The relationship of World Cup match results and
informational betting odds: Analyzing the abnormal
returns
Master Thesis
Author: Frano Peso
Student number: 6142001
Supervisor: dr. J.J.G. (Jan) Lemmen
Finish Date: 01-07-2017
UNIVERSITY OF AMSTERDAM Amsterdam Business School
MSc Business Economics Finance Track
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STATEMENT OF ORIGINALITY
This document is written by student Frano Peso who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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PREFACE AND ACKNOWLEDGEMENTS
To express the special significance of this thesis of my Master Finance study, I would like to express my gratitude to those who have been of great value in my study period. These are undoubtedly my parents, sister and girlfriend who took an important place in my life and also played an important part during my study at the University of Amsterdam. The unconditional support they always gave me in all I did and still do, the unlimited attention they gave me and always were a good ‘advisory body’, for which I have special thanks and appreciation. I would therefore be obliged, in respect and appreciation, to assign this doctoral thesis to them. Finally, I would like to take this opportunity to include my supervisor too, Jan Lemmen, for the good feedback, the result of my thesis would not be achieved without his critical view. Eventually this work has been a learning path for me again (it never stops!), on which I look back with a very satisfied feeling.
I hope you enjoy reading!
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ABSTRACT
I analyze the relationship between World Cup match results, betting odds and stock returns of all national football teams that participated. Using the event study analysis, I verify that abnormal returns are affected by match results. All the three possible outcomes (wins, ties, and losses) are followed by negative abnormal returns. Furthermore, I find that abnormal returns are greater with more goal difference and I conclude that the presence of both a year- and month-effect is supported by my data. Additionally, I test the explanatory power of betting odds in shaping market reactions to unexpected outcomes which have no significant effect. An extra check is needed using an alternative model for the seemingly unrelated regression model (SUR approach) to deal with bias of overlapping events. I use the generalized estimating equations (GEE) approach to handle the issue of contemporaneous correlations. Most of the GEE regression parameters could not achieve convergence after 100 iterations, except for two that were estimated for the subsample of top 27 teams. The full sample generated for the wins (ties) 0.33% (0.83%) lower abnormal returns. Further the results show that a loss (unexpected loss) of a match resulted in 0.69% (0.82%) lower
abnormal returns for the sample of 27 selected national teams for which the abnormal returns were calculated with national stock exchange indices. For the same top 27 countries and using the full sample of national MSCI and stock exchange generated abnormal returns, losses and ties generated respectively on average -0.85 and 53% lower abnormal returns, immediately on the first trading day after the match date.
Keywords: Football Match Results, Abnormal Returns, Betting Odds, Investor Mood and
Sentiment, Event Studies, GEE, SUR
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TABLE OF CONTENTS
STATEMENT OF ORIGINALITY ______________________________________________ II PREFACE AND ACKNOWLEDGEMENTS _____________________________________ III ABSTRACT _____________________________________________________________ IV LIST OF TABLES ________________________________________________________ VII LIST OF FIGURES _______________________________________________________ VII CHAPTER 1 INTRODUCTION _______________________________________________ 1 1.1 PROBLEM DEFINITION __________________________________________________ 3 1.2 RESEARCH APPROACH _________________________________________________ 4 1.3 RELEVANCE _________________________________________________________ 5 1.4 OUTLINE ___________________________________________________________ 5 CHAPTER 2 LITERATURE REVIEW __________________________________________ 7
2.1 INVESTOR BEHAVIOR AND STOCK RETURNS __________________________________ 7 2.2 DOMESTIC MARKET BIAS AND THE ECONOMY _________________________________ 9 2.3 TEMPORAL EFFECTS __________________________________________________ 10 2.4 PRE-MATCH BETTING ODDS _____________________________________________ 10 2.5 HOME ADVANTAGE ___________________________________________________ 12 CHAPTER 3 METHODOLOGY ______________________________________________ 16
3.1 ECONOMETRIC MODEL ________________________________________________ 16 3.2 ROBUSTNESS CHECK TO DEAL WITH CROSS-UNIT CORRELATIONS _________________ 21 3.3 HYPOTHESES AND THE MODELS _________________________________________ 29 3.4 DATA COLLECTION ___________________________________________________ 32 CHAPTER 4 EMPIRICAL RESULTS _________________________________________ 36
4.1 MAIN FINDINGS ______________________________________________________ 36
4.1.1 Market reaction to match results and goal differencse ___________________ 36 4.1.2 The temporal effects _____________________________________________ 39 4.1.3 Informational value of betting odds __________________________________ 42 4.2 ROBUSTNESS CHECKS ________________________________________________ 43 4.3 DISCUSSION ________________________________________________________ 48 CHAPTER 5 CONCLUSIONS _______________________________________________ 49
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5.2 LIMITATIONS AND RECOMMENDATIONS ____________________________________ 52 REFERENCE LIST ________________________________________________________ 54 APPENDIX A DISTRIBUTION OF THE TOP 27 PARTICIPATING COUNTRIES ________ 60 APPENDIX B DISTRIBUTION OF THE PARTICIPATING COUNTRIES _______________ 61 APPENDIX C NUMBER OF MATCHES PLAYED BY EACH NATIONAL TEAM ________ 62 APPENDIX D DISTRIBUTION OF THE EVENT DATES ___________________________ 63 APPENDIX E RANDOM EFFECTS REGRESSION RESULTS ______________________ 65 APPENDIX F CROSS-UNIT CORRELATIONS __________________________________ 66
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LIST OF TABLES
Table 1: Distribution of the post-event window after the match date. _________________________ 33 Table 2: Descriptive statistics _______________________________________________________ 35 Table 3: Linear regression with match results dummies ___________________________________ 37 Table 4: Linear regression with match goal differences ___________________________________ 38 Table 5: Linear regression with Monday or weekend effect ________________________________ 41 Table 6: Linear regression with match outcomes expectancy measures ______________________ 43 Table 7: Effect of football match results on stock price movements __________________________ 44 Table 8: Effect of football match results on stock price movements for the top 27 countries _______ 45 Table 9: Effect of football match expectancies on stock price movements _____________________ 46 Table 10: Effect of football match expectancies on stock price movements for the top 27 countries _ 47
LIST OF FIGURES
Figure 1: Conceptual model with independent and dependent variables ______________________ 20 Figure 2: Within-time correlation structure in Stata’s xtcsd command _______________________ 28 Figure 3: Distribution of the abnormal returns over the World Cup years by the match results ___________ 39 Figure 4: Distribution of the abnormal returns over the months by the match results _____________ 40
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CHAPTER 1 Introduction
The international football tournaments containing this thesis take place every four years, i.e. this year (2017) there will be no big football event but next year in 2018 the World Cup will take place. The World Cup can be seen, together with the Olympic Games, as one of the most important sport events in the world. According to Rouwen (2016) the World Cup is not only about the “game” but also commercially and economically it is an important event and success at the tournaments may lead to investor confidence for the future. In general, football is the most popular sport on the planet and is known as the “people’s game”. The World Cup is undoubtedly the sport’s global happening and, as a result, every four years football tends to dominate conversations in the global and national setting equally. However, for example the UEFA Euro Championship is globally less popular than the FIFA World Cup as it applies only to European countries and the World Cup obviously applies to all countries over the world. Also, less national teams participate at the Euro compared to the World Cup. It is obvious that the world’s fascination with the “beautiful game” transcends the game itself, where football is just as much as about culture. The importance of the World Cup is
noticeable in the large media coverage, the enormous TV audience, and the global interest. To support this while considering the recent World Cup (2014), the FIFA (Fédération
Internationale de Football Association) has released an in-depth document detailing the facts and figures that combined to make up the 2014 FIFA World Cup in Brazil1. A brief
introduction of some figure facts is that the total attendance was 3,429,873 for the 64 matches, the highest recorded at any World Cup since USA 1994. The average crowd of 53,592 was also the highest in two decades. More than one billion fans tuned in to watch the final of the 2014 FIFA World Cup Brazil, with the competition reaching a global in-home television audience of 3.2 billion people. The impressive figures are a result of intense global interest (Kaplanski & Levi, 2010). Football is an important economic factor where large amounts of money are spent in the football business. The indirect economic impact of football is noticeable in stock market returns (Lemmens, 2014). For academics, the interest here is that football results provide an easy and quantifiable proxy for mood and sentiment, and much of this research therefore comes under the scope of behavioral finance.
