crisis, was not per se more affected by other markets’ daytime rate of

return. Spillovers from Japan (Nikkei 225) to Germany being an exception here. Most likely this

is explained by the fact that most volatility, from the S&P 500, Toronto 300 Composite and FTSE

100, towards the German market spills over during trading hours. Compared to all the markets

Japan shows a different picture from the rest, as volatility spillovers of foreign daytime movements

during the crisis did not intensify. Except for the Japanese market: H2 is confirmed.

The second sub question and hypothesis 3 of this thesis were aimed at spillovers and its’

relation to time. Depending upon which market linkage is being investigated, H3 for some linkages

holds (e.g. DAX 30 versus S&P 500) but for other linkages clearly does not (e.g. Toronto 300

Composite versus Nikkei 225). Both GARCH and MGARCH-DCC depict results hinting at an

increased integration of financial markets. Although, spillover effects to the S&P 500 for the post-

31

crisis period are smaller than during the pre-crisis period, spillovers on the other markets,

generally, increased. Not only does this hint at an increased integration of financial markets, it also

implies that the importance of the American market over time, 2002 to 2015, intensified. Except

for the American market: H3 is confirmed.

The last sub question and hypothesis of this study yielded that market linkages are related

to geographical closeness and overlapping trading hours. The correlation analysis depicts strong

linkages between close geographical markets. Other markets, geographically separated, however

reported equally strong linkages. Correlations between close geographical markets, however, did

not intensify over time. Geography thereby can still be a determinant factor, but does not seem to

become more important. Contrary, the intraday volatility correlations showed increased linkages

between close geographical markets over time. The results can be interpreted as that markets with

overlapping trading hours are becoming more dependent on each other, on a daily basis, but does

not necessarily have to explain long-term co-movements’ of both markets. The results for H4

thereby are mixed. More research is needed in order to determine and measure the exact impact

and importance of markets’ geographical closeness.

32

5 Discussion & Conclusion

5.1 Introduction

This final Chapter summarizes the results of this study. Section 5.2 discusses the results and

elaborates on future implications. Section 5.3 states the limitations of this research. Section 5.4

comes up with recommendations with respect to future research. Section 5.5 briefly concludes on

the most important findings of this study.

5.2 Discussion

During crisis times, January 2008 to March 2009, overall correlations between the five indices

intensified. Intraday volatility correlations and the GARCH analyses confirm this finding. This

study has shown that volatility spillovers across developed equity markets increased substantially.

As the last decades have shown an increased digitalization and globalization of financial

markets one should think of the implications. It can be argued that an interrelated system is most

efficient, it also can be proposed that it is more vulnerable. This research has shown that during

the great financial crisis markets became more dependent on each other, how this relates to other

periods of instability for now remains unclear. An open question therefore remains: Are spillovers

during a crisis becoming more severe, compared to other crises, due to an increased globalization

of financial markets?

Another observation of this study is that, generally, developed equity markets, over time,

are becoming more related to each other. This finding does not only question long-term

diversification strategies it also yields broader implications for global policy makers and

multinational enterprises. Due to increased digitalization and integration of financial markets

former ‘local’ actions might originate into ‘global’ instabilities. It stipulates that global leaders

should be more aware of what happens elsewhere in the world. Constructive interregional

communications and a critical, but open, decision-making process seem to benefit market

participants most. Remarkable is that the importance of the American market over time, 2002 to

2015, intensified. Is this a trend which will continue? Within the next decade it could be equally

likely that America’s dominance will be offset by an increased dominance of the Asian markets.

33

5.3 Limitations

This study yields several limitations. First of all, a limited period (2002 to 2015) is observed.

Observing a longer time period, and multiple crisis periods, might reveal more details about how

spillovers evolve over time.

Secondly, this research focused on determining volatility spillovers across equity indices

of developed markets, which is a limitation by itself. Analyzing more equity, developed and

developing, markets might bring up new valuable insights.

Thirdly, observing more than just equity market interactions, e.g. by adding foreign

exchange, bond or commodity markets to the equation, might bring up valuable explanations with

respect to the origin of volatility spillovers across global equity markets. This requires more

advanced and deeper research models. Future studies therefore might want to apply higher-order

models, capable of sketching a multidimensional view.

5.4 Future research

The importance of trade flows, exchange rates, regional and global business cycle differences,

geography being a factor and different monetary policies all seem plausible factors explaining the

origins of spillovers on financial markets. It can be stated that volatility spillovers probably are the

result of the interplay between all of these factors, more advanced models are needed however in

order to quantify the exact impact of these factors with respect to volatility spillovers. In order to

explain the total picture, higher-order interactions between factors such as trade flows, exchange

rates, regional and global business cycle differences, overlapping trading hours and different

monetary policies need to be tested accordingly. Future work should aim at coming up with more

narrowed definitions and models explaining the origin of volatility spillovers.

