Algorithmic Trading, Market Efficiency and The Momentum Effect. Rafael Gamzo

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1 Algorithmic Trading, Markt Efficincy and Th Momntum Effct Rafal Gamzo Studnt Numbr: A rsarch rport submittd to th Faculty of Commrc, Law and Managmnt, Univrsity of th Witwatrsrand, in partial fulfilmnt of th rquirmnts for th dgr of Mastr of Managmnt in Financ & Invstmnt. Johannsburg, 2013 i

2 ד סב ABSTRACT Th vidnc put forward by Zhang (2010) indicats that algorithmic trading can potntially gnrat th momntum ffct vidnt in mpirical markt rsarch. In addition, upon analysis of th litratur, it is apparnt that algorithmic tradrs possss a comparativ informational advantag rlativ to rgular tradrs. Finally, th thortical modl proposd by Wang (1993), indicats that th informational diffrncs btwn tradrs fundamntally influncs th natur of asst prics, vn gnrating srial rturn corrlations. Thus, applid to th study, th thory holds that algorithmic trading would hav a significant ffct on scurity rturn dynamics, possibly vn ngndring th momntum ffct. This papr tsts such implications by proposing a thory to xplain th momntum ffct basd on th hypothsis that algorithmic tradrs possss Innovativ Information about a firm s futur prformanc. From this prspctiv, Innovativ Information can b dfind as th information drivd from th ability to accumulat, diffrntiat, stimat, analyz and utiliz colossal quantitis of data by mans of adpt tchniqus, sophisticatd platforms, capabilitis and procssing powr. Accordingly, an algorithmic tradr s accss to various complx computational tchniqus, infrastructur and procssing powr, togthr with th constraints to human information procssing, allow thm to mak judgmnts that ar suprior to th judgmnts of othr tradrs. This particular aspct of algorithmic trading rmains, to th bst of my knowldg, unxplord as an avnu or mchanism, through which algorithmic trading could possibly affct th momntum ffct and thus markt fficincy. Intrstingly, by incorporating this information variabl into a simplifid rprsntativ agnt modl, w ar abl to produc rturn pattrns consistnt with th momntum ffct in its ntirty. Th gnral thrust of our rsults, thrfor, is that algorithmic trading can hypothtically gnrat th rturn anomaly known as th momntum ffct. Our rsults giv crdnc to th assumption that algorithmic trading is having a dtrimntal ffct on stock markt fficincy. ii

3 ד סב DECLARATION I, Rafal Alon Gamzo, dclar that this rsarch rport is my own work xcpt as indicatd in th rfrncs and acknowldgmnts. It is submittd in partial fulfilmnt of th rquirmnts for th dgr of Mastr of Managmnt in Financ & Invstmnt in th Univrsity of th Witwatrsrand, Johannsburg. It has not bn submittd bfor for any dgr or xamination in this or any othr univrsity. Rafal Alon Gamzo: Signd at Wits Businss School On th 1st day of August 2013 iii

4 ד סב ACKNOWLEDGEMENTS My first apprciation gos to Hashm, G-d, King of th univrs, th most prcious thing in my lif. No words can fully xprss my dp affction, aw and rvrnc. My soul thirsts for You, my flsh longs for You, in a dry and wary land without watr. So may I look for You in th sanctuary to s Your powr and Your glory. Bcaus your lov is bttr than lif, my lips will glorify you. I will prais you as long as I liv, and in your nam I will lift up my hands. ( Thillim:63.) I would lik to xprss my gratitud to my rsarch suprvisor, Profssor Eric Schaling for his abl, insightful guidanc throughout th cours of my program. I would also lik to thank Profssor Frdrick Ahwirng-Obng and Profssor Christophr Malikan, from whom I hav bnfitd immnsly. I also xtnd my profound gratitud to all th staff at Wits Businss School for making my studis possibl. To Profssor Jann Zaidl-Rudolph and Profssor Michal Rudolph, your protction, car and wisdom hav bn a blssing to m. To my mothr and fathr, Yaron and Lindsay, whos xcptional slflssnss and ncouragmnt hav givn m mor than I could hav askd for. I am fortunat to call myslf your son. To my sistr Liat, whos unwavring support and blif has bn an inspiration to m. Last, but by no mans last, I would lik to thank my bautiful girlfrind Nisi, who has inspird m to bcom th prson I am today. For hr prayrs, patinc, lov and assistanc, I am truly gratful. iv

