University of Kent Department of Economics Discussion Papers

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1 Unversty of Kent Department of Economcs Dscusson Papers EXPERT ANALYSIS AND INSIDER INFORMATION IN HORSERACE BETTING: REGULATING INFORMED MARKET BEHAVIOR John Person and Mchael A. Smth November 2008 KDPE

2 EXPERT ANALYSIS AND INSIDER INFORMATION IN HORSE RACE BETTING: REGULATING INFORMED MARKET BEHAVIOUR John Person* Unversty of Kent Mchael A. Smth** Leeds Metropoltan Unversty ABSTRACT: We present a new model analyzng the effect of uncertanty faced by bookmakers. It s shown that bettors wth nsde nformaton or expert analyss decrease the odds set by proft maxmzng bookmakers. Data on prevously unraced two year old horses and those that have raced prevously are used to examne the mpact of the greater possblty of nsder nformaton on odds bas n relaton to unraced horses. The prce of a bet on unraced two year olds s found to be on average 15% hgher and the effect vares as the probablty of wnnng ncreases. The latter effect suggests a possble contrbuton to the favorte-longshot bas and the former shows the mportance of nsder nformaton n the settng of market prces. The regulaton of the use of nsder nformaton s dscussed n the lght of the smlar mpact of nsder nformaton and expert analyss on bookmaker odds. KEUWORDS: Bettng, horseracng, nsder nformaton, uncertanty JEL CLASSIFICATION: D82 & L83 Acknowledgements: We acknowledge the very helpful comments of Roger Vckerman, Jagjt Chadha and partcpants at the Conference on Gamblng, Predcton Markets & Publc Polcy, Nottngham, September Remanng errors and omssons n ths paper are the responsblty of the authors. * Department of Economcs, Keynes College, Unversty of Kent, Canterbury, Kent CT2 7NP; emal jdp1@kent.ac.uk; and tel ** Leeds Busness School, Bronte Buldng, Leeds Metropoltan Unversty, Leeds LS1 3HE; m.z.smth@leedsmet.ac.uk; and tel

3 I Introducton The settng of odds on gamblng events has been the subject of much academc attenton over the last thrty years, see the revews by Sauer (1998), Thaler and Zemba (1988), Vaughan Wllams (1999), Coleman (2004) and Clotfelter (2005). In partcular, the mpact of the use of nsder nformaton by gamblers has been examned n a large number of theoretcal and academc studes, see Dowe (1976), Tuckwell (1983), Crafts (1985), Henery (1985), Brd and McCrae (1987), Shn (1991, 1992 and 1993), Schnytzer and Shlony (1995, 2003 and 2005), Vaughan Wllams and Paton (1997), Paton,Vaughan Wllams and Fraser (1999), Jullen and Salané (2000), Law and Peel (2002) and Schnytzer and Snr (2008). The purpose of the present study s to develop a realstc model of nsder and expert gamblng and the correspondng odds offered by bookmakers. The mpact of nsder tradng and bettng by experts s to ncrease the uncertanty faced by bookmakers and lead them to reduce the odds offered on events where there s greater lkelhood of such bets. In the current study, ths effect s quantfed n order to measure drectly the effect of nsders on the odds offered to gamblers wthout access to superor nformaton. Unlke earler studes, we make a clear dstncton between the actons of gamblers wth nsde nformaton and those who process publcly avalable nformaton to gve objectvely accurate estmates of the probabltes of dfferent horses wnnng,.e. expert bettors. The settng of odds by bookmakers on often repeated sportng events provdes an excellent opportunty for economcs to nvestgate the prcng by a market maker of a fnancal asset wth an uncertan outcome n the face of the possblty of nsder knowledge. The analyss presented here allows the extent of the mpact of nsder tradng on asset prces to be measured more drectly than prevous models. Ths drect mpact s dfferent from the measurements of, for example, Shn (1991, 1992 and 1993), whose studes suggest the favourte-longshot bas s determned only by nsders gamblng. In contrast, our analyss shows that nsder models equally well descrbe the outcomes followng from the behavour of well nformed gamblers wth no access to prvleged nformaton. For ths reason, the emprcal nvestgaton of ths paper employs a dataset n whch the nfluence of expert opnon s lkely to be less marked, and that of nsder tradng to be of mportance. The need for regulaton of nsder gamblng s examned n the lght of our model and the quantfcaton of ts effect. The paper s n four further sectons. The second secton revews the lterature on the settng of odds n the face of nsder tradng. The thrd secton develops a new model of how bookmakers who maxmze expected profts set odds n the face of nsder and expert gamblng. The fourth secton tests the predctons of the model aganst extensve UK data sets of two year old horses that have never raced before, compared to those that have raced prevously. The fnal secton gves a concluson and analyses the need for regulaton of nsder gamblng and tradng n the lght of the theoretcal and emprcal evdence presented here. 3

