The Quarterly Review of Economics and Finance 49 (2009) 917–930

Contents lists available at ScienceDirect

The Quarterly Review ofEconomics and Finance

journa l homepage: www.e lsev ier .com/ locate /qre f

How quickly is temporary market inefficiency removed?

Ben R. Marshall ∗

Department of Finance, Banking and Property, Massey University, Private Bag 11-222, Palmerston North, New Zealand

a r t i c l e i n f o

Article history:Received 17 July 2008Received in revised form 15 January 2009Accepted 16 April 2009Available online 24 April 2009

JEL classification:G14

Keywords:ArbitrageMarket efficiencyBehavioral finance

a b s t r a c t

I provide evidence on the length of time it takes for arbitrageurs toexploit attractive investment opportunities. A unique data set fromthe Internet sports betting market allows me to focus on the speed ofinvestor response in an environment that is not affected by the jointhypothesis problem. The market does not instantly converge to anefficient level after mispricing occurs, but the adjustment processis rapid. Arbitrageurs remove many of these opportunities withinminutes of them being created and the majority are gone within anhour. Arbitrage opportunities that are more difficult to find last forlonger.

© 2009 The Board of Trustees of the University of Illinois.Published by Elsevier B.V. All rights reserved.

1. Introduction

Available information is fully reflected in prices in an efficient market (e.g., Fama, 1970), but inreality prices do not always react instantly to new information. Merton (1987, p. 485) states “theexpected duration between the creation of this investment opportunity and its elimination by rationalinvestor actions in the market place can be considerable.” Much research energy has been devotedto how quickly individuals respond to information which is unsurprising given the importance of theefficient market hypothesis to finance.

This literature involved too approaches, both of which have a weakness. The first strand considersthe convergence of prices to efficient levels, but in order to do so the authors first need to identify whatthe efficient price level is. This requires the use of a benchmark model, which as Fama (1998) points out,effectively means that two tests are jointly being undertaken. The first is speed of price convergenceand the second is ability of the benchmark model to correctly identify efficient price levels. The second

∗ Tel.: +64 6 350 5799; fax: +64 6 350 5651.E-mail address: B.Marshall@massey.ac.nz.

1062-9769/$ – see front matter © 2009 The Board of Trustees of the University of Illinois. Published by Elsevier B.V. All rights reserved.doi:10.1016/j.qref.2009.04.006

918 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

strand of literature, which considers convergence to efficient price levels by considering the speed atwhich arbitrage opportunities are removed, overcomes this joint hypothesis problem, however anotherissue is encountered. Most arbitrage in financial markets is not free of impediments to arbitrage suchas short-selling constraints (e.g., Shleifer & Vishny, 1997) so it is possible that mispricing persists forlong periods due to these rather than a lack of effort by investors to remove them.

I consider how quickly prices converge to efficient levels (i.e. arbitrage opportunities are removed)in an environment which does not suffer from either of the weaknesses outlined above, the Internetsports betting market. Durham, Hertzel, and Martin (2005) point out that sports betting markets aresimilar to financial markets in that they attract large volumes and information is widely available, butthey also have several strengths as an empirical laboratory.1 The particular advantages this paper isinterested in are: numerous price (or odd) quotations on the same event by different decentralisedmarket makers (bookmakers), diverse price quotations generating arbitrage opportunities, arbitrageopportunities being easily identified and valued based on odds that are perfect substitutes (i.e. nofundamental risk), the odds having a short life and a well defined termination point (i.e. no noise traderrisk), the arbitrage transaction being executed with minimal cost via the Internet (i.e. low transactionscosts), and the absence of short-selling constraints.

It is difficult to quantify exactly how many individuals are actively involved in sports betting arbi-trage. However a quick search on the Internet2 generates over 1.8 million links to websites discussingthe concept, providing advice on how best to capture the profits on offer, and giving feedback onhow much money individuals are making exploiting these arbitrage opportunities. Sports bettingarbitrage forums such as www.arbforum.co.uk and http://www.sportsarbitrageworld.com have over10,000 posts from individuals who appear to be actively engaged in this activity.

I show divergent price quotations on the same sporting event allow median arbitrage profits of justover 1.5% per trade to be made. Once created, these opportunities are quickly removed. Their medianduration is 15 min and 75% of all opportunities are removed within 50 min. Arbitrage opportunities thatare more difficult to find last for longer. These include opportunities involving three- rather than two-outcome sporting events and arbitrage opportunities created by bookmakers who do not typicallypost odds that create such an opportunity. The opportunity costs of checking these odds are largerthan those of checking the odds of bookmakers who frequently create opportunities so it is rationalfor arbitrageurs to check these bookmaker websites less frequently.

My results provide further support for the Merton (1987) suggestion that attractive investmentopportunities are not removed instantaneously. Investors take time to locate and exploit attractiveinvestment opportunities even in a market setting where fundamental risk, noise trader risk, transac-tions costs, and short-selling constraints do not impede the capturing of arbitrage opportunities. Myfinding that arbitrage opportunities that are more difficult to find last for longer is also consistent withthe propositions of Merton (1987). My results are not affected by the joint hypothesis problem that isinherent in most tests of the speed of convergence to market efficiency, as no model of efficient pricelevels is required. Sports betting markets are less liquid than financial markets and it is possible thatcredit concerns are more prevalent in sports betting markets. However, I propose that neither of thesefactors, which are discussed in detail later in the paper, affect my conclusions in a major way.

The remainder of the paper is organized as follows: Section 2 provides a discussion of relevantliterature. The market setting, data set and methodology used to determine if an arbitrage opportunityexists is described in Section 3. The results are presented in Section 4. Section 5 concludes the paper.

2. Related literature

In an efficient market, prices quickly react to information and rapidly converge to efficient levels asrational individuals seek to exploit attractive investment opportunities. However, many researchersshow that in reality mispricing persists for long periods of time. Lamont and Thaler (2003) find evidence

1 Others have indicated there are similarities between bets and certain financial assets. For instance, Vecer, Ichiba, andLaudanovic (2006) shows bets and credit derivatives have many similar properties.

2 The Google search for the term “sports arbitrage” was conducted on 27 September, 2007.

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 919

that a corporate spin-off did not trade at a rational price (based on the value ascribed to the companyit was carved out from) for a 6-month period. Ofek, Richardson, and Whitelaw (2004) documentviolations of the no-arbitrage put-call parity relationship in U.S. options over the 1999–2001 period.Froot and Dabora (1999) show that “twin shares” which have a fixed claim on the cash flow and assetsof the same company but trade in different countries trade at quite different prices for a 10-yearperiod. Dammon, Dunn, and Spatt (1993) document large, persistent differences in the pricing of threevirtually identical bonds over a 2-year period.