5 TABLE OF CONTENTS ABSTRACT II DECLARATION III ACKNOWLEDGEMENTS IV CHAPTER 1 : INTRODUCTION ) Purpos of th study ) Contxt of th study... 6 I. Th Efficint Markt Hypothsis... 6 II. Evolution and Forms of Markt Efficincy... 7 a. Wak-Form Efficincy... 8 b. Smi-strong Form Efficincy... 8 c. Strong-Form Efficincy... 8 III. Th Pric Adjustmnt Procss Implicit in th EMH... 9 IV. Markt Efficincy and th Momntum Effct V. Algorithmic Trading VI. Th Evolution of Algorithmic Trading VII VIII Algorithmic Trading and Financial Institutions Algorithmic Trading and th Momntum Effct ) Problm Statmnt ) Rsarch Objctivs... 18

6 1.6) Rsarch Qustions ) Significanc of th Study ) Structur of th Rsarch Chaptr 2: Litratur Rviw ) Introduction ) Rviw of th Currnt Litratur Concrning th EMH ) Rviw of th Currnt Litratur Concrning th Momntum Effct ) Possibl Explanations for th Momntum Effct a. Th Positiv Fdback Modl b. Th Ovrconfidnc Hypothsis ) Rational Modls and Information ) Concluding Rmarks on th Explanations for th Momntum Effct ) Rviw of th Currnt Litratur Concrning Algorithmic Trading a. Evidnc in Favour of Algorithmic Trading b. Evidnc Against Algorithmic Trading ) Th Intrplay Btwn Markt Participants and Information ) Algorithmic Trading and Asymmtric Information ) Information Driving Algorithmic Trading ) Othr Sourcs of Information Availabl to Algorithmic Tradrs ) A Possibl Explanation for Algorithmic Tradrs Informational Supriority ) Advancd Computational Tchniqus usd by Algorithmic Tradrs..47

7 ) Infrastructur and Procssing Powr ) Th Stylizd Facts about Algorithmic Tradrs ) Existing Thortical Modls ) Concluding Rmarks..63 Chaptr ) Introduction )Th Hypothsis ) Idntification of Rlvant Variabls and Stting Prior Expctations ) Rsarch Dsign and Modlling ) Rsarch Mthodology Chaptr 4: Th Modl ) A Rprsntativ Algorithmic Tradr-Agnt Modl ) Limitations..89 Chaptr 5: Discussion of th Rsults. 90 Chaptr 6 : Conclusion and Rcommndations ) Rcommndations for Furthr Rsarch 103 Rfrncs: APPENDIX A: 112

8 CHAPTER 1: INTRODUCTION Eugn Fama s (1970) Efficint Markt Hypothsis (EMH) has arguably bcom on of th most fascinating and highly contstd subjcts amongst financial profssionals and acadmics alik. Indd, th foundation of capital markt quilibrium lis on th Efficint Markt Hypothsis 1. Essntially, th Efficint Markt Hypothsis is an xtnsion of th zro profit comptitiv quilibrium condition from th crtainty world of classical pric thory to th dynamic bhavior of prics in spculativ markts undr conditions of uncrtainty 2 (Jnsn, 1978, p. 3). Inhrnt in th abov supposition is that givn th availabl information - scurity prics ar likly to xhibit unprdictabl bhavior. Accordingly, by and larg, no group of invstors should b abl to consistntly bat th markt by making consistnt positiv xcss rturns. Scurity rturn dynamics as wll as potntial trading stratgis ar fundamntally influncd by th natur and thus unprdictability of scurity prics, implicit in this Efficint Markt Hypothsis (Karmra, Ojah, & Col, 1999). Broadly spaking, th xtnt to which a financial markt is fficint has flicious consquncs for invstmnt and rsourc allocation in an conomy. This hypothsis has bn continuously and xtnsivly documntd, tstd and challngd vr sinc its incption 3. Howvr, thr has bn a growing body of financial litratur rcntly 4, highlighting aspcts of stock pric and rturn bhavior, which sm to dviat 1 It is of critical importanc that th (EMH) holds, or most of th statistical tchniqus in analyzing capital markt quilibrium such as th Capital Asst Pricing Modl (CAPM) ar opn to qustion (Huang & Yang, 1999). 2 Accordingly, a markt can b calld fficint whn prics always fully rflct availabl information (Fama, 1970, p. 383). 3 Its prominnc in financial litratur bcam most noticabl in th 1960s undr th rubric of th Random Walk Hypothss 4 Th growing availability of intraday data in th 80s and 90s allowd rsarchrs to tst informational ffcts on stock prics within minuts (Gosnll, Kown & Pinkrton, 1996). Howvr, this priod also