4 II Past Studes of Insder Informaton Gven the explct mportance of probabltes n relaton to odds n bettng markets, t s useful to adopt a defnton of bettor ratonalty suggested by Al: bettors are ratonal n the sense that no one prefers a bet wth a smaller wnnng probablty and the same or lower return, or wth a lower return and the same or lower wnnng probablty, to that avalable to hm. (Al 1977, p 809, footnote 9): Al goes on to dstngush ratonalty from sophstcaton, assertng that: bettors are sophstcated n the sense that the objectve wnnng probabltes are known to them. (Al 1977, p 809, footnote 9): Thus, one may regard potental gamblers who have objectve nformaton of the probabltes of an event occurrng as better nformed than other gamblers. There follows from Al s classfcaton an mportant dstncton that we beleve has been largely neglected htherto n the lterature. Namely, the dstncton s rarely made between bettors who process publcally avalable nformaton, to form accurate objectve estmates of the probablty of horses wnnng, and those who have access to prvleged nformaton. We refer to these two types of gamblers as experts and nsders respectvely. Informaton based models of odds bas have receved much attenton n recent emprcal studes of bettng markets. Hurley and McDonough (1985) explored the asymptotc behavour of nformed bettors by assumng that, n contrast to the unnformed bettors, they know the true probabltes of horses wnnng and have acqured ths nformaton at zero cost. Informed bettors are further assumed to respond to the actons of ther unnformed counterparts, pursung a symmetrc Nash game. The mplcaton of ther hypothess s that the bas ncreases wth the proporton of unnformed bettors n the market, as they bet dsproportonately on the longshot. The favourte-longshot bas on ths vew has two components: one drectly proportonate to transacton costs and the other component postvely related to the cost of acqurng race specfc nformaton to evaluate true probabltes. They proceeded to show that the model s generalsable to an n runner race so that t becomes amenable to emprcal testng n relaton to observed market data. In relaton to horse racng, Vaughan Wllams and Paton (1997) found that the favourtelongshot bas was more pronounced n low-grade races than n hgh class races. Ths fndng s consstent wth a reasonable assumpton that the cost of acqurng nformaton relevant to the race outcomes s hgher for low-grade races than hgh class contests, because there s lkely to be less publc and meda scrutny of low grade runners. 4