1 These figures are obtained from
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One of these aspects of behavioral finance is investor sentiment, which is the overall attitude of investors toward a particular security or financial market. Investor sentiment is the feeling or tone of a market, or its crowd psychology, as revealed through the activity and price movement of the securities traded in that market. For example, rising prices would indicate a positive investor sentiment, while falling prices would indicate a negative investor sentiment. The second aspect is investor mood, which is often described as the “mood” of the market or stock traders in emotional terms such as “anxious”, “depressed”, “calm” or “enthusiastic”. Moods are perplexed affective states that can originate from external events, prior emotional experiences, or the internal disposition of the person. In contrast to mood, investor sentiment is generally defined as “a belief about future cash flows and investment risks that is not justified by the facts at hand”. For example, investing in listed football clubs leads to overoptimistic win-chances of their club, which often results in true disappointments. Investors are not capable of making realistic and neutral predictions of the club’s match result, which leads to a systematic difference in the magnitude of their reactions after wins or losses. They project this explanation to the case of national football teams. Biased ex-ante beliefs can clarify why losses do have a greater impact on stock returns – knowing that wins in most cases are expected rather than losses – where Bernile and Lyandres (2011) state that this is solely due to overoptimistic beliefs. Furthermore, sport sentiment is the response of investors to the stock market as a result of sports events (Bernile & Lyandres, 2011). Investors cannot cope with these beliefs in order to link them with the impact on investor’s mood, and why moods are influence by biased beliefs. As a matter of fact, wins are always expected so no significant mood impact is the case whereas losses are unexpected and so will lead to true disappointments, which as a consequence will be projected on the stock market.
Looking at the history, there is a clear pattern of outperformance by the winning team in the weeks after the World Cup final. On average, a victory outperforms the global market by 3.5% in the first month. This is a meaningful amount, although the outperformance fades significantly after three months. Indeed, the winning nation does not tend to hold on to its gains and, on average, sees its stock market underperform by even around 4% on average over the year following the final. However, investor sentiment can only take you so far, in markets at least, and basically it comes down to “enjoy the gains while they last”. The pattern of outperformance following a victory at the World cup is fairly consistent over time
(Lemmens, 2014). All the winners since 1974 have outperformed in the post-final month, with only one exception, i.e. World Cup winner Brazil in 2002! However, in this particular case, macro events (a deep recession and currency crisis) overshadowed the impact of
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victories on the football field. The economic crisis was sufficient enough to drive the equity market down by 19% relative to the World Index in the month after the final and this followed an underperformance of 13% over the previous months. These remarkable market drops can be attributed to investor behavior driven by negative emotions, caused by football losses of their countries and also in a case of bad macro-economic events.
Recent studies considered the information content of pre-match bets in studying the relationship between football match results and football team market returns. Using bets as a proxy for investor expectations, Bernile and Lyandres (2011) analyze the returns of a sample of listed European soccer teams around important matches. Their findings show that investors are quite optimistic about their teams’ prospects ex ante, and quite disappointed ex post. This in turn leads to negative post-event abnormal returns. Bell et al. (2012) investigated over the period 2000-2008 a sample of English football teams and found that pre-match betting odds have an informational value. However, Palomino et al. (2009) find a strong relationship between market returns to match results whereas a weaker relationship to betting odds. This weakness may be because of the lack of informational content of betting information. Furthermore, Scholtens and Peenstra (2009) applied a multi-country analysis in the years 2000 till 2004 and find similar results when looking at the role of betting odds.
1.1 Problem definition
This thesis aims to contribute to the above-mentioned literature. In particular, I analyze the relationship between soccer match results, betting odds and stock returns of national soccer teams that participated in the World Cup. Since sport events affect mood, expected and unexpected soccer match results provide a unique way of studying the link between investor mood and stock market prices.
In football group stages (like in a World Cup) constellations can occur when a specific result helps both teams and this information will have an impact on the betting odds as well (Bray et al., 2005). Information about injured players, performance of players in domestic leagues or in rare cases even inside information and knowledge about match fixing might furthermore have an influence on the betting odds. Having said this, one can conclude that the predictor betting odd has apparently more explanatory power than for instance a predictor based solely on the ranking of teams. However, can this conclusion be proven in the field of this research? The following research question that arises is, do the betting odds of World Cup
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traditional investor sentiment and information salience they have? In case it does, we can
assume the bet market to be effective and all this information will contribute to a better quality of prediction in football.
It is possible that the betting odds do not contain any new information unknown to investors even though the bookmakers’ experts are almost perfectly predictors of the match results. Secondly, the odds can also contain new information, which is not considered by investors or is too costly to trade on. A possible explanation for this is the lack of
informational salience or by high bid/ask spreads causing the absence of a market reaction (Palomino et al., 2009). Since betting odds represent opinions about earnings-related information, this thesis is also related to the literature on (under-)reaction to revisions of earnings forecasts. With regards to the pre-match betting odds, this is inherent to the magnitude of the effect on stock returns, i.e., there is a weak relationship between the odds and the stock returns according to Palomino et al. (2009). Bonner et al. (2005) show that the investors' reactions to revisions of analysts' forecasts depend on the media coverage of these revisions. They combine analysts' forecasts and salience (media coverage) levels. However, there are also important differences between information released by bookmakers and that by equity-analysts. Bookmakers, whose expected profits are determined by betting odds, are less subject to the biases documented about these analysts, i.e., systematic optimism (Easterbrook & Nutt, 1999), conflicts of interests for analysts working for brokerage firms (Michaely & Womack, 1999), and common incentives (Clement & Tse, 2004).