9 from what is considrd th norm, rgarding th traditional paradigm. Ths abnormalitis ar both baffling and difficult to rconcil with markt fficincy du to thir implications rgarding prdictability. Ths irrgularitis ar rfrrd to as markt anomalis. Among ths anomalis, th momntum ffct is probably th most difficult to xplain and rprsnt, prhaps, th strongst vidnc against th Efficint Markt Hypothsis 5. Following Hong and Stin (1999), th momntum ffct can b viwd as an umbrlla trm ncompassing two prvasiv, intrconnctd phnomna. That is, firstly, th phnomna of xcss stock rturns tnding to xhibit unconditional positiv srial corrlation in th short to mdium-run (short-trm momntum) and scondly, th phnomna of xcss rturns tnding to xhibit ngativ srial corrlation in th long-run (long-trm rvrsals). Takn togthr ths two intrconnctd phnomna rprsnt th momntum ffct in its ntirty. Indd, studis on this subjct hav bgun to viw short-trm momntum and long-trm rvrsals as insparabl phnomna. (Hong and Stin, 1999). This momntum ffct is rgardd as on of th most puzzling anomalis of financ. Qustions surrounding th undrlying causs for th abov anomaly hav bn and may rmain mpirically unrsolvd for a whil. Adding to th complxity of th issu, financial markts ar sn to hav undrgon trmndous structural changs sinc th aformntiond studis wr conductd. Rcnt tchnological innovations hav facilitatd an xtraordinary volution in capital markt structur, as wll as considrably altring th procsss undrlying scurity rturns. witnssd th intllctual dominanc of th fficint markt hypothsis bcoming far lss univrsal. For xampl, Kim and Stambaugh (1986) found stock prics can b prdictd using crtain forcast tchniqus basd on crtain prdtrmind variabls. 5 Ths abnormalitis cast a considrabl doubt on th validity of th Capital Asst Pricing Modl, and hnc, markt fficincy. (Alagidd & Panagiotidis, 2009, p. 9). Indd, Fama and Frnch (1996) point out that th momntum ffct constituts th main mbarrassmnt for thir thr-factor modl (s also Fama and Frnch (2008)) 2

10 All things considrd it sms indcorous to nglct ths tchnological innovations and its possibl ffcts on markt fficincy whn analyzing th issus highlightd abov - this rmains a cntral thm of our rsarch. On of th ky dvlopmnts stmming from ths tchnological advancs falls undr th rubric of algorithmic trading. According to Zhang (2010), as of 2009, algorithmic trading accountd for as much as 78% of all U.S. quity trading volum. Algorithmic trading is commonly dfind as th us of computr algorithms to automatically mak trading dcisions, submit ordrs, and manag thos ordrs aftr submission (T. Hndrshott & Riordan, 2009, p. 2). Algorithms hav volvd into som of th most sophisticatd trading programs, making us of cutting dg mathmatical modls and xtraordinary procssing powr in ordr to implmnt profitabl trading stratgis. Thy mploy rlvant statistical and conomtric tchniqus via advancd computr and communication systms at xtrmly high spds and ar capabl of anticipating and intrprting rlativly short-trm markt signals, in ordr to implmnt profitabl trading stratgis. A dbat comprising widly opposing opinions has transpird rgarding th bnfits and risks associatd with algorithmic trading. Th Jury is still out, howvr, rgarding its ovrall ffct on th fficincy of financial markts. Proponnts of algorithmic trading hav linkd its prsnc to incrasd liquidity 6 and/or improvd pric discovry 7 in both forign xchang and quity markts. (Hndrshott, Jons & Mnkvld, 2011; Chaboud, Hjalmarsson, Vga & 6 Hndrshott, Jons and Mnkvld (2011) argu that for all stocks, and spcially larg-cap stocks, automatd trading incrasd liquidity. Chaboud, Hjalmarsson,Vga and Chiquoin (2009), using th 1993 to 1997 priod, posit that automatd trading tnds to slightly incras liquidity provisions in th forign xchang markts aftr xognous markt vnts such as nws announcmnts. 7 Brogaard (2010) in his analysis on th impact of algorithmic trading on markt quality finds that algorithmic trading adds to th procss of pric discovry, but finds mixd rsults on its ability to supply liquidity to th markt. Hndrshott and Riordan (2011) xamind th impact of algorithmic trading on th pric discovry procss in US quity markts. Ovrall th authors obsrvd that marktabl algorithmic trads activly driv prics towards thir long-trm fundamntal valu, thrby aiding th pric discovry procss. 3

