UNIVERSIDADE TÉCNICA DE LISBOA INSTITUTO SUPERIOR DE ECONOMIA E GESTÃO

UNIVERSIDADE TÉCNICA DE LISBOA INSTITUTO SUPERIOR DE ECONOMIA E GESTÃO MESTRADO EM: Economia Moneária e Financeira Explaining share price performance of fooball clubs lised on he Euronex Lisbon Nuno Alexandre Abranes Ferreira Orienação: Prof. Douor João Luís Correia Duque Ouubro de 2004 Documeno Provisório

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Explaining share price performance of fooball clubs lised on he Euronex Lisbon Nuno Alexandre Abranes Ferreira Absrac The lieraure concerning he effecs of sporing performance on fooball shares is scarce. Fooball clubs used o be non-profi organisaions and heir members had differen righs and views from hose which affec oday s shareholders perspecives and analysis. We were paricularly concerned wih sporing performance and how i impacs on share price reurns for fooball clubs. Using he fooball shares quoed in Euronex Lisbon Sock Exchange and he ARCH and GARCH mehodology we found a posiive relaionship beween sock price reurns and sporing performance. Therefore, we could provide empirical evidence for immediae impac of vicories, draws or defeas on price reurns. We also found ha impac o be relaed o he approach of he end of he season. This is in line wih previous research on he opic, alhough using a differen mehodology. When we look a volailiy, apar from showing srong clusering signs, a criical variable seems o be he rading volume around he sock ha comes wih he end of he season. Key Words: Economics of spors, Soccer club valuaion, Share price reacions. JEL Classificaions: G1, G14 3

Index Absrac 3 Index 4 Lis of Tables 5 Lis of Figures 6 1. Inroducion 7 2. Lieraure Review 9 3. Mehodology and Daa Analysis 15 3.1 Mehodology 15 3.2 Daa Sources and Variable Definiion 17 3.3 Daa Analysis 21 4. Empirical Resuls for Sock Reurns and Volailiy 27 5. Conclusion 37 6. References 39 4

Lis of Tables Table 1 - Sporing and Poro daily sock reurn saisics for he enire sample 25 Table 2 - Sporing and Poro daily sock reurn saisics aken by season 27 Table 3: Resuls of Regression Equaion 5 (Sporing) 30 Table 4: Resuls of Regression Equaion 5 (FC Poro) 30 Table 5: Resuls of Regression Equaion 6 (Sporing) 30 Table 6: Resuls of Regression Equaion 6 (FC Poro) 31 Table 7: Resuls of Regression Equaion 7 34 Table 8: Resuls of Regression Equaion 9 36 5

Lis of Figures Figure 1: Sporing Share Prices 22 Figure 2: Poro Share Prices 22 Figure 3: Sporing Sock Reurns 23 Figure 4: Poro Sock Reurns 23 Figure 5: Sock Reurn Clusering - Sporing 25 Figure 6: Sock Reurn Clusering - Poro 25 Figure 7: RPV of Sporing 34 Figure 8: RPV of Poro 34 6

Explaining share price performance of fooball clubs lised on he Euronex Lisbon 1. Inroducion Spor indusry has changed dramaically in he las weny years. All over Europe, fooball clubs have been ransformed ino profi oriened, public and lised companies. The same phenomena happened in Porugal. In 1997 wo of he major Poruguese fooball clubs (Sporing Clube de Porugal - from now on called Sporing, and Fuebol Clube do Poro from now on called Poro), creaed public companies independen from he original club. Today hey are floaed companies wih shares raded on he Euronex Lisbon Sock Exchange. Neverheless, he original clubs own 50% of heir shares and in each case he public companies have been urned ino one of he clubs affiliaed companies. The idea was o ransfer o he new companies some of he asses, such as he claims over fooball players, gae receips and merchandising relaed o fooball, leaving o he old clubs he propery of he sadiums and oher relaed asses, as well as he managemen of he remaining spor aciviies. 7

Shares of fooball companies have he ineresing characerisic of being raded based on wo possible reasons: he irraional eseem of heir supporers and on he economic raionale of any invesmen 1. We will assume, following a sudy of Brown and Harzell (2001) ha, alhough irraional facors may well be in he field he economic raionale dominaes rading volume and prices hroughou he marke. We base his assumpion on he hypohesis ha emoional invesors are less significan in he marke, being he free-floa in a marke secured by insiuional invesors and oher economically sound agens. Therefore i is a researchable quesion o undersand he facors ha may govern sock prices seled in exchanges. Using daa from 1998 o 2002 and analysing no only he enire sample, bu also four differen ime windows (each corresponding o a fooball season), we provide some evidence ha posiive sporing resuls in fooball are generally associaed wih good share price performances on he Sock Exchange, while a negaive sporing performance is associaed wih negaive sock price reurns. The sudy proceeds as follows. The second secion describes he lieraure review and he explanaions given by researchers for he relaions beween sporing performance and share price reacions on he Sock Exchange. The hird secion is dedicaed o he mehodology and daa analysis. In secion four we presen he resuls afer esing he model for reurns and volailiy behaviour and in secion five we presen he final conclusions. 1 Whils finishing his documen a crisis has jus arisen involving one of he leading fooball clubs of he world: Mancheser Unied. Rumours of an apparenly ineresing bid for he 8