1.2 Research approach
Using an event study approach, I measure abnormal returns following wins, ties and losses. Wins are expected to be associated with positive abnormal returns, and ties and losses with negative abnormal returns. Additionally, I analyze the role of bets in shaping market reactions to unexpected results. As a robustness analysis, I propose an alternative econometric approach using unrelated regression models to include the problem of overlapping events. To
accommodate this problem of the so-called ‘event clustering’ (Castellani et al., 2007), I apply a generalized estimating equations (GEE) model, which allows the correlations between the cross-units to be non-null. Firstly, by splitting the matches between wins, ties and losses, I want to see if these events lead to a different market reaction. Secondly, I test whether the intensity of the result, as measured by goal difference, has an effect on stock returns. Additional tests will be comprehensively explained in the Methodology chapter 3. Finally,
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using betting data, I divide all match results into expected and unexpected, and test whether the unexpected ones are associated with a larger effect on stock returns. According to the efficient market hypothesis, the stock prices of a football team should reflect all the available information, including the one on expected results, which is implicit in the pre-match betting odds. Using this interpretation framework, only unexpected events may be expected to generate abnormal returns.
1.3 Relevance
The rationale for analyzing World Cup match results is that football in general is not only just about the “game” but also economically it is an important sport, and success at tournaments may lead to investor’s confidence for the future (Rouwen, 2016). Due to the size of the World Cup in terms of attractiveness and the impact on the world’s population, it is obviously an interesting research topic.The data that is analyzed allows to support known results with new empirical evidence and to offer new insights on the effect of moods on soccer team stock prices. The existing literature focuses on national and international matches in single countries, or on international matches in several countries. Instead, this dataset includes all World Cup match results of all soccer teams in the period 2006–2018. The role of betting is analyzed only in recent studies. These studies consider the information content of the bets market as a proxy for investor expectations, and provide controversial results. This dataset includes the pre-match betting odds of all World Cup match results and allows us to deepen the empirical evidences on their information content. These rationales made it an interesting idea to analyze their effect on stock returns.
1.4 Outline
In the next chapter, the literature review will be provided, where the main theories in the existing literature will be discussed. Based on this literature review, in chapter 3 the methodology follows where data on stock returns, match results, betting odds, hypotheses, and the modelling framework will be presented. The potential problems or limitations will be taken into consideration in order to answer the research question. Also, the event study analysis and some descriptive statistics will be provided to produce some support and evidence for the given interpretations. Chapter 4 will follow this, where the main results of this research will be presented. The results will enhance economic meaning. The robustness
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checks need to be done which are provided in paragraph 4.2 by retesting some of the
hypotheses using the GEE approach. Finally, the conclusions and limitations in chapter 5 are based on the results to give a best possible answer on the research question. The thesis is closed with recommendations for further research.
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CHAPTER 2 Literature Review
In this chapter, investor behavior will be discussed. After this, the reflection of pre-match betting odds will be enlightened followed by a brief story about domestic market biases and the impact on an economy. Finally, this chapter ends with the phenomenon ‘home advantage’ in sport performance.
2.1 Investor behavior and stock returns
Football can be considered as the most popular game on earth. Football results represent a unique opportunity to study alternative explanations for share price movements, rather than explanations based on more standard business-related information that are the subject of much research on the pricing of equities and market efficiency (Bell et al., 2012). Considering that international tournaments like the World Cup have economical and sportive benefits for participating nations, a victory or a defeat clearly shifts investor mood but betting odds hardly have any impact on sentiment (Palomino et al., 2009). In the upcoming discussed papers, event studies were adopted to examine the impact of changes in investor’s mood on stock returns. This approach gives a clear distinction when it comes to the before and after situation of a particular event. Also, the consequences of some events can be captured with more certainty.
Just a friendly reminder, investor sentiment implies the attitude of their decision-making process for a certain activity on the stock market. It can cause the so called irrational investor behavior, which in turn can lead to suboptimal trade and misvaluations of stocks. Several papers have shown the impact of investor’s sentiment on stock returns which causes the deviations from expected returns. One of the earliest studies of the effects of football results on the share price was the research of Benkraiem et al. (2009). Their conclusion was largely consistent with those that found game results had an influence on returns and trading
volumes; their analysis further showed that the extent of the share price effect and timing of it was dependent on the type of result (win, draw, lose) and match venue (home, away).
Stockholders of participants of sports events can act rationally to these events, since its value can change based on the performance on the sports event. On the other hand, investors’ mood can be influenced by the performance of their supporting team, which can also lead to
emotional trading rather than rational trading. This behavior can lead to suboptimal trading and to stock mispricing. If football results are price sensitive information, i.e. testing whether
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they have an impact on stock prices, this represents a test of semi-strong form of efficiency. Even in the absence of any direct effects on company cash flows, football results can affect stock prices by changing the mood, confidence, and emotional state of investors (Ashton et al., 2003; Edmans et al., 2007).
From an economic perspective, it is assumed that investors are rational in their decision-making process. However, there have been a lot of researches done that proof the opposite, i.e. that investors are irrational. In this respect, the “mood” aspect of investors is an
explanation for their irrationality. Furthermore, in other researches this “mood” aspect has systemically been shown to be present. For example, Edmans et al. (2007) found a link between national soccer results of the market; for example, significant markets fall after soccer losses and has a stronger effect for smaller stocks, and in more important games. Additionally, Ashton et al. (2003) found a strong association between the England football team results and subsequent daily changes in the FTSE 100 index. However, the methodology employed by Ashton et al. (2003) was later criticized by Fock et al. (2009) who rejected the presence of any link. In response, Ashton et al. (2011) carried out new analysis, using a larger dataset, and re-asserted that a link does exist for the original study period of 1984-2002, although they report that the strength of the link has declined over the subsequent period 2002-2009. Fock et al. (2009) took into account that a lot of stocks are traded internationally so that investors are not influenced by the performance of their own national football team. Their analysis pointed out that there is no specific relation between a win or loss and the stock market following a football match. Despite this, if they would change their used models then surprisingly a significant result would occur, which would be consistent with other
researches. However, they emphasize that the influence of World Cup matches should be analyzed with caution concerning these inconsistencies. This in turn raised the problem at Ashton et al. (2003), i.e. if national team results do have an effect on stock returns during a World Cup, would this open the door for arbitrage opportunities? To answer this issue the study by Kaplanski and Levy (2010) is a good indicator which contradicts this. They did this by examining the US stock market and they found that there is a negative average return, whereby they state that arbitrage is not possible due to foreign investors on the stock
exchange market. Basically, multiple nationalities of investors are present and therefore they are differently influenced by any result of World Cup matches. Obviously, the existing literature resulted in an overall effect on the stock market whereas Fock et al. (2009) had a small “footnote” regarding World Cup matches. Overall, it can be assumed that the effect of a loss was larger than a victory following a football match.