11 Chiquoin, 2009; Brogaard, 2010, and Hndrshott & Riordan, 2011). Whilst, opponnts argu that it crats an atmosphr of instability and information infficincy (Smith, 2010, and Zhang, 2010). Evidnc to dat is still inconclusiv. Consistnt with th momntum ffct, Zhang (2010) finds that algorithmic trading hindrs th incorporation of fundamntal information into asst prics. His papr rvals that prics dviat systmatically from thir fundamntal valus whn algorithmic trading is mor vidnt, rsulting in thir rgrssion in subsqunt priods. Rlying on U.S. quity markt data, Zhang showd that in trms of conomic magnitud, on standard dviation incras in algorithmic trading also incrasd pric raction to fundamntal information by 8%. Although not xplicitly considrd in his papr, th findings suggst th prsnc of a momntum ffct- which was prviously attributd to bhavioral factors such ovrconfidnc and subjctiv slf-attribution bias 8 - and that this ffct can b bttr xplaind by algorithmic trading. Morovr, Smith (2010) finds that algorithmic trading is influncing th microstructur of quity transactions, xhibiting drastically highr dgrs of slf-similarity 9. Evidnc thus far sms to lnd itslf to th possibility of a rlationship btwn algorithmic trading and th momntum ffct. Howvr, attributing causality- by accrditing algorithmic trading with ngndring th momntum ffct- rmains prmatur. 8 S for xampl, Danil, Hirshlifr and Subrahmanyam, 1998, or sction of this papr, possibl xplanations for th momntum ffct, for a mor dtaild dscription of ovrconfidnc and subjctiv slf-attribution bias. 9 Slf-similarity is usually calculatd using th Hurst xponnt, H, which masurs th rlativ dgr of slf-similarity from pur Markovian Browninan Motion. For mor information s Smith (2010). His analysis posits that, as a rsult of algorithmic trading, markts ar bginning to xhibit fdback ffcts at xtrmly short timscals. 4

12 In brif, th momntum ffct and thus rturn prdictability has dominatd discussions on th Efficint Markt Hypothsis, yt no clar rasons or causs of th phnomna hav bn stablishd. Th initial prcption fails to tak into account th trmndous changs that hav takn plac in financial markts, consquntly, nglcting th rol playd by algorithmic trading in this complx dynamic rlation. Furthr, th vidnc put forward by Zhang (2010) indicats that algorithmic trading can potntially gnrat th momntum ffct vidnt in th rsarch, howvr, du to algorithmic trading s rlativly rcnt mrgnc, th litratur is yt to xamin this dirctly. Mor prcisly, th litratur is yt to produc a thortical modl that invstigats whthr algorithmic trading can gnrat th momntum ffct. Thrfor, this rsarch intnds to invstigat th contmporanous and dynamic rlationship btwn algorithmic trading, th momntum ffct and stock markt fficincy by focusing, formost, on th impact algorithmic trading has on scurity pricing and rturn dynamics (markt fficincy). Mor spcifically, algorithmic trading s ability to gnrat short-run momntum and subsqunt long-trm rvrsals (th momntum ffct). If on taks into considration th wll documntd nxus btwn th momntum ffct and stock markt fficincy as wll as considring th possibility of algorithmic trading ngndring this obsrvd phnomnon, it sms appropriat to invstigat algorithmic trading, th momntum ffct and stock markt fficincy in unison. 1.2) Purpos of th Study Th main purpos of this rsarch is to xamin th availabl litratur on capital markt fficincy in ordr to provid a prmis with which to discuss and valuat th critical issus raisd by th anomalistic fatur of th Efficint Markt Hypothsis, namly, th momntum ffct. This analysis intnds to complmnt still inconclusiv acadmic litratur on ths topics by drawing upon both concptual framworks and indicativ 5