5 Sobel and Ranes (2003) dentfed a lower favourte-longshot bas n hgh volume bettng markets, assumed to be better nformed, than low volume markets, assumed to be proportonately more heavly populated by casual bettors. The startng pont for the Sobel and Ranes nformaton model was to show that n the absence of any nformaton regardng race outcomes, the expected proporton of publc bets made on each runner n a par-mutuel market wll be 1/n, where n s the number of race entrants. Ths represents the lmtng case of extreme bas. To the extent that the bettng publc acqure race specfc nformaton to nform ther assessment of the true chances of ndvdual runners, the actual degree of bas wll depart from ths lmtng case and the proportons bet wll approach more closely the dstrbuton of objectve probabltes. The degree of bas s therefore largely a functon of the amount of nformaton avalable to bettors and the number of runners n the race. Usng a substantal dataset of greyhound racng par-mutuel prces, Sobel and Ranes found evdence of a conventonal favourte-longshot bas assocated wth a hgh proporton of casual bettors, and of an opposte favourte-longshot bas (due to over-reacton to nformaton) n the presence of a hgh proporton of serous bettors (experts and nsders on our defnton, though not dfferentated between n ther paper), substantatng ther nformaton model. Smth, Paton and Vaughan Wllams (2006) further substantated the nformaton based explanaton of bas n a comparatve study of bettng exchange and bookmaker markets, fndng bas to be postvely related to transactons costs and negatvely related to the amount of race specfc nformaton avalable to the publc. In contrast to bettors who process publcally avalable nformaton n a sophstcated manner - the experts - there exst bettors wth access to prvleged nformaton. These bettors are typcally labelled as nsders see, for example, Crafts (1985) and Paton, Vaughan Wllams and Fraser (1999). Schnytzer and Shlony (1995, 2003, 2005) develop models where the bookmaker responds to bettng by nsders by adjustng the odds n the bettng market. The most nnovatve, frequently cted and used nsder model of the settng of bookmaker odds, however, s that of Shn (1991,1992 and 1993). Shn explans the favourte-longshot bas observed n bookmakng markets as the consequence of bookmakers response to asymmetrc nformaton, where some bettors know the outcome of a race by vrtue of ther nsder status. Bookmaker response s modelled by Shn as an adverse selecton problem, wth the emprcal consequence that bookmaker odds on longshots as a class are depressed below far odds to prevent losses n the face of nsder actvty. Ths acton of bookmakers protects them aganst traders wth prvleged superor nformaton. In the Shn model, ths exposure to uncertanty s greater for low probablty horses. Thus, n the Shn model, ths effect of potental nsder nformaton declnes n magntude as the expected probablty of wnnng ncreases, and can consequently explan the favourte-longshot bas. The odds bases observed n emprcal studes employng nformaton based models are frequently attrbuted to the bettng of nsders. Models of expert and nsder gamblers are, n fact, dffcult to dstngush, as the mpact of the two types of gambler on bookmakers odds s the same (and wll also be the same for the odds gven by par-mutuel systems of gamblng). Thus, assumng that experts also possess superor estmates of probabltes of wnnng, models that 5

6 attrbute the cause of bas n bookmaker odds entrely to gamblng by nsders are ncorrect. The cause of bas could equally be the response of bookmakers to expert gamblers processng the publcly avalable nformaton or, more lkely, both types of gamblers could cause the bases. Addtonally, t s not clear that all the bas s caused by the bookmaker respondng to bettng by nformed gamblers. There may well be other causes of the favourte-longshot bas. Thus, there are two reasons why past studes may have overestmated the mpact on odds of nsders gamblng. Polcymakers need to be aware of ths overestmaton when framng regulatons to deal wth nsder tradng n such markets. In any model of odds, t s also necessary to consder the behavour of a thrd class of bettor, namely the less well nformed or casual gambler. Behavoural fnance studes typcally challenge the assumpton that decson-makers are profcent at assessng objectve probabltes,.e. they queston the sophstcaton of bettors, and attrbute the bas to an nablty of decson makng agents to compute objectve probabltes accurately (Kahneman and Tversky, 1979; Tversky, Kahneman and Slovc, 1982; Tversky and Kahneman 1992). For example, ndvduals are found to overestmate the probablty of catastrophc loss n the mputed calculaton of the expected value of a rsky proposton. In respect of large potental losses n wealth, they wll therefore behave n a rsk-averse manner and nsure, whereas faced wth large potental gans they wll gamble. The negatve expected value assocated wth premums n the case of nsurance, and stakes n the case of a gamble, are n such cases understated relatve to the potental losses and gans respectvely, due to ndvduals computng objectve probabltes wrongly or because they adopt mn/max or regret heurstcs (Shlefer 2000 and Shller 2001). In relaton to models of gamblng, these unsophstcated decson-makers correspond to the unnformed or casual gamblers dentfed n Hurley and McDonough (1985) and Sobel and Ranes (2003). It s suggested that the observed bases n odds are not just explaned by the bettng of nformed gamblers but that the behavour of unnformed and casual gamblers s lkely to contrbute to the effect. In the followng analyss, the behavour of unnformed or casual gamblers s not the focus of attenton; rather t s the mpact of nsders and experts on the odds offered by bookmakers that s of nterest. III The Bookmaker Model The reported odds for bettng on Brtsh horse races at off-course bettng offces are derved from a sample of on-course bookmaker odds, formng the bass of the startng prce, a unque odds value for each horse determned by offcal on-course odds nspectors. In the absence of a specfed fxed-odds value agreed between bookmaker and bettor, wnnng bets are settled at startng prce. In ths analyss, we make the assumpton, employed by Shn (1991, 1992 and 1993), that odds are set by a sngle representatve bookmaker. The major justfcaton for ths assumpton s that the settng of odds s an nfntely repeated game by bookmakers who can easly observe and respond to prce cuttng by rvals, are well known to each other, and meet 6