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Regarding the FIFA World Cup academic research tends to focus on two areas: the effect of the announcement of the World Cup host and market behavior during and
immediately after the World Cup. In this respect, Kaplanski and Levy (2010) found that the average return on the US equity market over the period of the World Cup was -2.6%
(compared to an average return of +1.2% for similar periods at other times). This effect did not depend on the games’ results and as the aggregate effect depended on many games; it was therefore robust. This result was supported by Baddour (2010) who also found an average return of -2% for the same conditions. Bernile and Lyandres (2011) have found also similar results, i.e. a relatively large fall of post-loss stock returns and modest positive post-win returns. They conclude that the market reactions are a consequence of investor’s ex-ante biased beliefs.
2.2 Domestic market bias and the economy
As the world is facing economic globalization and financial integration, this results in highly correlated stock markets. As a matter of fact, the investors are not only the countries’
inhabitants of a particular stock market but includes also all other investors on planet earth. This would imply that the impact of national football results on the national stock returns would decrease, since domestic investors have a natural incentive to support solely their own national football team, which in turn leads to domestic market bias in financial markets. Because of this, investors tend to invest a relatively large portion of their investments in their domestic market. One of the reasons to do this is due to a ‘confidence’ level, where investors tend to invest in stocks where they are familiar with. Another reason is to hold the so called ‘employer’ stock, where firms give their employees an incentive to hold their stock. Also, it seems to be difficult to gain information of foreign equities and particularly when trading in financial markets of less-developed countries. Furthermore, these reasons provide more insight in the effect on the national stock exchange if a relatively large portion of the market is held by domestic investors, because they are the most affected by the performance of their own national football team.
According to a Goldman Sachs report (2014) – based on outcomes of the World Cup 2014 on the economies of several countries – compared with the national team, I take Germany as an example because it has won this World Cup tournament. The German economy looked much more stable. German growth was also more balanced than before the crisis, when the economy was mainly dependent on exports and foreign demand. The main
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factor behind the weakness in private consumption has been weakness in household income, which in turn reflected declining employment and wage restraint over much of the pre-crisis period. In addition, a rising tax burden has weighted on the level of household income.
However, since the start of the crisis, household incomes have grown more rapidly, helping to fuel private consumption growth. Investment spending has also picked up meaningfully, although the level of investment spending remains rather low. Given the favorable backdrop for investment spending, in particular the very low funding costs for German corporates, the low level of investment spending implies there is scope for strong investment growth in the years ahead. Besides predicting a growth-rate over the years ahead, the report is not a guarantee that the growth-rate will maintain. So far it gives some insights on World Cup football and economic performance in Germany.
2.3 Temporal effects
The weekend effect is a phenomenon in financial markets in which stock returns on Mondays are often significantly lower than those of the immediately preceding Friday. Some theories that explain the effect attribute the tendency for companies to release bad news on Friday after the markets close to depressed stock prices on Monday. Others state that the weekend effect might be linked to short selling, which would affect stocks with high short
interest positions. Alternatively, the effect could simply be a result of traders' fading optimism between Friday and Monday. The weekend effect has been a regular feature of stock trading patterns for many years. For example, according to a study by the Federal Reserve, prior to 1987 there was a statistically significant negative return over the weekends. However, the study did mention that this negative return had disappeared in the period from post-1987 to 1998. Since 1998, volatility over the weekends has increased again, and the phenomenon of the weekend effect remains a much debated topic. I implement the weekend and Monday effects in my analysis together with the month and year effects. In paragraph 3.1 and 3.3, I describe the procedure and models implementing these effects.
2.4 Pre-match betting odds
The most common way to bet on soccer matches is the fixed-odds system (Palomino et al., 2009). This system is created by firms who offer these betting odds and obviously generate
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them for possible wins, defeats or draws. Betting odds are a reflection of the money that bettors will earn prior an initial stake. After the odds are placed, there is a small chance that they will change before the game starts whereas they will definitely not change during and after a match. In this respect, the fixed-odds betting system is different from other betting systems such as pari-mutuel or the point-spread betting, which reflect and react to the quantity of money bet on each possible outcome towards the beginning of an event. To illustrate a betting process, I elaborate on an example in paragraph 3.4 (Data collection) according to Palomino et al. (2009).
In general, it is very hard to make accurate predictions of complex future developments, so it is in this case for football matches too, in which they are enormous amounts of money that play a role in this sport industry. For example, experts seem to achieve similar levels of accuracy as non-experts based on stock forecasting (Memmert & Wunderlich, 2016). This statement is not so surprising looking at the principle of financial economics that assumes that stock prices should be more or less unpredictable (Memmert & Wunderlich, 2016). Football results also seem to have a considerable form of unpredictability and therefore discussing who will win is obviously an interesting feature for everyone who has passion for the sport. During the FIFA World Cup 2014 in Brazil, different groups of people like journalists, former
football players, betting organizations and so on try to forecast the results of games either in a work- or private-related environment (Memmert & Wunderlich, 2016). They also say that everyone can make a prediction based on some knowledge or simply on a feeling or mood, but making an accurate prediction is of course more complicated. A reason for this is simply due to the complexity of a match, so even so-called football experts and professional bettors cannot make better predictions than random persons (Memmert & Wunderlich, 2016). However, it is remarkable that the variable betting odds is a quite good predictor of the result of football games. Betting odds systems are frequently analyzed to improve their predictive power whereby numerous statistical prediction models have been used. As a result, the outcomes of the tests showed that the prediction quality of betting odds were quite good (Memmert & Wunderlich, 2016). It is very difficult to say which group has which influence on the betting odds, because the emergence of betting odds is a complex process and can be influenced by the opinion of experts as non-experts. The partially irrational behavior of sport bettors can declare that the odds are by definition not perfectly representative in determining the actual result of a match (Andersson et al., 2005). There are some factors that can influence
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factor in this field of research is the so-called “home advantage”, which will be discussed in the next section.
2.5 Home Advantage
First of all, in the context of this section there is no “traditional” home or away venue because a World Cup tournament is played in only one country (this is determined by FIFA electives), so the hosting country is always playing at home (therefore it has the home advantage) and the other countries are playing away. Despite this difference, the countries from the same continent as the hosting country can partially be considered as a home match too in order to explain the phenomenon home advantage. This is due to several factors like the influence of the crowd, the familiarity with the context, travel fatigue, and territory which will be all explained further on. Furthermore, the qualification matches do have the traditional home and away matches, so there is no difference in the upcoming discussion about the home
advantage.