This study has also shown that the Japanese equity market behaves fundamentally different

from the other, United States, Canada, United Kingdom and Germany, OECD equity markets. A

possible explanation is that Japan’s internal policy, business cycle and domestic central bank

policy differ. Future research is needed here to confirm, or reject, these possible explanations.

Most importantly, future work should focus on the broader implications, discussed in section 5.2,

of the integration of financial markets. Whether globalization leads to greater instabilities and if

America’s dominance on financial markets will become stronger, from my point of view, are topics

which require most attention.

34

5.5 Conclusion

Improved knowledge about volatility spillovers not only benefits the average investor and portfolio

managers but also yields important implications for policy makers and multinational firms. For

national firms, a globalized functioning of financial markets might offer opportunities with respect

to economies of scale but also poses risks in terms of diversification, and hedging, the firm’s

investment portfolio. For politicians, globalization across financial markets stipulates that political

and global leaders should be well aware of what happens elsewhere in the world. As the

implications of spillover effects eventually do affect us all, research regarding volatility spillovers

is self-evident. By use of several analyses, this study has shown that volatility within one equity

market is often leading the volatility of other equity markets. The main research question of this

thesis thereby is answered. Most important findings of this study are:

- All analyses underline that, during the years 2002 to 2015, volatility spillovers across the

S&P500, Toronto 300 Composite, FTSE 100, DAX 30 and Nikkei 225 indices existed.

- During the great financial crisis, January 2008 to March 2009, overall correlations and

spillovers between the five indices intensified.

- Strong evidence is found that market linkages, and thereby volatility spillovers, over time

are increasing. As an effect the dominance of the American equity market on other markets

seems to be increasing over time, 2002 to 2015.

- On several aspects the Japanese equity market behaves differently. More in-depth research

is needed to explain the different behavior of the Japanese equity market.

The results of this study thereby have provided insights and answers to several questions, but also

raises new ones. Quantifying the origin of spillovers requires more narrowed definitions and more

advanced research frameworks. Additionally, a globalized functioning of financial markets raises

questions with respect to the impact of a new financial crisis. Future research should aim at finding

more concrete answers to these important questions.

35

Appendix

Figure A. I – Global world trading hours

Figure A. II – Free float equity market capitalization*

*Source: World Economic Forum and Business Insider. Article: “What the world would look like

if countries were the size of their stock markets.” Published Aug. 21, 2015.

36

Figure A. III – intraday volatility movements

37

38

39


Table A. VI - GARCH (1.1.) models S&P 500 during the crisis (January 11, 2008 to March 31, 2009)

𝑅𝑆&𝑃,𝑡𝐶𝑂 𝑅𝑆&𝑃,𝑡

𝐶𝑂

VARIABLES (N = 236) VARIABLES (N = 236)

Constant -0.000519 Constant 6.03E-06

(0.000568) (0.000512)

𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.207*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡

𝑂𝐶 ) 0.340***

(0.032) (0.0568)

𝛽3 (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) -0.239***

(0.0901)

GARCH (1,1) GARCH (1,1)

Constant 9.61e-07** Constant 5.40E-07

(4.61E-07) (5.51E-07)

α 0.125*** α 0.137***

(0.0141) (0.0147)

β 0.906*** β 0.902***

(0.00671) (0.00623)



Table A. V – GARCH (1.1.) models S&P 500 prior to the crisis (March 1, 2002 to January 10, 2008)


𝐶𝑂 𝑅𝑆&𝑃,𝑡𝐶𝑂

VARIABLES VARIABLES VARIABLES

Constant 0.000156 Constant 0.000177* Constant -2.33e-06***

(0.0000994) (0.0000974) (0.000000179)

𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.0610*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡

𝑂𝐶 ) 0.0472*** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.0239***

(0.0057) (0.00408) (0.00765)

GARCH (1,1) GARCH (1,1) GARCH (1,1)

Constant -2.22e-06*** Constant -2.09e-06*** Constant 0.000133

(1.67E-07) (1.54E-07) (0.000106)

α -0.00282** α -0.00171 α -0.00283*

(0.00142) (0.0014) (0.0015)

β 0.708*** β 0.695*** β 0.718***

(0.0093) (0.00893) (0.00995)

Table A. VII - GARCH (1.1.) models S&P 500 after the crisis (April 1, 2009 to October 1, 2015)