2. Lieraure Review Wha do we know abou he influence of fooball performance on he corresponding fooball companies? Unil recenly, when Renneboog and Vanbraban (2000) from one side and Ribeiro (2001) from anoher, published heir resuls, here was no lieraure on he opic. However, only recenly have a significan number of clubs urned ino public companies, bringing he opic under he spoligh, hereby creaing he moivaion for his research and allowing for consrucion of saisically significan daases. Unil now he relaed lieraure was concerned wih oher spors or covered dependen variables oher han sock price reurns. However, recenly fooball firms have become a source of ineres and several references may be found in he lieraure o suppor he economic behaviour of hese corporaions. Paxson (2001) argues ha he major sources of income for acual fooball clubs are gae receips, TV righs, merchandising revenues, compensaion and ransfer fees and refers o hese firms as being a major field where real as well as financial opions heory is applicable. Realising ha audience is an imporan facor when explaining he economic performance of spor clubs, Bird (1982) ried o esimae a regression equaion in order o explain oal aendance for he four divisions of he English Fooball League. He used 92 shares (considered from he financial perspecive) by an American-based invesor, made some of he English supporers and fan invesors furious. 9

clubs and daa from 1948 unil 1980. In general he found ha icke prices, he number of goals scored during he season, as well he number of goals scored during he previous season were he major facors o explain he number of specaors aending games. Addiionally, he found variables such as he possibiliy of hooliganism, or he weaher condiions irrelevan when explaining game aendance. Domaslicky and Kerr (1990), sudying he same variable of aendance in he American Baseball League from 1968 o 1980 found several variables wih explanaory power, such as: he populaion living in he region, he average icke price, he income per capia, he wealh of he eam, he oal number of baseball eams in he region, he number of wins, he number of games observed, he score, he number of players in he eam, he physical condiions of he sadium where games ake place, and he division in which he eam is playing. They excluded vicory in he previous league as a sensiive variable. Burki and Cameron (1992) also sudied aendance a spor evens, bu observing insead he English Rugby League and using 30 clubs from 1966 o 1990. They found ha he posiion in he ranking is a key facor in explaining he number of specaors. Irani (1997) also found ha variables such as he icke price, he income per capia, he populaion in he region where he sadium is locaed, and he acual number of vicories are relevan o explain he demand for baseball in America for he ime period considered (from 1972 o 1991). A second major variable ha is presened in he lieraure as an explanaory variable for he undersanding of he economic success of spor clubs is income, and one of he 10

major sources of income is gae receips. They equal he number of specaors (already covered) imes he icke price. Akinson, Sanley and Tschirhar (1988) found he increase in he price of he ickes was direcly dependen on he previous year s sporing resuls. On average, hey observed ha a club raises is average icke price by US$12 afer having won he previous championship. Scully (1974) found ha he performance of he eam (measured by he difference beween vicories and losses), he number of inhabians of he region where he sadium is locaed and he physical condiions of he sadium were he variables wih saisical significance when sudying he income of he clubs in he American Baseball League. A hird source of spor clubs wealh is based on he value of is asses, namely he conracual claims on heir players. Players are no only good agens when exercising wihin heir specialiy, bu hey also acing as sars aracing fans o wach hem. For insance, Hausman and Leonard (1997) showed ha he elevision audience was direcly relaed o he presence of baskeball sars in NBA games, urning he TV pay-per-view sysem he main source of income of baskeball clubs. Sars increase he income of boh eams: heir own eam and he opposiion eam ha ges he benefi from having sars playing, wihou having he obligaion of paying heir salaries. And, of course, sars also increase he success of merchandising sales. A very ineresing and paricular issue ha characerises fooball firms is ha weekends are ime periods when a significan amoun of price sensiive informaion may arrive, and differenly from he well-documened weekend effec ha for oher lised firms 11

may be relaed o behavioural anomalies affecing sock prices, for fooball companies he weekend effec may have boh phenomena. In fac, he fooball games are mos commonly played a weekends (in Porugal from Friday evening o Sunday evening). As sock exchanges close during hese ime periods, price discovery is only clearly seen on Mondays. There is, herefore, a double weekend effec o consider in his analysis. The pioneering sudy on weekend effecs for sock prices of common firms was developed by Fields (1931) when he examined he Dow Jones Indusrial Average Index behaviour from 1915 o 1930. Fields (1931) concluded ha share prices end o increase on Saurdays 2, as a resul of closing down sock posiions before he weekend. The climae of insabiliy which exised a Wall Sree would no allow advised middlemen and financial agens o keep heir posiions exposed during weekends. The weekend effec also go he aenion of French (1980) who esed he "calendar eam hypohesis" saing ha Monday o Friday reurns should be hree imes larger han any oher day s esimaed reurn. This was an aemp o show he linear relaionship beween average sock price reurns and he ime period of invesmen. However, he mos classic reference for he weekend effec was described by Gibbons and Hess (1981). In heir sudy wih a sample of he daily S&P500 reurns hey showed ha compared wih oher weekdays, Monday reurns were significanly negaive, possibly as a resul of a biased human reacion o overcome weekends. Brown and Harzell (2001) sared by observing ha, differenly from ordinary firms for which invesors need o ge financial accouns and repors of research in order o 2 The American Sock Exchange was opened on Saurdays during his period 12

readjus expecaions for price formaion, lised companies ha manage baskeball eams are largely exposed o informaion release. Invesors can open he newspaper a leas 82 imes and check how he invesmen is going during an 82-game season. Bu is he marke sensiive o hese signals? They also confess o foreseeing some invesors buying hese shares basing heir decisions on irraional passion for heir eams and waning o own a slice of he eam. However, hey assume ha his is an insignifican number of invesors and, herefore, sock prices formed in he exchange may reflec he raional expecaions of informed invesors. They developed heir research based on wo sources of daa. Firs hey considered income and cash-flow and concluded ha here is a posiive and significan relaionship beween he number of vicories and cash-flow. Secondly hey considered marke daa and concluded ha sock price reurn was correlaed wih he sporing performance. However, volailiy and rading volume were no. They also observed an increase eiher in erms of volailiy or in erms of rading volume when sudying sporing season periods. Renneboog and Vanbraban (2000) were he only researchers o specifically invesigae wheher he sporing resuls had direc impac on fooball share price reurns. Analysing he clubs quoed on he London Sock Exchange, and on he Alernaive Invesmen Marke (AIM), he auhors concluded ha share prices were indeed influenced by sporing resuls. «Even sudies correced for hin Bayesian updaing reveal ha a he firs day of rading afer a game, posiive abnormal reurns of almos 1% can be expeced following a soccer vicory. In conras, defeas or draws are penalised, respecively, by negaive abnormal reurns of 1,4% and 0,6%». 13