Throughout the years researchers have tried to identify the factors that improve human sportive performances. According to Legaz-Arrese et al. (2013), the human sportive
performance is explained by multiple factors such as environmental and genetical factors. They say that home advantage in sports, in general, is well documented and there has been a lot of research about it, but the exact reasons for it is not well understood by the public. Despite this, several studies have shown a positive relationship between psychological and behavioral factors previous to competitive sport events and home advantage (Legaz-Arrese et al., 2013). In the paper of Legaz-Arrese et al. (2013) is said that home advantage is identified as a term that was used to show the consistent result that home teams regularly, i.e., more than 50% of the games played win their match or competition. They say that home advantage is defined as the percentage of home winning teams minus the percentage of away winning teams is greater than 5%. More recent studies suggest the same about home advantage which gives at first glance somehow “mysterious” unknown aspects about the causes. A
considerably higher advantage has been identified for disciplines in which referees directly can influence the results, possibly because of disproportionately high scoring for home competitors, and for disciplines that inherently entail the possibility of local variation in the facilities. The higher economic inversion created by the hosting country, the possibility to compete in all the matches, and the traditional home advantage could explain these findings.
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The relevant literature mentioned by now addresses the same causes that define the phenomenon home advantage, i.e., the influence of the crowd, the familiarity with the context, travel fatigue, rule factors that favor the home team, and territory. All these factors can influence on psychological- and health- states of players, coaches, and referees, whereby the home advantage partially is explained in empirical studies (Legaz-Arrese et al., 2013). The influence of the crowd is the first factor that can explain home advantage (Balmer et al., 2001). Countries from the same continent as the hosting country of a World Cup, have the advantage of less travel distance which gives them a higher chance of having more home supporters in the stadiums. Research has shown that referee bias is more likely to occur when dealing with a fanatic and massive crowd by favoring the home team (Legaz-Arrese et al., 2013). It is obvious that size, intensity of support or proximity to the field play are factors able to influence mood states or even attention level of players, coaches and referees, affecting sport performance and partially explaining the home advantage phenomenon. The familiarity with home playing or with familiar local climate circumstances as well as similar cultural aspects are significant contributing factors of home advantage. This is true for the countries from the same continent as the hosting country of a World Cup, as they can better adapt to these factors compared to countries from another continents. Legaz-Arrese et al. (2013) mention that English professional football teams who played on unusual big or small pitches or on unnatural surfaces (something different than real grass), might have benefited from a slightly increased home advantage. Balmer et al. (2001) identified a significant higher advantage for disciplines who have the possibility of a local variation in the facilities. In this respect, Pollard (2002) estimated that circa 24% of the home advantage may disappear when the team plays at another facility, but other studies observed that there are no significant effects that can be related to playing at another facility (Bray et al., 2005). Nonetheless, the main resuls appear to have only small effects to the contribution of familiarity with local conditions, such as physical characteristics of a stadium, distraction during a game, disruption of the game preparation, to the home advantage effect.
The intense travels that are accompanied with professional sport when playing away or at another facility, can favor the home advantage due to the fatigue that players suffer and because of breaking their normal routine. Obviously, this is related to less travel distance which in turn implies less jet lags and as a result less fatigue for countries from the same continent as the hosting country of a World Cup (Legaz-Arrese et al., 2013). The results show a weak or no significant effect of travel time and distance on performance, whereas the home advantage is less when playing local derbies where there is obviously no long trip involved
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(Bray et al., 2005). Despite this, only a small part of the variance of playing home can be declared by travel-related factors and therefore is the level of competition not that much affected by large travel distances (Legaz-Arrese et al., 2013).
Research is generally based on referee bias, whereby this phenomenon is seen as a cause of home advantage. Moreover, research has indeed observed referee bias in favor of the home team caused by for example more free kicks, less yellow or red cards, more extra time, higher scores etcetera, rather than a bias against the away team (Legaz-Arrese et al., 2013). In team sports like football, there are strong indications that a massive and fanatic crowd can influence the referee decision-making process, either by the noise the crowd produces or by the fact that referees are fully aware of that they are being evaluated for their honest
performance, which may be a potential contributing factor to the home advantage
phenomenon (Nevill et al., 2002). It seems like if the referee bias has an impact on home advantage, it is greater in sports that go along with a higher degree of subjective decisions. The home advantage is most probably derived from referee bias and is relied on several factors that depend on the sport in general, such as the crowd, political influence, and patriotism. Specific training methods for referees to improve their ability to cope with psychological stress, could reduce the subjective decisions and in turn also the home advantage effect.
Other research has observed the behavior of the last factor related to home advantage, that is, territoriality. This can be seen as a psychological aspect which implies that the home team has an “appearance” of a winning attitude towards the away team, because the home ground is considered to be “holy” (Pollard, 2006). Especially, from the Balkan-countries emerges the fact of large home advantages compared to other European regions (Legaz-Arrese et al., 2013). Most probably because of the geographical location of these countries, between the mountains and the emphasis on the historic ethnic religious conflicts, are responsible for a bigger territoriality characteristic. Similar results apply to countries in Asia and Latin America too.
As can be seen there is now overwhelming evidence of a relationship between football match results, stock prices, betting odds, and subsequently their impact on the countries’ economies in general. However, this literature has used linear specification in which all match results are treated as representing equally important information, and it is suggested by
Palomino et al. (2009) that betting odds contain new information to investors (which contrasts with the rational expectations hypothesis). Therefore, it is my assertion and also a
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analyzed by making use of the information on their pre-match betting odds. Also, the less important match results will be analyzed simultaneously because this can be seen as the counterfactual of the analysis of the important match results. To capture a measure in determining the predictive power of betting odds, I provide this in the next chapter (3), the methodology.
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CHAPTER 3 Methodology
Since the data analysis is based on more than one national soccer team, using the MSCI of each country’s soccer team is better because of mutual comparability. If these indices are not available, then indices of national stock exchanges is an alternative replacement. The matches and betting odds of the World Cup tournaments with the associated qualification matches (and explicitly their betting odds too) are included to examine the abnormal daily returns. The total sample period will contain matches that are defined as “less important” and “more important” matches that most probably affect the mood of investors more on the days of the more important football matches, i.e., the event dates. Less important matches are the matches between the countries outside the distribution of the top 27 countries (see Appendix A). Whereas the more important matches are the matches between the countries within the distribution of the top 27 countries. The sample is divided into three categories, i.e. (i) a category for all World Cup matches, including qualification matches, (ii) a category for solely qualification matches, and (iii) the last category that consists of solely the World Cup
tournament matches. I expect that the latter category, has the largest effect on the World Stock Market Index measured by MSCI world and/or national stock exchange indices, since these matches are considered to be the most important. The final total sample will contain the abnormal returns for all countries – occasionally referred to as national football teams – derived from their MSCI and stock exchange indices. Hence, in case I couldn’t find the MSCI index of a particular country I used the national stock exchange indices. Overall, initially I include all national football teams to capture the matches played by the participated countries, i.e., including the countries that in the end did not qualify for the World Cup head
tournament.