In the first two law of one price violations mentioned above investors were not simply slow to reactto the supposed profits on offer, they were in fact unable to exploit the profits. Lamont and Thaler(2003) and Ofek et al. (2004) show that the inability to short-sell at a reasonable cost explains theinefficiency they document. This is consistent with the evidence provided by Jones and Lamont (2002)regarding the link between stock price over valuation and short sale constraints. Market imperfectionsdo not appear to explain the arbitrage opportunities in the second two examples but it is possiblethe noise trader risk explains the lack of action from arbitrageurs. As De Long, Shleifer, Summers, andWaldmann (1990) show, irrational noise traders often bid prices further away from efficient levels inthe short term which forces arbitrageurs to close their positions at a loss.

Other authors, who consider the speed of convergence of prices to efficient levels based on modelsof normal returns, also find evidence of investors reacting relatively slowly. Chan (2003) finds that stockprices drift after bad news stories for up to 12 months, however this effect is centered in smaller, illiquidstocks, which suggests short-selling constraints may be the explanation. The findings of Hubermanand Regev (2001) are more difficult to explain from a limits-to-arbitrage perspective though. Theyshow that a stock’s price only began to move in meaningful way in response to a breakthrough inresearch the company was conducting once a story about its success was published in the New YorkTimes, even though news of the discovery was published in the scientific publication Nature some 5months earlier. There does not appear to be any impediment to investors acting on this news sooner.

There is also evidence of convergence to market efficiency occurring reasonably quickly. Rashes(2001) shows that deviation from fundamental value caused by confusion over ticker symbols tend tobe removed within several days. Chordia, Roll, and Subrahmanyam (2005) show there is serial correla-tion in order imbalances for stocks listed on the New York Stock Exchange but it only takes between 5and 60 min for rational investors to make offsetting trades which removes return persistence. Maloneyand Mulherin (2003) show that the stock prices of firms who supplied parts for the space shuttle Chal-lenger adjusted within minutes to news of its crash. Finally, Busse and Green (2002) find that pricesrespond to analyst reports on the Morning Call and Midday Call segments on CNBC TV very quickly.Prices begin to adjust within seconds of a stock being mentioned and positive reports are fully reflectedin prices within 1 min.

This paper adds to the literature discussed above by documenting the length of time it takes toremove attractive investment opportunities in an environment where there are no short-sales con-straints or noise trader risk. Studying this from the perspective of the length of time it takes for theremoval of arbitrage opportunities has the advantage of not being subject to the joint hypothesis prob-lem where tests are in effect a joint test of convergence to market efficiency and the accuracy of themodel used to determine “normal returns”.

Sports betting market data have numerous advantages as an empirical laboratory (e.g. they have atermination point at which values are known with certainty) so it is not surprising these data are usedby many researchers in the financial economics literature. Gandar, Dare, Brown, and Zuber (1998) useNational Basketball Association (NBA) data to document evidence consistent with market efficiency.Avery and Chevalier (1999) use National Football League (NFL) to show investor sentiment can affectprices. Durham et al. (2005) use college football betting market data to test the regime shifting modelof Barberis, Shleifer, and Vishny (1998).

More recently, many papers have re-examined the efficiency of betting markets from a number ofdifferent angles. Edelman and O’Brian (2004) use game theory techniques to document the possibilityof the existence of arbitrage opportunities based on exotic bets in horse races. Lane and Ziemba (2004)present arbitrage strategies and what they term “risk arbitrage bets” which involve little risk for the JaiAlai game. They show that it is possible to devise a range of profitable strategies. Paton and VaughanWilliams (2005) find the mid-point of the odds spread offered by the market in general gives a more

920 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

accurate forecast of the actual outcome than the mid-point of the spread quoted by an outlier book-maker. They then use this fact to develop profitable quasi-arbitrages or quarbs. In related research,Smith, Paton, and Vaughan Williams (2006) find that the development of person-to-person bettingexchanges has resulted in efficiency gains through the lowering of transaction costs.3

3. The market setting and data

3.1. Market background

It is difficult precisely estimate the size of the Internet sports betting market, but it appears to bewell in excess of US$20 billion per annum. Sinclair (1998) suggests that the size of the Nevada marketwas US$2.7 billion by 1997 and Strumpf (2003) estimates Internet betting on U.S. sports alone is now upto 10 times bigger than this market. There are now hundreds of Internet bookmakers simultaneouslyoffering odds on the same sporting event.

The sports betting market system is quite different from the pari-mutuel structure used by manyhorse race tracks. In pari-mutuel markets, market makers take their profits then return money towinning bettors in proportion to their individual stake. The actual payoffs to winning bettors aretherefore not known until the close of the betting period.4 In contrast, sports bookmakers offer fixedodds betting where a bettor is guaranteed to receive a certain payout (if they correctly pick the eventoutcome) regardless of how the odds change subsequent to their placing of the bet.

Prior to 2006 (i.e. the period of this study) non-U.S. based companies offering Internet bettingservices to U.S. based individuals were not violating any U.S. federal laws. This changed with theadoption of the Unlawful Internet Gambling Enforcement Act (2006). This legislation makes acceptingmoney for the purposes of gambling by banks or online bookmakers a criminal offence. Nevada, Oregon,and Delaware are still able to offer state regulated sports betting, but offering sports betting services inother states is illegal. This means that U.S. residents are no longer able to pursue the strategies outlinedin this paper, but these opportunities are still available to non-U.S. residents.

The level of regulation of Internet sports bookmakers in non-U.S. countries varies dramatically.Countries such as the U.K., Canada, and Australia conduct rigorous checks before issuing licenses. Inaddition, most U.K. bookmakers are regulated by the Independent Betting Arbitration Service which isan independent third party which offers adjudication for customers in dispute with their bookmaker.Moreover, many European and U.K. bookmakers are stock-exchange listed. However, in other countries(e.g. the Caribbean) a bookmaker only has to pay a fee to the Government in order to obtain a license.Minimal checks are carried out in these countries (see Rose, 1999, for more details).