The oher reference specifically relaed o our research opic is Ribeiro (2001). The auhor also sudied he wo Poruguese clubs quoed in he Poruguese sock exchange, using he ordinary leas squares (OLS) mehod o explain share price reacions of he Poruguese clubs o es he sock price reacion o sporing performance. Taking ino consideraion vicories, defeas, and draws, as well as a fourh variable called relaive poins o vicory (which expresses he difference in erms of poins beween he leader and he following eam in relaive o he available poins remaining o he end of he ournamen), he auhor concluded ha here was no relaion beween sporing performance and sock price reurns: «Wihin he period under analysis (wo years), sporing resuls of Sporing and Poro rarely originaed a raise or a fall in sock prices, excep [ ] on Monday, 15 h May 2000, when Sporing shares observed a 22,5% raise hiing heir maximum high. The cause of such a movemen seemed o be he reacion o he conques of he naional soccer championship on May, 14 h [ ] Vicories, defeas and draws don seem o have any explanaory power, unless eams urn ou o be champions. However, he relaive poins o vicory variable seems o have some explanaory power». This sudy had, however, severe shorcomings, namely he small sample size (only wo years of daa were available a ha ime), and his may well be one considerable reason for he weak economerical findings. In summary, he lieraure on sudying he effecs of sporing performance on spor company shares has been generaed using a wide variey of oher variables oher han sock price reurns, namely aendance a sadiums, gae receips, cash flows, ne profis and even he impac of he recruimen of sars. However, sock price reurns were widely forgoen and paricularly hose of fooball company shares. Soccer being a major, popular spor in 14

Europe i is ime o es wheher Poruguese invesors do reac o sporing resuls when pricing fooball company shares. 3. Mehodology and Daa Analysis As we presened earlier only wo sudies have direcly covered he opic under our consideraion: Ribeiro (2001) who covered he Poruguese fooball sock marke and Renneboog and Vanbraban (2000) who covered fooball club share prices quoed on he London Sock Exchange, and on he Alernaive Invesmen Marke (AIM). Boh sudies inend o inquire o wha exen sporing performance impacs on sock price reurns seled on he sock exchange. We aim o exend heir knowledge in erms of daa sample size (in comparison o Ribeiro, 2001) or in using a differen and supposedly sronger mehodology o cover wo differen aspecs of sock price behaviour: reurns and volailiy. 3.1 Mehodology As empirical financial lieraure abundanly proved, sock price volailiy is no consan, ending o show clusering paerns along ime, ha is, high volailiy periods end o be followed by high volailiy periods, while low volailiy periods end o be followed by low volailiy periods (see for insance Bollerslev, Chou and Kroner (1992), Bollerslev, 15

Engle and Nelson (1994) or Kroner and Ng, 1998). The Poruguese marke specifically seems o follow similar paerns o hose documened in Caiado (2004). We also empirically observed ha he consan hypohesis is rejeced for he colleced ime series of he Poruguese fooball share price reurns (Sporing and Poro). Therefore, he use of he ARCH-Auoregressive Condiional Heeroskedasiciy family models mehodology for modelling purposes seems appropriae. This allows us o esimae more robus models for ime series modelling, as opposed o using models ha assume consan volailiy hypohesis along he ime. As Harvey and Huang (1991) showed wih he release of cenral bank news on ineres raes, volailiy may significanly change is pah as a resul of he incorporaion of relevan price sensiive informaion. As a resul, when we hink of fooball shares, for which he weekend can be significanly relevan when maches occur, we hypohesised a significan impac of sporing performance on volailiy behaviour. Having assumed ha, we could increase our confidence in ARCH family models should being more appropriae han consan volailiy models for our research purposes. Hence, he use of ARCH family models combined wih an exended daabase will be a significan improvemen compared wih Ribeiro (2001). 16

3.2 Daa Sources and Variable Definiion The daabase colleced in his sudy is composed of Sporing SAD and F.C. Poro SAD share prices, quoed in he Second Marke of he Euronex Lisbon Sock Exchange from 2 nd June 1998 o 30 h July 2003 (1347 observaions each). Prices were colleced from Bloomberg and he summer ime observaions were excluded from he sample for offseason reasons. We have only aken ino consideraion he sporing resuls observed when games were played as par of he naional championship, leaving ou any oher resuls ha may have been observed, such as hose resuling from he European compeiions, as well as hose from he Poruguese Fooball Cup. As we have said previously, he ime period under analysis is a significan improvemen compared o Ribeiro s (2001) sudy. Insead of a wo-year daabase we more han doubled i o a five-year period. I is imporan o noe ha exended ime period allowed he inclusion of daa from one season in which neiher of he firms wih lised shares won he naional championship. Daily coninuously compounded sock price reurns were compued, ha is: S i, y i, = ln Si, 1 where S i, sands for he share price of firm i on rading day. 17