3.1 Econometric model
The employed statistical approach for the main research design, is the standard event-study analysis according to Campbell, Lo, and MacKinlay (1997). This is to investigate the
behavior of stock returns in the event of played World Cup matches. The variables of interest used in all regression models are derived from (i) the match scores, resulting in a win, loss or tie, (ii) goal differences for the match outcomes between two teams, (iii) the temporal factors, e.g. the year, month, day of the matches, (iv) the betting odds resulting in an expected win, loss or tie, and (v) the national stock market indices to compute the abnormal returns. To
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simplify the analyses I have calculated abnormal returns by calculating the difference between the national and market index returns. Of course more (sophisticated) models can be
employed to test the models under different market measures, e.g. proxies derived by market model or the CAPM model (Sharpe, 1964), Fama-French three-factor model (Fama & French, 1993) or Carhart’s four-factor model (Carhart, 1997). Yet, prior research have shown that event studies covering relatively short time spans, could not agree upon one superior model (Campbell et al., 1997). For instance, the four-factor model with size, value and
momentum would make no sense in the context of football, since I study just one sector and it is rather homogeneous. The used benchmark for the normal market return is the MSCI World Index2 at the same date. I use a market-adjusted return to take into account the systematic component of stock returns. Hence, this method implies a constant beta of 1 – if the CAPM framework would have been used - for all teams within the sample period. For instance, if I used the market model, I would need to estimate the betas for the country of each soccer team, of which the estimates would be inflated or deflated subject to the market movements.
Cross-sectional regressions are carried out through an ordinary least squares (OLS) models to find the effect of national football match results on the stock market movements, to test hypotheses 1 through 6. These hypotheses are described further in this paragraph. For my empirical tests I follow the setup of Castellani, Pattitoni, and Patuelli (2013) to assess the relation between the research variables and abnormal national index returns. The linear regression model in general form is specified in the econometric model:
𝑦!" = 𝑓 𝑥!"#, 𝜀!", 𝛽! . Eq 1
Where 𝑖 denotes the national football team, 𝑗 is the played match of the football team for any tournament phase described further in paragraph 3.4, 𝑘 is the match event related variable of interest, 𝛽! and 𝜀!" is respectively the coefficient of the independent variable 𝑘, and 𝜀!" are the residuals of the model assumed to be independent and identically distributed. The standard errors of the coefficients are corrected for heteroskedasticity. 𝑦!" are the abnormal returns derived from the stock exchange indices from the country of the national football team 𝑖 for the event date 𝑗. I estimate this model to detect whether football matches linked the World
2 Using a globally market index in case of such an event like the World Cup also might seem more appropriate when you consider that the MSCI is a market leader in global equity indexes.
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Cup tournament affect the market sentiment of the average football team’s nation, also explicitly described in the hypotheses to be followed. Specifically, the model variables in this general specification are outlined as follows. I change the main research variable 𝑥!" in each estimated model, depending on the hypothesis that is tested. Depending on the order of the hypotheses, that are outlined further in this paragraph, 𝑥!" becomes one of the following for: [H1]; three dummy variables, viz. 𝑊𝐼𝑁!", 𝐿𝑂𝑆𝑆!", and 𝑇𝐼𝐸!", i.e. if team 𝑖 wins (loses or ties) the match at an event date 𝑗, it is assigned the value one and zero otherwise, [H2]; 𝐷𝐸𝐿𝑇𝐴!" and 𝐷𝐸𝐿𝑇𝐴!"!, respectively the goal difference between team 𝑖 and its opponent for match 𝑗, and the squared goal difference of the same variable, [H3]; the interaction between 𝑊𝐼𝑁!", 𝐿𝑂𝑆𝑆!", and 𝑇𝐼𝐸!" and four dummy variables 𝑌06!", 𝑌10!", 𝑌14!", and 𝑌18!" for the years in which the World Cup tournaments are held or prepared for, respectively the years 2006, 2010, 2014 and 2018, [H4]; the interaction between 𝑊𝐼𝑁!", 𝐿𝑂𝑆𝑆!", and 𝑇𝐼𝐸!" and ten dummy
variables 𝐹𝐸𝐵!", 𝑀𝐴𝑅!", 𝐴𝑃𝑅!", 𝑀𝐴𝑌!", 𝐽𝑈𝑁!", 𝐽𝑈𝐿!", 𝐴𝑈𝐺!", 𝑆𝐸𝑃!", 𝑂𝐶𝑇!", and 𝑁𝑂𝑉!" for the months in which the matches are played, viz. February until November, [H5]; the interaction between 𝑊𝐼𝑁!", 𝐿𝑂𝑆𝑆!", and 𝑇𝐼𝐸!" and two dummy variables 𝑊𝑒𝑒𝑘𝑒𝑛𝑑!" and 𝑀𝑜𝑛𝑑𝑎𝑦!" for the weekend and the first day of the week, and [H6]; five dummy variables 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝑊𝑖𝑛!", 𝑈𝑛𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝑊𝑖𝑛!", 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝐿𝑜𝑠𝑠!!, 𝑈𝑛𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑𝐿𝑜𝑠𝑠!", and 𝑇𝑖𝑒!" measuring the
expectancy of the outcome for team 𝑖 and match 𝑗, derived from the betting odds. In some of the designs I have interacted the research variables with the win, loss or tie dummy variables to discriminate between the match outcomes with respect to the hypothesized variable. For instance interacting the win with the tournament (preparation) year 2006 produces the dummy interaction variable 𝑊𝐼𝑁!"× 𝑌06!". That means, this variable measures the average abnormal returns if team 𝑖 wins match 𝑗 and if this effect is significant at a particular level of
significance. I estimate the model for three (sub)samples, namely the complete sample, the sample of countries for which I have found the MSCI indices and the sample of countries for which I only could find the national stock exchange indices.
