Jean-Baptiste Dherbecourt

Bastien Drut
email: bastien.drut@gmail.com

Who will go down this year? The Determinants of Promotion and Relegation in European Soccer Leagues

Keywords: Economics of Sport, Organization of Sports Leagues, Soccer, Promotion and Relegation, Economic Forecasting, Regional Economy, Billionaires, Stock Market Classification: L83, R11, R58

Contributing to the lively debate on closed leagues (North American model) versus open leagues (European model) in professional sport league, this paper aims at determining the drivers of promotion and relegation in the major European soccer leagues. Using a large and original dataset (for example: club's link with a billionaire, club listed in the stock market, etc.) and logistic regressions, our results show that institutional factors matter to settle in the elite. It also indicates that open leagues system in European soccer championships is de facto very similar to closed leagues system. Furthermore, our forecasting model can be of interest for soccer investors or bookmakers.

Introduction

European soccer leagues are one of the most popular sportive organizations in the world. One of their major originality in comparison with American sport leagues (see [START_REF] Andreff | New Perspectives in Sports Economics: A European View[END_REF], for an exhaustive comparison) is that the membership is not fixed over time: sportive performances during the season determine whether a club shall be promoted in superior division or relegated to inferior division. [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF], [START_REF] Szymanski | Open Competition in League Sports[END_REF] and [START_REF] Szymanski | The Promotion and Relegation System[END_REF] detail how this format was put in place at the creation of English football league in 18881 . This format was expanded to other European soccer leagues and still remains2 . However, debates occured in the sport press and soccer institutions, for years. On one hand, some support the North-American model where leagues are closed and members are the same season after season and, on the other hand, there are supporters of the European model with open leagues based on promotion and relegation system. This debate also takes place on a European scale: [START_REF] Hoehn | The Americanization of European Football[END_REF] propose the architecture of a European Superleague.

The structure of professional soccer leagues has already been studied, especially its financial impact (Noll, 2002, Szymanski andValetti, 2005). [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] explores the economic impact of the promotion and relegation system in professional sport leagues in general: he argues promotion and relegation system tends to spread teams' quality in the higher division of a league. This would arise from the profit incentives balance created by such a system. Indeed, in a closed league, incentives are not affected by the fact that the weakest teams will be relegated, which results in reducing the gap between top and bottom teams. On the contrary, opportunity of promotion (and of getting related profits), and fear of relegation, will encourage teams to improve their own quality. Szymanski and Valetti (2005) further show that promotion and relegation system enhances sportive effort incentives (avoiding relegation strongly exacerbates the competition between bottom teams) but diminishes the incentive to share incomes: top teams would tend to invest so as to maintain a higher level, widening the gap with bottom teams. Both [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] and [START_REF] Szymanski | Promotion and Relegation in Sporting Contests[END_REF] bring empirical support to their theoretical model by taking the example of the English football League. However, they only focus on the economic impact of the promotion and relegation system and to our knowledge, and as noticed by [START_REF] Matheson | European Football: a Survey of the Literature[END_REF] in his literature review on European soccer and by [START_REF] Szymanski | The Promotion and Relegation System[END_REF], there has been no work focusing on the determinants of the teams' promotion and relegation. This is striking considering the stakes linked with promotion and relegation. Indeed, beside sport betting or fans' disappointment, sportive relegation is often a financial drama: the club has to sell its best players, it loses revenues from sponsors and broadcasting rights, it might have to fire staff members, etc. Thus, the possibility to forecast promotion and relegation could help to make economic decisions. [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] documents well the concentration of top teams in English Premier League, giving the intuition that elite teams are more likely to stay in the elite the season after. However, a wide range of statistics remains unused in the study of promotion and relegation. Though, it is interesting to understand whether cultural and economical factors play a role in the location of elite soccer teams: for example, [START_REF] Kuper | Why England Lose: and Other Curious Phenomena Explained[END_REF] relate soccer clubs location in Europe to the industrial revolution.

This paper aims at filling the gap, taking the particular cases of the five major European soccer leagues (England, France, Germany, Italy, and Spain); the promotion and relegation system being almost the same among these five championships. Our main objective is to propose a model able to forecast promotion for second division clubs and relegation for first division clubs. As relegation for a football club can be considered similar in the sportive sphere to a bond default in the financial sphere, we employ logistic regressions in the same way than papers studying sovereign bond defaults (for example [START_REF] Catao | Sovereign Defaults: the Role of Volatility[END_REF]Sutton, 2002, Manasse et al., 2003). Indeed, logistic regressions aim at explaining binary variables. In the vein of [START_REF] Manasse | Predicting Sovereign Debt Crises[END_REF], we propose an early warning system to detect, before the beginning of the sportive season, clubs for which the probability of relegation is high.

Besides, due to the lack of previous studies on this topic, this investigation is exploratory and not restrictive concerning the explanatory variables' choice.

The paper is organized as follows: in Section 2, we present the data we use in the study. In Section 3, we report the results of the promotion/relegation empirical determinants' analysis for the major European football leagues. Section 4 proposes an out-of-sample forecast of promotion and relegation for the 2008/2009 season. Section 5 concludes.

Data

We focus on the five most important European soccer leagues3 according to the Union of European Football Associations (UEFA) ranking in 2009, that is to say England, France, Germany, Italy and Spain. The study is restricted to the sportive seasons from 2004/2005 to 2008/2009 because the leagues' size and promotion/relegation rules were different during previous seasons. The system of relegation is the same among these five leagues: the three teams at the bottom of the first division are relegated to the second division. The promotion system is also very similar: in France, Germany and Spain, the three first teams of the second division are promoted in the first division while in England and Italy, the two first teams are directly promoted and the third team promoted is the winner of play-offs involving the third to the sixth teams of the second division. There is a particularity in Italy: play-offs may be avoided if the third ranked club of the second division has 10 points more than the fourth ranked club and if so, is promoted4 . The size of the first divisions ranges from 18 to 20 and the size of the second divisions ranges from 18 to 24, that makes possible the comparison across the leagues. Final league tables are downloaded from the websites of the different national leagues. This study only takes into account promotion and relegation through sportive results: for this reason, we do as if FC Messina Peloro was relegated for the season 2005/2006 in Italy instead of Juventus FC which was administratively relegated because of a match fixing scandal.

Considering the sample itself, we notice a kind of yo-yo effect, already noticed by [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] with eleven clubs (Birmingham City FC, SM Caen, MSV Duisburg, US Lecce, Levante UD, FC Metz, FC Nantes, CD Numancia, FC Hansa Rostock, RC Strasbourg, West Bromwitch Albion FC) relegated twice from the first division during the five seasons of the study and four clubs promoted twice (Birmingham City FC, MSV Duisburg, FC Köln, Sunderland AFC). The two most representative clubs of this phenomenon are Birmingham City FC and MSV Duisburg with two relegations and two promotions in five years.

The main issue in soccer-related studies is the lack of homogeneous data on football clubs.

Studying promotion and relegation requires data for each club involved in the first or second division for each league and for each season. It includes 259 distinct European football clubs: 55 in England, 47 in France, 48 in Germany, 55 in Italy and 54 in Spain. However, due to a lack of data availability, financial variables like total sales, players' wages or revenues from transfers cannot be used here: some reports like the yearly Deloitte Football Money League or the Forbes Most Valuable Soccer Teams 5 provide detailed financial data on top European soccer teams. However, to our knowledge, there is no such database or data source for alle the European clubs in the two first divisions in Europe -it is by the way surprising that the Deloitte and Forbes data are so little used in the literature 6 -. It is obvious that financial data would have a strong impact on the sportive results of the clubs: a rich club can hire good players and consequently makes its relegation probability lower and promotion probability higher. But working on a large group of clubs, as it is needed for our study, unfortunately implied to do without such a variable. Three types of variables are considered here: variables concerning the players and the staff, variables concerning institutional factors related to the clubs and variables concerning the economic context of the region in which the clubs are located.