3.2. Data source

The data are sourced from http://www.sportsarbitrageworld.com, a British company thatidentifies sports betting arbitrage opportunities in the odds quoted by Internet sports book-makers. http://www.sportsarbitrageworld.com uses proprietary software to scan bookmakerwebsites in real-time. It then alerts subscribers to an arbitrage opportunity as soon as itis created via an SMS message or “ArbAlarm”, which is proprietary software that transmitsto subscribers’ desktops in real-time (see www.sportsarbitrageworld.com for more informa-tion). http://www.sportsarbitrageworld.com data are unique in both their depth and breadth.http://www.sportsarbitrageworld.com started identifying and recording arbitrage opportunities elec-tronically in late 2002. Data for the full 2003 and 2004 years are unavailable due to the loss ofSeptember 2003 to March 2004 data by http://www.sportsarbitrageworld.com, so the data set spans

3 The interested reader should refer to Vaughan Williams (1990) for an excellent summary of studies that have consideredefficiency issues within betting markets.

4 Hausch and Ziemba (1990) show that is theoretically possible to earn “arbitrage” profits within a pari-mutuel setting fromcross-track betting. However, the odds determination mechanism of these markets means that an arbitrageur could not be certainthat such profits existed at the time they place their bets so they would have to be willing to incur risk in each transaction.

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 921

the January 2003 to December 2005 period, with the exception of the period for which data aremissing.5

The original data set contains 529,561 arbitrage opportunities. However, many of these are onthe same sporting event involving the same bookmaker. This occurs because when one bookmaker(say bookmaker A) posts an odd that is sufficiently different from the other bookmakers to cre-ate an arbitrage opportunity, http://www.sportsarbitrageworld.com records arbitrage opportunitiesbetween bookmaker A and every other bookmaker. In reality, an individual would be able to pur-sue only one of these opportunities due to time and/or bet maximum constraints with bookmakerA. Therefore this paper examines only one of such bookmaker duplicate arbitrage opportunitiesand those that do not involve one common bookmaker on the same sporting event. The approachoutlined above resulted in all but 19,882 arbitrage opportunities being removed from the dataset.http://www.sportsarbitrageworld.com focuses on arbitrage opportunities in sporting events thatinvolve two or three outcomes. The sports included in the http://www.sportsarbitrageworld.comdatabase are Cricket, Darts, Formula One Motor Racing, Golf, Major League Baseball (MLB), NascarMotor Racing, National Basketball Association (NBA), National Football League (NFL), National HockeyLeague (NHL), Rugby, Snooker, Soccer, and Tennis.http://www.sportsarbitrageworld.com has addedmore bookmakers to the universe it scans each year. To ensure the results are comparable acrossyears, this research includes only arbitrage opportunities that stem from the 50 bookmakers thathttp://www.sportsarbitrageworld.com tracked in each of the 3 years. These bookmakers were based inCosta Rica, Netherlands Antilles, West Indies (Curacao), Canada, Australia, Austria, Isle of Man, Gibraltar,U.K., Ireland, Malta, Cyprus.

3.3. Market conventions and mechanics

The formula required to determine if an arbitrage opportunity exists is relatively straightforward.Assuming a successful bet on outcome i gives a return (including the initial money bet) of Xi units andthat there are n outcomes in a contest, an arbitrageur must place 1/Xi on each outcome i for all 1 ≤ i ≤ n.This requires a total outlay (TO) of:

TO =n∑

i=1

1Xi

(1)

An arbitrage opportunity only exists if the total outlay required to guarantees a payoff of 1 unit (Eq.(1)) is less than one.

The total profit earned per unit bet is:

PROFIT = 1 −∑n

i=1(1/Xi)∑ni=1(1/Xi)

subject ton∑

i=1

1Xi

< 1 (2)

It should be noted that arbitrageurs do face minor costs such as Internet service provider costs so inthis sense the term PROFIT is referring to gross profits. I discuss the costs incurred in detail in Section4 and show they are small compared to the PROFITs on offer.

In order to achieve a certain PROFIT regardless of the outcome the proportion of the total outlay thearbitrageur should place on each outcome (i = 1, 2, . . ., n) is given by:

Proportion to bet on outcome i = 1/Xi

1/X1 + 1/X2 + · · · + 1/Xn(3)

An example of how the profits from an arbitrage opportunity are calculated is provided inAppendix A.

5 Extracting the data required for this research from the sportsarbitrageworld.com system is an onerous task. However, I checkmy core results are consistent with those generated from September and November, 2006 (the months immediately prior andfollowing the change in U.S. legislation) data and find they are.

922 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

3.4. Why are these arbitrage opportunities created?

The focus of this paper is the length of time it takes for arbitrage opportunities to be removed ratherthan the reasons they are created in the first instance. However, I briefly discuss possible reasons whythe odds offered by bookmakers may differ and why arbitrage opportunities are created. Bookmakerstend to display their opening odds for an event at approximately the same time. It is possible they offerdifferent odds because they have differing views on the likely outcome of any given match. Harris andRaviv (1993, p. 474) state “it seems to us that people share common information yet disagree as to themeaning of this information, not only in the evaluation of risky assets, but also in the evaluation ofpolitical candidates, economic policies, and the outcome of horse races.” Kuypers (2000) shows thatbookmakers who seek to maximize profits can set inefficient odds as a result of coming to differentconclusions regarding how bettors will place their bets.

Bookmakers could remove crossed odds themselves after viewing the odds of their competitorsbut there is little reason to do this if they believe their odds better reflect the outcome probabilitiesthan do those of their competitors. It is also possible that bookmakers purposely quote some odds at alevel above those of their competitors as a marketing ploy to attract customers to their website. Theseactions would be consistent with the Salop and Stiglitz (1977) and Varian (1980) theory of spatial pricedispersion.

4. Results

In this section I present the results and discuss their implications. The summary statistics displayedin Table 1 indicate arbitrage PROFITs range from 0.91% to 11.10%. The mean is 2.03% and the medianis 1.51%, indicating skewness. The data do not allow a conclusion to be drawn on the annual percent-age PROFITs available to an arbitrageur. Sporting events are typically concluded within 1 week of theodds first being offered (and the arbitrage opportunity potentially being created). Moreover, bookmak-ers return money to winning bettors on the day after an event’s conclusion. However, a reasonableestimate of annual arbitrage PROFITs is substantially less than the 216% implied by annualising theaverage PROFIT of 1.51% by 52 weeks. Arbitrageurs are unlikely to have accounts with all 50 book-makers in the http://www.sportsarbitrageworld.com database or the time required to pursue eachopportunity so no one arbitrageur would be in a position to take advantage of all the opportunitiesdocumented.

DURATION is the number of minutes it takes for an arbitrage opportunity to be removed. The DURA-TIONs indicate that arbitrages are typically removed very quickly. The median length of time they lastis 15 min and three quarters of the opportunities are removed within 50 min. There is strong positiveskewness in the data. The longest DURATION is just under a day.