Besides the main tests I apply a series of distinct procedures to test the main findings, i.e. I check whether the effects between the hypothesized measures are robust to statistical interventions. I only retest hypothesis 1 and 6 under the changed conditions to keep a clear overview of the findings in this thesis. Otherwise the overall comparability of the results would become complicated. The robustness checks are contemplated for the following reason. Castellani et al. (2013) emphasize that overlapping football matches, i.e. matches played on
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the same date, can cause correlations between the abnormal returns related to the sentiment of a particular match outcome. At a given event date, the disturbances of the different units (football teams) may be correlated. This reflects the possibility that unobserved influences may affect all units simultaneously. In such a situation it can be claimed that the error terms from the estimated regression model contain contemporaneous correlation. Neglecting the event date clustering may implicitly result in bias of the regression parameters, and indirectly to falsely accepting (rejecting) the hypotheses. On average 16 matches are played on a particular event date, thus the problem of cross-unit correlations is existent. To prevent potentially spurious outcomes from the main econometric design, I retest the aforementioned three hypotheses by means of an alternative statistical approach. The substitute for the OLS model is the generalized estimating equations (GEE) model. Castellani et al. (2013) use the
seemingly unrelated regression (SUR) model to deal with contemporaneous correlation. That
means, the model tests the relation between the (in)dependent variables if they seem to be unrelated. Nevertheless, as I have stated, football matches are related if the covariance
between the match outcomes is significant. The SUR approach or any model dealing with this kind of issue, models the correlation of the error terms implicitly. Influential factors like future anticipations and international prospects are hard to quantify, and their impact on all match outcomes is implicitly included in the unobserved error terms 𝜀!". However, for reasons I discuss in detail in the next paragraph 3.2, the SUR approach is not suitable to deal with my dataset for two important reasons, namely (i) it is does not have the same event dates across all units, i.e. my dataset is unbalanced, and (ii) the number of units – the football teams exceeds the average number of event dates per football team. Through, trial-and-error3 and
searching for an alternative model that can handle contemporaneous correlations, I strive to find the best model that can explain market fluctuations. Alternatively, through different routes I have found the GEE to be the best solution for issues related to correlations between units, to the best of my knowledge and research. While the basis event-study is inspired from Campbell et al. (1997), I substitute the estimation of this model with GEE approach as
suggested by Ballinger (2004) when I perform the robustness checks. For this purpose, I again retest with the complete sample, the sample of countries for which I have found the MSCI indices and the sample of countries for which I only could find the national stock exchange
3 I mention here trial-and-error, because some of the found solutions discussed in paragraph 3.2 forces
to adopt tests on (sub)samples to overcome the limitations of an unbalanced dataset, also discussed in the next part.
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indices. Finally, I retest with these three (sub)samples and limiting to only selected 27 national teams, for reasons I describe in detail in paragraph 4.2. In unreported results I
winsorized abnormal returns at the left and right one percent tales to correct potential outliers. Since the results are not much different, I proceed with the original abnormal returns in all statistical analyses. Further, I give the description or key features of the data, below each table and figure. All statistical operations are completed with Stata version 13.0, by writing the code the commands of all the pre-editing, filtering, import, merging, declaration and calculation of variables in Stata’s Do (syntax) file. At request, the program code can be provided. The conceptual framework of the models is presented below.
Figure 1: Conceptual model with independent and dependent variables
Abnormal
Returns
Dependent (scale) variable Tournament Result (Dummy variables) - Win - Loss - Tie Goal Difference (Scale variables) - Delta - Squared Delta Temporal Effects (Dummy variables) - Years 2006, ’10, ’14, ‘18 - Months February thru November- Weekend/ Monday effect
Betting Odds (Dummy variables) - Expected match win - Unexpected match win
- Expected match loss - Unexpected match loss
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3.2 Robustness check to deal with cross-unit correlations
Panel datasets possess potentially the property that the units are dependent, that can be the result of the presence of common shocks and unobserved influences that become part of the disturbances eventually. Some researchers think that this phenomenon is related to the global developments during the past few decades, viz. development of economic activities and financial integration of nations and financial institutions at a high pace. As a matter of fact, all these facets must cause a stronger interdependency between international organizations, markets and units of all sorts, including the units under study in this thesis. To give a sense a direction, in micro-economic settings, the likelihood that entities react to common shocks or unobserved influences, can be affected by neighbouring firm effects and herd behaviour (De Hoyos & Sarafidis, 2006). The impact of unobserved influences on cross-sectional units can be subject to the amount or the nature of the correlations. If it is assumed that the cross-sectional dependency arises from common shocks or unobserved factors and these are absorbed by the error terms, while not correlated with the independent variables. A fixed or random effects model can be estimated. These models produce consistent but inefficient betas, meaning that the betas are not estimated accurately. On the other hand, if these
unobserved influential common factors cause dependencies between the units – absorbed by the error terms – and are also correlated with the independent variables, these designs do not work. Fixed effects and random effects will produce biased and inconsistent betas. If
independent variables cannot be assumed stochastic and exogenous, i.e. that there is no correlation between the error terms and independent variables, other solutions have to be applied4. In such a case, it is difficult to estimate the individual contribution of each
independent variable onto the outcome of the dependent variable, e.g. abnormal returns. For such situations, one has to define instrumental variables (IV) to estimate two-stage least squares (2SLS) (Heij et al., 2004). However, from practical point of view, it is difficult to spot instrumental variables that are correlated with independent variables and not with the
unobserved common shocks or influences. What’s more, panel model estimations using cross-sectional interdependent datasets, experience inefficient betas of larger proportions, compared to OLS estimators. That means, if correlations between units are ignored and the units are pooled and run by a panel regression, the efficiency of the coefficients drops harder than if for each unit apart OLS had been run (Phillips & Sul, 2003). Therefore, it is crucial to take into
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account the cross-unit correlations if the dataset is constructed as such that each unit also contains a repeated time measure. Further below this part, I explain that if the number of times series observations is larger that the number of units, a Breusch-Pagan 𝐿𝑀-test is appropriate. But if the opposite is true, the 𝐿𝑀-test is due to its statistical properties not a suitable testing method.
A SUR approach can be applied to deal with contemporaneous correlations: 𝑦!" = 𝛼! + 𝑥!"! 𝛾
! + 𝜀!", Eq 2
With 𝐸 𝜀!"𝜀!" = 𝜎!" and 𝐸 𝜀!"𝜀!" = 0 for all 𝑖, 𝑗, and 𝑡 ≠ 𝑠. The equations for different units
seem to be unrelated, since all parameters 𝛼! and 𝛾! are different. Still, observations 𝑦!" and 𝑦!" are related if the covariance between these observations is non-zero. Translated to my subject, the relations between the football teams are modelled implicitly by the correlation of the disturbances 𝜀!". Further below, this insight is important to determine the best possible design to account for the cross-unit correlations.