𝐶𝑂 𝑅𝑆&𝑃,𝑡𝐶𝑂

VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1042)

Constant 0.000126 Constant 0.000143 Constant 0.000158

(0.000239) (0.000237) (0.000237)

𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.117*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡

𝑂𝐶 ) 0.0982*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.0399**

(0.0184) (0.019) (0.0171)

𝛽3 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.0879*** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.112***

(0.0194) (0.0194)


Constant 0.000101*** Constant 0.000101*** Constant 3.07e-05***

(4.73E-06) (4.44E-06) (0.00000434)

α -0.0102*** α -0.0100*** α -0.0106***

(0.00321) (0.0034) (0.0034)

β -0.773*** β -0.796*** β -0.812***

(0.0748) (0.0726) (0.0616)

40

Table A. VIII - GARCH (1.1.) models Toronto 300 Composite index prior to the crisis (March 1, 2002 to January 10, 2008)

𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂

VARIABLES VARIABLES VARIABLES

Constant 0.000865*** Constant 0.000848*** Constant 0.000872***

(0.000192) (0.000197) (0.000204)


𝑂𝐶 ) 0.0961*** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.102***

(0.015) (0.0115) (0.0181)


Constant 3.24e-05*** Constant 3.34e-05*** Constant 3.07e-05***

(0.00000246) (0.00000263) (0.00000434)

α 0.133*** α 0.141*** α 0.111***

(0.0202) (0.023) (0.0236)

β 0.00556 β 0.0105 β 0.117

(0.0634) (0.0652) (0.117)


Table A. VIII - GARCH (1.1.) models Toronto 300 Composite index during the crisis (January 11, 2008 to March 31, 2009) 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂



(0.000837) (0.000665) (0.000972)


𝑂𝐶 ) 0.161*** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.360***

(0.0288) (0.0547) (0.0559)


Constant 1.08e-05** Constant 1.73e-05*** Constant 4.02e-06*

(4.26E-06) (6.05E-06) (2.09E-06)

α 0.381*** α 0.562*** α 0.118***

(0.0571) (0.0989) (0.0267)

β 0.706*** β 0.598*** β 0.883***

(0.0332) (0.0456) (0.0249)


Table A. IX - GARCH (1.1.) models Toronto 300 Composite after the crisis (April 1, 2009 to October 1, 2015)

𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡

𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂



(0.000213) (0.000219) (0.000239)


𝑂𝐶 ) 0.198*** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.170***

(0.0167) (0.0162) (0.0192)


Constant 1.54e-06*** Constant 1.65e-06*** Constant 1.67e-06***

(2.48E-07) (2.80E-07) (3.46E-07)

α 0.0731*** α 0.0730*** α 0.0583***

(0.0065) (0.00604) (0.00552)

β 0.908*** β 0.908*** β 0.919***

(0.00846) (0.00795) (0.00888) Standard errors in parentheses *** p<0.01, ** p<0.05, * p<0.1

41


Table A. XI- GARCH (1.1.) models DAX 30 during the crisis (January 11, 2008 to March 31, 2009)

𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝑅𝐷𝐴𝑋,𝑡

𝐶𝑂 𝑅𝐷𝐴𝑋,𝑡

𝐶𝑂 𝑅𝐷𝐴𝑋,𝑡

𝐶𝑂

VARIABLES (N= 235) VARIABLES (N = 235) VARIABLES (N = 235) VARIABLES (N = 236)

Constant -0.00129** Constant -0.00120** Constant -0.00138** Constant -0.000999

(0.000609) (0.000568) (0.000632) (0.000676)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.156*** 𝛽2(𝑅𝑇𝑋,𝑡−1

𝑂𝐶 ) 0.127*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0501 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.313***

(-0.0408) (-0.0487) (-0.0325) (-0.03)

GARCH (1,1) GARCH (1,1) GARCH (1,1) GARCH (1,1)

Constant 1.82e-06*** Constant 1.72e-06** Constant 1.36e-06** Constant 1.56e-06***

(0.000000611) (0.000000677) (0.000000661) (0.000000598)

𝛼1 0.121*** 𝛼1 0.125*** 𝛼1 0.126*** 𝛼1 0.0985***

(0.0132) (0.0143) (0.0139) (0.0116)

β 0.890*** β 0.888*** β 0.890*** β 0.907***

(0.0094) (0.00883) (0.00817) (0.00873)


Table A. XII- GARCH (1.1.) models DAX 30 after the crisis (April 1, 2009 to October 1, 2015)