The list of our potential explanatory variables includes:

 the team's average age (Source: http://www.eufo.de/).

 the percentage of foreign players (Source: http://www.eufo.de/).

 the club seniority in the division.

 the coach seniority in the club at the beginning of the season (Source: authors's calculation).

 the participation to an European competition (Source: UEFA).

 the fact that the club has ever won the national cup or the championship since 1980 7 .

 the financial link with a billionaire 8 (Source: http://www.forbes.com) 5 Deloitte publishes each year a report with detailed financial data on the 20 more lucrative European soccer clubs. Forbes also publishes each year a report on the 25 "most valuable soccer teams" with detailed statistics. 6 The data could be used to test structural models about top European soccer. 7 1980 being the date we retain for the beginning of our football era with the important increase of TV broadcasting rights. 8 As businessmen and billionaires in particular are more and more involved in European soccer, we built a billionaire dummy with the help of the magazine Forbes, the common reference for billionaires. To do so, we  club listed on the stock market.

 the presence of a club of the same city in first division.

 the stadium capacity (Source: clubs' websites).

 the club creation date (Source: clubs' websites).

 the city population (Source: http://www.wikipedia.org/ 9 ).

 the GDP per capita of the region in which the club is located (Source: Eurostat).

 the 5 years average of GDP growth of the region in which the club is located (Source: OECD).

 the population density of the region in which the club is located (Source: Eurostat).

 the percentage of agriculture and industry in the total employment (Source: OECD).

 the unemployment rate of the region in which the club is located (Source: Eurostat).

 the percentage of the labour force with secondary and tertiary education (Source: OECD).

Descriptive statistics for these variables are in the Table 1 in Appendix for the season 2008/2009. They already give interesting insights. For several variables, there is a strong distinction between first and second division clubs: the percentage of foreign players, the average coach seniority in the club, the stadium capacity, the city population, the percentage of service in total employment in the region and the population density in the region are higher in first division clubs than in second division ones. Then, we notice some heterogeneity across the different leagues: for example, the percentage of foreign players and the stadium capacity are much more important in England and Germany than in France, Italy and Spain. On average, English and German clubs have also been created before French, Italian and Spanish ones.

In order to maximize the sample size, we focus on pooled regressions for the five countries. To do so, we run two panel logistic 10 regressions, one for promotion and the other for relegation, because this model aims at explaining binary variables. In the first (resp. second) one, we consider variables of first division (resp. second division) clubs and the collected all the soccer-related news on http://www.forbes.com and we attribute 1 when mention is made of a financial link between a soccer club and a billionaire and 0 otherwise. 9 Wikipedia proposes the latest data from the national offices of statistics in almost every case. 10 Probit regressions have also been tried with very similar results. dependent variable is a dummy being 1 when the club is relegated (resp. promoted) and 0 otherwise. In order to remove biases between distinct leagues and seasons, we take reduced centered figures related to the teams from the same league and season. As many variables appear to be correlated, we adopt a "backward elimination" procedure with a retention threshold of 0,30.

Results

In Table 2 (respectively Table 3), the logit regression results are available for relegation

All variables After backward elimination

First, the pseudo R² after the "backward elimination" procedure is pretty low for both regressions (0.19 for the relegation regression and 0.13 for the promotion regression). By order of comparison, the same regression is run with a dependent variable being 1 if the club is champion at the end of the season and 0 otherwise, and obtains a pseudo R² equal to 0.45 (see Table 4 in Appendix). An explanation could be that forecasting top teams' results is easier than bottom teams' ones but also mainly that there is a strong heterogeneity between the five different leagues. Despite this quite low predictive power, some interesting insights emerge. After the "backward elimination" procedure, several regional variables remain significant. This indicates clearly that the regional context matters in the location of elite soccer teams.

Concerning the relegation from the first division (see Table 2), the regional context plays a highly significant role: it appears that the more the percentage of services in the total employment and also the more the percentage of educated regional people, the less the relegation probability. Noticing that almost all the best football clubs in Europe are located in industrial cities (Manchester or Milan for example), [START_REF] Kuper | Why England Lose: and Other Curious Phenomena Explained[END_REF] Concerning the promotion regression (Table 3), the most significant variable is the stadium capacity. Again, having a big stadium allows clubs to obtain important revenues and induces a strong relative difference between second division clubs. This could encourage the return in the elite of top clubs "accidentally" demoted, that is to say demoted while they had the financial and sportive means to stay in the first division. Besides, the impact of the seniority in second division is asymmetric, depending on the origin (first or third division): it is only significant for clubs coming from the first division (p-value=0.03). As suggested by [START_REF] Hoehn | The Americanization of European Football[END_REF], demoted clubs from first division are more likely to be promoted the years following the relegation. After what, they get bogged down in second division, a priori because they progressively lose first division financial means. This is related to the yo-yo effect underlined by [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF].

Another interesting point is that presence of another team of the same city in first division significantly (p=0.06) decreases the promotion probability, indicating that Barcelona, Liverpool, London, Manchester, Milan or Madrid would stay exceptions in European soccer.

Like [START_REF] Kuper | Why England Lose: and Other Curious Phenomena Explained[END_REF], we interpret this by fact that the majority of resources in terms of attendance and matchday revenues already belongs to the principal football club of the city and is unable to develop durably.

The significance of the growth and unemployment variables in the promotion regression is striking: clubs of regions with high growth and low unemployment, that is to say in good economic shape, are less likely to be promoted. We do not have credible interpretations for this. Regions in bad economic shape could desire a football club in the elite in order to develop social and entertainment activities for people in economic distress. For cities, it is also a matter of prestige to have a successful football club and it can improve or even build the media-related image of the city. But this interpretation stands also for regions in good economic shape.

Both "Billionaire" and "Stock Market" variables remain after the "backward elimination" procedure in both regressions but their significance strongly differs. The "Billionaire" dummy increases significantly (p-value=0.05) the promotion probability. This is not surprising if one considers the huge amounts of money invested by billionaires in soccer, what tends globally to increase the team's level. Nevertheless, we have to admit that this dummy could be improved by also considering multimillionaires and non billionaires tycoons12 but we are not aware of such data sources. An astonishing point is the influence of the stock market dummy: it is significant neither for promotion nor for relegation but the sign is the same.

In both regressions, indicators concerning the teams' average age and the percentage of foreign players fail to be significant at conventional levels. For these two variables, several contradictory phenomena play a role. For example, very young talents can improve the staff quality but this argument holds also for confirmed thirty-year-old players. For the same reasons, the percentage of foreign players has no significant impact here on promotion and relegation: the percentage of foreign players can be an indicator of teams' quality (for example, Liverpool, Chelsea, Arsenal and Internazionale Milano have around 80% of foreign players) but a perfect counterexample is the Athletic Bilbao that has only Basque players and that is the only Spanish club together with Real Madrid and FC Barcelona to have always been member of the first division.

Out-of-sample forecast for the season 2008/2009

In this section, we discuss the practical accuracy of our model by running an out-of- First, if we retain a threshold probability of 0.20 as early signal of promotion and relegation, the model predicts well 10 clubs out of 15 for the relegation and 6 out of 15 for the promotion. In the other way, the model predicts wrongly 19 relegations and 21 promotions.