I now consider whether arbitrage opportunities that are more difficult to find exist for longer.Arbitrage opportunities exist in sports with two possible outcomes (A wins or B wins) three possi-ble outcomes (A wins or B wins or there is a draw). Two-outcome arbitrage opportunities are easierto locate than their three-outcome counterparts because they require an arbitrageur to only com-pare two sets of odds rather than three. This suggests two arbitrage opportunities should be foundand removed more quickly. The results relating to these tests are presented in Table 2. An event out-come dummy variable, EVT OUT, which equals zero if there are two possible outcomes involved inan opportunity (i.e. those that are relatively easy to find) and one if there are three possible out-

Table 1Summary statistics.

Number Mean S.D. Minimum LQ Median UQ Maximum

PROFIT 19882 0.0203 0.0149 0.0091 0.0114 0.0151 0.0229 0.1110DURATION 19882 59.424 127.219 0.017 6.333 15.358 50.046 1177.667

The data are sourced from http://www.sportsarbitrageworld.com. The arbitrage opportunities occur in the 2003–2005 period.PROFIT is the gross payback arbitrageurs receive for conducting an arbitrage transaction. DURATION is the length of time (inminutes) each arbitrage transaction lasts for before being totally removed.

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 923

Table 2DURATION regression results.

1 2 3 4 5 6 7 8

Intercept 2.844 2.777 2.103 1.869 2.606 1.788 2.056 2.332EVT OUT 0.822 0.858 0.873 1.106 −0.381 0.887 0.929 0.963CTRY RISK −0.198 −0.206 −0.213 −0.164 −0.169 −0.204 −0.136HOME CTRY −0.113 −0.099 0.518 0.052 −0.139 −0.083 −0.151OTHER REG 0.184 0.166 0.156 0.162 0.169 0.140 0.143PUBLIC 0.085 0.079 0.048 0.026 0.081 0.028 0.023PROFIT −0.172 −0.220 −0.217 −0.213 −0.157 −0.229Cricket −0.078Darts 0.107F1 0.589Golf −1.203MLB 1.035Nascar 0.590NBA −0.732NFL −0.131NHL −0.265Rugby −0.022Snooker −0.358Soccer 0.955Tennis −0.8982003 0.4732004 0.7362005 −0.855

Adj. R2 0.034 0.041 0.045 0.081 0.122 0.064 0.088 0.130

The data are sourced from http://www.sportsarbitrageworld.com, bookmaker websites, Bookmakers Review(http://www.bookmakersreview.com), and the Independent Betting Arbitration Service (http://www.ibas-uk.com). Theseresults are derived from the entire sample. DURATION, which is the number of minutes it takes for an arbitrage opportunityto be removed, is the dependent variable in each instance. EVT OUT is a dummy variable that equals zero if there are twopossible outcomes involved in an opportunity and one if there are three possible outcomes. CTRY RISK is a dummy variablethat equals zero if all bookmakers are from a strongly regulated country and one if one or all bookmakers are from a weaklyregulated country. PUBLIC is a dummy variable that equals zero if all bookmakers are public companies and one if one or all arenot. OTHER REG is a dummy variable that equals zero if all bookmakers are members of IBAS and one if one or all bookmakersare not members. HOME CTRY is a dummy variable that equals zero if all teams/players are from the same country and oneotherwise. PROFIT is the gross profit on offer expressed as a percentage. Sport and Year dummy variables are also included. Allregressions are estimated using White (1980) heteroskedasticity adjusted standard errors. Coefficients that are statisticallysignificant at the 10% level or higher are highlighted in bold.

comes (i.e. those that are relatively difficult to find) is used and numerous control variables areincluded.

The likelihood of suffering major loss of capital through bookmaker default does not appear tobe high. No bookmaker tracked by http://www.sportsarbitrageworld.com defaulted in the period Istudy. In addition, an arbitrageur’s capital is typically distributed among 20 or more bookmakersso the effect of the default of one bookmaker on the arbitrageur’s capital is not extreme. Despitethe above, I investigate whether bookmaker default or the risk of a bookmaker not acting hon-ourably in a transaction is so high that longer DURATIONs are explained by more-risky bookmakersbeing involved. I investigate this by including three dummy variables for bookmaker credit/reputationrisk.

One measure of bookmaker risk is related to the country they are domiciled in BookmakersReview, an independent organisation, considers “each country’s economical and political stability,the presence of government’s control over the betting industry and/or the existence of a gamingauthority or commission, the procedures and requirements for a betting company to be licensed,the international reputation as a betting jurisdiction, the ease of information access and the availabil-ity of modern communication infrastructures, and classifies each jurisdiction into one of five tiers”(http://www.bookmakersreview.com/Jurisdictions/).

924 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

The first dummy variable CTRY RISK is based on the risk attached to bookmakers in different coun-tries by Bookmakers Review. The most distinct increase in risk occurs between Tier 2 and Tier 36 soCTRY RISK equals zero if all bookmakers are from a strongly regulated country (Tiers 1 or 2) and oneif one or all bookmakers in an arbitrage opportunity are from a weakly regulated country (Tiers 3–4).Strongly regulated countries include Canada, Australia, Isle of Man, Malta and the U.K. Weakly regu-lated countries include Costa Rica, Netherlands Antilles, West Indies, Austria, Gibraltar, Ireland, andCyprus.

A second way of measuring the credit risk inherent in dealing with a bookmaker relates to thelevel of disclosure of the bookmaker’s financial position. Of the 50 bookmakers included in my sample19 are stock exchange listed public companies. These companies have a considerably higher level ofdisclosure than their private counterparts. This information can be used by arbitrageurs to reduce therisk of having money with a bookmaker close to collapsing so the second dummy variable to proxy forrisk, PUBLIC, equals zero if all bookmakers in an arbitrage opportunity are public companies and oneif one or all are not.

Bookmakers can choose to be members of the Independent Betting Arbitration Service (IBAS), whichis an independent third party, which offers adjudication for customers in dispute with their bookmaker.A bookmaker who is a member of IBAS undertakes to be bound by the rulings of its arbitrators. If theydo not comply with an IBAS ruling they would be publicly de-registered from the service (IBAS, 2006).Being an IBAS member is therefore a signal that a bookmaker is likely to act honourable with clients.The third variable I introduce as a risk proxy, OTHER REG, equals zero if all bookmakers are membersof IBAS and one if one or all bookmakers are not members.