We sared by compuing he average, volailiy (given by he sandard deviaion), kurosis and skewness of sock price reurns for each group of observaions. Economeric and any oher saisical analysis was carried ou by using he sofware E-Views version 3.0. As our aim was o sudy he impac of fooball performance on sock price reurns we sared by assigning one ou of he hree possible oucomes for a fooball game (vicory, draw and defea) o dummy explanaory variables. For example, he dummy variable vicory, assumes 1, when he club wins and zero oherwise. I is imporan o underline ha, as we are considering daily daa, we can use hree dummy variables (vicory, draw and defea), wihou running he risk of incurring a dummy rap. This is because we have some days wih no games, when all hese dummies assume he value zero. As fooball games always have o end in one of he hree possible oucomes (vicory, draw or defea), we added a fourh dummy variable. This dummy was called «game», being assigned 1 when a club played a game, and zero oherwise. This fourh dummy variable was used o es wheher on he day or on he eve of he mach, share prices showed signs of abnormal volailiy. Oher variables were addiionally aken ino consideraion as a consequence of he lieraure review, in order o explain he daily reurns: rading volume, PSI-20 reurn (he index benchmark for he Poruguese sock marke), he lagged daily sock price reurns and he so-called relaive poins o vicory raio (RPV). This raio was successfully inroduced 18

by Ribeiro (2001) when he reacion of fooball shares o fooball performance in Porugal was firs explained. We sared by hypohesising ha daily volume could be a relevan variable for his sudy, mainly because fooball shares are hinly raded on he Euronex Lisbon. This is easily deeced when comparing heir rading volumes wih he rading volume recorded by oher companies in he Poruguese marke. In order o ge a rough idea of how hin he marke is we mus sae ha here were days in our daabase wih no more han 30 shares as oal daily rading volume. Deloie (2004), he consulancy company, saes in is sudy: «The soccer marke has a reduced liquidiy. For insance, Poro and he Sporing rade in a monh less han Porugal Telecom (he mos liquid asse in he Poruguese Sock Exchange) rades in a day». Addiionally, Nicolau (1999), in a sudy where ARCH mehodology is used in order o explain he course and he correlaion beween PSI-20 and Dow Jones, refers o he fac ha he specificaion of he condiioned variance is subsanially beer when he variable daily volume is added o he model. «I is naural: larger daily volumes, ranslaed ino larger variabiliy of share prices and, herefore, in a larger volailiy». The use of a marke benchmark like he PSI-20 index is obvious. I may overcome he need for esimaing he sysemaic risk of sock price reurns, and akes ino consideraion he abnormal reurn effec ino he model. For insance, Renneboog and Vanbraban (2000) used he Sharpe-Linner-Treynor CAPM (Capial Asse Pricing Model) 19

o esimae he abnormal sock price reurn in order o sudy he fooball performance impac on share price behaviour for fooball clubs lised in he UK marke 3. The concep of relaive poins o vicory raio (RPV) is no new. I was firs inroduced and esed wih posiive resuls by Ribeiro (2001). I expresses he idea ha one vicory in a mach and he consequen hree poins obained for ranking purposes does no mean he same when we are six poins as when we are hiry poins from he end of he ournamen. Therefore, if he firm s eam is leading he championship, he difference in erms of poins beween he firm under analysis and is mos direc compeior should be aken in relaive erms, reflecing he number of poins ha are sill under dispue up o he end of he ournamen. Hence, he he relaive poins o vicory raio ( RPV i, ) of firm i a momen, is he difference expressed in poins, beween he firm and he leader (or beween he firm and he challenger, if he firm leads he ournamen), relaive o he number of poins sill under dispue up o he end of he ournamen. Is analyical definiion is: RPV i, N N i, j, = eq. 1 3K where: N i, is he number of poins of he eam i, a ime ; 3 They esimaed he abnormal reurn as R i, E[ Ri, ] where i sock i on day, and E [ Ri, ] E[ Rf, ] + [ E[ Rm, ] E[ Rf, ] = β i. R, sands for he observed price reurn of 20

N, represens he number of poins obained by he challenger (second place in j he able) if firm i leads he championship a ime, or represens he number of poins obained by he leader if firm i is no leading he championship a ime. K is he number of maches sill o play up o he end of he championship. The RPV raio is posiive when he firm leads he championship, being negaive whenever he firm chases he leadership of he ournamen. When he RPV raio is null i means ha he eam under scope shares he lead of he championship able wih anoher eam. Therefore, he larger and posiive he RPV raio is, he greaer he probabiliy of eam i o win he championship. 3.3 Daa Analysis We sared wih some daa mining in order o exrac a firs look a he daase and o infer some economic inuiion as well as some plausible implicaions concerning research design. From Figures 1 and 2 a consan rend for price declines over all of he period under scope seems eviden, alhough once in a while some sharp upward movemens are clearly noiced. These irregular posiive shocks, as we will see laer in his sudy, are associaed 21

wih he sporing success of he eams. Sporing share prices are an illusraive example of wha has been said. Along he ime series, he club won he championship wice (during he 1999/2000 and he 2001/2002 seasons). This is clearly signalled in he char wih wo sharp peaks. FC Poro won he naional championship ile in he 2002/2003 season, ha is, a he end of he ime series. The char shows ha, a he end of he ime series, Poro SAD prices rose significanly, alhough wih an unexpeced break during he las days of he sample. However, we speculae ha his may be he resul of some profi aking movemen in he marke, because i would be difficul o replicae in he near fuure wha he eam had jus achieved, which was wining he naional championship ( Superliga ), he UEFA Cup and he Poruguese Cup. Figure 1: Sporing Share Prices (2 nd June 1998 30 h July 2003) Figure 2: Poro Share Prices (2 nd June 1998 30 h July 2003) 9 9 8 8 7 7 6 6 5 5 4 4 3 3 2 200 400 600 800 1000 1200 2 200 400 600 800 1000 1200 We will define y scp, and y fcp, as he daily reurns of share prices for Sporing and Poro, respecively, measured by he differences in log-prices. 22