The model forecasts better relegation than promotion, which has to be related with the better pseudo R² of the relegation regression. However, promotion and relegation appear to be not fully predictable by our variables, which is not a surprise given the low predictive power of forbade the promotion because of insufficient financial resources. Second, the experience of the players was not exceptional: two years before the promotion in Ligue 1, the club was in the third division and one year before, they had to struggle until the lat game to stay in Ligue 2. Third, the stadium "Stade de la Libération" could accommodate around 8000 spectators at that time, what was few even for a French second division club. Fourth, the coach had not any record14 . Fifth, Boulogne-sur-Mer had never been in the elite before while there was already three clubs in the region Nord-Pas-de-Calais 15 established in the first or second division for many years. In the case of Boulogne-sur-Mer, the most plausible explanation is the system of play quality put in place and the collective power of the players. Typically, this promotion will offer the "David and Goliath contests" mentioned in [START_REF] Hoehn | The Americanization of European Football[END_REF].

The structure of promotion and relegation leagues lets us think that in the second leagues, except clubs benefiting from exceptional institutional advantages (billionaire on the board, big stadium capacity, etc.), almost each club stands a chance to finish in the upper level.

Conclusion

The aim of this paper was to study the empirical determinants of promotion and relegation in the major European soccer leagues. Even if our approach is exploratory, we believe that it yields insights complementing the works of [START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] and [START_REF] Szymanski | Promotion and Relegation in Sporting Contests[END_REF].

In European soccer leagues, a hard core of clubs in the first divisions appears to be very unlikely to be demoted to the lower division. The present study shows that this phenomenon is self-reinforcing. There is a kind of top-league inside the first league:

institutional factors like the stadium capacity, the club background, and the link with businessmen contribute to clubs' successfulness. This has for consequence that these clubs are able to compete at the highest level over seasons. Moreover, if one of these top clubs happens to be relegated "accidentally" in the second league, the return in first division the next season is very likely. For these clubs, it results in a yo-yo effect because the club's competitiveness is not high enough to remain in first division but institutional factors support their return in first division. By contrast, the other clubs have strong difficulties in establishing themselves durably in the first division. To put it in a nutshell, the promotion and relegation system of European football leagues does not correspond to a real open league in which there would be a lot of renewals but rather already looks like closed leagues completed with four or five rotating clubs.

Further research could focus on the reasons why some top clubs established for many years in the first division are sometimes demoted, a possible reason being governance issues.

On the contrary, it could be interesting to study the determinants of success stories where clubs originally playing in the third or fourth division succeed in reaching quickly the elite:

subsidies, coach personality, staff stability, etc. We also believe that the drivers of promotion and relegation are time-varying and further research could cover their evolution across time.

(

  respectively promotion) in the European football leagues for the seasons 2004/2005 to 2008/2009.

  describe the role of the industrial revolution in the location of soccer clubs in Europe: at this period, soccer was a way for newcomers in industrial towns to socialize. We interpret the significant negative impact of the industry variable on relegation by the decline of industries in Europe in relation with the globalization, this would explain the decline in the elite of clubs from industrial regions, for example Strasbourg and Birmingham in our sample, compared to clubs of services areas.It sounds obvious that the seniority in the first division and the qualification in European Cup decrease significantly the relegation probability. Indeed, clubs in first division have had access to first division broadcastings rights for several years, important matchday revenues and had the time to build high level teams. Moreover, clubs qualified in European Competition must have had very good players the former season to qualify. The stadium capacity variable, even if less significant, goes in the same way: this can be interpreted by the fact that having a big stadium allows you to receive important matchday revenues and in some cases stadium naming revenues 11 . It can also ease access to credit. Actually, these variables are the illustration of elite reproduction and fully validate the theoretical findings ofSzymanski and Valetti (2005): incomes are little shared in the soccer elite and a hard core of a bit more than 10 clubs is durably set in each league. The process is self-reinforcing because belonging to the elite for years makes the club earn more money and allows hiring good players, what diminishes the relegation probability.

  sample forecast of promotion and relegation for the season 2008/2009. We run both logistic regressions with data from 2004/2005 to 2007/2008 and compute promotion and relegation probabilities by applying to this model clubs' characteristics known at the beginning of the season 2008/2009. The forecasted probability of relegation (resp. promotion) is presented in

  the regressions shown in Section 3. Two main reasons can be invoked: the lack of financial data and the leagues' heterogeneity. Nevertheless, it gives interesting guidelines for further developments of the model.In each country, there is a hard core from 8 clubs in Germany to 11 clubs in England in the first division for which the relegation probability is very low (below 0.10). These clubs are also the best ranked at the end of the season 2008/2009. This is linked with findings of Section 3: these groups of top clubs are durably set in the first division and attract financial resources in order to stay in the elite. From these hard cores, only Newcastle was relegated in 2008/2009. This can be considered as an "accident" but one can also assume that the seniority in first division 13 can increase the relegation probability if the club does not win any trophy because it has not access to top clubs revenues (from European championship for example). Concerning the promotion, results are more dispersive. Forecasts are good in the Italian case with the three clubs promoted (Parma, Bari and Livorno) having the highest promotion probability at the beginning of the season. Except in Germany, the clubs with the highest promotion probability have been promoted (Birmingham FC, RC Lens, Parma and Zaragoza). However, forecasts are clearly inaccurate in Germany with no promoted club in the six clubs with the highest promotion probability. Some cases are very difficult to forecast. A very good example is Boulogne-sur-Mer in France. This club from Nord-Pas-de-Calais was promoted to Ligue 1 at the end of the season 2008/2009 while its promotion probability was very low (0.06). Explanations of this exploit are very scarce. First, Boulogne-sur-Mer club is not rich at all: when it was promoted from National (the third division) to Ligue 2 at the end of the season 2006/2007, the Direction Nationale du Contrôle de Gestion (DNCG), the French watchdog of football clubs almost

Table 2

 2 Logit regression results for relegation in European football leagues 2004/2005 to 2008/2009

	Coefficient	Prob.	Coefficient	Prob.

Table 3

 3 Logit regression results for promotion in European football leagues 2004/2005 to 2008/2009

	Coefficient	Prob.	Coefficient	Prob.

Table 5 (

 5 resp. Table6) for each club with the final rank at the end of the season 2008/2009.

Promoted and relegated clubs are in bold.