It is also possible that some “investor biases” are prevalent in betting markets to a larger degreethan they are in stock markets and these are driving the results. The most plausible bias is a “HomeCountry Bias” where individuals bet on their teams from their own country even when it is not rationalto do so based on the odds on offer and the probability of their team winning. Kang and Stulz (1997)find that stock market investors favour investments in their own country. This may be related to theHeath and Tversky (1991) competence hypothesis. These authors suggest that individuals would ratheroperate in an environment that they are familiar with instead of one where they feel ignorant. Thissame hypothesis could be expected to apply to sports betting markets, and it is reasonable to assumethat it might be exacerbated by bettors favouring their home country team due to some emotionalattachment that would not exist with stocks. I test for a home country bias using a dummy variableHOME CTRY which equals zero if all teams/players are from the same country and one otherwise. Sportand Year dummy variables, which equal 1 if an observation pertains to a given sport or year and zerootherwise, are also included.

As mentioned earlier, there is skewness in the DURATION variable. To ensure that this is not affectingmy regression results I follow the approach adopted by Allayannis and Weston (2001) and many otherresearchers, and take the natural logarithm of this variable before using it in my regression analysis.The results presented in Table 2 have LN(DURATION) as the dependant variable in each instance anddifferent combinations of control variables. White (1980) heteroskedasticity adjusted standard errorsare used in each instance. Variables that are statistically significant at the 10% level or higher are inbold. The equation 1 results indicate that there is a positive relation between the length of time anarbitrage opportunity lasts for and the number of event outcomes. Three-outcome sports that requirethree sets of odds to be compared lead to arbitrage opportunities that are more difficult to find sothese opportunities last longer.

This result is robust to the inclusion of a range of different control variables. The relation betweenDURATION and bookmaker credit risk is mixed. Arbitrage opportunities involving bookmakers fromstrong regulation countries last longer, while arbitrage opportunities involving listed bookmakers andthose belonging to IBAS are removed more quickly. Arbitrage opportunities involving teams from the

6 Tier 2 is “assigned to jurisdictions offering a good combination between a stable economical and political environment anda regulatory framework setting out high standards to protect bettors’ interests. Tier 3 is assigned to the jurisdictions that, evenin presence of a stable economical and political environment, are lacking one or more of the following characteristics: propergovernments’ controls, strong gaming authorities or commissions, stringent licensing requirements, therefore transferring toomany risks to bettors” (http://www.bookmakersreview.com/Jurisdictions/).

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 925

same country last longer. There is evidence of a negative relation between the profits on offer from anyparticular arbitrage opportunity and the length of time the opportunity last for. This is expected as it islogical that opportunities involving larger profits are exploited more quickly by arbitrageurs. There isevidence of different DURATIONs across different sports, which is unsurprising given that some sportshave more two-outcome events and others have more three-outcome events. DURATIONs are lower,on average, in 2005 than in 2003 and 2004.

Fifty bookmakers are consistently tracked by http://www.sportsarbitrageworld.com over the 3-yearperiod of this study. However, there is wide variation in the number of times one of these bookmakersposted an odd that is sufficiently different from the rest of the market to create an arbitrage opportu-nity. One bookmaker posted only one such odd, while another posted 784 such odds. To determine ifthere are different characteristics across the odds quoted by bookmakers involved in a few and manyarbitrage opportunities the 50 bookmakers are sorted according to the number of arbitrage opportu-nities they create. The top and bottom 20% (10) bookmakers are then identified. A dummy variable,LOW HIGH, which equals zero if the bookmaker is in the top 10 bookmakers (20%) based on the totalnumber of arbitrage opportunities created (i.e. those that are relatively easy to find) and one if thereare in the bottom 10 (20%) (i.e. those that are relatively difficult to find).

Differences in the length of time arbitrage opportunities last at these bookmakers can be used togive added insight into the relationship between the costs involved in finding arbitrage opportunitiesand how long they last. An arbitrageur with limited time has to decide which bookmaker odds to checkfirst and it is rational for them to focus on those where there is the greatest likelihood of finding anarbitrage opportunity. From this perspective the opportunity cost of searching the odds of bookmakerswhere few arbitrage opportunities are present are higher than those faced by an arbitrageur searchingthe odds of those where numerous opportunities are likely to be present.7

The results presented in Table 3 reveal the relationship between the DURATION and the numberof opportunities a bookmaker generates. The results pertain to the subset of bookmakers that arein the top or bottom 20% based on opportunities to allow the creation of the LOW HIGH dummyvariable. White (1980) heteroskedasticity adjusted standard errors are used in each instance. Thereis a positive relation between the length of time arbitrage opportunities exist for and the LOW HIGHvariable. Opportunities generated by bookmakers in the bottom 20% of opportunities that involve alarger opportunity cost last for longer. This result is robust to the inclusion of the control variablesused in Table 2. These control variables have them same sign in this subset of data as they do in theentire data with the exception of PUBLIC which has a negative relation.

While the length of time that arbitrage opportunities persist for is the major focus of this paper, Ibriefly consider another dimension of arbitrage in sports betting markets, namely the profits on offer.The regression results presented in Table 4 have PROFIT as the dependant variable. As with the DURA-TION regressions, I attempt to minimise the impact of skewness on my results by taking the naturallogarithm of this variable before using it in my regression analysis. White (1980) heteroskedasticityadjusted standard errors are used in each instance.

The results presented in Table 4 indicate that there is a positive relation between PROFIT and thenumber of event outcomes involved in an arbitrage opportunity. This indicates that while opportunitiesinvolving three-outcome sports are more difficult to find, they also offer large profits on average. Thereis no evidence that the profits on offer are compensation for credit risk. The coefficients of CTRY RISK,OTHER REG, and PUBLIC are negative which given how these are specified (dummy variables whichequal zero for low risk and one for high risk) indicates that PROFIT is, on average, higher when the riskof default is lower. PROFIT was higher in 2003 than it was in 2004 or 2005.

A key difference between Internet sports betting markets and financial markets is the lack of depthin sports betting markets. Internet bookmakers have bet maximums, which preclude placing verylarge bets on any one contest. These maximums are typically equivalent to US$2000. While this is

7 It might appear that this is picking up holding costs on the basis that there is a higher opportunity cost of having moneysitting with a bookmaker that does not generate many opportunities. I propose this is not the case as such funds could still beapplied to an arbitrage opportunity as the “market odds”. Each opportunity typically involves one company posting odds out ofline with the rest of the bookmakers in the sample.

926 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

Table 3DURATION regression results including LOW HIGH variable.

1 2 3 4 5 6

Intercept 2.709 2.058 2.931 2.058 2.214 2.514LOW HIGH 0.544 0.442 0.298 0.482 0.436 0.436EVT OUT 0.884 1.297 −0.140 1.080 1.152 1.180CTRY RISK −0.334 −0.288 −0.252 −0.301 −0.219HOME CTRY −0.124 −0.369 −0.510 −0.486 −0.569OTHER REG 0.028 −0.002 −0.038 −0.094 −0.062PUBLIC −0.097 −0.083 −0.078 −0.138 −0.127PROFIT −0.224 −0.219 −0.214 −0.190 −0.237Cricket 0.253Darts 0.133F1 1.379Golf −0.952MLB 1.195Nascar 1.810NBA −0.874NFL −0.270NHL −0.343Rugby 0.076Snooker −0.112Soccer 0.734Tennis −0.9292003 0.4082004 0.7242005 −0.776

Adj. R2 0.053 0.106 0.112 0.080 0.108 0.137

The data are sourced from http://www.sportsarbitrageworld.com, bookmaker websites, Bookmakers Review(http://www.bookmakersreview.com), and the Independent Betting Arbitration Service (http://www.ibas-uk.com). DURATION,which is the number of minutes it takes for an arbitrage opportunity to be removed, is the dependent variable in each instance.These results are for the subset of bookmakers that are in the top or bottom 20% based on opportunities created. LOW HIGHis a dummy variable that equals zero (one) if the bookmaker generating an arbitrage opportunity is in the top 10 (bottom)bookmakers (20%) based on the total number of arbitrage opportunities created. EVT OUT is a dummy variable that equalszero if there are two possible outcomes involved in an opportunity and one if there are three possible outcomes. CTRY RISK isa dummy variable that equals zero if all bookmakers are from a strongly regulated country and one if one or all bookmakersare from a weakly regulated country. PUBLIC is a dummy variable that equals zero if all bookmakers are public companies andone if one or all are not. OTHER REG is a dummy variable that equals zero if all bookmakers are members of IBAS and one if oneor all bookmakers are not members. HOME CTRY is a dummy variable that equals zero if all teams/players are from the samecountry and one otherwise. PROFIT is the gross profit on offer expressed as a percentage. Sport and Year dummy variables arealso included. All regressions are estimated using White (1980) heteroskedasticity adjusted standard errors. Coefficients thatare statistically significant at the 10% level or higher are highlighted in bold.

obviously quite different to financial markets, I propose that this does not affect my conclusions aboutthe link between the difficultly in exploiting mispricing and how long the mispricing persists for.Firstly, maximum bet sizes are an important element of bookmaker marketing so they tend to be verysimilar across all bookmakers in my sample. Secondly, my key conclusions are based on differences inDURATION between two- and three-outcome events, which are both offered by all bookmakers in mysample.

While it is not possible to directly test, I propose that the traditional explanations for arbitrageopportunities are unlikely to be driving the opportunities in these data. Fundamental risk, as describedby Barberis and Thaler (2002), is non-existent in sports betting arbitrage as the odds offered by differentbookmakers are perfect substitutes for each other. The short time frame between placing an arbitrageand the sports event taking place means that noise trader risk (risk that the mispricing being exploitedby the arbitrageur worsens in the short run, forcing arbitrageurs to liquidate their positions earlyresulting in losses) is also not a big factor in sports betting arbitrage.

The fact sports betting arbitrage opportunities are removed with a median time of 15.4 min ratherthan persisting for the entire duration leading up the game commencement suggests implemen-tation costs are not the explanation. Anyone wishing to pursue sports betting arbitrage needs to

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 927

Table 4PROFIT regression results.

1 2 3 4 5 6 7

Intercept −4.079 −3.924 −3.959 −3.749 −3.966 −3.919 −3.884EVT OUT 0.115 0.090 0.134 0.045 0.093 0.088 0.098CTRY RISK −0.048 −0.045 −0.040 −0.037 −0.048 −0.041HOME CTRY 0.079 0.016 −0.074 0.067 0.078 0.074OTHER REG −0.106 −0.094 −0.083 −0.103 −0.104 −0.107PUBLIC −0.036 −0.033 −0.029 −0.035 −0.034 −0.041Cricket 0.292Darts 0.332F1 0.299Golf −0.013MLB 0.195Nascar 0.221NBA −0.271NFL −0.340NHL −0.128Rugby −0.126Snooker 0.011Soccer −0.161Tennis −0.2232003 0.1302004 −0.0322005 −0.075

Adj. R2 0.005 0.014 0.030 0.035 0.025 0.015 0.0189

The data are sourced from http://www.sportsarbitrageworld.com, bookmaker websites, Bookmakers Review(http://www.bookmakersreview.com), and the Independent Betting Arbitration Service (http://www.ibas-uk.com). Theseresults are derived from the entire sample. PROFIT, which is the gross profit in percentage terms, is the dependent variable ineach instance. EVT OUT is a dummy variable that equals zero if there are two possible outcomes involved in an opportunityand one if there are three possible outcomes. CTRY RISK is a dummy variable that equals zero if all bookmakers are from astrongly regulated country and one if one or all bookmakers are from a weakly regulated country. PUBLIC is a dummy variablethat equals zero if all bookmakers are public companies and one if one or all are not. OTHER REG is a dummy variable thatequals zero if all bookmakers are members of IBAS and one if one or all bookmakers are not members. HOME CTRY is a dummyvariable that equals zero if all teams/players are from the same country and one otherwise. Sport and Year dummy variablesare also included. All regressions are estimated using White (1980) heteroskedasticity adjusted standard errors. Coefficientsthat are statistically significant at the 10% level or higher are highlighted in bold.

open accounts with a range of bookmakers (http://www.sportsarbitrageworld.com advise that 20is a good number). Money can be deposited with and withdrawn from bookmakers using creditcards and online banks like NETeller. A fee of between 1% and 3% is incurred on credit carddeposits, however deposits via NETeller incur no fees. Bookmakers often offer a deposit bonus ofup to 10% of the funds deposited, so an arbitrageur’s account generally has a higher balance (afterthe deposit fees have been subtracted and deposit bonus has been added) than the amount theydeposited. Bookmakers offer accounts denominated in a wide range of currencies so it is pos-sible to remove currency risk (see http://www.sportsarbitrageworld.com for more details on theabove). I seek to provide further evidence that transactions costs do not have a major bearing onthe results presented by generating results based on a database that excludes all PROFIT observa-tions that are less than the lower quartile PROFIT of 0.0151. It is these arbitrage opportunities, whichgenerate lower profits that are most likely to not be worth pursuing if transaction costs are anissue.