In Figures 3 and 4, we plo daily reurns for Sporing and Poro share prices. One ineresing and relevan issue is ha Sporing share prices seem more volaile during he seasons when hey won he championship. However, Poro share prices did no seem o suffer he same phenomenon. The highes volailiy happened during he 2001/2002 season, when hey fough wih Benfica up o he las day of he ournamen for he hird place in he ranking able of he championship. This was imporan because for ha paricular season, he hird place in he final compeiion ranking gave direc access o he UEFA Cup. A end of heir successful 2002/2003 season, daily sock reurns did no evidence high volailiy, probably because he marke soon anicipaed heir conques of he championship. In fac four monhs before he end of he compeiion, Poro already had a significan advanage of 10 poins over is mos direc compeior. 0.3 0.2 0.1 Figure 3: Sporing sock reurns (2 nd June 1998 30 h July 2003) 0.3 0.2 0.1 Figure 4: Poro sock reurns (2 nd June 1998 30 h July 2003) 0.0-0.1-0.2-0.3 0.0-0.1-0.2-0.3 200 400 600 800 1000 1200-0.4 200 400 600 800 1000 1200 Figures 3 and 4 confirm wha we have saed before and are indeed represenaive of he volailiy clusers: srong (weak) variaions are more likely o be followed by srong 23

(weak) variaions and vice-versa. In hese circumsances, assuming consan volailiy may be seriously misleading. One of he commonly admied assumpions in Finance is he normal disribuion of 2 sock prices reurns ( ~ N( µ ; σ ) ). While his may be a reasonable assumpion for long y horizon reurns (more han one year), for shor horizons, he lieraure has been abundan in showing non-normaliy of sock price reurns. Since Mandelbro (1963), confirmed by Fama (1965), we collec evidence of non-normaliy of sock reurns. Smih (1981), Gray and French (1990), Peiró (1994), Praez (1972), Blaberg and Gonedes (1974), Kon (1984), Harris and Küçüközmen (2001), McDonald and Xu (1995), Theodossiou (1998), McDonald and Newey (1988) or Geinby e al. (2004) are examples of papers where alernaive disribuions are esed o fi empirical sock price reurns. Their resuls show ha he momens of he empirical disribuions srongly differ from wha we expec of a normal disribuion. When we calculaed kurosis 4 and skewness 5 from daily reurns of Sporing and Poro, we found wha previous empirical evidence has shown: boh samples srongly differ from he skewness and kurosis expeced in a normal disribuion. In Table 1 kurosis shows much larger values han 3 for boh share price reurns, which means heavier ails han 4 µ 4. I measures he peak or flaness of he disribuion of he series. The kurosis of a n = 1 σ normal disribuion is 3. If he kurosis exceeds 3, he disribuion is peaked (lepokuric) relaive o he normal; if he kurosis is less han 3, he disribuion is fla (playkuric) relaive o he normal. 3 n 5 Is given by: 1 ( y µ ) SK = y 3. I measures he asymmery of he disribuion of he series around is mean. The n = 1 σ skewness of a symmeric disribuion, such as he normal disribuion, is zero. Posiive skewness means ha he disribuion has a long righ ail and negaive skewness implies ha he disribuion has a long lef ail. n 4 1 Is given by: ( y ) K y = 24

normal disribuion for boh socks. In oher words, exreme value observaions are observed more frequenly han in a normal disribuion. The skewness saisic helps us o show ha he disribuions are non-symmeric wih exreme negaive reurns more pronounced and frequen han exreme posiive reurns. For normal disribuions, his saisic is zero. In Table 1, he skewness saisics show negaive values meaning ha he lef ail of he disribuion is heavier han is righ ail. Table 1 - Sporing and Poro daily sock reurn saisics for he enire sample Mean Variance Maximum Minimum Kurosis Skewness Y SporingSAD -0.000691 0.000975 0.285047-0.293830 22.085-0.714503 Y PoroSAD -0.000741 0.000712 0.234461-0.322020 26.2331-0.647077 Anoher imporan aspec ha wih which we are concerned is he volailiy clusering of he ime series. If presen, i would be a srong signal for he appropriaeness of ARCH models in our research. This can be easily idenified in Figures 5 and 6 where y is ploed agains y 1. Figure 5: Sock Reurn Clusering - Sporing Figure 6: Sock Reurn Clusering - FC Poro 0. 4 0. 4 Y 0. 2 0. 0 Y 0. 2 0. 0-0.2-0.2-0.4-0.4-0.2 0. 0 0. 2 0. 4-0.4-0.4-0.2 0. 0 0. 2 0. 4 Y - Y - 1 1 25

As a consequence of such empirical paerns from our daabase i seems ha he mos appropriae means for modelling and esing he phenomena under scope are nonlinear modelling. As Franses and van Dijk (2000) sae: «Needless o say, such asymmeries should be incorporaed in a ime series model used for descripion and ou-of-sample forecasing, oherwise one may obain forecass ha are always oo low or oo high. We will call such ime series models, which allow for an explici descripion of asymmeries, nonlinear ime series models». Apar from previous research in he opic, a firs saisical analysis wih our sock price reurns daa sample led us o suspec ha some associaion could be observed beween hem and sporing performance. When he saisical analysis previously underaken by firm was repeaed by firm and season, i became clear ha fooball share prices ended o experience larger valuaions when heir eams won he naional championship. This was rue for FC Poro shares in 1998/1999 and 2002/2003 and for Sporing shares in 1999/2000 and 2001/2002. In 2000/2001, he season in which none of he eams won he championship (Boavisa won i) prices fell for boh companies (wih average negaive sock reurns). As we can observe in Table 2, he mean daily reurn is larger when he club wins he naional championship. 26