Table 5

 5 Out-of-sample forecast of the relegation probability in European football leagues for the season 2008/2009

		England			France		Germany			Italy			Spain
	Club	Relegation Probability	Final Ranking	Club	Relegation Probability	Final Ranking	Club	Relegation Probability	Final Ranking	Club	Relegation Probability	Final Ranking	Club	Relegation Probability	Final Ranking
	Stoke	0.57	12	Valenciennes	0.38	12	Karlsruher	0.74	17	Atalanta	0.46	11	Numancia	0.52	19
	West Brom	0.49	20	Grenoble	0.37	13	Bochum	0.30	14	Chievo	0.45	16	Osasuna	0.39	15
	Hull	0.36	17	Sochaux	0.32	14	Bielefeld	0.26	18	Lecce	0.39	20	Malaga	0.31	8
	Wigan	0.27	11	Caen	0.32	18	Cottbus	0.26	16	Catania	0.26	15	Valladolid	0.28	16
	Bolton	0.24	13	Le Havre	0.29	20	Hannover	0.22	11	Bologna	0.25	17	Almeria	0.24	11
	Fulham	0.21	7	Le Mans	0.27	16	Moenchengladbach	0.19	15	Siena	0.19	14	Huelva	0.24	20
	Portsmouth	0.19	14	Nantes	0.20	19	Köln	0.18	12	Juventus	0.17	2	Villarreal	0.23	5
	Blackburn	0.18	15	Lorient	0.18	10	Leverkusen	0.17	9	Reggina	0.17	19	Gijon	0.13	14
	Middlesbrough	0.16	19	Lille	0.18	5	Wolfsburg	0.13	1	Cagliari	0.14	9	Valencia	0.12	6
	Sunderland	0.10	16	Lyon	0.11	3	Stuttgart	0.13	3	Palermo	0.13	8	Betis	0.12	18
	West Ham	0.06	9	Auxerre	0.10	8	Frankfurt	0.09	13	Torino	0.10	18	Getafe	0.08	17
	Aston Villa	0.05	6	Nancy	0.09	15	Dortmund	0.08	6	Napoli	0.10	12	Sevilla	0.07	3
	Everton	0.03	5	Nice	0.06	9	Hoffenheim	0.07	7	Genoa	0.05	5	Espanyol	0.07	10
	Tottenham	0.03	8	Toulouse	0.04	4	Bayern	0.06	2	Fiorentina	0.05	4	Santander	0.06	12
	Newcastle	0.01	18	St. Etienne	0.03	17	Bremen	0.06	10	Inter	0.03	1	Ath. Bilbao	0.06	13
	Manchester City	0.01	10	Bordeaux	0.02	1	Schalke	0.03	8	Udinese	0.02	7	Mallorca	0.04	9
	Chelsea	0.01	3	Monaco	0.02	11	Hertha	0.02	4	Sampdoria	0.02	13	La Coruna	0.02	7
	Liverpool	0.01	2	PSG	0.01	6	Hamburger	0.01	5	Lazio	0.02	10	Atl. Madrid	0.01	4
	Arsenal	0.00	4	Rennes	0.00	7				AS Roma	0.00	6	Barcelona	0.00	1
	Manchester Utd	0.00	1	Marseille	0.00	2				AC Milan	0.00	3	Real Madrid	0.00	2

Table 6

 6 Out-of-sample forecast of the promotion probability in European football leagues for the season 2008/2009

		England			France			Germany			Italy			Spain
	Club	Promotion Probability	Final Ranking	Club	Promotion Probability	Final Ranking	Club	Promotion Probability	Final Ranking	Club	Promotion Probability	Final Ranking	Club	Promotion Probability	Final Ranking
	Birmingham	0.55	2	Lens	0.64	1	Duisburg	0.41	6	Parma	0.41	2	Zaragoza	0.35	2
	Sheffield Utd	0.41	3	Strasbourg	0.50	4	Rostock	0.35	13	Bari	0.28	1	Elche	0.26	12
	Derby	0.27	18	Metz	0.41	5	Kaiserslautern	0.28	7	Livorno	0.22	3	Celta Vigo	0.25	17
	Sheffield Wed	0.26	12	Sedan	0.21	9	Frankfurt	0.26	15	Empoli	0.21	5	Real Sociedad	0.24	6
	Coventry	0.19	17	Amiens	0.21	18	Oberhausen	0.23	9	Avellino	0.17	21	Alicante	0.23	20
	Southampton	0.19	23	Troyes	0.20	19	Aachen	0.21	4	Triestina	0.16	8	Hercules	0.22	4
	Wolves	0.17	1	Montpellier	0.11	2	Mainz	0.17	2	Ascoli	0.16	16	Sevilla Atl.	0.20	22
	Preston	0.16	6	Reims	0.10	20	Nurnberg	0.15	3	Salernitana	0.15	14	Levante	0.19	8
	Burnley	0.11	5	Tours	0.09	6	Munich 1860	0.14	12	Modena	0.14	15	Murcia	0.16	14
	Barnsley	0.10	20	Nimes	0.09	17	St. Pauli	0.14	8	Mantova	0.14	13	Castellon	0.11	7
	Charlton	0.09	24	Dijon	0.08	8	Wehen	0.11	18	Albinoleffe	0.14	9	Alaves	0.10	19
	Crystal Palace	0.06	15	Clermont	0.06	12	Freiburg	0.11	1	Rimini	0.12	18	Gimnastic	0.10	10
	Norwich	0.06	22	Angers	0.06	7	Ahlen	0.10	10	Pisa	0.12	20	Salamanca	0.10	9
	Watford	0.06	13	Boulogne	0.06	3	Koblenz	0.10	14	Piacenza	0.11	10	Xerez	0.09	1
	Swansea	0.05	8	Guingamp	0.04	13	Augsburg	0.09	11	Treviso	0.09	22	Eibar	0.07	21
	QPR	0.04	11	Ajaccio	0.04	16	Furth	0.07	5	Sassuolo	0.09	7	Cordoba	0.06	13
	Doncaster	0.04	14	Brest	0.04	14	Osnabruck	0.06	16	Grosseto	0.08	6	Huesca	0.06	11
	Plymouth	0.04	21	Chateauroux	0.03	15	Ingolstadt	0.02	17	Brescia	0.07	4	Albacete	0.05	15
	Nottingham	0.03	19	Bastia	0.02	11				Ancona	0.05	19	Girona	0.05	16
	Cardiff	0.03	7	Vannes	0.01	10				Cittadella	0.04	17	Tenerife	0.04	3
	Ipswich	0.03	9							Frosinone	0.03	11	Las Palmas	0.04	18
	Reading	0.03	4							Vicenza	0.02	12	Vallecano	0.03	5
	Blackpool	0.02	16
	Bristol City	0.02	10

of the labour force with Tertiary Education

		England	France	Germany	Italy		Spain
	Average of players' age	26.0	25.7	25.6	25.6	25.6	25.9	26.7	26.4	26.8	26.8
		(1.5)	(1)	(1.4)	(1.2)	(1.1)	(1)	(1.3)	(1.2)	(0.7)	(1.6)
	% of foreign players	61.54%	46.53%	39.18%	27.23%	55.53%	35.99%	38.80%	21.14%	37.70%	16.86%
		(13.32%)	(14.22%)	(11.54%)	(12.49%)	(8.43%)	(13.89%)	(13.44%)	(9.05%)	(18.87%)	(10.74%)
	Years of presence of the current coach	3.1	1.6	1.5	1.3	1.6	0.9	1.5	0.4	0.9	0.5
		(5.3)	(1.2)	(1.7)	(1.6)	(2.2)	(1.2)	(1.8)	(0.6)	(1.1)	(0.9)
	Stadium Capacity	38506	25386	26940	17195	44852	27451	47412	19672	37175	22689
		(13981)	(6631)	(13053)	(9334)	(20043)	(16319)	(22435)	(11541)	(23346)	(11094)
	Creation date	1886	1885	1916	1921	1911	1912	1912	1918	1920	1928
		(15)	(12)	(22)	(28)	(23)	(27)	(16)	(18)	(28)	(18)
	City Population	2113106	1179251	353590	114592	686088	392579	709041	109725	768974	324451
		(3230911)	(2470605)	(552551)	(77450)	(817291)	(457876)	(795428)	(74468)	(950018)	(235462)
	Region: population density	3416	1836	174	107	778	498	240	249	214	184
		(3525)	(2948)	(196)	(85)	(931)	(515)	(102)	(103)	(228)	(150)
	Region: GDP per capita	38310	31988	24200	22020	29939	30389	24358	26864	24905	24314
		(24414)	(18754)	(4140)	(1360)	(6810)	(7312)	(5970)	(4986)	(5058)	(4568)
	Region: % Agriculture in Total Employment	0.80%	1.38%	3.88%	4.94%	1.76%	2.20%	4.63%	3.42%	4.82%	4.88%
		(0.45%)	(0.69%)	(2%)	(1.66%)	(0.96%)	(0.89%)	(3.27%)	(1.54%)	(3.17%)	(3.22%)
	Region: % Industry in Total Employment	19.22%	20.55%	23.26%	23.56%	24.61%	25.36%	25.63%	31.65%	28.81%	30.47%
		(5.14%)	(4.47%)	(4.25%)	(3.66%)	(5.16%)	(4.09%)	(7.31%)	(5.89%)	(4.94%)	(4.79%)
	Region: % of the labour force with Secondary Education 45.21%	45.22%	45.98%	44.53%	56.80%	57.69%	44.20%	44.44%	22.61%	22.52%
		(2.82%)	(2.07%)	(3.65%)	(7.26%)	(3.44%)	(1.91%)	(4.37%)	(3.16%)	(2.35%)	(2.13%)
		29.95%	28.91%	25.40%	22.94%	24.08%	23.51%	14.59%	14.51%	32.07%	31.63%
		(5.52%)	(4.36%)	(4.43%)	(4.01%)	(3.65%)	(1.82%)	(2.15%)	(1.34%)	(6.42%)	(7.2%)
	Region: % of unemployment	6.88%	5.95%	7.82%	8.48%	8.52%	7.16%	6.59%	4.71%	8.39%	8.24%
		(1.43%)	(1.54%)	(1.67%)	(2.06%)	(2.94%)	(2.93%)	(3.65%)	(2.76%)	(2.79%)	(2.37%)

Region: %

A second division was set in 1893 and the system of promotion of the best teams of the second division and relegation of the worst of the first division was set in 1898.

The promotion and relegation system remained in Europe, even if many rules changes occurred in practice.[START_REF] Noll | The Economics of Promotion and Relegation in Sports Leagues[END_REF] details these changes in the case of the English league since its creation.

The Deloitte Football Money League report(2007) and the Financial Action Task Force (2009) also identify these five leagues as the five "big ones". The Deloitte Football Money League (2007) reports that the overall revenues for the top tier clubs of these five leagues represent € 5.2 billions.

On the five study seasons, play-offs were avoided only in the season 2006/2007 where the third club had ten points more than his direct follower, Piacenza Calcio. But the promoted club was always the third ranked club, except in 2004/2005 where Ascoli Calcio, sixth-ranked, won the play-offs.

The most famous example is Arsenal FC: the club concluded a 15 years naming deal for its new stadium with Emirates airlines for more than GBP 100 millions.

For example, Mohamed Al Fayed invested in Fulham F.C. in 1997 while the club was in the third division (currently called Football League One) and made the club go in Premier League but he is not considered as billionaire by Forbes.

Newcastle had been in the Premier League since the season 1993/1994.

Before being Boulogne-sur-Mer coach, Philippe Montanier had just been the assistant of Robert Nouzaret when he was in charge of Côte d'Ivoire.

Acknowledgments

The authors thank Bas Hamers, Valérie Mignon, Kim Oostelinck, Jérémy Poirot and Ariane Szafarz for their helpful comments. Errors, if any, remain ours.

Appendix

All variables After backward elimination

Regional variables matter less than for the promotion and relegation regressions. Top teams managed to abstract themselves of the regional context and their performances are more driven by specific variables. Besides, contrary to the promotion and relegation regressions, the percentage of foreign players matters here: the capacity to attract international players helps to win the championship.

A very interesting point is that the probability to be champion decreases with the population of the city. Actually, this finding has to be related to the previous findings of [START_REF] Kuper | Why England Lose: and Other Curious Phenomena Explained[END_REF] who explain that the major clubs are not located in capital cities, these latter having the biggest population. They notice for example that no London club has ever won a European cup.


Hélène Raymond

-

Keywords: Sovereign Wealth Funds, Event Study. JEL Codes: G14, G34

This study assesses the reaction of stock markets, when Sovereign Wealth Funds (SWFs) announce that they have taken a stake in a listed company. It adds useful empirical results to the debate on the effect of SWFs on financial markets, which remains so far largely reliant on guess work. We perform an event study using a sample of 50 SWF acquisitions of equity stakes in listed companies around the world, from May 2005 to April 2008. According to our results, the announcement of an acquisition by a SWF has a transitory positive impact on the share price of the target company, but there is no lasting effect. This stands in contrast to the results obtained in the academic literature for the investments of private equity funds, and to a lesser extent pension funds. The tests conducted on a sub-sample of announcements targeting banks only made during the subprime crisis (between July 2007 and April 2008) do not exhibit more lasting effects. This may suggest that markets are not convinced that SWFs alone are capable of restoring the position of the banks concerned. These results are however subject to some caveats, and notably, the relatively small size of the sample as well as a selection bias in favour of transparent SWFs, due to the lack of information on other funds.

The growing attention to SWF investments

The recent acquisitions made by Sovereign Wealth Funds (SWFs) in international banks have been receiving growing attention in the public debate.

A sovereign wealth fund can be broadly defined as a government-owned or a government-controlled investment fund with a long-term investment horizon and very few explicit liabilities. It invests the surpluses of foreign exchange reserves, fiscal resources or commodity exports in international financial markets, often in instruments with higher risk/return profiles (e.g. equities)

than the usual foreign exchange reserve management funds. The higher involvement of these funds as investors and shareholders in financial markets raises questions as to their ability to influence market functioning and valuation.

The governance, transparency and management objectives of SWFs remain an open issue. Some funds show a willingness to remain passive shareholders with a long-term strategy. However, taking into account their sheer size and its future increase, it is unlikely that they will have absolutely no influence on the share price and governance of target companies and on market dynamics in general. By the same token, they could also have a bearing on asset valuation and risk premia.

The purpose of this study is to measure the reaction of stock markets, when Sovereign Wealth Funds (SWFs) announce that they have taken a stake in a listed company. To our knowledge, only four very recent papers deal with a similar issue.

The first of these papers is an occasional paper by the ECB by [START_REF] Beck | The impact of sovereign wealth funds on global financial markets[END_REF], which is focused on the announcements of disinvestments made by the Norwegian SWF. It concludes that these announcements have no effect on stock prices, as they are only made after the disinvestments have been completed. However, this result may just reflect the specific policy of the Norwegian SWF which, unlike most other SWFs, explicitly aims at minimising its market impact.

The event study of Fotak et alii (2008) is closer to the scope of our paper, as it excludes the investments by the Norwegian SWF. It also shares with our paper a selection bias in favour of Asian SWFs, which is difficult to avoid considering the lack of detailed information on many middle-eastern SWFs. 1 However, there are two differences with our approach. First, Fotak et alii (2008) do not seem to control for heteroskedasticity which is a major characteristic of daily stock price changes, whereas we fit conditional volatility by GARCH(1,1) processes and use these fitted series to standardize abnormal price changes.

Second, Fotak et alii (2008) try to assess the long-term effect of SWF acquisitions whereas this study focuses solely on the short-term effects (horizon of 10 business days). They find more lasting but non-linear effects: positive in the short run and negative in the long-term.

The two other papers are by [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] and by Kotter and Lel (2008). These papers are very similar in essence, as they both use an event study in a first step and, then, in a second step, attempt to explain the abnormal price reaction by the transparency score of the SWF. To the best of our knowledge these two papers do not control for heteroskedasticity in their event study. However their main conclusions are consistent with ours as they find positive short-term effects of SWFs acquisitions. This paper is organized as follows: section 2 details the method and the sample used, section 3 summarises the main results, and section 4 concludes and suggests ways to expand and improve our study.

