Volatility Spillovers Across Stock Indices: Empirical Evidence from Developed Markets

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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

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1

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?

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5

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

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6 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.

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7 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).

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8 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.

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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.

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11 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:

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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:

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13 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.

𝑅_𝑖,𝑡𝐼𝑁𝑇𝑅𝐴 = ln(𝑝_𝑖,𝑡𝐻) − ln(𝑝_𝑖,𝑡𝐿 ) (3.1)

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14 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:

𝑅_𝑖,𝑡𝐶𝑂 = ln(𝑝_𝑖,𝑡𝑂) − ln(𝑝_{𝑖,𝑡−1}𝐶 ) (3.2)

The continuously compounded close-to-open return, 𝑅_𝑖,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:

𝑅_𝑖,𝑡𝑂𝐶 = ln(𝑝_𝑖,𝑡𝐶) − ln(𝑝_𝑖,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.

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15 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 𝑅_𝐷𝐴𝑋𝐶𝑂 _,𝑡 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

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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 𝜎_𝑡2 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) 𝜎_𝑡2 = 𝛼0+ 𝛼1 ∈𝑡−12

where 𝑦_𝑡 denotes the stock return in one market, and 𝑥_𝑖𝑡 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

𝜎_𝑡2 = 𝛼₀+ 𝛼₁ ∈_𝑡−12 + 𝛽𝜎_𝑡−12

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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:

𝑅_{𝑆&𝑃,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝐹𝑇𝑆𝐸,𝑡}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2) 𝜎_𝑡2 = 𝛼₀+ 𝛼₁ ∈_𝑡−12 + 𝛽𝜎_𝑡−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: 𝑅_{𝑆&𝑃,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅𝑂𝐶_{𝐷𝐴𝑋,𝑡}+ 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2) American market with respect to spillovers from the Japanese market:

𝑅_{𝑆&𝑃,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎

Toronto 300 Composite index

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

𝑅_{𝑇𝑆𝑋,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅𝑂𝐶_{𝐹𝑇𝑆𝐸,𝑡}+ 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎ Canadian market with respect to spillovers from the German market:

𝑅_{𝑇𝑆𝑋,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝐷𝐴𝑋,𝑡}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎ Canadian market with respect to spillovers from the Japanese market:

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DAX 30

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

𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 = 𝛽1+ 𝛽2 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2) German market with respect to spillovers from the Canadian market:

𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝑇𝑆𝑋,𝑡−1}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎ German market with respect to spillovers from the British market:

𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝐹𝑇𝑆𝐸,𝑡−1}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎ German market with respect to spillovers from the Japanese market:

𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 = 𝛽1+ 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

NIKKEI 225

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

𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 = 𝛽1+ 𝛽2 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2) Japanese market with respect to spillovers from the Canadian market:

𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 = 𝛽₁+ 𝛽₂𝑅_{𝑇𝑆𝑋,𝑡−1}𝑂𝐶 + 𝜖_𝑡, ∈_𝑡 ~ 𝑁 (0, 𝜎_𝑡2₎ Japanese market with respect to spillovers from the British market:

𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 = 𝛽1+ 𝛽2 𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2) Japanese market with respect to spillovers from the German market:

𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 = 𝛽1+ 𝛽2 𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 + 𝜖𝑡, ∈𝑡 ~ 𝑁 (0, 𝜎𝑡2)

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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

𝑦_𝑡 = 𝐶𝑥_𝑡+ ∈_𝑡 ∈𝑡 = 𝐻𝑡

1/2 𝑣𝑡

where 𝑦_𝑡 is a m-vector of dependent variables, C is a m x k parameter matrix, 𝑥_𝑡 is a k-vector of explanatory variables, 𝐻_𝑡1/2 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

𝑦_𝑡 = 𝐶𝑥_𝑡+ ∈_𝑡 ∈𝑡 = 𝐻𝑡 1/2 𝑣𝑡 𝐻_𝑡= 𝐷_𝑡1/2𝑅_𝑡𝐷_𝑡1/2 𝑅_𝑡= diag(𝑄_𝑡)−1/2𝑄_𝑡diag(𝑄_𝑡)−1/2 𝑄_𝑡= (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;

𝑥_𝑡 is k x 1 vector of independent variables, which may contain lags of 𝑦_𝑡;

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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

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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

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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.