7 frequently. Consequently, we expect that there s a hgh degree of trust between them. These condtons make t very lkely that bookmakers set prces that maxmze jont expected profts (see Bnmore, Krman and Tan, 1993). Thus, we consder prces to be set smultaneously on all n horses n a race, by a sngle bookmaker. The prce of a tcket that pays 1 on the th horse wnnng s q. The expected probablty of the th horse wnnng p s known to the bookmaker. The bookmaker knows the expected probabltes p but ths expectaton s determned by a probablty densty functon for the dfferent probabltes of wnnng for each of the compettors. The bookmaker knows the probablty densty functon,.e. understands the degree of uncertanty, but not the actual outcome of the probablty for any horse wnnng. X s the number of bets by unnformed bettors and s pad out by the bookmaker on the th horse wnnng. Unnformed bettors are defned as those whose objectve expected return s negatve, as they bet on horses whose objectve probablty of wnnng s less than the prce. N s the number of dentcal nformed bettors who bet on the th horse. Y s the number of bets by an nformed bettor on the th horse and N Y s the amount pad out by the bookmaker to nformed bettors on the th horse wnnng. Informed gamblers are lmted n number and defned as bettors who know the outcome of the draw from the probablty densty functon. 1 Informed gamblers ether bet nothng or a postve amount wth an expected return that s postve. The expected bookmaker profts are n where p* s a column vector. n * * * * = X (q - p ) + N Y (p, q ) (q - p ) ( p ) dp (1) j j j j j j j j j 1 1 Informed bettors are assumed to bet on (at most) only one horse n a race 2 and the expected proft maxmum s gven by the condton: 1 It s possble to generalse the analyss and allow nsders to have dfferent probablty densty functons. Thus, nformed gamblers degree of understandng of the probablty densty functon vares. For example, n partcular crcumstances known to one type of nformed gambler, they know that the probablty of a horse wnnng s p j, whereas another nformed gambler wth superor nformaton may know the underlyng probablty densty functon that has the mean p j.ths mprovement s relatvely straght forward to nclude n the model but slghtly complcates the presentaton of the analyss, though the results reman the same. For ths reason we omt the more general model. 2 It s very unlkely that an nsder has prvleged nformaton on more than one horse n a race and ths justfes the assumpton that nsders only bet on (at most) one horse n race. It s possbly that expert gamblers may hedge ther bets and bet on more than one horse n a race. Ths greatly complcates the analyss but the results presented here carry over approxmately to the more general case of the possblty of an nformed gamblng bettng on more than horse n a race, see for detals Sung, Johnson and Person (2008). 7

8 q X n j = (q j - p j) + X j=1 q Y + N (q - p ) ( p ) d p + N Y ( p ) d p 0 * * * * * q (2) All terms wth Y n them are postve as nformed bettors only bet when the expected return s postve,.e. (q j - p j ) and Y q are negatve. The uncertanty facng the bookmaker has two components and s mportant, n the manner of Shn, n determnng the prces set. Frstly, the bookmaker faces uncertanty about the number of nformed gamblers, and secondly, uncertanty about the nature of the dstrbuton of the probablty densty functon. An ncrease n uncertanty follows from ether an ncrease n the number of nformed gamblers or a mean preservng movement of probablty mass outwards from the mean of the densty functon. An ncrease n the uncertanty facng the bookmaker from a greater number of nformed gamblers smply ncreases the terms wth Y n them. Thus, both the terms n Y ncrease n magntude. An ncrease n the number of nformed gamblers does not affect the bettng by outsders. Consequently, ths change n uncertanty ncreases the frst order condton (2) and rases the proft maxmsng prce. An ncrease n the degree of uncertanty n the probablty from a change n the probablty densty functon has a dfferent effect. Investgaton of ths effect requres consderaton of the determnaton of the amount bet by a bettor. An nformed bettor s assumed to have a subjectve assessment p of the probablty of the jth horse wnnng a gven race. s Whether the trader places a bet, and the sze of the bet, are determned by the probablty assessment, the prce of the bet and the utlty functon. It s assumed that an nformed gambler makes only one bet on a race. Expected utlty s gven by: EU = p U(w + (1-q ) Y ) + (1 - p ) U(w - q Y ) (3) s s where w s the ntal wealth of the gambler and Y, s the number of bets placed on horse. It s smple to show that the optmal number of bets Y s gven by EU/ Y = (1 - q ) p U (w + (1 - q ) Y ) - q (1 - p ) U (w - q Y ) = 0 (4) s s where R s the level of absolute rsk averson. 8