What are the possible outcomes of SWFs acquisitions on stock markets ?

Following the announcement of a SWF investment in a listed company, the share price of a target company can move according to three different dynamics.

The first possible outcome is that the share price of the target company tracks closely the movements of the global market index in the days immediately following the announcement. In this instance, the transactions of the SWFs have no influence on the market. This outcome is most likely to occur if the 1 36 of the 75 events (48%) covered by their study are from Singaporean SWFs , compared with 26 out of 50 events (52%) for our study. 19 of the 75 events they cover are from two Malaysian and relatively marginal SWFs, which brings the total of Singaporean plus Malaysian stake announcements to 55/75 = 73% of the total number of events surveyed by Fotak et alii (2008).

SWF takes a small stake or if the news is already integrated in market prices due to early leaks.

A second possibility is that the announcement has a short-lived influence. The expected outcome in this case is that the share price of the target company outperforms the market index ("abnormal" positive price change) on the days immediately following the announcement. This can be due to a mere liquidity effect: the price increases in response to the expected rise in the demand of shares. This outcome is most likely to occur when the SWF takes large stakes.

Another interpretation is that the SWF investment relaxes the short-term financial constraints of the company, even though it does not improve its longterm profitability. Such an immediate reaction of the market reflects semistrong efficiency: the new information is immediately reflected in the stock price.

The final possibility is that the announcement has a lasting influence on the behaviour of the share price of the target company. In this case, the market expects the SWF to have a significant leverage over the governance of the company and hence its profitability. The direction of this long-term effect can go either way depending on the circumstances: positive if, as a long-term shareholder, the SWF improves the long-term return of the company [START_REF] Shleifer | Large Shareholders and Corporate Control[END_REF]; or negative, if as a state-owned entity, the SWF pursues strategic goals inconsistent with the maximization of the company"s profitability.

The method used

The simplest way of testing the different hypotheses is to have recourse to the method of event studies. Efficient markets process information immediately [START_REF] Fama | The Behavior of Stock-Market Prices[END_REF][START_REF] Campbell | The Econometrics of Financial Markets[END_REF]: the arrival of new information -such as a stake taken by a SWF in a company -should immediately be reflected in the share price. It is therefore possible to detect an "abnormal" reaction in response to an announcement by looking at the behaviour of the share price of the target company around the date of the announcement. In what follows we define the "abnormal" price change as the difference between the actual change of the share price of the target company and its normal change, measured with the help of a market model, which controls for the sensitivity of the share price to the market developments (for more details see Appendix).

Abnormal price changes are computed for each target company, on the day of the "event" and the days of the "event window". The "event" is defined as the public announcement of the participation of a SWF in a listed company. The "event window" is the period surrounding the announcement over which tests are conducted, with the day of announcement being defined as day 0. To capture the reaction of the financial markets in case of a leak before the announcement, or an announcement after the acquisition of the shares, event studies often make the event window begin two days before the official day of the announcement. In the tests for abnormal price variations we use the event window: [-2, +10].

The parameters of the market model are estimated during a period of estimation, prior and unconnected to the event window (to avoid all disturbances in the estimation of the parameters). The period of estimation used in this study covers a period of 163 days, finishing 11 days before the event.

We use parametric and non parametric tests, following the standard event methodology (see Appendix for details) to test whether the average abnormal price change is significantly different from zero. In a first step we compute daily average abnormal price changes (averaged over all events for each day of the event window, including the event day) and cumulative average abnormal prince changes (average abnormal price changes cumulated through time), then we test whether they are significantly different from zero. As stock price changes are heteroskedastic and volatility can vary throughout the event window, we choose to standardize the abnormal price variation using a GARCH process, in order to control for heteroskedasticity before applying parametric tests and the Corrado rank test.

2.2

The sample

Our database of events covers 50 acquisitions made from May 2005 to April 2008 by SWFs from 5 countries: China, Hong-Kong, Qatar, Singapore and the United Arab Emirates. The target companies are listed in 23 different countries ranging from Canada to Vietnam. The database of events has been constructed using sources such as Bloomberg, financial publications and information coming from the SWFs themselves. The bulk of the information is therefore biased towards recent events, and investments by the most transparent funds. Market data (share have been extracted from Bloomberg, such as the stock price of the company concerned and the stock index of the market considered, focusing on a period of 500 days around the date of the event.

Main results

The test results are shown using two different samples: the complete sample comprising the 50 stakes" announcements and a reduced sample limited to recent acquisitions made during the sub prime crisis.

An outperformance of the share price immediately after the announcement…

The test results for all 50 events are displayed in Table 1. They show that on average, there is a positive reaction in the markets on the day of the announcement of the acquisition of a stake by a SWF. Around the announcement (nearly always the day of the announcement or a few days before or after), there is an abnormal positive reaction of the stock price (columns 2 and 3 of Table 1). For both the standard parametric test and the Corrado non-parametric test (last line of Table 1), the abnormal daily variation of the stock price (AR) is strictly positive on the day of the event at the 1% percent significance level. On average, the abnormal rate of change is around 6%. But as two events on emerging markets clearly appear as outliers with positive abnormal price changes over 15% on the event day, we repeated the tests excluding these two events. The results of these tests on the database reduced to 48 events are displayed in the last four columns of table 1. The main results stay the same though the average abnormal price change on the event day drops to "only" 3,85%. This illustrates the sensitivity of the estimate of the average abnormal price change to the extreme abnormal price variations that can be observed on emerging markets, despite the correction for volatility that we apply. The outliers excluded are two announcements of acquisitions on emerging markets that where accompanied by a spectacular outperformance of the stock"s price. 2 2 One of the company is China Eastern Airlines, for which quotation was suspended a few days before the announcement. On the whole we agree with the first part of the conclusion made by Fotak et alii (2008) and with the results of [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] and of Kotter and Lel (2008): there is a positive immediate effect of the announcements of SWFs acquisitions on the share prices of the companies. the fifth day following the announcement, the effect on the cumulated abnormal price change is no longer significant (columns 4 and 5 of Table 1).

This seems to indicate that there is neither a long lasting positive nor negative effect following the entry into the capital of a company by a sovereign wealth fund.

This conclusion must be treated with caution. The average results for the fifty announcements collected could conceal heterogeneity in the effect of the stake hold by the SWF. This could be due to the differing perception of investors towards the different funds as well as the differing strategy of the funds, depending on the markets they are investing in. Part of this positive transitory effect could be explained by SWFs investments in distressed companies [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF], large stakes [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] and the SWF"s transparency (Kotter and Lel, 2008).

Contrary to Fotak et alii (2008) and to [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] we have not extensively tested the long-term impact of SWFs investments and therefore are unable to confirm their findings of a negative long term effect. 3We are limited to stating that according to our results the cumulative abnormal price increase seems to disappear a few days after the impact of the instantaneous market reaction, which does not exclude the possibility that in the long-term the markets" reaction could turn negative. However the standard methodology of the events study does not lend itself well to long-term tests [START_REF] Kothari | Friends or Foes? The Stock Price Impact of Sovereign Wealth Fund Investments and the Price of Keeping Secrets[END_REF]. The primary reason for this is that by extending the window of events the risk is increased that events other than the acquisition of shares by a SWF will have an effect on the share price, thereby distorting the results. There is also a range of more technical reasons, notably the fact that an extension of the window of events to test the long-term effects is usually accompanied by an increased cross correlation between the securities abnormal price changes, as well as the fact that specification errors of the normal price changes are magnified over a long-term horizon. As it appears that SWFs often invest in distressed companies [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] it is of particular importance to compare the long-term performance of their investments with the long-term performance of similar companies, before drawing any definitive conclusions.