Table 2 - Sporing and Poro daily sock reurn saisics aken by season Y SporingSAD Y SporingSAD Season 1998/1999 1999/2000 2000/2001 2001/2002 2002/2003 Naional Champion FC Poro Sporing Boavisa Sporing FC Poro Mean -0.12% 0.24% -0.24% 0.07% -0.08% S. Deviaion 1.11% 3.71% 2.27% 5.30% 2.02% Mean 0.10% 0.06% -0.21% -0.13% 0.06% S. Deviaion 0% 2.39% 1.89% 4.11% 2.89% Bu i seems ha volailiy also suffers from he naional championship effec. In fac, when companies eams win he naional fooball championship no only do hey seem o evidence higher average sock reurns, hey also experience an increase in volailiy. 4. Empirical Resuls for Sock Reurns and Volailiy As previously saed, he purpose of he paper is o es he effec of sporing performance on sock marke behaviour. We will es his by using he effecs on sock price reurns as well as on sock price volailiy. Our preceding analysis showed ha he process for fooball share reurns ( y scp, ; y fcp, ) could be well modelled by a mulivariae AR+GARCH model, alhough oher models could also be considered. We sar by assuming ha sock price reurns can follow a pah reurn given by: y = µ + u eq. 2 where, = [ y y ] ; µ = [ µ ] and [ u u ] y scp, fcp, scp, µ fcp, =. We will u scp, fcp, ake µ scp, and fcp, µ as he condiional expecaions for y scp, and for y fcp,, while u is he error erms vecor wih a generic disribuion wih zero mean. 27

The variance-covariance marix Ω (marix 2x2), is given by: E uu ' f 1 = Ω σ = σ 2 scp, fcp, scp, σ scp, fcp, 2 fcp, σ eq. 3 where f 1 is all he available informaion up o ime -1 (or he σ-algebra generaed b y up o ime -1). The condiional averages describe he dynamics of sock reurns while Ω describes he dynamics of volailiy. We will assume a linear specificaion for daily reurns, on which y depends, based no only upon heir pas figures, bu also on exogenous variables. Therefore, if he price reurn dynamics depend exclusively upon condiional averages, he model can be saed as follows: y y scp, fcp, c = c scp fcp γ + γ φ + φ β + β 1, scp 1, fcp 0, scp 0, fcp scp,1 γ γ fcp,1 φ φ 2, scp 2, fcp 1, scp 1, fcp β β scp,2 fcp,2............ Wni βscp,3 Dr i + β fcp,3 Dfi yi, 1 γ n scp y, i, 2 + γ n, fcp... yi, n y j, φ n scp y, j, 1 + BW φn, fcp... y j, n eq. 4 In equaion 4 c i represens he consan erm characerisic of sock i, Wn i, Df i sand for he dummy variables (win, draw and defea) of sock i, and marix Dr i and W 28

represens he exogenous variables no ye considered, such as PSI-20 daily reurns, daily volume, risk free ineres raes, and he relaive poins o vicory variable (RPV), aken a ime. Solving he model we ge: yscp, = cscp + β scp,1wnscp + β scp,2drscp + β scp,3dfscp + n n + γ scp, i yscp, i + φscp, j y fcp, j + BscpWscp i= 1 j= 0 y fcp, = c fcp + β fcp,1wn fcp + β fcp,2dr fcp + β fcp,3df fcp + n n + γ fcp, i y fcp, i + φ fcp, j yscp, j + B fcpw fcp i= 1 j= 0 eq. 5 Concerning Ω we will assume a mulivariae GARCH(1,1) specificaion, ha is: σ σ 2 scp, 2 fcp, c = c scp fcp a + b 1 1 a u 2 b u 2 2 scp, 1 2 fcp, 1 α 1 + β1 α σ 2 β 2 σ 2 scp, 1 2 fcp, 1 + CZ eq. 6 where Z is a four imes one marix for he exogenous variables and C is he marix for he exogenous variables parameers. According o Nicolau (1999) «mulivariae GARCH specificaions wih lags superior o 1 are unreaable from he esimaion poin of view, unless hey are considered appropriae resricions of he parameers». Franses and Dijk (2000) sae ha «even hough he general GARCH(p,q) model migh be of heoreical ineres, he GARCH(1,1) model ofen appears adequae in pracice». Tables 3 o 6. The resuls of applying our daabase o equaion 5 and equaion 6 are shown in 29