The results present in Table 5 indicate that the positive relation between DURATION and EVT OUTdocumented for the entire data also exists in the high profit subset. This indicates that the finding ofarbitrage opportunities that are more difficult to find (i.e. those that require the comparison of threesets of odds) lasting for longer is not being driven by arbitrage opportunities that have the lowest profits.Similarly, the finding that arbitrage opportunities last for longer when they are created by bookmakerswho only post odds that generate arbitrage opportunities relatively infrequently is also robust to theexclusion of arbitrage opportunities with lower profits. Finally, the finding of more profitable arbitrage

928 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

Table 5Robustness checks on high profit subsets.

1 2 3

Dependent variable DURATION DURATION PROFIT

Intercept 2.720 2.983 −3.761LOW HIGH 0.372EVT OUT 0.844 1.078 0.047CTRY RISK −0.175 −0.243 −0.031HOME CTRY −0.151 −0.575 0.067OTHER REG 0.209 −0.011 −0.124PUBLIC 0.100 −0.092 −0.016

Adj. R2 0.042 0.062 0.012

The data are sourced from http://www.sportsarbitrageworld.com, bookmaker websites, Bookmakers Review(http://www.bookmakersreview.com), and the Independent Betting Arbitration Service (http://www.ibas-uk.com). Eachregression is based on data that excludes observations that generate a PROFIT that is lower than the lower quartile PROFIT of0.0151. LOW HIGH is a dummy variable that equals zero (one) if the bookmaker generating an arbitrage opportunity is in thetop 10 (bottom) bookmakers (20%) based on the total number of arbitrage opportunities created. EVT OUT is a dummy variablethat equals zero if there are two possible outcomes involved in an opportunity and one if there are three possible outcomes.CTRY RISK is a dummy variable that equals zero if all bookmakers are from a strongly regulated country and one if one or allbookmakers are from a weakly regulated country. PUBLIC is a dummy variable that equals zero if all bookmakers are publiccompanies and one if one or all are not. OTHER REG is a dummy variable that equals zero if all bookmakers are members ofIBAS and one if one or all bookmakers are not members. HOME CTRY is a dummy variable that equals zero if all teams/playersare from the same country and one otherwise. All regressions are estimated using White (1980) heteroskedasticity adjustedstandard errors. Coefficients that are statistically significant at the 10% level or higher are highlighted in bold.

opportunities being available in three- rather than two-outcome sports is also robust to the exclusionof the least profitable arbitrage opportunities.

Bookmakers do not pay interest on funds deposited with them so an arbitrageur incurs a holdingcost (in the form of foregone interest) on money deposited with each bookmaker. The higher therequired rate of return on an arbitrageur’s money, the greater the number of bookmakers an arbitrageurdeposits money with, and the larger the deposit with each bookmaker the larger the holding costincurred. However, the fact that these opportunities are removed reasonably quickly suggests thatholding costs are not at a level that removes the incentive to exploit them. This fact is borne outby a simple example. Assume an arbitrageur has a required return of 10% p.a. Assume further thatthey decide to allocate US$100,000 to this activity, spread across 50 bookmakers. Assuming that theyplace the maximum “bet” possible each time of US$2000 they will have US$4000 at stake on eachtwo-outcome event. If they earn the average PROFIT of 2% they will receive US$80 per arbitrage. Tobreak even based on their required return of US$10,000 (US$100,000 × 10%) they will therefore needto conduct 2.5 arbitrages per week or 125 per year.

5. Conclusions

Security prices fully reflect all available information in an efficient market but in reality prices donot always react instantly to new information. Researchers such as Merton (1987) suggest that thetime between an attractive investment opportunity being created and removed can be considerable.I consider the speed at which prices converge to efficient levels by examining how long it takes forarbitrage opportunities to be removed in the Internet sports betting market. This environment has theadvantage of allowing a test that is free of the joint hypothesis problem. No model of expected returnsis required. Sport betting markets have several other attractive features. There are numerous price(or odd) quotations on the same event which generate arbitrage opportunities and these arbitrageopportunities can be executed with minimal cost via the Internet.

I show divergent price quotations on the same sporting event allow median arbitrage profits ofjust over 1.5% per trade to be made. These opportunities do not last for long. Their median durationis 15 min and 75% of all opportunities are removed within 50 min. I also find that opportunities thatare more difficult to find last for longer. Taken together, my results provide support for the Merton

B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930 929

(1987) proposition that attractive investment opportunities are not removed instantaneously. Investorstake time to locate and exploit attractive investment opportunities even in a market setting wherefundamental risk, noise trader risk, transactions costs, and short-selling constraints do not impede thecapturing of arbitrage opportunities. My finding that arbitrage opportunities that are more difficult tofind last for longer is also consistent with the propositions of Merton (1987).

Acknowledgements

I would like to thank Jason Thompson of http://www.sportsarbitrageworld.com (formerlywww.zero-risk-arbitrage.com) for kindly providing the data. The views expressed in this paper arenot necessarily those of http://www.sportsarbitrageworld.com. I would also like to thank seminarparticipants at the 2005 Western Finance Association Annual Meeting, the 2006 Asian FA/FMA annualmeeting, the 2007 New Zealand Finance Colloquium, and Victoria University, and Hamish Anderson,Jonathan Batten, Henk Berkman, Glenn Boyle, Charles Corrado, Toby Daglish, Nont Dhiensiri, JohnGandar, Pinghsun Huang, Ben Jacobsen, Stephen Keef, Martin Lally, Chris Malone, Lyndon Moore, JohnPowell, Larry Rose, Allan Smee, Fei Wu, Martin Young, Eric Zitzewitz, and Rick Zuber for valuablecomments. This paper was previously distributed under the names “Arbitrage Opportunities in SportsBetting Markets”, “The Profitability and Persistence of Internet Sports Betting Arbitrage Strategies”,and “The Impact of Search and Holding Costs on Persistent Mispricing”.

Appendix A. Appendix A

This appendix contains an example of how arbitrage profits are calculated. The interested readershould refer to http://www.sportsarbitrageworld.com for more information.

On the 28th of August 2003 the following odds were on offer for a Major League Baseball (MLB)match between the Boston Red Sox and Oakland Athletics:

• Boston Red Sox to Win at Stan James at 1.83.• Oakland Athletics to Win at ToteXpress at 2.38.