The weak persistence of the effect of the entrance by a SWF into the capital of a company could seem paradoxical as our sample contains events corresponding to the recapitalisation of companies by SWFs following the losses or depreciations occurring during the sub prime crisis.

In order to test whether the acquisitions made by SWFs during the period of the crisis have a longer lasting effect, we have set up a sub-sample of events observed during the sub prime crisis.

During the sub prime crisis : an apparent scepticism of markets towards

SWFs as 'lenders of last resort'

We have tested the effect of the acquisitions of SWFs on a sub-range of 14 events, occurring between July 2007 and April 2008. These events include investments by SWFs in Citigroup, UBS, Morgan Stanley, Merrill Lynch and Crédit Suisse.

To capture the effect of the crisis on the companies we start the estimation period closer to the day of the event whilst still ending it 11 days before the event, thereby reducing the estimation window to 119 days. This reduction of the estimation period allows us to take a better account of the increased sensitivity of stock prices to market developments during the crisis. 4 The results obtained are displayed in Table 2 and show some differences with those seen in the study using the complete sample. The positive effect is somewhat weaker in the short-term. The daily abnormal price change on the day of the announcement of the investment by a SWF is significant at the threshold of 10%, yet is only around 2% (instead of 6% for the complete sample). This very short lived positive effect -confirmed by Corrado"s Rank Test -is too weak to remain statistically significant when it is aggregated in cumulated abnormal price changes (columns 4 and 5 of Table 2). Even if cumulated abnormal price changes remain positive over 30 days after the event (Chart 2), they are not statistically significant. 4 According to some preliminary tests not reported here, the alphas in the market model do not change much, but the betas increase during the crisis.

These results are subject to some caveats: there are few events in this subsample and the crisis constitutes a factor common to all events which invalidates the hypothesis of independent abnormal price changes. Moreover, the investors are probably uncertain of the long-term impact of these investments in this particular context. One possible interpretation of our results is that investors are not convinced of the capacity of the investment by SWFs to restore, on a permanent basis, the position of the companies concerned.

Comparison with the event studies on the investments of Private Equity and Pension Funds

This absence of a lasting positive effect for the two samples studied is wholly consistent with the findings of the others event studies on SWFs acquisitions.

But it contrasts with some of the results of the empirical literature on the investments of pension funds, and above all with the main conclusions of the event studies on the investments of private equity funds. This difference in results could be easily explained if SWFs were totally passive investors. This is obviously not the case for a number of SWFs: SWFs from emerging countries often hold some controlling shares (Miracky et alii, 2008) and some SWFs holding minority stakes -such as the Norwegian GPF -global or the French FRR -actively use their voting rights to promote a better governance of the companies in which they invest 5 .

The literature on private equity operations and leveraged buy outs generally concludes that there is a notable and lasting positive effect on the value and the performance of the target companies (Cumming et alii, 2007). The difference with our results -and more generally with the results of the event studies on SWFs-can be explained by the under-valuation of the companies targeted by private equity funds, by the fiscal advantages gained from the interest relating to their debt programme and by the positive effect they are assumed to have on the governance of the company. The private equity funds are known for their policy of aggressive restructuring of the companies they 5 Recall that the GPF and the FRR are excluded from this event study. The FRR is a relatively small fund and its investment horizon is not as long term as the horizon of "permanent" sovereign funds such as the GPF. The GPF stands apart amongst the main sovereign funds: it has a very specific strategy of minimizing the impact of its investments and disinvestments on stock markets.

have acquired, allowing them to quickly increase the profitability of the company.

Some of the literature on pension funds shareholdings finds a positive effect of the investments of the Californian Pension Fund CalPERS on stock prices.

These results have been labelled as the "CalPERS" effect. Alongside shareholder resolutions to change the management of the underperforming companies, CalPERS uses its communication policy as a tool to identify and disclose underperforming managers: CalPERS has published an annual 'Focus List of Underperformers' since 1992. Nevertheless, the positive effect of CalPERS activism on the share prices of the companies in which it holds stakes remains controversial. Thus, English et alii (2004) confirm the CalPERS effect, whilst [START_REF] Nelson | The CalPERS effect revisited again[END_REF] finds that after a methodological bias has been corrected, the effect becomes non-significant. Despite the size of CalPERS, its long history as an active shareholder and the publicity around its announcements there is no consensus on a positive and lasting "CalPERS" effect. Therefore, it is not very surprising to have not found a lasting positive effect of the investments made by SWFs.

As sovereign foreign investors, SWFs have to be more cautious than private long run investors. Also, SWFs do not have homogeneous practices as to the transparency of their investment policies and market participants may have some difficulties in interpreting their involvement in the governance of the companies. What is more, even the most transparent SWFs often pursue macroeconomic goals, besides purely financial goals such as the maximisation of returns relative to risks. Some SWFs aim at stabilizing the incomes drawn from commodity exports, some are development funds, some aim at stabilizing their exchange rates, etc. None of these motives are of course illegitimate, but objectively it is more complex for market participants to assess the motives of SWFs investments than those of private equity funds or pension funds.

For a better assessment of the long run impact of SWFs on the governance of the companies in which they invest, more robust results from long run event studies are needed. As has been indicated, the scope of our event-study is limited to the assessment of short run effects. Pursuing the study into the long-term is however difficult in regards to the robustness of the obtained results: whilst the methodology used in the short-term events study is well prepared, the long-term methodology still needs to be improved [START_REF] Kothari | Friends or Foes? The Stock Price Impact of Sovereign Wealth Fund Investments and the Price of Keeping Secrets[END_REF]. Using a standard long-term methodology, Fotak et alii (2008) find that the acquisitions of SWFs have a negative long-term impact on the profitability of the acquired company. However the elimination of 11 events out of 53 is sufficient to remove this negative effect. Considering the illiquidity and the volatility of many of the shares on emerging markets and the fact that SWFS often invest in distressed companies [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF],

it cannot yet be excluded that this negative impact has other causes than solely the governance policy of these SWFs.

SWFs: Guardian angels or strategic investors?

The ongoing debate on the role played by SWFs on financial markets is far from being settled. But with elevated oil prices, the accumulation of excess FX reserves and the difficulties of the banking sector, the investments of SWFs have attracted growing attention.

As confirmed by four other recent studies on the subject, as well as by this study, the use of event studies can help us to understand how the markets react to the announcement of a SWF taking a stake in a listed company. These first studies yield interesting results but are subject to some caveats. Due to the lack of comprehensive data on SWF investments we inevitably focus on the most publicized investments. Therefore, these primary results have to be considered with caution.

Overall, for the fifty events of our database we confirm the result of Fotak et alii (2008), Kotter and Lel (2008) and [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF], according to whom there is an immediate, strong and positive effect of SWF investments on share prices. Part of this positive short-term effect could be explained by SWF investments in distressed companies [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF], large stakes [START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] and the SWF"s transparency (Kotter and Lel, 2008).

Contrary to Fotak et alii (2008) we do not confirm that SWFs have a negative long-run effect on the target companies. However, we do not attempt to gauge the effect of the announcement of SWFs acquiring stakes beyond 10 days after the event.

The tests we conduct on a sub-sample of announcements made during the Subprime crisis yield results similar to those obtained with the whole sample.

The announcements of the SWFs investments have a short-term positive effect on the share price. But we do not find more lasting effects. One possible interpretation is that markets are not convinced that SWFs alone are capable of restoring the position of the banks concerned.