9 Takng the total dervatve of equaton (4) for a change n the prce of a bet we obtan: dy - 1/((1-q )q ) + Y R(w+ (1-q ) Y ) - Y R(w - q Y ) = dq (1-q ) R(w+ (1-q ) Y ) + q R(w - q Y ) (5) The amount an nformed bettor gambles s gven by the ntegral of the dervatve (5) between the subjectve probablty assessment (p s ) and the market prce (q j ). Thus, for a mean preservng shft of the probablty densty functon that moves probablty mass to the tals of the dstrbuton, the amount bet by ndvdual bettors wll ncrease. Thus, the Y term n (2) ncreases. The effect of probablty mass shfts on the dervatve term n Y s more complex. The term (q j - p j ) ncreases n magntude. The terms Y q would be expected to ncrease or perhaps approxmately reman constant, but ths result s not necessarly unambguous. The mpact of the probablty mass shft s to ncrease the amount bet. Ths effect s nvestgated by takng the dervatve of (5) wth respect to Y. 2 dy = dq dy (-1+2q - q ) R'(w+ (1-q ) Y ) + q R'(w - q Y ) - 1/((1-q )q ) + Y R(w+ (1-q ) Y ) - Y R(w - q Y ) ((1-q ) R(w+ (1-q ) Y ) + q R(w - q Y )) R(w+ (1-q ) Y ) - R(w - q Y ) + Y (1-q ) R'(w+ (1-q ) Y ) + q R'(w - q Y ) (1-q ) R(w+ (1-q ) Y ) + q R(w - q Y ) The expresson (6) s zero for constant absolute rsk averson. The second term of expresson (6) s negatve for decreasng absolute rsk averson. The square bracketed term n the frst term s postve and the whole term negatve f (1-2q) s postve and R s constant and negatve. Thus, ether for constant absolute rsk averson or for prces less than 0.5 and decreasng absolute rsk averson wth an approxmately fxed R, the expresson (6) s negatve. A negatve expresson (6) ensures that for an ncrease n uncertanty from a change n the probablty densty functon there s an ncrease n the magntude of the term Y q. Consequently, there s an ncrease n the term contanng Y q. An ncrease n uncertanty does not affect the bettng by outsders as the expected probablty remans the same and terms n X take the same value. Consequently, for an ncrease n the second cause of uncertanty, the frst order condton becomes postve and the proft maxmsng q ncreases. Thus, whatever the cause of an ncrease n uncertanty for the bookmaker, the response s to ncrease the prce of a bet. In the present model, compared to the Shn models (1991, 1992 and 1993), nformed 2 (6) 9