Table 3: Resuls of Regression Equaion 5 (Sporing) Dependen Variable: y scp Mehod: ARCH Coefficien S. Error Z-saisic p-value c 0.00399 0.00061 6.58600 0.00000 Wn 0.01470 0.00164 8.96546 0.00000 Dr -0.01326 0.00393-3.37028 0.00080 Df -0.00997 0.00272 3.66113 0.00030 y scp (-1) -0.09770 0.03174-3.07846 0.00210 y scp (-2) -0.12604 0.02899-4.34796 0.00000 y fcp 0.38125 0.02040 18.68499 0.00000 y psi 0.13726 0.04770 2.87737 0.00400 Table 4: Resuls of Regression Equaion 5 (FC Poro) Dependen Variable: y fcp Mehod: ARCH Coefficien S. Error Z-saisic p-value c -0.00146 0.00047-3.07985 0.00210 Dr -0.01248 0.00200-6.23087 0.00000 y fcp (-1) -0.26070 0.03009-8.66302 0.00000 y fcp (-2) -0.15188 0.01681-9.03471 0.00000 y scp 0.07103 0.01769 4.01570 0.00001 Table 5: Resuls of Regression Equaion 6 (Sporing) Dependen Variable: σ 2 scp Mehod: ARCH Coefficien S. Error Z-saisic p-value c 0.00005 0.00002 2.99734 0.00270 ARCH(1) 0.14997 0.02282 6.57154 0.00000 GARCH(1) 0.59996 0.01928 31.11418 0.00000 Vol 0.00002 0.00000 12.94266 0.00000 30

Table 6: Resuls of Regression Equaion 6 (FC Poro) Dependen Variable: σ 2 fcp Mehod: ARCH Coefficien S. Error Z-saisic p-value c 0.00013 0.00001 19.31980 0.00000 ARCH(1) 0.11703 0.02376 4.92520 0.00000 Vol 0.00001 0.00000 18.72496 0.00000 Where vol scp and vol fcp represen 1/100 of he daily rading volume for Sporing and Poro shares. Saring wih he Sporing reurns regression equaion, we conclude ha share price reacion for he posiive sporing resuls seems o be posiive. Sporing share price ends o increase, on average, 1.5% immediaely afer winning a mach. On he oher hand, defeas and draws have a negaive impac on share price, he draws apparenly being more negaive in erms of price punishmen han defeas. I seems ha he marke had already anicipaed defeas, a leas parially. When he eam draws, share prices end o depreciae, on average, 1.3% while, when i loses, reurns only fall by abou 1%. The oher variables ha seem significan are lagged sock reurns (showing a negaive dependence), Poro share reurns and PSI20 index reurn. The posiive relaion beween Sporing and Poro shares may seems srange, aking ino accoun heir rivalry in he field. However, his may be a resul of some indusry effec ha should be considered. Finally, he posiive associaion of Sporing shares wih he PSI20 index may resul from is sysemaic risk. 31

Poro shares differ somehow from resuls shown by Sporing shares. For insance, win and defea dummies seem o have no effec on sock reurns. However, similar o wha was found for Sporing shares, draws show a negaive effec. When he eam draws, shares end o depreciae 1.2% on he day afer. On op of his, lagged reurns and he indusry effec, also observed in he Sporing reurns equaion, also seem significan variables for Poro shares. These resuls are somehow surprising when compared wih hose found by Renneboog and Vanbraban (2000) where posiive sporing resuls seem o exer a significan posiive effec on he enire sample. As we have observed, our resuls do no permi such a conclusion o be exended o he enire sample. The same somehow surprising findings happen wih he analysis of defeas, and paricularly when we compare hem wih he resuls for draws. In our findings he draw effec ends o be very significan and applicable o he enire sample. This may be a resul of a profound confidence of invesors in exreme sporing resuls, only showing a sysemaic surprise when eams draw maches. Concerning he effecs of sporing performance on sock price volailiy, we observe ha ARCH(1) and GARCH(1,1) models seem o be appropriae for modelling he effecs of Poro and Sporing share volailiy, respecively. Bu on op of he sandard ARCH / GARCH model variables, daily rading volume should also be considered as a significan variable for explaining volailiy. For boh equaions rading volume has a posiive and significan impac when explaining volailiy. As we were expecing, he increase in rading volume seem o bring new agens o he marke wih a corresponding increase in volailiy. 32

We sared by hypohesising ha he RPV variable («relaive poins o vicory») should play an explanaory role when modelling fooball reurns and volailiy. However, differenly from Ribeiro (2001) we could find no such effec for eiher company. However, due o is srucure, we suspeced ha i could be difficul find any significan effec of RPV on sock reurns. In fac, RPV is a raio ha says suck from one mach up o momen of he nex mach. Then, new poins are deduced from he denominaor of he raio, and someimes some poins are added o he numeraor of he raio. For he majoriy of he days (when playing wih daily daa), he raio does no change and, herefore, we may be biasing he equaion regression wih a subsanial amoun of spurious daa. There are wo mehods o avoid his: eiher by calculaing weekly reurns (as in Ribeiro, 2001) and assuming ha no oher significan effecs play a role in explaining weekly reurns; or exclude he daily reurns which were no immediaely subsequen o a mach (which is he same as o say ha we would only consider one daily reurn per week, which would be he one ha immediaely followed a game). The inconvenience of his mehodology is ha he number of observaions falls significanly. As a soccer season has only 34 maches, in order o ake more informaion ou of he daa se and assuming ha here are no reasons o suspec ha firms would reac differenly, we decided on a panel daa model wih fixed effecs running he same equaions wih boh companies in i: y i, = α i, + βi, RPVi, + εi, eq. 7 The regression equaion resuls are presened in Table 7: 33

Table 7: Resuls of Regression Equaion 7 Season FCP_C SCP_C RPV Coefficien Coefficien Coefficien p-value 1998/1999-0.003160-0.004660-0.019316 0.0053 1999/2000 0.006492 0.009004 0.073444 0.2482 2000/2001-0.005550-0.004590 0.000627 0.7127 2001/2002-0.010500 0.007620-0.036633 0.4141 2002/2003 0.001504-0.011820-0.002704 0.4488 In spie of our aemp o improve he research mehod we sill regisered no saisical significance for he RPV variable. However, as we may observe from Figures 7 and 8, hese insignifican resuls may sill be a consequence of he way in which he variable was defined. Figure 7: RPV of Sporing Figure 8: RPV of Poro 2 4 0-2 2-4 0-6 -8-2 -10 20 40 60 80 100 120 140 160 180 200-4 20 40 60 80 100 120 140 160 180 200 The RPV variable suffers a significan increase (or decrease) in he las maches of a season and is clearly non-linear. When he eam is leading he ournamen and wins he championship, he RPV variable suffers a dramaic increase in he las weeks of he season. 34

Tha was he case of Poro for he 1998/1999 and 2002/2003 seasons and he case of Sporing in he 1999/2000 and 2001/2002seasons. However, when he eam is no leading he championship, he approach of he end of he season means an abrup fall of he variable. In order o correc his effec we did a simple ransformaion in he variable, replacing i by he firs difference beween wo consecuive RPV values (he difference beween he RPV in week and he RPV variable in week -1). This procedure correcs he abrup increases and decreases in he variable, smoohing is pah. VRPV = RPV RPV 1 eq. 8 When VRPV (he variaion in RPV raio) is posiive i means good news. As he denominaor of RPV decreases wih he approach of he season s end, he eam mainains an unimpeachable disance beween iself and is closes opponen, expressed in erms of poins. When VRPV is negaive his means a loss in erms of poins relaive o is mos direc opponen and he marke can read i as bad news. equaion: Replacing his new variable in he daase we go he following esable regression y i, = α i, + βi, VRPVi, + ε i, eq. 9 The resuls for equaion 9 are summarized in Table 4. 35

Season Table 8: Resuls of Regression Equaion 9 VRPV FCP_C SCP_C Coefficien p-value Coefficien Coefficien Winner of he Championship 1998/1999-0.014870 0.0573-0.004190-0.000810 FC Poro 1999/2000 0.126285 0.0058-0.000180 0.003220 Sporing CP 2000/2001-0.011650 0.1785-0.005660-0.005450 Boavisa FC 2001/2002 0.161435 0.0407 0.002571 0.010230 Sporing CP 2002/2003 0.110438 0.0348 0.001100-0.008450 FC Poro As expeced, apar from hose years when he VRPV coefficien is insignifican, we find ha in general here is a posiive relaionship beween sock price reurns and VRPV. During he firs season, and as a resul of he IPO reurns, i behaved in an apparenly srange way. However, his negaive behaviour for boh socks is simply he resul of he well-documened IPO overpricing. This overpricing was also documened for he Poruguese marke (see Almeida and Duque, 2000). Moreover, he VRPV coefficien is saisically insignifican a a 95% confidence level, which leads us o discard i from our analysis. In general VRPV is posiive and saisically significan. There is anoher excepion: during he hird season of he sample, he VRPV is also saisically insignifican, bu his happened when none of he company eams won he naional championship. For he res of he seasons, here seems o be a posiive relaionship beween he daily sock price reurns afer he mach and he change in he relaive poins o vicory. This posiive sign of he VRPV parameer means ha whenever he firm approaches he leader or, if i is he leader already, i increases is difference in poins beween i and he mos direc compeior, sock prices seem o reac posiively. 36

Comparing he independen parameers of boh firms, hey also end o differ from each oher. In fac he winner of he championship ends o show a premium wih an independen parameer greaer han he corresponding parameer of he non-winner, and when Boavisa won he naional championship he independen parameer of boh firms (Sporing and Poro) were negaive! 5. Conclusion This paper invesigaes wheher share prices of wo soccer clubs lised on he Poruguese Sock Exchange (Sporing and Poro) are influenced by he soccer eam s weekly sporing performances. Following he same research opic as Renneboog and Vanbraban (2000), we used a differen mehodology for esing he impac on sock price reurns and exended he analysis o volailiy. In paricularly we inroduced a new mehodology and a new variable in order o explain reurns and volailiy of fooball shares. We sared by observing price chars and we concluded ha for he las 5 seasons (1998-2003), i seems obvious ha here is some visual associaion beween prices and end of he season vicories in he naional championship. Oher price reurn characerisics such as kurosis and skewness are in line wih he findings for oher socks and, herefore, fooball shares do no seem o differ from hem. Moreover, hey also show some signs of clusering leading us o admi ha an ARCH-family model could be appropriae for esing fooball share behaviour. 37

Addiionally we found ha whenever he eam wins he naional championship share prices always presened a posiive mean reurn, and he opposie when no winning he ournamen. This rule has no excepion for he ime period under analysis. Then, using he ARCH family mehodology and he same daase composed of 5 seasons prices and sporing resuls, we provide some evidence ha posiive sporing performance in fooball firms is posiively associaed wih good share price performances in he Sock Exchange, while negaive sporing performances (defeas and draws) are associaed wih negaive sock price reurns. In paricular, Sporing shares reac posiively o vicories and negaively o defeas and draws. For Poro, we only found saisical significance for draws. These resuls are in line wih Renneboog and Vanbraban (2000) resuls for oher markes, using a differen mehodology. We also found oher variables wih a significan impac on sock price reurns such as he previous day sock price reurn (he exhibiing of a negaive dependence reinforces he volailiy clusering hypohesis) and an indusry effec wihin he Poruguese marke for fooball shares. In addiion, we inroduced a new variable in order o measure sporing success. We hypohesised ha a vicory in a game a he sar of he season should have a differen (weaker) effec on sock prices han a vicory when he season is almos over and he company is leading or chasing he leader (sronger effec). Therefore, we inroduced he measure of relaive poins o vicory (RPV) ha measures he difference calculaed in erms of number of poins from he firm o is follower (if he firm leads he ournamen) or 38

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