Much work remains to be done on SWFs. In the field of event studies, major improvements would be to construct databases which are more representative of the relative sizes of the SWFs and to study in detail the investment policies of the main funds. SWFs still have heterogeneous investment policies, though the recent agreement on a set of voluntary best practices (IMF, 2008) could lead to some homogenization of their practices as investors.

Appendix: Testing for abnormal price changes

The abnormal price change for security i and time observation t is computed as the difference between the actual logged price change and a theoretical "normal" logged price change that would prevail in the absence of the event 6 :

N it it it R R AR Where it AR , it R , N it
R are, respectively, the abnormal, actual and normal logged price changes.

The "normal" price change is computed, as is usual, from the market model 7 : Cumulative abnormal price changes (CAR i [ 1 , 2 ]) can then be computed by totalling the abnormal price changes recorded during the event window [ 1 , 2 ], which begins two days before the announcement and ends ten days after: Standardized cumulative abnormal price changes can then be computed as:

mt i i N it R R
6 Taking the difference of the logged price rather than the exact rate of growth of the price has the advantage of reducing the kurtosis of the series.

7 The market model is generally fitted on the stock return -including the dividend -rather than on the rate of growth of the stock price. However at a daily frequency the two series are close and yield very similar results. Besides, the short-term expected effect of the announcement of the stake taken by a SWF is only on the stock price. Contrary to the CAPM model the market model does not rely on interest rates for which homogeneous data are difficult to collect for both emerging and developed countries. However, over short event windows the results of event studies are not very sensitive to the model used (Campbell et alii, 1997). The standard error can be estimated using different hypotheses on the variance of the abnormal price change. In this study, we estimate the standard error alternatively assuming the homoskedasticity of the abnormal price change and assuming heteroskedasticity. Heteroskedasticity is modelled here using the GARCH(1,1) process [START_REF] Bollerslev | Generalized autoregressive conditional heteroskedasticity[END_REF]. To save space, only the results for GARCH standardized abnormal price change are reported. But the results of the tests are similar under both methods of standardization:

controlling for heteroskedasticity reduces, on average, the size of abnormal price change over the event window, but does not change the main results.

The following step is to compute the average of SCARs for all N securities included in the event study:

Finally the test statistic J2 is defined as (Campbell et alii, 1997):

2 1 1 1 , 4 4 2 SCAR L L N J
Where L1 is the length of the period over which the market model has been estimated.

J2 has a standard normal distribution in large samples. When J2 is above the threshold associated with a 5% significance level, the hypothesis of zero cumulative abnormal price changes is rejected. J2 can of course also be computed over periods of only one day: therefore in tables reporting the test results we display J2 for each day of our event period, which begins 2 days before the day of the event and ends 10 days after. We also report J2 for subperiods progressively extended towards the end of the event window; that is for the following sub periods: [-2,-2], [-2,-1], …, [-2,+10].

In this paper the graphs of cumulative abnormal price changes display standardized cumulative abnormal price changes computed over a larger window (usually [-11,+30]) to give a more general picture of the evolution of the SCARs. But the tests themselves are not reported for sub-periods extending over 10 days after the event because our results show that the effect of the event vanishes very quickly: ARs are not significantly different

N SCAR SCAR N i i 1 2 1 2 1 , ,
from zero after the day of the event. Extending the tests beyond 10 days after the event entails the risk of capturing the effects of events other than the announcement of a stake taken by a SWF.

Non-parametric tests are generally used to check the results of parametric tests such as the tests based on the statistic J2. In this paper we use the Corrado rank test, which is based on the rankings of abnormal price changes (see Campbell et alii, 1997[START_REF] Serra | Event Study Tests: A Brief Survey[END_REF] for a detailed description). The main advantage of non-parametric tests is that they do not rely on a specific assumption about the distribution of price changes.

  The red vertical line indicates the day of the acquisition, i.e. day 0 The red vertical line indicates the day of the acquisition, i.e. day 03.2 ...which dissipates rapidlyNevertheless, as illustrated by Chart 1A, the effect dissipates rapidly. It is impossible to discern a significant effect on the average abnormal price change on the day following the announcement. This is shown by the relatively quick return back to zero of the cumulated abnormal price variation (Chart 1B): from

ˆ

  Where mt R is the market price index change, i ˆ and i ˆ are estimated over an estimation period ending 10 days before the day of announcement of the investment.

Usually

  ARs are computed for each day of the event window and CARs are computed over windows progressively extended from the first day of the event and the days following it.

Table 1

 1 Abnormal price changes standardized with GARCH

			50 events database			48 events database
	Day AR	Signif.	Cum AR.	Signif.	AR	Signif.	Cum	Signif.
			level		level		level	AR.	level
	-2	0.939	34.8%	0.939	34.8%	0.985	32.46%	0.985	32.5%
	-1	-0.880	37.9%	0.042	96.7%	-0.826	40.88%	0.112	91.0%
	0	6.075*** 0.001%	3.542*** 0.04%	3.847*** 0.012%	2.313** 2.07%
	+1	0.212	83.2%	3.173*** 0.15%	0.264	79.17%	2.135** 3.28%
	+2	1.251	21.1%	3.398*** 0.06%	1.097	27.28%	2.400** 1.64%
	+3	-1.764*	7.8%	2.381**	1.7%	-1.879*	6.02%	1.424	15.4%
	+4	0.670	50.3%	2.458**	1.4%	0.654	51.29%	1.566	11.7%
	+5	-1.234	21.7%	1.863*	6.2%	-1.245	21.32%	1.024	30.6%
	+6	-1.166	24.4%	1.368	17.1%	-1.131	25.82%	0.589	55.6%
	+7	-1.313	18.9%	0.883	37.7%	-1.236	21.65%	0.168	86.7%
	+8	0.601	54.8%	1.023	30.6%	0.722	47.04%	0.378	70.6%
	+9	-1.034	30.1%	0.681	49.6%	-1.227	21.98%	0.007	99.4%
	+10 -0.084	93.3%	0.631	52.8%	-0.053	95.77%	-0.008	99.4%
	Corrado rank test [0]: 3.235*** (0.12%)	Corrado rank test [0]: 2.8*** (0.5%)
	Corrado rank test [-2,+10]:-0.438 (66%)	Corrado rank test [-2,+10]: -0,6 (55%)

*** Significant at 1%, ** significant at 5%, * significant at 10%.

Table 2 Abnormal price changes standardized with GARCH -14 events during the Subprime crisis

 2

	Day	AR	S.l.	cum. AR	S.l.
	-2	0.54607	58.5%	0.54607	58.5%
	-1	-0.87274	38.3%	0.23099	81.7%
	0	1.81571 *	6.9%	0.85970	39.0%
	+1	0.54087	58.9%	1.01495	31.0%
	+2	0.55168	58.1%	1.15452	24.8%
	+3	-0.68503	49.3%	0.77427	43.9%
	+4	0.86488	38.7%	1.04372	29.7%
	+5	-0.45645	64.8%	0.81494	41.5%
	+6	0.53516	59.3%	0.94671	34.4%
	+7	-0.80640	42.0%	0.64312	52.0%
	+8	0.26577	79.0%	0.69333	48.8%
	+9	-1.40032	16.1%	0.25957	79.5%
	+10	1.10993	26.7%	0.55723	57.7%
	Corrado rank test [0]: 2.21120** (signif. level 2.7%)
	Corrado rank test [-2,+10]: 1.25795 (signif. level 21%)
	*** Significant at 1%, ** significant at 5%, * significant at 10%.

[START_REF] Chhaochharia | Sovereign Wealth Funds: Their Investment Strategies and Performance[END_REF] find a negative long term impact at a 10% significance level only for one subsample of investments.