Longshots, Overconfidence and Efficiency. on the Iowa Electronic Market *

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1 Longshos, Overconfidence and Efficiency on he Iowa Elecronic Marke * Joyce E. Berg and Thomas A. Riez Tippie College of Business Universiy of Iowa Iowa Ciy, Iowa January 2002 * We hank he faculy and saff who run he Iowa Elecronic Markes. For helpful commens and suggesions, we hank Mahew Bille, Rober Forsyhe, Forres Nelson, George Neumann, Toni Whied and seminar paricipans a Tulane Universiy.

2 Longshos, Overconfidence and Efficiency on he Iowa Elecronic Marke Absrac A basic proposiion of behavioral finance is ha individual decision-making biases will manifes hemselves in observable financial marke phenomena. While his may help explain financial marke anomalies, i is no necessarily he case. Here, using Iowa Elecronic Marke (IEM) daa, we ask wheher he longsho bias affecs marke prices. We also ask wheher rader overconfidence affecs prices. In conex, hese give opposing predicions. The IEM is ideal for answering hese quesions because i mixes many desirable feaures from racerack being markes wih a closer parallel o naurally occurring financial markes. While he longsho bias affecs many spors being markes robusly, no such bias appears here. Nor does overconfidence influence prices a shor horizons. If here is a bias, i resuls from overconfiden raders a long horizons. While he markes incorporae informaion efficienly a shor horizons, non-marke daa indicaes some long-horizon inefficiency. When markes appear inefficien, we calculae Sharpe raios for saic rading sraegies and documen reurns for dynamic rading sraegies o show he economic conen of he inefficiencies.

3 Longshos, Overconfidence and Efficiency on he Iowa Elecronic Marke The Longsho Bias is commonly observed in being markes. 1 A he racerack, beors are willing o pay more for longsho bes (hose ha are unlikely o pay off) han hey are acually worh. This resuls in relaively large negaive average reurns for longsho bes. A he same ime, beors are no willing o pay he full value for favorie bes (hose ha are mos likely o payoff). This resuls in relaively small negaive (because of he rack ake ) or, someimes, posiive average reurns for favorie bes. These biases seem quie robus (see Ziemba and Hausch, 1986). Thaler and Ziemba (1988) discuss exacly how he longsho bias resuls in inefficiencies ha can be exploied profiably. The implicaion is ha he racerack being marke is inefficien. If invesors behave similarly in financial markes, hen financial markes should be inefficien as well. Furher, he longsho bias could explain some financial marke anomalies. For example, if he longsho bias resuls from over-esimaing low-probabiliy evens (as Kahneman and Tversky, 1979 sugges) and his carries over o financial markes, hen markes will be overly sensiive o low-probabiliy evens. Riez (1988) shows ha lowprobabiliy marke crashes can help explain he equiy risk premium puzzle (Mehra and Presco, 1985). If invesors overesimae he chances of unlikely marke crashes, hen he puzzle would be ha much easier o explain. Furher, if raders over-reac o small changes in he perceived probabiliies of crashes, hen he expeced values of socks will reac more han hey should o such changes in probabiliies wihou correspondingly large changes in acual fuure oucomes (e.g., dividends). This may help explain he excess volailiy puzzle (Shiller, 1981). While hese may be analizing explanaions for financial marke anomalies, hey rely on he assumpion ha biases and behaviors from one conex (being markes) will carry over o anoher conex (financial markes) and ha hey will have robus, observable effecs in he second conex. However, here are several reasons he bias may no affec financial markes. Firs, convenional wisdom suggess ha a few raional raders will arbirage biases ou of exisence in markes. This is a debaable issue because, if he bias arises from a pervasive cause, i may be impervious o arbirage. For example, all raders may be affeced by prospec heory s over-weighing of low probabiliy evens (Kahneman and Tversky, 1979). If so, none of he raders will recognize he bias in prices and, hence, none will drive prices o efficien levels. Even if a few do recognize he bias, wheher hey will have he abiliy or incenive o 1

4 drive markes o efficien levels is an open quesion. Grossman and Sigliz (1980) sugges ha raders will never wan o drive ou all arbirage opporuniies because o do so would eliminae all profis for informaion collecion and arbirage aciviies. Second, he conex may influence wheher anomalies generalize o financial markes. Again, he issue is debaable. Slovic (1972) argues ha conex may affec observed risk preferences. Cosmides (1989) argues ha conex may influence he incidence of a differen bias (he confirmaion bias ). Because a financial marke is a differen conex han a being marke, conex effecs may reinforce, weaken or eliminae he longsho bias. Third, he marke srucure may reduce or reverse he bias. While i is no apparen wha he effec will be in conex, some evidence suggess ha srucure maers. Woodland and Woodland (1994) sugges ha a difference in srucure (he abiliy o be agains eams) reverses he bias in baseball being. Furher, while Gandar, Zuber, O Brien and Russo (1988) ge mixed resuls, Gray and Gray (1997) show ha being home-eam underdogs in fooball being markes can have posiive profis. This could be inerpreed as a parial reversal of he longsho bias in hese differenly srucured markes (poin-spreads, insead of odds, adus o guaranee he bookie s ake). Because financial markes differ in srucure as well, one migh expec srucural differences o affec how biases manifes hemselves. For example, Thaler and Ziemba (1988) cie he inabiliy o shor racing bes as a possible conribuing facor o he longsho bias. Since raders can shor sell in ypical financial markes, his srucural difference may miigae or eliminae he manifesaion of he bias in financial markes. Fourh, evidence suggess ha he exisence of a wo-sided dynamic marke iself will miigae he effecs of irraional or biased raders. Gode and Sunder (1993) show ha markes do no necessarily need o be populaed by perfecly raional, opimizing raders o observe prices and allocaions consisen wih efficien markes. Insead, hey show ha he marke iself can drive efficien oucomes even when populaed wih zero-inelligence robo raders. Forsyhe, Nelson, Neuman and Wrigh (1992) and Forsyhe, Ross and Riez (1999) show ha some biases commonly observed in poliical science research (he false consensus effec and he assimilaion conras effec) affec raders in poliical markes on he Iowa Elecronic Markes. 2 However, in hese markes, more raional raders se marke prices and, hrough hem, he effecs of he biases are removed from marke prices. Thus, significan numbers of irraional or biased raders will no necessarily impac marke phenomena. Wheher i does here is an empirical issue. Here, we ask wheher he longsho bias carries over o very simple financial markes in which raders buy and sell asses ha closely resemble bes purchased in being markes. Do raders appear o over-value asses ha 2

5 will pay off wih low probabiliy and under-value asses ha will pay off wih high probabiliy? This would mirror he longsho bias in hese markes and would be consisen wih over-weighing low-probabiliy evens. Alernaively, does he bias disappear or even reverse iself? A reverse longsho bias would mean ha prices of asses ha pay off wih low probabiliy will fall even lower han he obecive probabiliies would sugges while asses ha pay off wih high probabiliy would have prices even higher han he obecive probabiliies. Such an effec could resul from raders overconfidence in heir own assessmens. For example, if raders receive bad news abou a paricular asse s chances of payoff, hey should price his asse lower. If hey overreac o his news or are overconfiden in heir inerpreaion of i, hey will depress he price even furher. 3 Thus, our analysis is a es beween unbiased pricing and wo poenial biases, one reflecing over-weighing of low probabiliy evens ha mirrors he longsho bias and one reflecing over-weighing of high probabiliy evens ha consisen wih an overconfidence bias. Wheher longsho or overconfidence biases affec prices is very difficul o answer using naurally occurring financial marke daa. 4 Unlike a being marke, here is no definiive poin in ime when he value of a sock is known wih cerainy. This makes i difficul o deermine wheher prices a any poin in ime are acually biased. In addiion, socks, opions and fuures are all very complex bes. The value of a sock should depend on he disribuion of dividends over he infinie horizon. The value of an index depends on he values of is componen socks. The values of opions and fuures, in urn, depend on he fuure disribuions of he values for underlying socks or indices. The complexiy of hese bes would make i difficul o deec he effecs of simple biases like he longsho bias even if we knew he rue values of he underlying asses. Furher, repeaed observaions under similar condiions give being markes a definie edge in esing. Bu, as discussed above, being markes have heir own significan drawbacks and resuls may no generalize o financial markes. Thus, neiher being markes nor naurally occurring financial markes are he ideal esing grounds o deermine wheher hese biases affec financial markes. Here, we use he Iowa Elecronic Markes (IEM) o es for longsho bias effecs in real-money, real-ime, repeaed and simple financial markes. There are many advanages of using he IEM. Firs and foremos, i is a real financial marke in which raders buy and sell asses on heir own accoun, bearing he real-money risks and reaping he real-money rewards of heir aciviy. IEM paricipans rade simple coningen claim asses (called conracs ) ha payoff $1 in one sae of he world and $0 oherwise. These conracs parallel he simpliciy of racerack bes (which eiher pay off or no depending on he oucome of he race). IEM conracs liquidae a pre-deermined daes 3

6 wih no uncerainy abou heir value a ha ime and he marke repeas iself under essenially idenical condiions monhly. Finally, he srucure of he marke and he conracs raded imply ha he price of a paricular conrac a any poin in ime should equal he marke consensus probabiliy ha he conrac will pay off $1 on he liquidaion dae. Thus, prices can be compared o obecive esimaes of payoff probabiliies (from mulinomial logi models) o deermine wheher biases exis. A a given poin in ime, prices should be sufficien saisics for esimaing payoff probabiliies. This makes esing for efficiency simple. If adding pas price informaion or ouside informaion o IEM price informaion increases he explanaory power of logi models in predicing payoffs, hen he markes are no efficien. While hese feaures make using he IEM well suied for sudying he longsho bias because of similariies beween IEM conracs and racerack bes, many srucural feaures of he IEM more closely resemble naurally occurring financial markes han raceracks. The IEM runs as a wo-sided marke wih an inermediae horizon (up o 5 weeks). News abou relaive payoff probabiliies is revealed during rading on he IEM. Traders can synheically shor sell in he IEM. 5 Because IEM raders know he price a he ime hey rade, hey effecively know he odds a he ime hey place heir bes, in conras o US raceracks. IEM raders can reverse heir posiions a any ime by underaking opposie ransacions a marke prices. All of his rading can be done wihou paying he rack s ake wih each posiion change. Insead, raders pay he bid/ask spread as hey would in any oher financial marke. Because hese feaures parallel naurally occurring financial marke, he IEM will help deermine wheher we migh expec he longsho bias o generalize o financial markes in a sraighforward manner. Our resuls show he dangers of simple generalizaion from one conex and marke srucure o anoher. The longsho bias no only disappears, i reverses iself. Asue raders could have made significan profis rading agains he resuling overconfidence bias. In he conclusions, we discuss wheher his resul migh have been prediced given a common explanaion of he longsho bias and differences in srucure beween being and financial markes. I appears so, bu a final udgmen mus awai furher evidence. In he nex secion, we discuss he IEM in more deail and show how biases would manifes hemselves in hese markes. Then, we describe he esing procedure in deail, give he resuls and end wih conclusions and discussion. 4

7 I. Biases, Efficiency and Marke Price Predicions A. The Iowa Elecronic Markes and Conracs The Iowa Elecronic Markes (IEM) are real-money, real-ime, fuures markes operaed as a no-for-profi eaching and research ool by he Tippie College of Business a he Universiy of Iowa. Relaive o ypical experimenal markes, hey are large scale and long duraion. The markes discussed here have housands of regisered raders and, ofen, hundreds or more acive ones. They run from four o five weeks and have liquidaed and reiniialized monhly for more han five years. The IEM also differs from ypical experimenal markes in ha he raders buy and sell asses on heir own accoun, bearing he real-money risks and reaping he real-money rewards of heir aciviy. 6 The IEM marke srucure closely parallels naurally occurring financial markes. I operaes as a coninuous elecronic double aucion ha raders access hrough he Inerne. Traders can place boh limi and marke orders. Ousanding bids and asks are mainained in price and ime ordered queues, which funcion as coninuous elecronic limi order books wih he bes price in each queue made public. The markes discussed here are he Microsof Price Level and Compuer Indusry Reurns Markes. 7 Prospecuses for hese markes appear in he appendices. We describe hem briefly here. Each marke runs eiher four or five weeks (from he Monday afer he hird Friday of one monh o he Monday afer he hird Friday of he nex monh). 8 Each marke conains a complee slae of conracs, one of which will liquidae a $1 depending on he sae of he world on he liquidaion dae. All oher conracs in he marke liquidae a a value of $0. Thus, all conracs are simple sae-coningen claims, similar o bes ha eiher pay off or no, depending on he sae of he world. In he Microsof Price Level Marke, a slae consiss of wo conracs. One of hese conracs (he H conrac, denoed generically as MSH ) will liquidae a $1 if Microsof s acual sock price closes above a predeermined cuoff value on he hird Friday of he monh. The oher conrac (he L conrac, denoed MSL ) will liquidae a $1 if Microsof s price closes less han or equal o he cuoff. 9 Thus, hese conracs are simple binary opions. (See he prospecus in Appendix I for more deails.) In he Compuer Indusry Reurns Marke, a slae consiss of four conracs. Each conrac corresponds o an underlying securiy (company sock or index). The underlying securiies are Apple Compuer (AAPL), IBM (IBM), Microsof (MSFT) and he Sandard and Poor's 500 Index (SP500). Each conrac will payoff $1 if he 5

8 underlying securiy had he highes reurn from hird Friday o hird Friday. 10 Thus, hese conracs are also simple sae coningen claims, hough somewha more complex han he conracs in he Microsof Price Level Marke. (See he prospecus in Appendix II for more deails.) B. Prices, Predicions and Models In each marke, he complee slae of conracs is a risk-free porfolio. One of he conracs will always liquidae a $1 while he ohers expire worhless. Cash holdings are also risk-free. Boh of hese risk-free asses earn a zero reurn. There are no ransacion fees. Complee slaes can be purchased from or sold o he exchange a any ime for a fixed price of $1. This implies ha he numbers of conracs of each ype in a marke are always he same. Thus, here is no aggregae uncerainy in his marke. Because of hese feaures, conrac prices should always equal expeced values of he conracs regardless of risk preferences and ime remaining o liquidaion. 11 Le p be he price of conrac on dae and q(v = 1 I ): = q be he probabiliy ha conrac will liquidae a $1 T ( V =1) on dae T given informaion available on dae (I ). In heory, we should observe: T ( = 1 I ) $1+ [ 1 q( V = 1 I )] q { 1,2,..., J}, T : p = q V 0 = (1) T where indexes he slae of J conracs ha pay off in differen saes of he world and represens any dae up o he dae T when liquidaion values are deermined. 12 Tesing will be very simple. Firs, following he exising racerack lieraure, we use a simple frequency analysis. Then, we refine and expand he analysis using logi models 13 o esimae he rue probabiliies of $1 liquidaions (i.e., he q s) and see wheher hey deviae sysemaically from marke prices (i.e., he p s). To see how his works, consider he mulinomial logi model: X b e { 1,2,..., J}, T : q = (2) J i Xb e i= 1 where, in addiion o he variables defined above, X is a vecor of independen variables a dae and coefficien vecor for conrac a dae. To idenify he model, J b is arbirarily se o 0 and conrac J becomes he base conrac. 14 probabiliies of all oher conracs are compued relaive o he base conrac as: 6 T b is a Then, he

9 q Xb { 1,2,..., J 1}, T : = e (3) q J Now consider using log raios of conrac prices as independen variables. 15 Since he conrac price should represen he probabiliy ha a conrac will liquidae a $1 condiional on all available informaion, price raios should be sufficien saisics for forecasing probabiliies of payoffs. In paricular, consider using as independen variables: X 1 p = 1,ln,...,ln J p p p J 1 J q q J = e 1 J 1 1, + p J 1, α + + p β ln... β J ln J p p (4), i, If prices do indeed equal probabiliies, hen i should be he case ha α = 0 and β = 1 for all and β = 0 for all i. Only in his case does q = p for all. Furher, if prices incorporae all available informaion abou he probabiliies of payoffs (as efficien markes would sugges), hen, apar from co-lineariy issues, coefficiens on any oher independen variables will be zero. Even if co-lineariy creaes he appearance of significance, adding oher variables should no increase explanaory power of he model. This will serve as he basis for deecing any biases and inefficiencies ha exis. C. Biases, Efficiency and he Logi Model Esimaes If raders are unbiased and he marke is efficien, we should observe esimaes consisen wih α = 0, i, and β = 1 for all and β = 0 for all i in he logi model equaion (4). If we graph he logi model esimaed probabiliies agains prices in his case, we would ge a 45-degree line labeled bea=1 in Figure 1. In he, wo-sae case, a longsho bias would show up if β > 1. This leads o he bea>1 mapping in Figure 1 where prices exceed he probabiliy of payoff for low payoff probabiliies and fall shor of he probabiliy of payoff for high payoff probabiliies. 16,17 Paying oo much for a low-payoff-probabiliy conrac here corresponds o being oo much on he longsho in a horse race. This is consisen wih Kahneman and Tversky's (1979) proposiion from Prospec Theory ha people over-weigh he likelihood of low probabiliy evens. In conras, an overconfidence, bias would show up if β < 1. This leads o he bea<1 mapping in Figure 1 where prices fall below he probabiliy of payoff for low payoff probabiliies and exceed he probabiliy of payoff for high payoff probabiliies. 7

10 This effec, which is he opposie of a longsho bias, can easily resul from raders being overconfiden in heir forecass (e.g., he overconfidence bias of Lichensein, Fischhoff and Phillips, 1982). If he raional probabiliy of payoff is acually 90%, overconfiden raders may assess he probabiliy a an even higher level and be willing o pay, say, 95 cens for he conrac. 18 Thus, esing for he longsho bias and overconfidence will ake a paricularly simple form: run logi models wih logged price raios as he independen variables and check he resuling coefficiens. Tesing for efficiency is also simple. If a conrac's log price raio is sufficien for explaining is own probabiliy of payoff, here should be no difference in explanaory power beween an unresriced logi model and a logi model wih he resricions ha cross-price raio coefficiens are zero ( β i, = 0 i ). If markes are weak-form efficien, adding recen prices or price changes should no increase explanaory power. Finally, if markes are semi-srong-form efficien, adding addiional informaion (e.g., sock marke reurns or prices) should no increase explanaory power. These proposiions can be esed using likelihood raio ess in a series of nesed logi models (hough he quaniy of daa available resrics he amoun of esing ha can be done). We also ask wheher he horizon affecs any biases ha exis. Rubinsein (1985) shows a ime-oexpiraion bias in ou-of-he money call opions. The racerack lieraure suggess ha he smar money is be lae and ha his miigaes he longsho bias somewha lae in he being process (see Thaler and Ziemba, 1988 and Asch and Quand, 1986). This may generalize o financial markes creaing horizon effecs in any biases or inefficiencies ha exis. By looking a differen horizons (numbers of days o liquidaion value deerminaion), we can sudy wheher horizon effecs exis. We use 1 o 21 day horizons o sudy hese issues. 19 D. The Advanages of using he Iowa Elecronic Markes For many reasons he IEM makes for an ideal place o sudy expecaions in financial markes and hese biases in paricular. Some of hese reasons mirror hose cied o usify using racerack daa. For example, similar o being markes, bu in conras o mos naurally occurring financial markes, here exis well defined poins in ime a which he values of IEM conracs are realized wih cerainy. The frequency of his realizaion can be compared o he proeced probabiliy of occurrence given by marke prices a any prior poin in ime. This is a clear advanage over using sock marke reurns because sock values always depend on unknown fuure oucomes. Several disinguishing feaures make he IEM beer han being markes for sudying hese issues. Firs, i is a real-money, wo-sided financial fuures marke. Srucurally, i much more closely resembles naurally 8

11 occurring financial markes and financial markes as modeled in heory. Traders can ake boh sides of bes and unwind bes a any ime as informaion is revealed. Traders self-selec in o or ou of markes a any ime or can be driven ou of he markes hrough bad rading. This resemblance o naurally occurring markes may maer. Some explanaions for he longsho bias cie paricular characerisics of he being marke. For example, Shin (1992) argues ha he longsho bias arises from bookies seing prices o mainain heir ake while recognizing ha knowledgeable insiders place some bes. On he IEM, here are no ransacions coss (no ake for he rack or bookie). Of course, raders who place limi orders in he IEM face adverse selecion as well, bu i should be symmeric and should more closely resemble ypical marke microsrucure heory han racerack being markes. Two differences beween he IEM and racerack being markes lie in he rading/being horizon and informaion flow of IEM markes. Asch and Quand (1986) argue ha lae changes in odds help predic racing oucomes. Thus, he horizon and informaion flow ino he marke may affec he efficiency of he marke and profiabiliy of various sraegies. Bu, analysis from he racerack is limied by he relaively shor being horizon. Similarly, radiional experimenal asse markes las for a few hours a mos, wih rading periods ha ypically las a few minues. The IEM's inermediae marke horizons (four or five weeks for he markes discussed here) address he gap beween he shor-erm prospecs of racerack being or radiional experimens and he infinie horizon of sock markes. Avoiding he valuaion problems caused by he sock marke's infinie horizon, his allows for analysis a various horizons while keeping repeaed observaions. Being markes are evaluaed for efficiency using odds during he being period before he race is run. While he being process aggregaes informaion during he being period, lile news is produced during his ime. Things migh look considerably differen if beors could coninue placing and wihdrawing bes during he race, as news abou acual performance is being produced, evaluaed and incorporaed ino odds. In he sock marke, news is consanly being generaed abou companies and heir prospecs. The marke boh incorporaes news and aggregaes informaion across raders. Paralleling he sock marke, news comes ou during IEM rading abou he likely oucomes. Much is available o all raders, bu subec o inerpreaion. Some may only be known by one or a few raders. All of i should be incorporaed in IEM prices if he marke is efficien. This allows for esing of a much more dynamic ype of informaion efficiency, and one ha more closely resembles naurally occurring financial markes, han being odds allow. Finally, wo oher feaures make esing in he IEM paricularly nice. The bes here are much simpler han many bes in gambling markes and cerainly simpler han he bes implied in mos naurally occurring financial 9

12 markes. There are no paricularly difficul erminologies or convenions o learn. In fac, he IEM is quie ransparen. In addiion, markes are designed so ha risk preferences should no maer. This is ofen a difficuly for radiional experimenal research. Overall, in a relaively simple environmen, he IEM keeps many of he desirable feaures of he racerack being markes for analysis (simple asse srucure and repeiion) while more closely paralleling naurally occurring financial markes (marke srucure and rading mechanics), making for fewer worries abou exernal validiy. II. Tess for Biases and Efficiency A. A Simple Mehod To compare o previous research, we sor he daa ino cells according o observed prices and compare he average price in each cell o he obecive probabiliy deermined by he acual payoff rae wihin he cell. This is analogous o he analysis in much of he racerack lieraure where researchers aggregae bes (conracs) across odds (prices) and compare average bes wihin each cell (average prices) o average payoffs (liquidaion values). Table 1 shows he average price of conracs in $0.20 ranges aggregaing across all conracs and markes a differen horizons (1, 2, 4, 7, 14 and 21 days o liquidaion deerminaion). This is similar o aggregaing ranges of odds across all horses and races in a daa se. The able also shows average payoffs for conracs in each range and he differences beween average payoffs and prices. Finally, he able shows he number of observaions in each range and simple -ess for differences beween payoffs and prices. A longsho bias would resul in significanly higher prices han payoffs for low-priced (longsho) conracs and significanly lower prices han payoffs for highpriced (favorie) conracs. If anyhing, he daa show he opposie. Prices fall significanly below payoffs for conracs falling in he $0.0 o $0.2 range a mos horizons longer han one day. Prices are significanly above payoffs for conracs falling in he $0.8 o $1.0 range a 4- and 14-day horizons. Inermediae conracs appear o be priced efficienly. Table 2, which aggregaes across price quiniles, shows similar, hough slighly weaker, resuls. There are several limiaions inheren in his simple frequency analysis (and similar racerack being analyses). I raises aggregaion issues and is no a paricularly efficien use of he daa. Frequency analysis ignores he inerdependen naure of he conrac payoffs. I fails o ake ino accoun he fac ha only one conrac in a muliple-conrac marke can payoff a $1. Analogously, only one horse can win a race, only wo can show and only hree can place. This creaes a negaive correlaion across oucomes ha can be addressed by logi models (for he 10

13 Microsof marke wih wo conracs) and mulinomial logi models (for he compuer markes wih four conracs each monh). In addiion, analysis of he possible sources of inefficiency and he search for daa ha may provide beer predicions boh require a more deailed analysis han simple frequency analysis. Neverheless, he frequency analysis serves as a quick comparison o he exising racerack lieraure. In spie of weaknesses, is resuls mirror he logi models ha follow, hough he logi models allow much more exensive invesigaion while overcoming he weaknesses discussed here B. Logi Models for he Microsof Price Level Marke For he wo-conrac Microsof Price level marke, he model becomes a simple logi model. I accouns for he perfec negaive correlaion beween he MSH and MSL conracs by recognizing ha he normalized price of he MSL conrac is one minus he price of he MSH conrac and using he logged price raio for analysis. The Model I rows in Table 3 give he resuls of a simple logi model wih he log price raio as he only explanaory variable. Table 3 shows several sample horizons while Figure 2 summarizes esimaed β coefficiens a all horizons. Recall ha, if prices are unbiased esimaes of rue probabiliies of payoffs, hen he coefficien on he log price variable should be 1 and he coefficien on he inercep should be zero. As Figure 2 shows, esimaed slope coefficiens generally fall below one. A one and wo day horizons, his null is no reeced. However, a all horizons of hree days and longer (including he 4, 7, 14 and 21 day sample horizons shown in Table 3), he coefficiens on he logged price raio fall significanly below one (a he 95% level of confidence), indicaing an overconfidence bias. Thus, he resuls from simple logi models mirror he resuls from he simple frequency analysis. Logi models can go beyond simple frequency analysis in esing for efficien markes. If markes are efficien in incorporaing all relevan informaion ino prices, hen adding addiional informaion should no improve he abiliy o predic payoffs. Model II asks wheher adding he mos recen change in log price raios adds o he explanaory power of prices. Asch and Quand (1986) sugges ha lae changes in odds help predic winning frequencies a raceracks. 20 This migh carry over o financial markes if raders over- or under-reac o news, creaing serial correlaions in prices. Likelihood raio ess for Model II agains he (resriced) Model I show ha adding he change in log price raios seldom adds explanaory power. As shown in Figure 2, he only significan likelihood raio saisics (a he 95% level of confidence) are a he 2-, 6- and 20-day horizons. 11

14 Finally, if markes are efficien, hen adding informaion abou he curren Microsof sock price relaive o he cuoff should no increase explanaory power. The raio of he curren Microsof sock price o he cuoff is added as an independen variable in Model III. This represens he percenage change in Microsof s sock price required o change he payoff oucome in he IEM marke. Table 3 (a sample horizons) and Figure 2 (a all horizons) give he resuls of likelihood raio ess for Model III agains (he resriced) Model I. The resuls are mixed. A several inermediae horizons (5, 7, 8, 10, 12, 14, 15, 16, 17 days), i appears ha adding his informaion increases power. Tha is o say, a rader a hese horizons would do beer a predicing he chances of payoff by knowing he curren relaive level of Microsof's price o he cuoff insead of knowing only he H conrac price on he IEM. 21 Thus, here is limied evidence agains marke efficiency using Model III. In Secion III, we discuss he risks and reurn o invesmen sraegies designed o exploi hese inefficiencies. C. Mulinomial Logi Models for he Compuer Indusry Reurns Markes Since here are four conracs in he Compuer Indusry Reurns Marke, we use a four-sae mulinomial logi model for esimaion. Table 4 liss hree models for his marke and gives resuls for sample horizons. Figure 3 summarizes his informaion for all horizons. In each model, he base conrac is he S&P500 and log price raios are relaive o he price of his conrac. 22 Each model has hree componen equaions: one o esimae he probabiliy of an AAPL payoff (relaive o S&P500), one for IBM and one for MSFT. The simples version (Model I) resrics he coefficiens o zero on all erms excep he conrac s own log price raio. This model is he mulinomial analog of Model I for he Microsof Marke. I recognizes he mulinomial naure of he payoffs, bu assumes ha each conrac's own log price raio is sufficien for forecasing is probabiliy raio. The able gives individual -ess for he null ha each individual own price raio coefficien equals one. I also gives a oin χ 2 es saisic for he null ha all hree own price coefficiens equal one for each horizon. The upper par of Figure 3 shows he own log price raio coefficiens for all conracs. The resuls mirror he Microsof marke resuls. A horizons of 2 or more days, all oin ess for all own-price coefficiens equaling one are reeced a he 95% level of confidence wih one excepion: he 10-day horizon (wih a 94% level of confidence). Individual coefficiens ofen fall significanly below one. The coefficiens generally fall as he horizon increases. As one would expec from Table 1, inspecion of he mappings beween prices and probabiliies overwhelmingly show overconfidence biases. Thus, he evidence for an overconfidence bias from he Microsof marke is paralleled in he more complex Compuer Indusry Reurns marke. 12

15 Model II asks if he cross-price resricions imposed in Model I are reasonable or if removing hem can significanly increase explanaory power. Likelihood raio ess of Model II agains (resriced) Model I show no significan effecs of relaxing hese resricions a any horizon. (Table 4 shows sample horizons and Figure 3 shows he likelihood raio es saisics across all horizons relaive o he criical value.) Model III asks wheher he markes fully incorporae he informaion abou he relaive reurns of he underlying socks by adding relaive reurn sandings o he Model I regressions. The addiional variable is he reurn on he sock underlying a given conrac minus he maximum of he oher underlying reurns. 23 Cross-price resricions are kep in ligh of he Model II resuls. Likelihood raio ess of Model III agains (he resriced) Model I show ha a all horizons adding relaive reurn informaion increases explanaory power. (Again, Table 4 and Figure 3 show hese resuls.) Thus, he markes are no making fully efficien use of all of he available informaion. In summary, he IEM markes appear quie efficien a shor horizons, bu suffer from overconfidence biases a longer horizons. Furher, ypically a inermediae or long horizons, addiional informaion can help improve explanaory power in logi models for predicing payoffs. In he nex secion, we discuss he risks and reurn o invesmen sraegies designed o exploi hese inefficiencies. III. Invesmen Sraegies Given he overconfidence bias eviden in he IEM, one migh conecure ha here are profiable invesmen opporuniies based on price alone. This is analogous o he observaion ha being heavy favories a he horse rack can generae posiive expeced reurns. In fac, profiabiliy should be easier o aain in he IEM because here are no explici ransacions coss (i.e., here is no rack ake ). To evaluae risk and reurns for differen conracs, we assume ha he logi models give he bes predicion of he acual probabiliy of payoff. This is analogous o he usual assumpion in he racerack lieraure of assuming he ex-pos frequencies of winning are he bes esimae of he ex-ane acual frequencies. While he racerack work ypically calculaes win frequencies relaive o odds or he expeced reurns o bes a various odds levels, we exend resuls here o he risk-reurn radeoff and o he reurns o dynamic rading sraegies. A. Sharpe Raios for Buy and Hold Sraegies The relaionships beween price, expeced reurn and risk for he Microsof Price Level marke under Model I are paricularly simple and can be graphed easily. Figure 4 shows he prediced probabiliies versus he 13

16 prices for he MSH conracs a various horizons. The under-pricing of low-priced conracs and over-pricing of high-priced conracs is apparen from his graph. This resuls in exremely high-reurn profi opporuniies a low prices, bu also high risk. Figure 5 shows Sharpe raios for conrac purchases a available prices and various horizons given he payoff probabiliy predicions of Model I. I shows how much a rader could profi relaive o he risk underaken by buying conracs a available prices and holding unil liquidaion. The highes raios are aained by purchasing conracs in he $0.10 range a wo-week or four-day horizons. Graphs for he Compuer Indusry Reurns markes are somewha more complicaed because of he inerdependen, mulinomial naure of he conracs. Neverheless, similar paerns can be seen a similar horizons. Figure 6 shows he Sharpe Raios for conracs in he Compuer Indusry Reurns Marke for a 14-day horizon. Across mos prices, he highes raios are for AAPL. For any given conrac, he highes raios are in he $0.15 and under range. A his 14-day horizon, he average AAPL Sharpe raio was I s median was and he 75 h percenile was The same saisics for IBM were , , and 1.29, respecively. For MSFT hey were , and Finally, for SP500, hey were , and For comparison purposes, he Sharpe raios compued on hird-friday o hird-friday reurns for AAPL sock, IBM sock, MSFT sock and he S&P500 index from January 1996 o December 2000 were 0.079, 0.276, and 0.305, respecively. In summary, Sharp raios show a posiive reward and, ofen, a high reward relaive o risk for saic buyand-hold rading sraegies for low-priced conracs across inermediae o long-erm horizons. B. Dynamic Trading Sraegies Suppose a hypoheical invesor knew how o forecas payoff probabiliies according o he logi model esimaes before he markes sared. How would such an invesor rade and how much would he or she earn if he or she could rade each nigh a closing marke prices condiional on hese payoff probabiliy assessmens? This gives some measure of he economic significance of he bias documened here. To deermine his, consider an invesor wih a mean-variance uiliy funcion given by U(x) = E(x) γvar(x), where x is he level of payoffs a he dae of liquidaion and γ measures he invesor s risk aversion. Suppose ha he invesor maximized his or her uiliy a each dae from 21 days o one day before liquidaion value deerminaion given curren prices and forecas payoff probabiliies. Given an iniial budge of, say $100, i is easy o deermine he holdings and reurn for such an invesor a any given poin in ime given he consrains ha cash and conrac holdings may never fall below zero and conrac holdings mus be in ineger values. This sraegy could no acually have been implemened. I requires 14

17 he invesor o know more han he or she possibly could have known a he ime of rading and i allows he rader o rade any desired quaniies a closing marke prices wihou adverse price effecs. Neverheless, his shows he poenial for profiabiliy of dynamic rading sraegies in hese markes. Table 5 summarizes he holdings and reurns for such an invesor in he Microsof Price Level marke. Using Model I, he rader would have generaed reurns ha average 0.31% o 1.2% a monh for risk aversion parameers ranging from 0.5 o 0.1. These reurns are generaed wih surprisingly low volumes of 0.21 o 1.22 conracs raded per day on average and a maximum of 10 conracs raded. Over all of he markes, he rader's porfolio would have increased in value from an iniial $100 o final values in he $120 o $207 range depending on risk aversion. If he rader used he curren price of Microsof sock relaive o he cuoff as exra-marke informaion in Model III, reurns increased dramaically. For he mos par, volume remained small, ranging from 1 o 5 conracs daily on average. However, on one rading day, he rader would have waned volumes ranging from 366 o 1,826 conracs depending on he risk aversion parameer. Much of he reurn o his sraegy, which ranges from 4.76% o 11.32% per monh on average and gives final porfolio values ranging from $411 o $1,655, resuled from his day s rading. If he rader were no able o rade on his day, reurns sill would have averaged 0.80%, 1.31% and 2.31% per monh for risk aversion parameers of 0.5, 0.25 and 0.1, respecively. Final porfolio values sill would have ranged up o $404. Table 6 summarizes he holdings and reurns for such an invesor in he Compuer Indusry Reurns marke. Using Model I, he rader would have generaed reurns ha averaged 0.16% o 0.84% a monh for risk aversion parameers ranging from 0.5 o 0.1. These, somewha lower, reurns require higher volumes han he Microsof Price Level marke sraegy (averaging 0.94 o 4.77 conracs per day). Over all he markes, he rader's iniial $100 porfolio would have increased in value o $109 o $166 depending on risk aversion. If he rader used curren relaive reurns as exra-marke informaion in Model III, reurns increased dramaically as in he Microsof Price Level marke. The rader frequenly hi he budge consrain and volumes were ofen high. Hypoheical reurns ranged from 2.09% o 3.96% per monh on average and gave final porfolio values ranging from $430 o $1,299. To aain hese reurns, he rader would have had o rade from o conracs per day on average. Because he rader frequenly hi shor sale and budge consrains, reurns could have been even higher wih a larger iniial endowmen. In conras o he Microsof Price Level marke, high volumes and reurns occurred on numerous days. 15

18 Overall, he overconfidence bias in he marke had he poenial for generaing considerable excess reurns for raders using dynamic rading sraegies designed o exploi hese biases. IV. Summary and Discussion The longsho bias is well documened for racerack being markes (see Thaler and Ziemba, 1988). In oher markes, i may be miigaed (e.g., Gray and Gray, 1997, for fooball being) or even reversed (e.g., Woodland and Woodland, 1994, for baseball being). These differences may arise because of differences in conex or marke srucure. The overconfidence bias has been documened for individual assessmens of probabiliy and choices (Lichensein, Fischhoff and Phillips, 1982). Because such biases may affec significanly financial markes and because financial markes differ boh in conex and srucure from being markes and individual choice asks, i is imporan o deermine wheher such biases carry over o and acually do affec financial markes. Here, we ask wheher he longsho bias or he overconfidence bias appears o generalize o and affec prices in he Iowa Elecronic Markes (IEM). These are acive, wo sided markes in a financial conex. IEM raders have he abiliy o synheically creae shor posiions. There are no explici ransacions coss. These feaures may be imporan in allowing raders o drive ou mis-pricing caused by biases. In fac, he longsho bias appears o reverse iself in a series of IEM markes. Insead, prices seem biased by overconfidence of he par of raders in heir abiliy o forecas wha will happen in hese markes several days o weeks in advance. Inefficiencies arising from his bias could resul in considerable profis for asue raders. Can he exisence of he longsho bias in some being markes, is absence in ohers and reversal in he IEM be explained in a consisen manner? Perhaps. Mos of he explanaions for he exisence of he longsho bias depend on a combinaion of beor biases and srucural characerisics of he being markes. For example, Thaler and Ziemba (1988) sugges a possible explanaion as follows: Some beors may choose horses for essenially irraional reasons, like he horse s name. Since here is no possibiliy of shor sales, such beors can drive he odds down on he wors horses, wih he smar money simply aking he beer bes on he favories. Ohers have developed his idea more formally. 24 Mos of he models use irraional reasons which each could easily be inerpreed as an overconfiden reacion o some informaion, or even us a hunch, ha a paricular horse migh win. Each explanaion relies on some addiional feaure of he being marke ha creaes an asymmeric effec o make is case (e.g., no shoring, he pari-muuel pricing mechanism, ec.). Excepions o he longsho bias occur when hese oher feaures change. For example, Woodland and Woodland (1994) speculae ha he reason ha he bias 16

19 reverses for baseball being is ha beers can be agains eams. Gray and Gray (1997) cie he fac ha, in fooball being, he poin spreads (insead of odds) adus o keep he bookie s ake consan. Hurley and McDonough (2000) cie he rack ake. This leaves he debae over wheher biases will exend o financial markes compleely unseled. For he IEM and oher financial markes, wo maor srucural facors change and hese may miigae longsho and overconfidence bias effecs. Firs, here is no ake for he rack (se in response o an asymmeric being srucure) in eiher he IEM or naurally occurring markes. Insead, here is a bid/ask spread, presumably se by marke makers who face symmeric adverse selecion issues. Second, ofen raders in naurally occurring markes can shor sell. While raders canno direcly shor-sell on he IEM, hey can se up synheic shors and hese posiions are feasible because of he absence of explici ransacions coss. Thus, raders are free o sell agains prices ha are oo high in heir view. The differences in hese feaures may remove he asymmeric effecs of overconfidence. This would leave only an overall endency for overconfidence on he pars of raders ha would drive up prices of conracs ha raders are relaively sure will pay off and drive down prices on he conracs ha raders are relaively sure will no pay off. 25 The evidence from he IEM suggess he overconfidence bias is he one likely o appear in wo-sided financial markes. Finally, i is ineresing o noe ha he resuling overconfidence bias is ransiory. I disappears and he markes become efficien as he liquidaion dae for conracs approaches. Neverheless, raders who were aware of he biases could have reaped subsanial profis by exploiing he resuling mis-pricing. Mirroring he ypical paern of open ineres in fuures markes, mean-variance uiliy maximizing rading sraegies generally purchase or sell mis-priced conracs a inermediae horizons and hen close ou hese posiions as he liquidaion dae approaches. This is he sraegy one would expec arbirageurs o follow when exploiing mis-pricing. Traders acing in his manner here could be he reason for prices converging o efficien levels near liquidaion. Thus, rading dynamics, no us he marke srucure, of he IEM parallels naurally occurring markes. This insills even greaer confidence in he exernal validiy of he IEM and is usefulness for sudying facors driving convergence, price dynamics and efficiency in naurally occurring markes. 17

20 Foonoes 1 Snyder (1978) cies eigh early sudies. See Thaler and Ziemba (1988) for a more recen and complee lis of papers on i. 2 The false consensus effec is he belief ha ones own views are more represenaive of he general populaion han hey are in realiy (see Ross, Greene and House, 1977). The assimilaion-conras effec occurs when people inerpre news more favorably wih respec o mainained posiions ha warraned (see Parducci and Marshall, 1962). 3 This is similar o he over-reacion dynamics hypohesized by Gandar, Zuber, O Brien and Russo (1988) and Gray and Gray (1997) for fooball being markes. 4 Many of he following poins are also used o usify he racerack lieraure. See Thaler and Ziemba (1988). 5 Traders can obain a shor posiion by buying a complee se of conracs from he marke for is fixed known payoff of $1 and selling he conrac(s) hey wan o shor. This creaes he same cash flows and ne posiions as a shor, bu proecs he exchange from losses. I consiues a shor ha is cash covered o he wors oucome. 6 Because hese are real fuures conracs, he IEM is under he regulaory purview of he Commodiy Fuures Trading Commission (CFTC). The CFTC has issued a no-acion leer o he IEM saing ha as long as he IEM conforms o cerain resricions (relaed o limiing risk and conflic of ineres), he CFTC will ake no acion agains i. Under his no-acion leer, IEM does no file repors ha are required by regulaion and herefore i is no formally regulaed by, nor are is operaors regisered wih, he CFTC. 7 These are he wo series of IEM markes ha rade only binary ($1 or $0 payoff) conracs and ha are repeaed under essenially idenical condiions monhly. We do no use IEM conracs wih oher ypes of payoffs because we canno inerpre prices as probabiliies for oher ypes of conracs. We focus only on repeaed markes o insure he saionariy needed for economeric analysis across markes. 8 These daes were chosen because he conrac values are linked o underlying values of socks on opion expiraion daes (he hird Fridays of each monh) as discussed laer. 9 Cuoffs are chosen o be he srike price of he closes-o-he-money raded opion for he sock (i.e., he closes $5 incremen o he curren sock price). This insures ha, a leas a he ouse, boh conracs have inermediae values. Conracs can be spli (see Appendix I) when sock prices deviae significanly from he cuoff and 18

21 conrac prices reach exreme levels (close o 0 or 1). Only one spli has occurred in he daa se used here. This spli creaed a middle range conrac in addiion o he L conrac (ha pays off if Microsof closes below a cuoff) and he H conrac (ha pays off if Microsof closes above a cuoff). For consisency, only he L and H conracs are used in he daa analysis here. Neiher making a differen choice nor hrowing ou daa from his monh changes any of he resuls. 10 We use dividend-adused reurns for he socks and he capial gains reurns for he index. If wo or more securiies ie, he payoffs are evenly spli among he ied conracs. This has never happened. 11 See Malinvaud (1974) for a general equilibrium proof of his proposiion. I also resuls from CAPM or APT along he following lines of argumen: According o each heory, he equilibrium reurn of any securiy (including our conracs) should equal he risk-free rae plus a risk premium associaed wih each aggregae risk facor. Since here is zero aggregae risk, he risk premiums will be zero. Since he risk-free rae is also zero, he expeced reurn for each conrac will be zero. This will only be rue if, a every poin in ime, he price of each conrac is equal o is expeced fuure value. Technically, hese will be risk-neural probabiliies and hedging demand may drive hem away from rue probabiliies. However, he markes are resriced o sudens and wih maximum invesmens of $500. This should minimize any such effecs. Furher, work from he poliical markes on he IEM suggess ha raders do no hedge agains heir own poliical preferences (see Forsyhe, Ross and Riez, 1999). 12 Some readers may have difficuly wih a zero risk-free rae. One migh speculae ha a posiive risk free rae would resul in p q =, where r is he (posiive) risk-free rae for days. (Since here is sill no aggregae 1 + r risk, here will sill be no risk premium.) However, his would violae arbirage resricions since his implies ha J = 1 J p < q = 1 = 1. If his were so, raders could buy he porfolio from oher raders a a combined price of less ha $1 and sell i back o he exchange for $1, making a sure profi. This aciviy would drive he discoun rae on each conrac o zero. Even if raders ignored his arbirage opporuniy, he discoun raes would fall ou of he analysis discussed laer because normalized prices and price raios, no raw prices, are used. 19