10 gamblers bet at the same tme as outsders. Informed gamblers and outsders vary the amount they bet n a manner related to the prce of the bet and ther vew of the chance of a horse wnnng. Informed bettors are assumed to be rsk averse, and do not know exactly what s gong to happen n a race but are better nformed than the bookmaker settng the book on the race. The book prces are set smultaneously on all horses runnng n a race and the demand for bettng on one horse depends on all prces. These aspects of the present model represent mprovements over the Shn models (1991, 1992 and 1993). IV Emprcal Investgaton In our model of bas, the prncpal explanatory factor s uncertanty about nsders usng prvleged nformaton and experts usng publc nformaton. In order to solate the mpact of nsder gamblng and the response of bookmakers, t s therefore necessary to examne races and horses on whch t s lkely that there s a sgnfcant amount of nsder tradng rather than a relatvely large proporton of experts gamblng. In relaton to our chosen markets, the observatons are prces correspondng to bookmaker odds, and objectve probabltes derved from race results. Our dataset s made up of two year old racehorses competng n Flat races run n the UK durng the perod , comprsng four Flat racng seasons. We make the reasonable assumpton that the degree of uncertanty regardng the use of nsde nformaton wll be greater for unraced two year olds than for those that have had prevous racetrack runs. Our reasonng s that knowledge concernng the ablty, temperament and racng style of unraced two year olds can only be nferred ndrectly from breedng, tranng, and home trals conducted by traners off-course, not observed drectly on the racecourse. Ths nformaton s lkely to be protected by traners, stable staff and owners. For unraced two year old horses, we expect greater odds bas than for prevously raced horses, on two counts. Frstly, consstent wth the Hurley and McDonough, and Sobel and Ranes hypotheses, the dstrbuton of subjectve probabltes contaned n the odds wll be on average closer to 1/n than s justfed by the ex post objectve probabltes. Ths s a consequence of not knowng mportant attrbutes of horses that affect the outcome of a race, whch are not yet revealed because of the absence of hstorcal race data. Secondly, followng Shn s reasonng, bookmakers may reasonably antcpate a greater nsder advantage than the norm possessed by, for example, stable connectons n relaton to unraced horses, and protect the book aganst the unknown ncdence of potental losses by depressng odds offered on unraced two year olds. The emprcal consequence s that, for the same objectve probablty of wnnng, an unraced two year old horse would be set at lower odds,.e. the prce of a bettng tcket to wn a gven amount wll be hgher for unraced horses. The testng methodology used two sets of data: the results and prces for prevously unraced and raced two year old horses. The horses were separated nto prce categores correspondng to odds. The hypothess of the analyss was tested on the equvalent null hypothess that the probabltes of wnnng n the two data sets are equal for matchng odds categores. A test statstc was constructed on the bass that a horse race can be consdered as a bnomal experment wth all horses n the same prce category havng the same probablty of 10

11 wnnng. Wthn each prce category, estmated probabltes were calculated from the number of wnners and runners for the two datasets. The dfference of the estmated probabltes has a normal dstrbuton under the null hypothess and when the number of observatons and expected wnners/losers s suffcently large. Thus, when the number of observatons was less than 30 and/or the number of expected wnners/losers was less than fve for ether raced or unraced horses, the prce category was dropped. Ths left 40 matched prce categores. The test statstc was normalsed by an estmate of the standard devaton of the samplng dstrbuton to gve a standardsed normal varate as a test statstc. Table 1 reports for the 40 ndvdual prce categores: the test statstcs; the bas for raced and unraced two year olds; 3 a summed test statstc for the four groups of ten prce categores normalsed to gve a standardsed normal varate; and the correspondng average dfferences n bas. The results show a statstcally sgnfcant greater bas up to prces of about 0.4 and the addtonal bas s of mportance. The addtonal bas dsappears for prces greater than 0.4. Thus, as predcted by the theory, the statstcal nvestgaton shows that for horses wth prces of less than 0.4, bookmakers offer prces on unraced two year old horses that are statstcally sgnfcantly dfferent and the dfference s represents on average an addtonal bas of 15%. V Implcatons and Conclusons A model s developed of the settng of odds by proft-maxmzng bookmakers that explctly ncorporates the mpact of nsder and expert gamblng. The model s tested aganst data from races n whch two year old horses run. The use of ths data allows estmaton of the degree to whch bookmakers respond to nsder gamblng by worsenng the odds offered to other less nformed gamblers. The mert of the data used n the present study s that t refers to crcumstances whch, amongst all possble horse races, are the most lkely to reflect strong evdence of nsder gamblng. It s argued that prevous theoretcal and emprcal studes have made lttle or no dstncton between nsder and expert gamblers n ths way. Ths s understandable as the effects of the two types of bettors on the odds offered by bookmakers are lkely to be very smlar. However, t s not approprate to attrbute all bas to the gamblng of nsders and gnore the mpact of expert gamblers who have a smlar effect on bookmaker prces. Addtonally, the behavour of more casual or nformed gamblers may also determne some of the observed bas n prces. The reported results suggest that the potental presence of nsders leads bookmakers to ncrease the prce of bets by a sgnfcant amount for unraced two year old horses. It should be noted that the comparson s wth the bas n the prces for raced horses whch may contan a bas caused by nsder gamblng on these horses. The addtonal bas n the prces for unraced two year olds s not present for hgh prces. Ths may be explaned by the greater nformaton avalable and meda attenton gven to unraced horses wth a hgh probablty of wnnng. Such nformaton and attenton s lkely to prevent the exstence of prvleged nformaton on the probablty of a horse wnnng. 3 The bases are calculated from the expresson (1-p/q) where p s the probablty estmated from the number of wnners and runners n the prce category. 11