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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}

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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,𝑡𝐶𝑂 𝛽2 𝑅𝑆&𝑃,𝑡𝐶𝑂 𝛽2

pre-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.0610*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.0472*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.0239*** crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.340*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) -0.239*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.207*** post-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.0982*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.0399** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.117*** TORONTO 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂 𝛽2 pre-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.164*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.0961*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.102*** crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.181*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.161*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.360*** post-crisis (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 0.295*** (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.198*** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.170*** DAX 30 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝛽2 pre-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.235*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.174*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0137 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.152*** crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.156*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.127*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0501 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.313*** post-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.140*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.149*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0778** (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.330*** NIKKEI 225 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂 𝛽2 pre-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.483*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.404*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.315*** (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 0.311*** crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.317*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.251*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.217*** (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 0.233*** post-crisis (𝑅𝑆&𝑃,𝑡−1𝑂𝐶 ) 0.616*** (𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 ) 0.494*** (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.431*** (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 0.448*** *** p<0.01, ** p<0.05, * p<0.1

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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).

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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,𝑡𝐶𝑂 𝑅𝐷𝐴𝑋,𝑡𝐶𝑂 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝐶𝑂

VARIABLES VARIABLES VARIABLES VARIABLES

𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.156*** 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.151*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.228*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.379*** (0.0283) (0.0247) (0.0377) (0.042) 𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.0588** 𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 0.0025 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 -0.0194 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 -0.0199 (0.0245) (0.0194) (0.0451) (0.0489) 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 -0.021 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.0717*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.130*** 𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 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).

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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

𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.284*** 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.389*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 -0.0745* 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.375*** (0.0587) (0.117) (0.0404) (0.0527) 𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.207*** 𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 -0.272** 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 0.0277 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 -0.0566 (0.0706) (0.12) (0.0405) (0.0526) 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.141*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.358*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.481*** 𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 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).

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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

𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.0986*** 𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 0.231*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.121*** 𝑅𝑆&𝑃,𝑡−1𝑂𝐶 0.432*** (0.023) (0.0315) (0.0438) (0.0503) 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.0876*** 𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 0.0521* 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 0.0713 𝑅𝑇𝑆𝑋,𝑡−1𝑂𝐶 0.0169 (0.0242) (0.0282) (0.0557) (0.0513) 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 0.106*** 𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 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).

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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.

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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.

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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?

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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.

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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.

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35

Appendix

Figure A. I – Global world trading hours

Figure A. II – Free float equity market capitalization*

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

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,𝑡𝐶𝑂

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

Constant -0.000519 Constant 6.03E-06

(0.000568) (0.000512) 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 0.207*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡𝑂𝐶 ) 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)

𝑅𝑆&𝑃,𝑡𝐶𝑂 𝑅𝑆&𝑃,𝑡𝐶𝑂 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,𝑡𝑂𝐶 ) 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)

𝑅𝑆&𝑃,𝑡𝐶𝑂 𝑅𝑆&𝑃,𝑡𝐶𝑂 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,𝑡𝑂𝐶 ) 0.0982*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡𝑂𝐶 ) 0.0399**

(0.0184) (0.019) (0.0171)

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

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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,𝑡𝐶𝑂 𝑅𝑇𝑆𝑋,𝑡𝐶𝑂

VARIABLES VARIABLES VARIABLES

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

(0.000192) (0.000197) (0.000204)

(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)

(0.000837) (0.000665) (0.000972)

(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)

(0.000213) (0.000219) (0.000239)

(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)

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

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

𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 𝑅_{𝐷𝐴𝑋,𝑡}𝐶𝑂 𝑅_{𝐷𝐴𝑋,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−1𝑂𝐶 ) 0.127*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0501 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 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)

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−1𝑂𝐶 ) 0.149*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0778** 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 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−1𝑂𝐶 ) 0.174*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) -0.0137 𝛽2 (𝑅𝑁𝐼𝐾𝐾𝐸𝐼,𝑡𝑂𝐶 ) 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***

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

𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,𝑡}𝐶𝑂 𝑅_{𝑁𝐼𝐾𝐾𝐸𝐼,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−1𝑂𝐶 ) 0.404*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.315*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 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)

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−1𝑂𝐶 ) 0.251*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.217*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 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−1𝑂𝐶 ) 0.494*** 𝛽2 (𝑅𝐹𝑇𝑆𝐸,𝑡−1𝑂𝐶 ) 0.431*** 𝛽2 (𝑅𝐷𝐴𝑋,𝑡−1𝑂𝐶 ) 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)

Volatility Spillovers Across Stock Indices: Empirical Evidence from Developed Markets