𝑅𝐷𝐴𝑋,𝑡𝐶𝑂




VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1042) VARIABLES (N = 1043)

Constant 0.000608* Constant 0.000647** Constant 0.000714** Constant 0.000773**

(0.000323) (0.000322) (0.000326) (0.000308)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.140*** 𝛽2(𝑅𝑇𝑋,𝑡−1

𝑂𝐶 ) 0.149*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0778** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.330***

(0.034) (0.0438) (0.0321) (0.0248)


Constant 4.00e-06*** Constant 4.72e-06***

Constant 4.65e-06***

Constant 3.88e-06***

(9.57E-07) (1.08E-06) (1.06E-06) (9.49E-07)

𝛼1 0.0477*** 𝛼1 0.0546*** 𝛼1 0.0599*** 𝛼1 0.0558***

(0.00805) (0.00867) (0.00922) (0.00825)

β 0.922*** β 0.911*** β 0.907*** β 0.913***

(0.0137) (0.0149) (0.0149) (0.0142)


Table A. X - GARCH (1.1.) models DAX 30 prior to the crisis (March 1, 2002 to January 10, 2008)






Constant 0.000648*** Constant 0.000679*** Constant 0.000647** Constant 0.000632**

(0.000244) (0.000249) (0.000259) (0.000247)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.235*** 𝛽2(𝑅𝑇𝑆𝑋,𝑡−1

𝑂𝐶 ) 0.174*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0137 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝑂𝐶 ) 0.152***

(-0.0171) (-0.0278) (-0.0227) (-0.0258)



(0.0000000604) (0.0000000702) (0.0000000733) (0.0000000694)

𝛼1 0.133*** 𝛼1 0.0305*** 𝛼1 0.0301*** 𝛼1 0.0293***

(0.0202) (0.0023) (0.00225) (0.00217)

β 0.00556 β 0.967*** β 0.967*** β 0.968***

(0.0634) (0.00237) (0.00227) (0.00231)

42

Table A. XIII - GARCH (1.1.) model Nikkei 225 prior to the crisis (March 1, 2002 to January 10, 2008)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡

𝐶𝑂


Constant 0.000394 Constant 0.000530* Constant 0.000448 Constant 0.000414

(0.000281) (0.0003) (0.0003) (0.000292)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.483*** 𝛽2(𝑅𝑇𝑋,𝑡−1

𝑂𝐶 ) 0.404*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.315*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡−1

𝑂𝐶 ) 0.311***

(0.021) (0.0395) (0.0205) (0.0187)



(0.000000153) (0.000000186) (0.000000174) (0.000000197)

α 0.0193*** α 0.0196*** α 0.0209*** α 0.0209***

(0.00316) (0.00367) (0.00362) (0.0036)

β 0.973*** β 0.973*** β 0.972*** β 0.971***

(0.00422) (0.00455) (0.0045) (0.00485)


Table A. XIV - GARCH (1.1.) models Nikkei 225 during the crisis (January 11, 2008 to March 31, 2009)

𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂





Constant -0.000787 Constant -0.000372 Constant -0.000373 Constant -0.000741

(0.000912) (0.00106) (0.00102) (0.000982)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.317*** 𝛽2 (𝑅𝑇𝑋,𝑡−1


𝑂𝐶 ) 0.233***

(0.0514) (0.0354) (0.0434) (0.0513)


Constant 0.000377*** Constant 0.000463*** Constant 0.000478*** Constant 0.000453***

(2.42E-05) (2.91E-05) (3.60E-05) (3.13E-05)

α -0.0230** α -0.0218*** α -0.0408*** α -0.0329***

(0.0109) (0.00666) (0.0148) (0.0103)

β -0.897*** β -0.890*** β -0.870*** β -0.881***

(0.07) (0.0519) (0.0713) (0.0534)


Table A. XV - GARCH (1.1.) models Nikkei 225 after the crisis (April 1, 2009 to October 1, 2015)






Constant 0.000136 Constant 0.000587 Constant 0.000518 Constant 0.000489

(0.000342) (0.000376) (0.000357) (0.000342)

𝛽2 (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.616*** 𝛽2 (𝑅𝑇𝑋,𝑡−1


𝑂𝐶 ) 0.448***

(0.0279) (0.0488) (0.0249) (0.028)



(7.51E-07) (9.55E-07) (7.85E-07) (7.02E-07)

α 0.0465*** α 0.0626*** α 0.0697*** α 0.0667***

(0.008) (0.00873) (0.0112) (0.00797)

β 0.923*** β 0.905*** β 0.903*** β 0.907***

(0.0135) (0.0135) (0.0145) (0.0113)


43

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