12 It mght be argued that a negatve effect of nsder gamblng s the possblty of bookmakers sufferng losses. Ths effect s lkely to be reflected n bookmakers allowng for and protectng aganst such losses through settng hgher tcket prces (lower odds). The more mportant negatve effect of nsder gamblng s less nformed gamblers facng hgher prces, see Crafts (1985) and Paton, Vaughan Wllams and Fraser (1999). The evdence presented here suggests that the bas n bookmakers prces may be rased n the regon of 15% (a rough average of the values n the fnal column of Table 1) by the possblty of nsder gamblng on unraced two year olds. Ths addtonal cost mposed on less well nformed gamblers would appear to be of mportance and consttutes an argument for regulatng aganst nsder gamblng. It has been suggested that nsder gamblng s an acceptable reward for those nvolved n ownng and tranng horses (see the dscusson n Crafts, 1985). However, n most countres of the world, the use of nsder busness nformaton s llegal and t s dffcult to argue that horse racng has any features that would make nsder gamblng acceptable. Thus, there s a strong economc argument for regulaton of nsder gamblng. However, the detecton of nsder gamblng rases many practcal problems. The analyss of the present study shows that there s lttle dfference between the mpact of the operaton of nsder and expert gambler on the prces set by bookmakers. However, the latter use the power of publcly avalable nformaton and analyss to support ther gamblng. By comparson wth the busness world, t s dffcult to argue that such gamblng should be made llegal. Rather, t s to be applauded just as much as data drven analyss leadng to successful fnancal market nvestment. 12

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14 Schnytzer, A. and Shlony, Y. (2005) Insder Tradng and Bas n a Market for State-Contngent Clams, n Vaughan Wllams, L.(edtor), Informaton Effcency n Fnancal and Bettng Markets, Cambrdge: Cambrdge Unversty Press. Schnytzer, A., and Snr, A. (2008) Herdng n Imperfect Bettng Markets wth Insde Traders, Journal of Gamblng Busness and Economcs, 2 (2), pp Shn, H. S. (1991) Optmal Bettng Odds Aganst Insder Traders, Economc Journal, 101, pp Shn, H. S. (1992) Prces of State Contngent Clams wth Insder Traders, and the Favourte- Longshot Bas, Economc Journal, 102, pp Shn, H. S. (1993) Measurng the Incdence of Insder Tradng n a Market for State-contngent Clams, Economc Journal, 103, pp Smth, M.A., Paton, D. and Vaughan Wllams, L.(2006) Market Effcency n Person-to-Person Bettng, Economca, 73, pp Sobel, R. S. and Ranes, S. T. (2003) An Examnaton of the Emprcal Dervatves of the Favourte Longshot Bas n Racetrack Bettng, Appled Economcs, 35, pp Sung, M.C., Johnson, J.E.V. and Person, J. (2008) Understandng the Weekend Effect: Insghts from a Market for State Contngent Clams, Workng Paper, Centre for Rsk Research, Unversty of Southampton. Thaler, R. and Zemba, W. (1988) Parmutuel Bettng Markets: Racetracks and Lotteres, Journal of Economc Perspectves, 2, pp Tuckwell, R. (1983) The Thoroughbred Gamblng Market: Effcency, Equty and Related Issues, Australan Economc Papers, 22, pp Tversky, A. and Kahneman, D. (1992) Advances n Prospect Theory: Cumulatve Representaton of Uncertanty, Journal of Rsk and Uncertanty, 5, pp Vaughan Wllams, L. and Paton, D. (1997) Why s there a Favourte-Longshot Bas n Brtsh Racetrack Bettng Markets?, Economc Journal, 107, pp Vaughan Wllams, L (1999) Informaton Effcency n Bettng Markets, Bulletn of Economc Research, 51 (1), pp

15 Prce Table 1 Test Statstcs for Dfferences of Estmated Probabltes Probablty Test Statstc Bas Unraced TYOs Bas Raced TYOs Average Test Statstc Average Increase n Bas ** 7.4% * 11.7% * 24.4% % ** statstcally sgnfcant at 5% * statstcally sgnfcant at 1% 15