Even though the number of played matches for each country is not balanced, still the SUR approach is not applicable, as this model requires fewer subjects than the longest time span. For instance, the maximum (average) length of the time-series per team is 65 (40). Further, I show alternative solutions that I tried to apply SUR to my unbalanced dataset. The maximum possible matches per event date are 36 and the average matches per event date are 16. All dates in the sample are the business dates earliest after a particular match date. So, each match is tied with at most two distinct abnormal returns if both the countries of a match have retained in the final dataset. In other words, if Argentina – Brazil has played a match on November 13th 2015, Argentina (Brazil) is combined with the abnormal returns earliest available on November 16th 2015, since the match was held on a Friday. This date lies at most three days after a football match. The event date, i.e. the match date, is not considered, since I look at the effect of all match results on stock market movement the day after the match. For SUR to be applicable, all match dates should be balanced across countries, that means no different match dates should exist for any team5. I test for contemporaneous or cross-sectional correlation in a panel model. I estimate this model on an unbalanced dataset where the
5 For instance Stata gives the screen message “match_date has different values across panels”, since
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number of units is much larger than the number of time points. For this matter FGLS models cannot be applied to deal with contemporaneous correlation. Applying the sureg command to estimate the parameters of a set of seemingly unrelated regressions to an unbalanced dataset is not possible. That is, there is unequal number of observations for a specific event date across countries. Alternatively, the testing of GLS regression with correlated
disturbances for dataset with contemporaneous correlation is unfortunately not possible with Stata’s xtgls command. This command fits panel data models by using GLS, subject to datasets that are balanced across units. Still, an equation-by-equation regression is possible if and only if cross-unit correlations are absent. Alternatively, OLS regressions for each unit may be feasible. If all units have the same independent variables 𝑋! = 𝑋 or if the different units are uncorrelated so that 𝜎!" = 0 for all 𝑖 ≠ 𝑗, SUR is no longer needed. In that case the GLS-estimator in the SUR model reduces to the OLS estimator for every unit. Since the independent variables are not constant for all units, I make sure that the disturbances of the different units are not correlated, before estimating OLS regressions for each unit. A final solution is to apply the cross-unit correlation test - Breush-Pagan Lagrange Multiplier (LM) test - described in Heij et al. (2004) and Greene (2000). I employ the test to assure cross-sectional independence in the residuals. A nice user-written Stata command xttest2 calculates the Breusch-Pagan statistic for cross-sectional independence in the residuals after a fixed effect regression model is estimated. The issue arises since in an unbalanced panel only the observations are used to calculate the test statistic if those observations are available across all units. The resulting test statistic is distributed 𝜒! !
!𝑚 𝑚 − 1 with 𝑚 the number of cross-sectional units, under the null hypothesis of cross-sectional independence. This test statistic is computed over observations common to all cross-sectional units, i.e. the countries. However, applying this test to my dataset, Stata gives the message ‘too few common
observations across panel’. From the table in appendix D, it is evident that each event date is
not evenly distributed across the units. For instance, the event date November 18th 2004, appears two times while there are 87 countries, just like other event dates that are very few. To compute the contemporaneous correlations, there should be sufficient number of event dates that are common to all units. Besides, this command is suitable if the number of time series observations per unit is large compared to the number of units. Finally, there is another method to test whether independence of country teams is true. A user-written Stata function xtcsd seems to be the suitable program to deal with unbalanced datasets, according to the provided description. Besides, it complements the Stata command xttest2. The module is
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a post-estimation function that is applicable to cross-sectional time-series data following a fixed or random effects model. Error terms across units are a standard assumption in panel structure datasets. In the case that the number of time series observations 𝑛 are large and the number of units 𝑛 are small. The 𝐿𝑀-test, defined above, is appropriate to test for absence of cross-sectional correlations (𝜎!" = 0 for all 𝑖 ≠ 𝑗). Yet, cross-sectional time series datasets in most instances have a smaller timespan 𝑛 compared to the number of units 𝑚. In those cases the Breusch-Pagan 𝐿𝑀-test is not valid, apparently also not for my dataset, since I have 87 distinct national football teams and on average 40 football matches per team. This module tests the hypothesis of cross-sectional independence by giving the choice between two semi-parametric tests (Friedman, 1937; Free, 1995, 2004), and a semi-parametric test (Pesaran, 2004). The Pesaran test statistic follows a standard normal distribution, while it is capable of managing balanced and unbalanced datasets. The Friedman test employs a 𝜒! (read as: Chi-squared) distributed test statistic, and even though it is capable of handling unbalanced datasets, it uses only the observations that are common to all cross-sectional observations. This implies, that if one observation for a particular event date is present for one national team, the same event date must exist for all national teams, which is not likely. Otherwise, uncommon dates are not evaluated at all. Free’s test assumes a different distribution and handles unbalanced data similar to the Friedman test. Thus, all these three tests are capable of dealing with the testing of contemporaneous correlations. De Hoyos and Sarafidis (2006) have studied cases in which these tests are performed under various model specifications. The authors assert that this module closes an important gap in applied research.
I perform the Pesaran test, as it is capable of dealing with unbalanced data, even if there are event dates that are not available for all cross-sectional units. I am testing for a subsample of 27 national teams, for reasons mentioned previously. The reason why this works, is
because the larger sample does not allow the Pesaran test to work properly. Stata gives the screen message that the panel is highly unbalanced, i.e. there are not enough common
observations across panel to perform Pesaran's test. The test seems initially to assure to work for unbalanced datasets, but there is a restriction for this module, namely that the dataset should not be too unbalanced. The module guidelines do not mention what the degree of
unbalancedness should be to work properly. Eventually, I have conducted the Pesaran test for
a number of subsamples, including only the event dates that prevail in multiple cross-sections. The subsamples are chosen with trial-and-error, however, the tests did not succeed in
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aforementioned 27 national teams. What’s more, the Pesaran test should be employed after a fixed or random effects regression is estimated. I chose to estimate a random effects
regression for the following reasons. In a panel model with fixed effects, the characteristics of national teams should be constant over time. One must assume that the marginal effects of the independent variables on the abnormal returns are equal for all national teams. This notion is the same as restricting the parameters to 𝛾! = 𝛾, making them constant across the units. To capture the unit-specific characteristics of the data, the constant terms 𝛼! can vary across units.
𝑦!" = 𝛼! + 𝑥!"! 𝛾 + 𝜀
!", 𝜀!" ~ IID 0, 𝜎! . Eq 3
Panel model with fixed effects
However, I would like to capture the differences of the match outcomes over time, for which the random effects model is appropriate. In other words, the random effects model does not absorb the unit- or time-specific characteristics in the constant terms 𝛼!, but allow the disturbances 𝜔!" to correlate over time. Rewriting 𝛼 in the fixed effects model gives 𝛼! = 𝛼 + 𝜂!, with 𝜂! ~ IID 0, 𝜎!! , and
𝑦!" = 𝛼 + 𝑥!"! 𝛾 + 𝜔
!", 𝜔!" = 𝜀!" + 𝜂!. Eq 4
Panel model with random effects
The model assumes that the disturbances are subject to: 𝐸 𝜔!" = 0, 𝐸 𝜔!"! = 𝜎!+ 𝜎
!!, 𝐸 𝜔!"𝜔!" = 𝜎!! (for 𝑡 ≠ 𝑠), 𝐸 𝜔!"𝜔!" = 0 (for all 𝑡, 𝑠, and 𝑖 ≠ 𝑗).
The results of the random effects model for the 27 selected national teams dataset is given in appendix E and the correlation matrix of the cross-unit correlations is given in appendix F. Accordingly, once I have accounted for random effects, none of the match outcome dummy variables have an effect upon the MSCI or national stock exchange abnormal returns. The model implicitly assumes that the cross-sectional units are independent within at a given time or over time. The test permits to test the null:
