Insights into the Market Impact of Different Investment Styles

Transcription

1 Insighs ino he Marke Ipa of Differen Invesen Syles Ron Bird a*, Lorenzo Casavehia a, aul Woolley b The aul Woolley UTS Working aper Series May 2008 a The aul Woolley Cenre for Capial Marke Dysfunionaliy, Universiy of Tehnology, Sydney, Cnr Quay Sree and Ulio Road, O Box 23, 2007, Sydney, Ausralia b The aul Woolley Cenre for he Sudy of Capial Markes Dysfunionaliy, London Shool of Eonois, Houghon Sree, London WC2A 2AE, Unied Kingdo Absra: Modern day equiy arkes are populaed by invesors pursuing a nuber of invesen syles. In his paper we siulae he behaviour of invesors pursuing various ypes of hese syles in order o exaine wheher heir ineraion is a ajor onribuing faor o ineffiienies wihin arkes and pariularly o he anoalous priing behaviour idenified in he lieraure. We found ha sall arke fraions onsiued by oenu and growh invesors are very disrupive o arkes, signifianly inreasing heir volailiy and ausing ispriing for exended periods of ie. They also indue an inrease in boh he risk and rading volue experiened by he oher ypes of invesors. We onlude ha oenu and growh invesing ay be a soure of he any arke anoalies and serious hough should be given o poliy, eonoi and soial ipliaions of equiy priing onsisenly no refleing fundaenal value. JEL Codes: G2, G4 Key Words: Heerogeneous Agens; Marke Effiieny; Mispriing * Correspondene Address: Shool of Finane and Eonois, Universiy of Tehnology, Sydney, O Box 23, Broadway, NSW, Ausralia, 2007, Tel.: +6 (2) , Fax: +6 (2) , Eail: ron.bird@us.edu.au

2 Seion : Inroduion Over he las half enury, he growh of he anaged fund indusry has spawned he developen and ipleenaion of a yriad of invesen syles. Whereas a one sage equiy arkes were doinaed by fundaenal invesors, who adop inforaion-driven sraegies, oday arkes are populaed by invesors pursuing a uliude of syles any of whih pay lile or no aenion o he available inforaion ha is oonly hough o drive sok pries. Exaples of suh syles inlude index and oenu invesing. Index (passive) rading ignores all inforaion oher han he arke weighs of he soks inluded in he index. As Lorie and Hailon (973) ephasised, a assive fly-o-passive invesing has he effe of reduing he opeiion and he effiieny wihin arkes. Likewise, oenu (ehnial) rading disregards any inforaion oher han he iediae pas hisory of sok reurns. I is signifian ha one iporan neessary ondiion o prooe inforaional effiieny in arke priing is aive opeiion beween invesors, who seek ou all relevan inforaion in heir searh for ispried seuriies, rade on any pereived ispriings, and so ensure he exisene of fully-revealing pries (Faa, 965). The fa ha a signifian proporion of arkes is now in he hands of invesors who uilise a liied subse of inforaion is suggesive of he possibiliy ha seuriy pries igh depar fro heir fair value for exended periods of ie. In his paper we siulae an arifiial arke populaed by invesors pursuing differen invesen syles: fundaenal, prie oenu, onrarian, index and noise (rando). Our fous is on he ipa ha differen obinaions of hese sraegies ould exer on reurns and risks experiened by eah syle of invesor 2 and he onsequen effe on he arke prie dynais. Our proposiion is ha, nowadays, he oposiion of arkes sees o depar quie radially fro ha assued for an effiien priing o ake plae. Therefore, we ipound ino our odel proxies for invesen syles oonly adoped in real arkes wih he ai o esablish wheher he resuling arifiial arke appears o display sylised haraerisis siilar o hose oonly idenified in he arke anoalies lieraure. We will also provide evidene on he exen o whih eah pariular syle rader ipas on he reurns, risks, and rading volues realised by oher raders. In Seion 2 of he paper, we provide a brief review of he lieraure. In Seion 3, we odel he behaviour of eah of he invesen syles o be used in our siulaions of he behaviour of arkes oposed of various obinaions of hese differen syle invesors. We presen and disuss he ain findings in Seion 4 paying speial aenion o he insighs ha hey provide ino he proess of prie foraion and he exen o whih hey are in aord wih he lieraure. Our disussion will highligh ha i is prie oenu and over-exrapolaing fundaenal invesors onribue o generaing a desabilising influene in rending arkes. We onlude in Seion 5 wih a suary of our findings and a disussion of possible direions for fuure researh. Seion 2: The Evidene on Marke and Invesen Syle Behaviour Alhough he iniial ess of he inforaional effiieny of apial arkes dae bak over a enury, i was only wih he wriings of Faa in he 60 s and early 70 s ha he epirial researh in his area began o ushroo 3. Aording o he Effiien Marke Hypohesis (EMH), seuriies are orrely pried o he exen ha invesors anno forulae invesen sraegies, based upon inforaion relaed o fir s haraerisi (e.g. size), soe By syle we ean he sraegy or proess by whih an invesor hooses he soks o be inluded in his porfolio. 2 In resuls no repored here we also exained he ipa of eah ype of invesor on rading volue. 3 Faa (970) 2

3 valuaion uliple (e.g. book-o-arke) and/or soe orporae announeen (e.g. a new share issue), ha onsisenly generae reurns over and above he level neessary o reward he invesor for he inheren risks of he invesens. There are hree general ondiions ha us exis wihin arkes for effiien priing o be esablished in he sense oulined above. Firs, inforaion flows oslessly o he arke wihin a shor ie of i being generaed. Seond, invesors iediaely analyse he ipliaions of new inforaion for a sok s valuaion and rade where hey believe ha a sok is inorrely pried. The final ondiion being ha ransaion oss should no inhibi he profiabiliy fro rading o exploi any pereived ispriings. Where hese ondiions hold, effiien priing should be esablished as invesors will quikly opee away any profiable opporuniies. In his paper, we onenrae our aenion on he seond of he previous ondiions, naely he presupion ha he arke is populaed wih invesors whose deisions (based upon heir analysis of all available inforaion) are geared o exploiing any ispriing opporuniy. We adop his as our working definiion of he age-old syle oonly referred o as fundaenal invesing. Indeed, he poenial for fundaenal invesors o add value depends on boh he agniude of ineffiienies in arkes and heir abiliy o auraely idenify and exploi he in a iely fashion. We will speifially onsider wo ypes of fundaenal invesors: (i) aurae fundaenal invesors, who are always able o idenify he rue (fair) value of a sok; and (ii) biased fundaenal invesors who signifianly over-exrapolae he os reenly released earnings growh. We will refer o he laer as growh invesors. The epirial evidene on he disappoining perforane of aive invesen anagers, daing bak o he early work of Treynor (965), Sharpe (966) and Jensen (968), provided he siulus for any invesors o urn o index invesing (Malkiel, 2003). This drif has resuled in upwards of 25% of he invesible funds in any of he developed equiy arkes being in he hands of passive invesors. Moreover, liens andaory guidelines (e.g. benhark seleion for easuring anagers risk and reurn) have ade aive anagers ore aounable for heir perforane. This proess has resuled in any anagers oving o being lose indexers (or quasi-indexers) wih respe o a signifian porion of heir aive porfolios. I would no be unreasonable, hene, o assue approxiaely a hird or ore of anaged funds in he ajor world equiy arkes being subje o eiher over or over passive invesing 4. This phenoenon generaed a liquidiy drag, wih a signifian proporion of invesible funds ou of he arke as a resul of index invesor oally ignoring all inforaion releases when deerining heir porfolio index weighings (Woolley and Bird, 2003). The reaining porion of equiy invesen is separaed beween wha is known as onrarian and oenu invesing. The origin of onrarian invesing daes bak over 70 years o he publiaion of he ex Seuriy Analysis auhored by Graha and Dodd (934), even hough he ineres fro he aadei ouniy has largely been resried o he las 5 years (Faa and Frenh, 992, Lakonishok e al., 994). One of he explanaions for he exisene of a value preiu (value soks ouperfor growh soks) is ha invesors end o overexrapolae he urren poor (good) perforane of an under- (over-) valued sok (judgeenal isakes), wih he onsequene of a reversion in he perforane in he following one o 3 years. Hene, a onrarian sraegy onsiss of buying (selling) heap (expensive) soks, in order o profi fro expeed subsequen ean reversion. Conrarian invesors ypially rely upon siple valuaion uliples (e.g. prie-o-book, prie-o-earnings, and dividend-yield) in order o idenify heap or expensive seuriies. Therefore, alhough hey uilise inforaion in heir deision proess, i is only a narrower subse han is he ase wih fundaenal invesors. The siilariy beween onrarian and fundaenal invesors is ha boh ry o idenify heap and expensive soks, hough basing heir assessen on 4 Exep where oherwise referened, suh esiaes ade in his paper represen a onsensus fro inforaion gahered fro a survey of he ajor inernaional asse onsulans. 3

4 differen inforaion signals and, hene, iing. Indeed, onrarians end o rea slower o new inforaion as in os ases here will be a ie delay before new inforaion is ipounded ino valuaion eris used o separae he ross-seion. Moreover, as ephasised by Asness (997), hese valuaion uliples provide only a very rude easure as o wheher a pariular sok is ispried 5. For exaple, a onrarian invesor igh regard a pariular sok as being heap based upon is valuaion uliples when in fa i is fairly pried when one onsiders a wider se of inforaion ha ypially does no ener ino heir deision proess. Despie hese defiienies, he epirial evidene suppors he exisene of a posiive value preiu whih suggess ha he disiplined ipleenaion of a onrarian invesen syle will on average ouperfor he arke 6. enu invesing is an invesen syle ha has only ahieved proinene in reen years in he aadei lieraure, hough i was undoubedly being praied well before index invesing ahieved any for of populariy. The os oon for of prie (reurn) oenu invesing involves purhasing (selling) winner (loser) soks whose reen arke perforane has been good (poor). Jegadeesh and Tian (993, 200) exained various ipleenaions of his for of invesen and found evidene o sugges ha he bes of he signifianly ouperfored he arke. Several oher wriers have onfired hese findings suggesing a arke ineffiieny whih has proved diffiul o explain in he ligh of radiional odels (Faa, 996, 2006). Alhough no any invesors aually represen heselves as oenu invesors, here is lear evidene ha oenu onsiues a signifian par of any invesen sraegies and is reinfored by he herding behaviour of boh insiuional and individual invesors 7. As oenu invesors base heir invesing solely on pas prie oveens hey have he poenial o be a desabilising fore by exaerbaing rends ha already exis in arke and aking i ore diffiul for ean reversion o our even in he fae of hanging fundaenals 8. Finally, we also inlude in our analysis hose invesors who do no rade on he basis of available inforaion in any disiplined way: he noise raders. Noise rading is no a syle ha any invesors lai o follow alhough i is likely o provide a reasonable represenaion of he rading behaviour of any individual and, possibly soe, insiuional invesors. The issue of he ipa of suh invesors on arkes has been debaed for he las 50 years wih Friedan (953) suggesing ha hey would end o buy high and sell low and onsequenly have no signifian ipa on priing as heir rading would effeively be offse by arbirageurs. De Long e al. (990), insead, argued ha arbirage ay no be as effeive as Friedan igh surise, and raising he possibiliy of noise raders being quie disrupive in arkes, possibly experiening good reurns over exended period of ie and no neessarily underperforing in he long-er. In our sudy, we adop opuaional heerogeneous agen-based odels (hereafer, HAM), whih have beoe a oon approah in he analysis of he ipliaions of he ineraions beween raders wih differen beliefs and differen invesen sraegies. In he reen lieraure, any HAM have been invesigaed hrough nuerial siulaion, given he oplex analyial raabiliy of he raders ineraions. In he nex seion, we will briefly urn o onsidering he evidene on arke anoalies as we are pariularly ineresed in 5 Bird and Casavehia (2007). 6 For evidene on he agniude of he value preiu aross arkes and aross ie, see Capaul e al (993), Faa and Frenh (998) and Dison e al (2003). 7 For evidene on invesor herding, see Grinbla e al (995), Werers (999) and Wylie (2000) 8 Earnings oenu is anoher oenu invesen sraegy ha involves rading soks based upon signals generaed by eiher heir aual or foreased earnings. One exaple being o purhase (sell) soks whose urren earning is graer (less) han he average earnings over he previous n quarers. This phenoenon has been exensively invesigaed in he lieraure wih he evidene suggesing ha pries are only slow o adjus o earnings announeens (Foser e al 984, Bernard and Thoas, 990). We have odelled earnings oenu and evaluaed is ipa on arkes and invesors pursuing oher invesen syles and found ha invesors pursuing his syle have lile or no deleerious ipa on arkes and oher raders. We do no inlude he in he siulaed arkes repored in his sudy as heir inlusion would only furher exend he es ases onsidered wihou providing any addiional insighs in priing bahaviour wihin arkes. 4

5 wheher he paerns of prie behaviour observed by any previous auhors an be a leas parially explained by he ipa of one or ore of hese syles on he prie foraion proess. Evidene on Marke Anoalies Over he os reen 30 years, we have seen a ouning volue of epirial evidene whih has brough ino quesion he EMH a all levels and fuelled he debae as o wheher even he os developed and regulaed arkes an really be assued as being effiien 9. I is no our inenion o provide a review of he evidene on arke effiieny bu raher o ouline wo of he ore iporan priing ipliaions ha any have drawn fro he exising evidene on arke anoalies 0 : (i) ries will under-rea o individual piees of inforaion bu over-rea o an aggregaion of inforaion: any sudies have highlighed a slow reaion in pries o inforaion releases whih in soe insanes would appear o exend over a nuber of years (Foser e al [984]. In onras he work of DeBond and Thaler [985] and ohers would sugges ha pries ofen evenually ove o unsusainable levels fro whih hey orre. A nuber of sudies have aeped o provide an explanaion for he siulaneous exisene of boh under- and over-reaion wih Hong and Sein [999] being os in he spiri of his sudy by suggesing ha i is a dire resul of he arke ineraion of wo ypes of invesors: news followers (fundaenal) and rend followers (oenu). (ii) There are exended periods of ie when a sok s prie is reoved, a soe ie exessively, fro is fair value: he evidene suggess possible deparures fro effiien priings boh a he relaive and absolue level and ha hese deparures an be large in agniude and persis for exended periods of ie. A he sok level (relaive disorions) we have evidene o sugges ha i an soeies ake up o five years for a arke o adjus o erain orporae evens (e.g. Harris, 2004; Lakonishok e al, 994). A he arke level (absolue ispriing), we have reenly experiened he longes arke yle ever in any ounries resuling in he bubble of he lae 90 s followed by a ajor orreion (Siegel, 2003]. We will rea hese as sylised fas agains whih o evaluae he priing behaviour ha we generae in our siulaions wihin arkes populaed by various obinaions of he several invesen syles ha we will disuss in ore deail in he nex seion. Seion 3: Mehodology Iniial Se Up Our ai is o reae a arke wih jus suffiien oplexiy o provide us wih ineresing insighs ino priing behaviour and his is ahieved by resriing our analysis o a arke wih one risky asse (whih ould be an index) wih quarerly reurn r, and one risk-free asse wih quarerly reurn r 2 f. The risk free asse is perfely elasially supplied a a gross reurn of R f =+ r f /K, where K sands for he frequeny of rading period per quarer whih is assued o be weekly (hus K= 3 periods per quarer). The sole soure of inforaion ha affes pries is quarerly earnings announeens where he quarerly growh in earnings is: 9 This lieraure daes bak o he June-Sepeber 978 volue of Journal of Finanial Eonois oally devoed o wha beae known as arke anoalies. 0 Brief reviews of he lieraure on arke effiieny are o be found in Dison and Mussavian (998) and Srivasava (2004). There are also noieable siilariies o he paper of De Long e al (990) 2 This ould be odeled o follow soe sohasi proess. 5

6 o eiher randoly drawn (eah quarer fro a disribuion wih an assued ean and sandard deviaion of per en), or o serially orrelaed, osillaing around a long-er growh rae of % per quarer, where he oplee yle akes hree years (i.e. 2 quarers), eah oposed of a upward drif in earnings growh for six quarers followed by a ean reversion in earnings growh (i.e. ean reversion) over he subsequen six quarers. This 2-quarer yle is hen repeaed 3. Afer eah quarerly earnings announeen, a new fundaenal value for he sok is deerined by applying a dividend disoun odel as desribed below and a new round of weekly rading is generaed. Deerinaion of aenal rie The fundaenal value for he sok, whih also ould be referred o as is fair value or inrinsi value, is deerined iediaely afer eah earnings announeen by exrapolaing ou he earnings growh for he nex 2 quarers (he ie lengh of he earnings growh rae) a he average earnings growh rae for he urren and he previous hree quarers. Beyond hese 2 quarers, i is assued ha earnings will grow a he long-run quarerly growh rae for earnings. These projeed earnings figures are hen disouned in a dividend disoun odel a a risk-adjused rae o deerine he fundaenal prie. The fundaenal prie * an be expressed as follows: * T 2 i 2 3 i + gt + g o + gt + gt + r + g o = λ E = + T, + 3 λet () 0 i= + r i= + r r gt + r r g + r where E T represens he earning per share of he sok over he quarer T, g 0 onsiues he long-er growh rae of % per quarer, λ is he payou raio (assued equal o 0.8), and g T is an average growh rae alulaed eah quarer on he assupion ha earnings will grow over he nex 2 quarers a he average of he earnings growh raes over he urren quarer and he las hree quarers ( g T ). As a speial ase when gt = g0, we obain he Gordon valuaion forula: * + g 0 T = λ E T. (2) r g 0 Heerogeneous Trading Sraegies As enioned previously, we assue ha here are seven differen ypes of invesors pursuing five differen ypes of invesen syles: wo fundaenal invesors (one who foreass auraely and he oher, referred o as a growh invesor, who over-exrapolaes pas earnings growh), wo oenu invesors (one whose ipleenaion is uh shorer er han he oher), onrarian invesor, index rader, and noise rader. In he following disussion, we ouline he naure of he deand funion of eah ype of invesor. The fundaenal invesors ake he following assupions. They believe ha he arke prie is ean revering o heir pereived fundaenal prie. Consequenly, hey purhase 3 This paern is onsisen wih he findings of Soffer and Walher (2000) for US soks. 6

7 (sell) he soks when he arke prie is below (above) his pereived fundaenal prie. The fundaenal invesors deerine heir pereived fundaenal prie by applying a dividend disoun approah as in equaion. We odel wo ypes of fundaenal invesors: one ype ha orrely foreass fuure earnings growh and so effeively always knows he fundaenal prie and a growh invesor who over-exrapolaes pas earnings growh whih is a judgenal error ha is oonly refleed in sok pries (Lakonishok e al, 994). In boh ases i is assued ha beyond an iniial period earnings will grow a he long-er earnings growh rae. We also assue ha eah of he wo ypes of invesors only rade when he * deviaion of he urren prie fro heir pereived prie,i is eiher above or below a erain peren, say s [ 0, ], of he urren prie level in reogniion of he risks, and various rading and finaning oss, assoiaed wih he invesen. Moreover, given heir role in sabilising he arke, heir deand is proporional o he deviaion of he arke prie fro he fundaenal prie. Therefore, we an express he deand of he fundaenal invesors ( z, ) a ie as follows: z s, s = 0 s s * [ ( + ) ],i * [ ( ) ],i s s if if if *,i *,i *,i > ( + ) s < < ( ) where, s (greaer han zero) easures he deand inensiy, s (greaer han zero) easures required preiu ha inorporaes boh ransaions oss and a opensaion for he risks assoiaed wih he invesen. The deand funion expressed in unis of shares indiaes ha he fundaenal raders only purhase (sell) soks when hey believe ha he poenial * gain (loss) is above (below) s.,i represens he pereived fundaenal prie, wih i equal o he lengh of he exrapolaion of he fundaenal rader onsidered. In he ase of he aurae fundaenal invesors i is equal o 2 quarers (as in he ase of ) whereas for he growh invesors i equals 40 quarers. I should be noed ha he perepion of he fundaenal prie by he aurae fundaenal invesors is, by onsruion, always orre and as suh hey provide a useful benhark. Indeed, a arke oposed 00% of hese invesors is always effiien. s s * (3) As aforeenioned, we also siulae he rading of wo prie oenu invesors. In our forulaion, oenu invesor purhases (sells) soks ha have hanged in prie over he previous f weeks (foraion period) a a rae greaer (less) han g 0, whih is he average growh rae per quarer, and o hold he posiion reaed for h weeks before reversing he ransaion. This is akin o he rading sraegies se ou in Jegadeesh and Tian [993, 200] who evaluaed he perforane of oenu sraegies ipleened wih various obinaions of foraion periods (f) and holding periods (h). The wo suh ipleenaions onsidered in his paper inlude a shor er version, wih a foraion period of 3 weeks and a holding period of 6 weeks (or f = 3, h =6), and a longer er version wih a foraion period of 26-weeks and a holding period of 26-weeks (or f = 26, h = 26) 4. More preisely, for he oenu invesors, we assue ha: (i) heir rading signals are generaed by he differene beween he urren prie and he prie auulaed in he previous f weeks a he rae g 0 ; (ii) hey are risk averse, naely hey inrease heir (long/shor) posiions iniially 4 Given he periodiiy of he priing yle produed in our siulaions, he shorer-er oenu invesor is soewha akin o he earlysage oenu invesor idenified in Lee and Swainahan (2000) while he longer-er oenu rader is ore akin o he lae-sage oenu invesor. 7

8 8 when he rading signals generaed are srong enough, bu hey are auious when suh signals are oo srong (heir deand funion is a nonlinear inreasing funion of he rading signals while he arginal deand is dereasing); and (iii) hey hold heir posiions for h weeks and hen reverse he. Based on he above assupions, he deand funion of he oenu invesors, z a ie ay hus be defined by he following piee-wise nonlinear funion: [ ] [ ] + < + + < > + + = f f f f f f g if g ) g ( ) g ( if g if g z ) )( ( ) )( ( anh 0 ) )( ( ) )( ( anh , σ β σ β (4) where, 0 > easures he deand inensiy, 2 0 σ > easures he volailiy of he arke prie, whih is assued o be a onsan, 0 > easures he rading os, and β easures how quikly he raders adjus heir deand when he rading signals are sall. The onrarian invesors purhase (sell) soks ha are undervalued (overvalued) as indiaed by he sok s (yearly) earnings-yield ( T E, ). The level of under- (over-) valuaion is defined relaive o he (yearly) long-er earning-yield ( ), alulaed as he inverse of he perpeual Gordon onsan growh rae odel. Again, hey rade on his signal only when he differene is above (below) a erain ransaion os [ ] 0,, As a resul, he deand of a onrarian invesor ( z, ) is expressed by he following funion: < + < + > + = T T T T T ) ( E ) ( E σ β ) ( E ) ( E ) ( E σ β z if if 0 if,, 2,,, 2, (5) where, again > 0 easures he deand inensiy, σ 2 >0 easures he volailiy of he arke prie, assued o be a onsan, β easures how quikly he raders adjus heir deand when he rading signals are sall, and T E, is he urren yearly earnings alulaed as he su of he earnings released in he os reen four quarers. A sok whose urren earning yield is above (below) he long-er earnings-yield (he iniial earnings are equal o ), is designaed as an under- (over-) valued sok. Consisen wih oher auhors, we forulae he noise raders as invesors whose deand are randoly deerined. In his fraework, he noise rader is a pariular aegory of hose invesors who rade on noise [as] hey [were] rading on inforaion (Fisher, 986). Their deand is expressed as a rando draw fro a noral disribuion: n z, ~ N (0, 3). (6)

9 The noise raders, hene, rade on rando perepions raher han soe heurisi rading sraegy as in he ase of he oenu or onrarian invesors 5. Finally we have he index invesors as always 00% invesed in he risky asse. Hene, he deand of he index invesors z i, is always zero. Wealh funion In our odel eah invesor has a hoie beween holding his wealh in eiher shares (risky asse) or a risk-free asse (whih we will refer o as ash). I is possible for hi o hold a shor posiion in soks and o borrow (i.e. negaive ash). The wealh posiion of an invesor a any poin in ie an be is alulaed as follows 6 : [( W N )( + r 3 ΔN ] W p, = N p, + p, p, f ) p, (7) where W p denoes he wealh of he p h invesor a ie, N p denoes he nuber of shares held, denoes he prie of eah share, and r f denoes he quarerly risk-free rae. We an see fro Equaion 7 ha he wealh posiion eah week is equal o he value of he shares held plus he ash holdings he week iediaely before, adjused for boh ineres and he ash flows assoiae wih rading in shares. The aual nuber of shares o be purhased by eah invesor is deerined by heir wealh relaive o he oal wealh of all invesors (whih a ie for he p h invesor is denoed as n p, ) and he level of heir deand as deerined fro heir deand funion (whih is denoed as z p, ) Based on he previous disussion, he exess deand of he risky asse z e, a ie is hen given by: ze, n p z p, (8) where p= z p, denoes he deand funions of he differen raders as defined in (3)-(6). Marke Maker and Marke Clearing rie In addiion o he seven ypes of invesors, we also have a arke aker whose role is o lear he arke eah period of any exess deand. Hene he arke aker will ake a long posiion when z e, < 0 and a shor posiion when z e, > 0. A he end of period afer he arke aker has ransaed, he adjuss he prie for he nex period in aordane wih he experiened exess deand. Using μ o denoe he orresponding speed of prie adjusen of he arke aker in he fae his exess deand, and η o denoe a rando noise, hen he arke-learing prie a ie + is given by: + = + μ ze, + η (9) The arke aker behaviour in his odel is highly sylised. For insane, we do no onsider he invenory level of he arke aker buil up as a resul of he auulaion of various 5 For sipliiy, we do no onsider he ase of a posiive or a negaive bias in he noise raders deand, even hough i is possible o analyse he ipa of heir oods by uliplying heir deand by a onsan (see Alfarano e al, 2005, De Long e al, 990). 6 See also Levy, M., Levy, H., and Soloon, S.,

10 long and shor learing posiions. This ould affe his behaviour, e.g. he arke aker prieseing role in (0) ould also be a funion of he invenory level. Seion 4: Findings We oulined in Seion 2 ha our objeive is o invesigae he prie foraion proesses ha evolve in arkes oposed of invesors pursuing differen syles and also o onsider he ipa of hese differen obinaions on he risks and reurns realised by, and he rading behaviour of, invesors pursuing eah of hese syles. In Seion 3, we developed a odel oposed of five differen invesen syles o allow us o siulae priing behaviour wihin a arke oposed of seven ipleenaions of hese five invesen syles. The fous in his seion is o vary he oposiion of arkes by hanging he proporions ha eah syle of invesor represens in he arke in order o provide insighs ino he resuling prie behaviour and also he resuling reurns, risk and rading aiviy for eah syle of invesing The various obinaions of invesors wihin he es ases ha we exaine in he firs par of our analysis are se ou in Table. For eah es ase we ran 300 Mone Carlo siulaions of he arke behaviour for boh rando and serially-orrelaed earnings growh over a period of 25 years (,300 weeks). Moreover for purposes of oparabiliy, we use he sae Mone Carlo earnings pah for all he differen arke sruures. This eans ha all he resuls we douen are generaed fro he sae series of rando or serially orrelaed earnings growh. We alibraed he odel as developed in Seion 3 wih he objeive ha an equivalen signal will ranslae ino a siilar level of rading for eah of he raional aive invesors: fundaenal, oenu and onrarian. For all siulaions, he seleed paraeers are as follows: λ = 0.8, = = s μ = 0.5, =, s = 0.03/3, W p,0 = 5, = 2e + 03, = 5e + 05 β p = σ 2 p =, Effiien riing The evidene os relevan o our ajor findings is o be found in Tables 2 and 3 and os of he disussion in his seion will be based on hese Tables suppleened where appropriae. Table 2 provides us wih inforaion abou he risk and reurn haraerisis for boh he arke and eah individual invesor syle under eah of our 27 es where quarerly earnings growh is generaed randoly while Table 3 repeas his inforaion where serial orrelaion and ean reversion is buil ino he growh of quarerly earnings One iporan piee of inforaion, no repored in he ables, is he ean of he differene beween he aual and he fundaenal pries esablished eah week 7. The fa ha his ean is effeively zero for all es ases under boh rando and serially orrelaed earnings growh infors us ha he prie is on average orre over he 25 years overed by our siulaions. This is a neessary bu no a suffiien ondiion for arke effiieny whih would require ha he prie be orre hroughou he 25 years raher han o be orre on average over hese years. Wih his in ind he easure repored in Tables 2 and 3 ha bes apures he poenial for arke ineffiieny is he sandard deviaion of he differene beween he aual and he fundaenal pries whih we repor in he ispriing olun. In a arke wih no poenial for ineffiienies his ispriing easure would have a value of zero so we an use is agniude o provide us wih insighs ino exen of any ispriing opporuniies. We have defined an ineffiien arke as one where invesors anno use available inforaion o forulae an 7 The ean of he differene beween he weekly prie and he fundaenal prie is alulaed for eah siulaion and hen he average of hese eans is alulaed. 0

11 invesen sraegy ha onsisenly generaes exess reurns. We disuss below his ispriing easure firs in he ase of rando earnings growh and hen where we have serial orrelaion in earnings growh. Subsequenly we exaine he perforane of he invesors uilising he differen invesen syles in order o deerine he exen o whih he opporuniies indiaed by he ispriing easures are exploied by he various ypes of invesors. Mispriing under Rando Markes Under es ase where he arke is enirely oposed of invesors who effeively know he fundaenal prie, he ispriing easure is 0.42 (unis of urreny) whih is indiaive ha pries very quikly adjus o he release of new inforaion and suggess ha he arke in his ase is highly effiien 8. A review of he inforaion onained in he ispriing olun of Table 2 reveals several es ases where he level of ispriing is uh higher han i is in es ase 9. The greaes deparures, boh in exess of seven dollars, are be found in es ases 4 and 9, whih represen a obinaion of he fundaenal or he growh invesor wih he longer-er oenu invesor. In order o obain a greaer insigh ino he naure of he priing proess assoiaed wih hese wo es ases, we repor in Figure a ypial es pah and he average serial orrelaion for eah es ase. These hars learly indiae ha i akes several weeks for he prie o adjus o new inforaion bu hen pries overshoo heir fundaenal value whih is a finding ha is onsisen wih he under and over-reaion idenified in any previous sudies 20. There are any less severe insanes of arke ispriings ha an be observed fro reviewing he oher es ases and hese provide us wih furher insighs ino he effe of he oposiion of invesen syles wihin arkes on effiieny of he prie foraion proess: The level of ispriing is higher in hose es ases where here is a growh invesor raher han an aurae fundaenal invesor (.f. he ispriing easure for es ase 3 wih ha for es ase 8, es ase 3A wih es ase 6A, and so on). This oes as no surprise as he growh invesor onribues o prie deparures by valuing soks oo highly a ies of srong earnings growh and plaing oo low on he a ies of weak earnings growh; The shorer-er oenu invesor onribues less o ispriing han does he longerer oenu invesors (.f. es ase 3 wih es ase 4, es ase 8 wih es ase 9 and so on). This refles ha he longer-er oenu invesors ake longer o adjus heir buying behaviour in response o a hange in he paern of repored earnings growh and hen hold on o heir soks longer one hey have been aquired ; Index invesors and noise raders neiher enhane nor iigae any ispriings in arkes aused by invesors following oher invesen syles (.f. es ase 3 wih ess ases 4 and 5, es ase 6 wih es ases 7 and 8). This is beause ispriings in arkes do no enourage index invesors o rade while noise raders effeively rade randoly independen of he exisene of any ispriing in arkes alhough hey inrease he level of volailiy experiened in arkes. The invesen syles ha do os o redress any ispriings in arkes are he aurae fundaenal invesor and he onrarian invesor (.f. 6A wih 6, 20 wih 9) who boh rade when hey pereive ha he aual prie has diverged fro is fundaenal value. 8 The average prie over he 25 years is approxiaely $40 and so a sandard deviaion of 42 ens is 0.3% of he prie. Alhough we igh expe ha he sandard deviaion would be zero in a arke 00% oposed of aurae fundaenal invesors, his sall sandard deviaion refles ha here is a one week gap beween he earnings announeen and he firs opporuniy o rade. 9 There are five es ases where he ispriing easure represens ore han 4% of he average prie. 20 One riiis ha ould be levied is ha he ispriing idenified largely refles he no rade zone ha we have iposed on invesors o aoun for ransaions os and risk. When we repeaed our analysis wihou his no rade zone, he ispriings only fell by beween 0% and 5%.

12 Mispriing under Serially-Correlaed Markes Alhough he growh invesors, in assoiaion wih he oenu invesors, onribue o ispriing in arkes where earnings announeens are rando, heir ipa on ispriing approxiaely doubles in arkes where earnings growh is serially-orrelaed (see Table 3). There are nuerous insanes of es ases having a ispriing easure of around 5 or higher and he unique aspe of eah of hese es ases is ha hey inlude growh invesors 2. Furher, hese exrees in ispriing even our in arkes ha inlude no oenu invesors (i.e. es ases and 2). Our findings highligh ha he growh invesor is he ain onribuor o ispriing in arkes haraerised by serially-orrelaed earnings growh (Soffer and Walher, 2000). An exaple of a ypial priing pah under one of hese es ases (es ase 9) and he assoiaed serial orrelaion har is repored in Figure 2. These hars highligh ha he growh invesors by over-exrapolaing earnings growh ause levels of overshooing in pries ha we do no see in arkes where earnings growh is rando hrough ie. The periodiiy of he priing yle is longer (.f. es ase 9 in Figure wih ha in Figure 2) refleing ha adjusen proess is longer and he exen of overshooing is greaer. Whereas previously wih rando earnings growh, i was he oenu invesors who were he ain onribuors o a higher level of arke ispriing wih he growh invesor playing a seondary role, hese roles are basially reversed when we experiene rends in earnings growh. The level of ispriing is basially lef unhanged by he inroduion of oenu invesors, whih leads us o sugges ha he desabilising influene of he oenu invesors is no greaer in he serially-orrelaed arkes han i is in he rando arkes. This proposiion gains suppor fro he fa ha obinaions of he aurae fundaenal invesors wih oenu invesors resul in he sae level of ispriing in boh ypes of arkes (.f. ess ases 3 and 4 in Table 2 wih he sae es ases in Table 3). One aspe of he priing proess ha is oon o boh rando and serially-orrelaed arkes is ha obinaions of growh and oenu invesors do resul in boh under- and over-reaions o earnings announeens (see Figures and 2), wih he resuling disorions in priing being ore susained in he ase of serially-orrelaed earnings announeens. Oher insighs ha we gain fro he findings repored in Table 3 are very siilar o hose previously oened on fro our review of Table 2: The shorer-er oenu invesor onribues less o ispriing han do he longerer oenu invesors (.f. es ase 3 wih ess ase 4, es ase 8 wih es ase 9 and so on). Boh index invesors and noise raders neiher enhane nor dapen any ispriings in arkes inrodued by invesors following oher invesen syles (.f. es ase 3 wih ess ases 4 and 5, es ase 6 wih es ases 7 and 8). The wo invesen syles ha redress any arke ispriings os are he aurae fundaenal invesors and he onrarian invesors (.f. 6A wih 6, 20 wih 9) In suary, i is he growh invesors and/or he oenu invesors ha are he ajor onribuors o ispriing in arkes and a soure of he under- and over-reaion in pries o inforaion releases and he susained periods of ispriing ha have been oonly found in any epirial sudies. The aurae fundaenal and onrarian invesors are he greaes iigaing fores agains suh ispriings bu even hey anno preven ispriings persising over long ie periods. Neiher he index invesors, by effeively wihdrawing funds fro he arke and he rando invesen behaviour of he noise raders ake a signifian 2 There are nine es ases in whih he ispriing easure represens 0% or ore of he average prie 2

13 onribuion o ispriings in arkes nor do hey play a role in orreing any ispriings. However, i is ineresing o observe he four-fold drop-off in ispriing fro es ase 9 (75% oenu and growh invesors) o es ases 2 and 22 (boh 60% oenu and growh invesors), whih leads one o observe ha exen of any ispriing is quie sensiive o he proporion of he arke represened by growh and oenu invesors. Reurns fro Alernaive Syles We now urn our aenion o firs he reurns, and hen he risks, experiened by he differen invesor syles under he various es ases. We have repored in Tables 2 and 3 he absolue and relaive reurns and risks realised by eah ype of invesor for eah of he 27 es ases where he earnings growh is boh rando and serially orrelaed 22. We hoose o firs oen on he reurns as hey have ipliaions for (i) he exploiable opporuniies flowing fro he idenified ispriings disussed in he previous sub-seion and (ii) he longer-er susainabiliy of invesors following eah of he various invesen syles. One obvious winner is he aurae fundaenal invesor who onsisenly ouperfors under all arke ondiions bu realises heir greaes ouperforane in arkes where hey are in opeiion wih growh and/or oenu invesors. The oher ouperforer in he ajoriy of he es ases is he onrarian invesor who realises handsoe gains a he expense of he sae growh and/or oenu invesors. Indeed in arkes driven by randoly generaed earnings growh, he added value realised by he onrarian invesor is very siilar o ha realised by he aurae fundaenal invesors. However here are insanes in arkes driven by serially-orrelaed earnings growh where he perforane of he onrarian invesor is uh inferior o ha realised by aurae fundaenal invesors. This is pariularly rue when he onrarian invesor is in single opeiion wih he aurae fundaenal invesor and/or when he wo ypes of oenu invesors are also presen in he arke. The onrarian invesors aually underperfor in hose arkes driven by serially-orrelaed earnings growh where hey are in opeiion wih fundaenal invesors (see es ases 4, 3A and 23 fro Table 3) whereas hey have he greaes upside in hese sae arkes when fundaenal invesors are absen (see es ases 0, 6A and 24 in Table 3). This refles ha alhough he aurae fundaenal and he onrarian invesors boh see o have he abiliy of idenifying when a sok is heap, i is he fundaenal invesor who is able o do so wih greaer auray and superior iing. The index invesors and he noise raders effeively realise he arke reurn under all arke oposiions irrespeive of wheher earnings growh is rando or serially-orrelaed. This should oe as no surprise in he ase of index invesors whose ain objeive is o repliae he arke reurns bu is ore ineresing in he ase of noise raders and iplies ha onrary o wha Friedan suggesed, he ruly rando invesor igh survive under os arke oposiions. This leaves us wih he wo os ineresing ypes of invesors; he growh and he oenu invesors. The growh invesors perfor relaively well in rando arkes ypially eking ou sall profis, alhough heir reurns are always inferior o hose of he fundaenal invesors and/or he onrarian invesors. The ouoe hanges in arkes ipaed by seriallyorrelaed earnings growh, where he growh invesor experienes signifian underperforane in arkes populaed by fundaenal and/or onrarian invesors in obinaion wih oenu invesors. The srong rends in suh arkes ause he growh invesor o signifianly isprie soks in boh up and down arkes wih he resuling ispriing opporuniies being exploied by he aurae fundaenal and/or onrarian invesors. 22 The reurns ha we repor are he average of he 25-year reurns over he 300 siulaions and he risks are he sandard deviaion of hese reurns. 3

14 The long-er oenu invesors are he onsisen losers largely as a onsequene of arkes no rending over suffiienly long periods o aoodae heir ipleenaion of he oenu syle. Indeed, hese invesors underperfor in all of he es ases exained, bu ore so in he rando arkes ha obviously do no sui an invesor whose syle is dependen upon rending arkes. In onras he shor-er oenu invesors do ouperfor in all es ases as a resul of heir ipleenaion being ore in une wih priing behaviour, wih he exepion of where hey are in sole opeiion wih fundaenal and growh invesors. The bes perforane of shor-er oenu invesors is realised in rando arkes populaed by fundaenal and longer-er oenu invesors. As well as providing insighs ino perforane of differen syles in differen arkes seings, he above disussion also has ipliaions for (i) he exen o whih he ispriing opporuniies ha we have previously highlighed are exploiable and (ii) he likelihood of survival of invesors pursuing differen invesen syles. We will onsider (ii) a a laer poin in his paper bu a his sage will ake soe observaions regarding (i). The onsisen winners aross all arke seings are he aurae fundaenal invesors while he onrarian invesors also ouperfor in he vas ajoriy of insanes. Boh of hese ypes of invesors follow a raional inforaion-driven approah and ahieve heir greaes value added in hose arkes seings in whih our ispriing easure are greaes. This leads us o onlude ha our findings provide evidene o suppor he proposiion ha he inerplay beween invesors pursuing differen arke syles an be he soure of ineffiienies in arkes. A onlusion ha is srenghened by he fa ha he prie behaviour generaed in any of our es ases is onsisen wih he sylised fas drawn fro he arke anoalies lieraure. Risks assoiaed wih Alernaive Syles We will now urn our aenion o onsidering he risks experiened by eah syle of invesor and, in pariular, he risks ha hey ipose on hose pursuing oher syles. Before oening he review we should poin ou ha we have presened wo easures of risk: an absolue risk easure being he sandard deviaion of he weekly reurns generaed for eah invesen syle and a relaive easure being he raking error as easured by he sandard deviaion of he differene beween he weekly reurns of a pariular syle and ha of he arke. The low absolue risk and raking error experiened by all ypes of invesors involved in es ases, 5 and 6 as presened in Table 2 and Table 3 would lead us o disiss fundaenal, onrarian and index invesors as being he soure of any signifian level of risk eiher o heselves or o hose following oher invesen syles. Therefore, in he following disussion we an onenrae our aenion on he risk faed by he growh, oenu and noise raders and he ipa ha hese hree ypes of invesors have on he risk faed by he oher ypes of invesors. Risks under Rando Markes An exainaion of he risks under es ases 2, 0 and in Table 2 onfir ha he growh invesors are also no a ajor soure of risk eiher o heselves hrough heir ipa on arkes or o he fundaenal, onrarian and index invesors in arkes where earnings grow randoly hrough ie. We observe in suh arkes ha he absolue risk of all invesors inreases signifianly one one or ore oenu invesors and/or noise raders are inrodued ino he oposiion. However i is raking error raher han absolue risk ha have oe o be aeped as he ain easure of risk of an individual invesor and our findings beoe ore oplex one we onsider raking error as he risk easure for invesors in a rando arke seing (see he righ-hand panel of par B). I shows ha he raking errors experiened by he oenu invesors and noise raders are ypially uh less han ha experiened by he invesors pursuing oher invesen syles. Good exaples 4

15 of his an be found in es ases 23 and 24 where in boh insanes oenu invesors and noise raders experiene relaively low raking error while he growh and onrarian invesors, and o a lesser exen he fundaenal invesors, experiene uh higher levels of raking error. Wih he exepion of he index invesors, he shor-e oenu invesors experiene he lowes risk, followed by he noise raders and he long-er oenu raders. Risks under Trending Markes In he ajoriy of our es ases he absolue risk of he arke inreases by less han 0% where he arke is driven by serially-orrelaed earnings growh as opared o arkes where i is driven by randoly generaed earnings. However, here are isolaed insanes in arkes heavily populaed by fundaenal invesors of inreases in arke risk in he range of 50% o 00%. The swih fro rando arkes o rending arkes resuls in hardly any inrease in absolue risk for he oenu, index and noise invesors. The invesor syle os ipaed by he ove o rending arkes are he onrarian invesors who experiene in several es ases a ore han a doubling of absolue risk bu we also noe ha fundaenal and growh invesors also experiene sizable inreases in absolue risk under erain es ases. In onras o he relaively sall inrease in absolue risk experiened by he various invesen syles under rending as opared o rando arkes, any of he invesen syles experiene uh larger inreases in heir raking error (i.e. relaive risk). This is no rue for he oenu and index invesors and noise raders, whose raking error reains alos he sae under he rending arkes as i was under rando arkes. However he fundaenal, growh and onrarian invesors experiene uh greaer raking error under he rending arkes and pariularly in hose arkes ha are also oposed of growh, oenu and/or noise raders This an be seen fro a review of he ore oplex arke oposiions (i.e. es ases 9 o 26 in Table 3), where we see levels of raking errors for fundaenal, growh and onrarian invesors ha are en- o 20-ies hose experiened by oenu, noise, and index invesors. The exree risks faed by he hree ore valuebased invesors as deonsraed in hese es ases is largely a onsequene of he rading oo early in arkes ha rend away fro fundaenal value for exended periods resuling in hese invesors experiening exended periods of underperforane prior o he benefiing fro he evenual ean reversion in priing. Indeed, we an see in a arke oposed of a balaned represenaion of all of our invesen syles (es ase 25) ha he shor-er oenu rader realises an inforaion raio uh higher han ha of he aurae fundaenal and onrarian invesors, due o he uh higher relaive risk experiened by hese wo laer syles of invesing. Therefore i would no be surprising o find ha in suh arke seings, invesors (and asse anagers) being drawn away fro ore value-based approahes of invesing and owards oenu invesing (alhough our findings highligh ha no all ipleenaions of oenu ouperfor). Of ourse, if his drif fro valuebased o oenu invesing ours hen i will resul in even ore volailiy and ispriing wihin arkes. Seion 5: Suary and Conluding Coens The oposiion of invesen syles in arkes has hanged signifianly over ie. The epirial evidene highlighs a reduion in he influene of he inforaion-driven fundaenal invesors due o ore funds flowing o invesen syles whih rely on signals oher han hose ha are supposedly relevan o arke pries. In his sudy we have used arifiial heerogeneous agen odel o sudy he behaviour of arkes populaed by invesors following ipleenaions of invesen syles suh as fundaenal, oenu, onrarian, index and noise. Our priary objeive was o invesigae he exen o whih he ajor arke anoalies idenified in he epirial lieraure an be explained o soe exen by he inerplay of invesors pursuing sraegies represenaive of hose oon syles adoped in real arkes. Our ineress also exended o he analysis of he perforane of he various 5

16 invesors populaing onsiuing he arke fraions onsidered and, in pariular, he ipliaions of he presene of eah invesen syle on he perforane of he oher syles. In his regard, we onsidered wo ypes of arkes: one in whih inereporal inforaion signals (in our odel represened by he growh of quarerly earnings) are rando as assued in an effiien arke; he oher where here is serial orrelaion buil ino he earnings growh, whih is ore in line wih he epirial findings. In boh insanes we found ha arkes oposed of various obinaions of aurae fundaenal, onrarian, index and noise raders are fairly effiien. Furher, he firs hree of hese invesor syles an be regarded as arke-friendly in ha hey no only inrodue negligible inreenal arke risk and rading volues, bu hey also have lile ipliaions for he risks faed by he oher invesors 23. In onras, and onsisen wih previous finding in he lieraure, he noise raders are he soure of a large porion of arke risk, and ause he arkes o be ore risky for hose pursuing oher invesen syles. In relaion o he oher wo syles invesigaed - fundaenal exrapolaors (growh) and oenu invesors - hey boh individually and ogeher see o be he soure of onsiderable desabilisaion in priing, wih his being pariularly so when he inforaion flows are serially-orrelaed. This is iporan as boh ypes of oenu invesors and he growh invesors see o exend he rends in pries reaed by he serially-orrelaion in earnings announeens and so onribue o aual pries diverging fro he fundaenal pries for exended periods of ie. In he rando arkes i is he long-er ipleenaion of oenu invesors ha is he ajor soure of ispriing, wih he shorer-er oenu invesors and he growh invesors also onribuing bu o a less exen. In he ase of serially-orrelaed inforaion flows, i is now he growh invesor ha perfors he priary role in generaing ispriings, wih oenu invesors, along wih index invesors and noise raders, playing wha is bes desribed as a supporing role. The ajor quesion ha reains ousanding is wheher he arke sruures ha give rise o anoalous priing are susainable. In oher words, he explanaion ha we pu forward o explain ispriings in arkes ay only persis if he arke oposiions ha give rise o he persis. Wih his in ind, we evaluaed he perforane of he various invesors and esablished he long-er viabiliy of he various invesen syles and found ha i is only he longer-er prie oenu invesors ha are likely o prove non-viable under all arke ondiions wih he growh invesors also proving non-viable under rending arkes. The fa ha he wo leas viable invesors are he sae ones ha ake he ajor onribuions o anoalous priing raise he quesion as o wheher hey will susain suh ispriing ino he fuure if hey indeed give rise o i in he firs plae. However in foreasing heir deise we should reeber ha invesors over-exrapolae and pursue oenu invesing (herding) for a variey of reasons, any of whih are no srily perforane relaed. This does no deny ha any invesors using suh syles will eiher reire fro he arke or drif o soe oher syle of invesing. However, i is likely ha hey will be replaed by novies who are araed by hese syles for he sae reasons ha have been araing invesors for any deades. 23 We do find ha a signifian proporion of index invesors slows down he rae a whih pries adjus o new inforaion (Bird and Woolley, 2003) 6

17 Referenes Alfarano, S., Lux, T., Wagner, F., Esiaion of agen-based odels: The ase of an asyeri herding odel, Copuaional Eonois,26, 9-4. Ball, R. and Brown,., 968. An epirial evaluaion of aouning inoe nubers. Journal of Aouning Researh, 6, 2. Bird, R., Casavehia, L., Value enhaneen using oenu indiaors: he European experiene, Inernaional Journal of Managerial Finane, forhoing Bird, R., and Woolley, 2003, Eonoi ipliaions of passive invesing. Journal of Asse Manageen, 3, 4. Capaul, C., Rowley, I., Sharpe, W., 993. Inernaional value and growh soks. Finanial Analyss Journal, 49,. De Bond, W., Thaler, R., 985. Does he sok arke overrea? Journal of Finane, 40, 3. De Long, J.B., Shleifer, A., Suers, L., Waldann, R., 990. Noise rader risk in finanial arkes. Journal of oliial Eonoy 98, Dison, E., Nagel, S., Quigley, G., Capuring he value preiu in he Unied Kingdo. Finanial Analyss Journal, 59, 6. Faa, E., 970, Effiien apial arkes: A review of heory and epirial work, Journal of Finane, 37, 2. Faa, E.,995. Rando walks in sok arke pries, Finanial Analyss Journal, Vol. 5, Iss. ; p. 75 Faa, E., The FEN one-on-one inerview: Eugene F. Faa, Finanial Engineering News, Noveber 3 rd Faa, E., Frenh, K., 992. The ross-seion of expeed sok reurns, Journal of Finane, 47, Graha, B. and Dodd, D Seuriy analysis, MGraw Hill, New York. Grinbla, M., Tian, S., Werers, R., 995. enu invesen sraegies, porfolio perforane and herding: A sudy of uual fund behavior. Aerian Eonoi Review, 85 Harris, S The long-er perforane of UK soks afer aking righs issues, Journal of Asse Manageen, 4.5. Hong, H., Sein, J., 999. A unified heory of underreaion, oenu rading, and overeaion in asse arkes, Journal of Finane, 54, 6. Ikenberry, D., Lakonishok, J., Veraellen, T., Sok repurhases in Canada: perforane and sraegi rading, Journal of Finane 55, 5. Jegadeesh, N., Tian, S., 993. Reurns o buying winners and selling losers: Ipliaions for sok arke effiieny. Journal of Finane, 48, Jegadeesh, N., Tian, S., 200. rofiabiliy of oenu sraegies: An evaluaion of alernaive explanaions, Journal of Finane. 56, 2. Lakonishok, J., Shleifer, A., Vishny RW., 994. Conrarian invesens, exrapolaion, and risk, Journal of Finane: 49, 5. Lee, C., Swainahan, B., rie oenu and rading volue. Journal of Finane, 55,5. Levy, M., Levy, H., Soloon, S., 995. Mirosopi siulaion of he sok arke. Journal of hysis I, 5, 8. Malkiel, B., assive invesen sraegies and effiien arkes, European Finanial Manageen, 9,. Rier, J., Welh, I., A review of IO aiviy, priing and alloaions. Journal of Finane, 57, 4. Siegel, J., Wha is an asse bubble? An operaional definiion. European Finanial Manageen, 9,. Soffer, L., Walher, B., Reurn oenu, reurn reversals and earnings surprise. Working aper: Universiy of Illinois a Chiago Srivasava, A., Capial arke effiieny: A lieraure review. Working aper: Jaipura Insiue of Manageen Werers, R., 999. Muual fund herding and he ipa on sok pries. Journal of Finane, 54 Wylie, S., anager herding: Tess of he auray of easures of herding using UK daa. Working aper: Darouh Universiy 7

18 Figure. rie ah and Auoorrelaions for Differen Tes Cases: Rando ES. The figure shows he prie pah relaive o he fundaenal prie (lef side) and he auoorrelaion funion over 40 lags of he log reurn (righ side) for differen es ases for he siulaions where he earnings are assued o follow a rando walk. anel A depis he resuls for es ase 4 where he arke is iniially 50% oposed of he aurae fundaenal invesor (F 2) and 50% oposed of he long-er oenu invesor who is denoed hroughou he paper as 26 M 26. In anel B, we provide he sae inforaion for es ase 9 where he arke is iniially 50% oposed of he growh invesor (F 40), who overexrapolaes reen earnings growh, and he oenu raders 26 M 26. 8

19 Figure 2. rie ah and Auoorrelaions for Differen Tes Cases: Serially Correlaed ES. The figure shows he prie pah relaive o he fundaenal prie (lef side) and he auoorrelaion funion over 40 lags of he log reurn (righ side) for differen es ases for he siulaions where he earnings are assued o be serially orrelaed. We depi he resuls for es ase 9 where he arke is iniially 50% oposed of he growh invesor (F 40), who overexrapolaes reen earnings growh, and he oenu raders 26 M 26. 9

20 Table The Iniial Weighs in he 27 Tes Cases In his able, we douen he iniial perenage of raders for eah es ase (or arke sruure). These perenages hen vary aording o he weekly proporion of he raders wealh in relaion o he oal wealh in he arke. There are wo fundaenal invesors who rade on he differene beween a sok s urren prie and is pereived fair value. F 2 exrapolae reen earnings growh for 2 quarers while F 40 over-exrapolae ou reen earnings growh for 40 quarers. There are wo oenu invesors who rade on he basis of he prie oveen over soe previous defined foraion period and who hold he soks for a fixed holding period. 3 M 6 operaes wih a foraion period of 3 weeks and a holding period of six weeks while 26 M 26 operaes wih a foraion period of 26 weeks and a holding period of 26 weeks. Conrarian raders based heir signal on a arke-based indiaor ha is represened by a sok s earnings-yield. The Index raders repliae he index whereas he Noise invesors siply rade on a rando signal. aenal (orre) aenal (Overexrapolaor) enu (Shor) enu (Long) Conrarian Index Noise A A