To determine if an arbitrage opportunity exists, the arbitrageur should calculate:

TO =n∑

i=1

1Xi

= 11.83

+ 12.38

TO = 0.9666.TO is less than 1 so an arbitrage opportunity does exist.To receive guaranteed PROFIT regardless of the outcome the arbitrageur must bet

(1/1.83/(1/1.83 + 1/2.38)) or 56.53% his/her total bet on Boston Red Sox and (1/2.38/(1/1.83 + 1/2.38))or 43.47% on Oakland Athletics. Assuming the arbitrageur has $966.60 to bet, s/he should bet $546.40on Boston Red Sox to win at odds of $1.83 at Stan James and $420.20 on Oakland Athletics to win atodds of $2.38 at ToteXpress.

Based on these bets the PROFIT per $1 bet is (1 − 0.9666)/0.9666 = 0.0346.In this situation, the arbitrageur earns $0.0346 for every $1 bet regardless of the outcome of the

event. The arbitrageur commits $966.60 to the event so s/he receives $33.44.

References

Allayannis, G., & Weston, J. (2001). The use of foreign currency derivatives and firm market value. The Review of Financial Studies,14(1), 243–276.

Avery, C., & Chevalier, J. (1999). Identifying investor sentiment from price paths, the case of football betting. Journal of Business,72, 607–636.

Barberis, N., Thaler, R. (2002). A survey of behavioural finance, In G. Constantinides, M. Harris, R. Stulz (Eds.), Handbook of theeconomics of finance.

Barberis, N., Shleifer, A., & Vishny, R. (1998). A model of investor sentiment. Journal of Financial Economics, 49, 307–343.Busse, J., & Green, T. (2002). Market efficiency in real time. Journal of Financial Economics, 65, 415–437.

930 B.R. Marshall / The Quarterly Review of Economics and Finance 49 (2009) 917–930

Chan, W. (2003). Stock price reaction to news and no-news, drift and reversal after headlines. Journal of Financial Economics,70(2), 223–260.

Chordia, T., Roll, R., & Subrahmanyam, A. (2005). Evidence on the speed of convergence to market efficiency. Journal of FinancialEconomics, 76, 271–292.

Dammon, R., Dunn, K., & Spatt, C. (1993). The relative pricing of high-yield debt, the case of RJR Nabisco Holding CapitalCorporation. American Economic Review, 83(5), 1090–1111.

De Long, J., Shleifer, A., Summers, L., & Waldmann, R. (1990). Noise trader risk in financial markets. Journal of Political Economy,98, 703–738.

Durham, G., Hertzel, M., & Martin, J. (2005). The market impact of trends and sequences in performance, new evidence. Journalof Finance, 60(5), 2551–2569.

Edelman, D., & O’Brian, N. (2004). Tote arbitrage and lock opportunities in racetrack betting. The European Journal of Finance, 10,370–378.

Fama, E. (1970). Efficient capital markets, a review of theory and empirical work. Journal of Finance, 25, 383–417.Fama, E. (1998). Market efficiency, long-term returns, and behavioural finance. Journal of Financial Economics, 49, 283–306.Froot, K., & Dabora, E. (1999). Are stock prices affected by the location of trade? Journal of Financial Economics, 53, 189–216.Gandar, J., Dare, W., Brown, C., & Zuber, R. (1998). Informed traders and price variations in the netting market for professional

basketball games. Journal of Finance, 53(1), 385–386.Harris, M., & Raviv, A. (1993). Differences of opinion make a horse race. The Review of Financial Studies, 6(3), 473–506.Hausch, D., & Ziemba, W. (1990). Arbitrage strategies for cross-track betting on major horse races. Journal of Business, 63, 61–78.Heath, C., & Tversky, A. (1991). Preference and belief, ambiguity and competence in choice under uncertainty. Journal of Risk and

Uncertainty, 4, 5–28.Huberman, G., & Regev, T. (2001). Contagious speculation and a cure for cancer, a nonevent that made stock prices soar. Journal

of Finance, 56(1), 387–396.Independent Betting Arbitration Service (2006). www.ibas-uk.com.Jones, C., & Lamont, O. (2002). Short-sale constraints and stock returns. Journal of Financial Economics, 66(2–3), 207–239.Kang, J.-K., & Stulz, R. (1997). Why is there a home bias? An analysis of foreign portfolio equity ownership in Japan. Journal of

Financial Economics, 43, 3–28.Kuypers, T. (2000). Information and efficiency. An empirical study of a fixed odds market. Applied Economics, 32(11), 1353–1363.Lamont, O., & Thaler, R. (2003). Can the market add and subtract? Mispricing in tech stock carve-outs. Journal of Political Economy,

1112, 227–268.Lane, D., & Ziemba, W. (2004). Jai Alai arbitrage strategies. The European Journal of Finance, 10, 353–369.Maloney, M., & Mulherin, J. (2003). The complexity of price discovery in an efficient market, the stock market reaction to the

Challenger crash. Journal of Corporate Finance, 9, 453–479.Merton, R. (1987). A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42, 483–510.Ofek, E., Richardson, M., & Whitelaw, R. (2004). Limited arbitrage and short sales restrictions, evidence from the options markets.

Journal of Financial Economics, 74(2), 305–342.Paton, D., & Vaughan Williams, L. (2005). Forecasting outcomes in spread betting markets: Can bettors use ‘Quarbs’ to beat the

book? Journal of Forecasting, 24, 139–154.Rashes, M. (2001). Massively confused investors making conspicuously ignorant choices (MCI-MCIC). Journal of Finance, 56(5),

1911–1927.Rose, I. N., 1999. The Law of Internet Gambling. I Nelson Rose.Salop, S., & Stiglitz, J. (1977). Bargains and ripoffs, a model of monopolistically competitive price dispersion. Review of Economic

Studies, 44, 493–510.Shleifer, A., & Vishny, R. (1997). The limits of arbitrage. Journal of Finance, 52, 35–55.Sinclair, S. (1998). Casino gambling and the Internet. New York: Christiansen/Cummings Associates.Smith, M., Paton, D., & Vaughan Williams, L. (2006). Market efficiency in person-to-person betting. Economica, 73, 673–689.Strumpf, K. (2003). Illegal sports bookmakers, Unpublished Working Paper.Varian, H. (1980). A model of sales. American Economic Review, 70(4), 651–659.Vaughan Williams, L. (1990). Information efficiency in betting markets: A survey. Bulletin of Economic Research, 54(1), 307–337.Vecer, J., Ichiba, I., Laudanovic, M. (2006). Parallels between betting contracts and credit derivatives. Working Paper, Columbia

University.White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econo-

metrica, 48, 817–838.