13 vidnc obsrvd in th U.S. markts. Mor importantly an assssmnt will b mad on whthr this obsrvd phnomnon can b xplaind by algorithmic trading in th capital markt. In an ffort to advanc on causality, this study will attmpt to produc a rprsntativ modl, incorporating faturs that fit wll with th stylizd facts about algorithmic trading. This is don in ordr to idntify th thortical mchanism through which algorithmic trading may possibly gnrat this obsrvd phnomnon. 1.3) Contxt of th Study i) Th Efficint Markt Hypothsis Whn Fama (1970) assmbld a comprhnsiv rviw of thortical and mpirical vidnc of markt fficincy h proposd a thory known as th Efficint Markt Hypothsis (EMH). Accordingly, a markt can b calld fficint whn prics always fully rflct availabl information (Fama, 1970, p. 383) Th concpt of an fficint markt can b illustratd by th following short story: A studnt and hr financ profssor ar both walking down th busy campus hall whn thy both notic a $100 not lying on th floor. As th studnt bnds down to pick up th mony sh notics a disappointd look on hr profssor s fac. Th profssor subsquntly says to th studnt, Don t bothr. If th mony was rally thr, somon ls would hav pickd it up alrady (Malkil, 2003). Th Efficint Markts Hypothsis is simpl in principl, but rmains lusiv. Undr th rubric of th Random Walk Hypothsis, th Efficint Markt Hypothsis suggsts that th path that a stock pric follows should display no discrnibl pattrn, thus prcluding any knowldg of past prics as a mans of prdicting futur stock prics. A simpl vrsion of th Random Walk Hypothsis is that th 6

14 pric of a stock today is th pric of a stock ystrday plus an unprdictabl rror trm: Y t = a + Y t 1 + t Mor prcisly th abov quation is rfrrd to as a random walk with a drift 10. This ida has bn applid xtnsivly to thortical modls and mpirical studis of financial scuritis prics, gnrating considrabl controvrsy as wll as fundamntal insights into th pric-discovry procss 11. Th importanc of th Random Walk Hypothsis cannot b undrstatd. It is crucially important that th random walk hypothsis holds, or most of th statistical tchniqus in analyzing capital markt quilibrium such as CAPM ar opn to qustion (Huang & Yang, 1999, p. 3). ii) Evolution and Forms of Markt Efficincy A markt is said to b fficint rgarding som particular information if that information is not ffctiv in arning positiv xcss rturns. Historically th volution of mpirical work on markt fficincy bgan primarily with what is rfrrd to as wak form tsts. Hr, studis wr concrnd mrly with past pric (or rturn) historis. This typ of tst is considrd th outcom of random walk litratur. Aftr numrous tsts confirmd fficincy at this lvl, studis bgan to focus on smi-strong form tsts which wr concrnd with th tim takn for prics to adjust to all publically availabl information 12. Finally, strong form tsts, whr, monopolistic accss to information by any invstors, was of intrst. As a rsult thr diffrnt forms of markt fficincy mrgd. Ths forms ar laboratd blow: 10 In th tru random walk modl a would = If stock prics ar gnratd by a random walk (possibly with drift), thn, for xampl, th varianc of monthly sampld log-pric rlativs must b 4 tims as larg as th varianc of a wkly sampl. (Lo & MacKinlay, 1988, p. 53) 12 For xampl, dividnd announcmnts, sasond public offrings or stock splits. 7

15 A) Wak-Form Efficincy This typ of fficint markt suggsts that th currnt pric of a shar rflcts its own past prics. In othr words all information about historical prics has alrady bn incorporatd into th currnt shar pric. Thus prics fully rflct th historical information of past prics and rturns. B) Smi-Strong Form Efficincy Smi- strong form fficincy is rgardd as th most controvrsial fficincy form. It proposs that all publicly availabl information 13, including all historical information is rflctd in th shar pric. C) Strong-Form Efficincy With strong form fficincy, all information, both public and privat is rflctd in currnt markt prics. This form of fficincy is probably bst viwd as a bnchmark against which any dviations from markt fficincy can b analyzd. It is of particular intrst to not that any information st in th strong form includs th information st in th smi strong form, which in turn includs th information st in th wak form and thrfor th particular sts of information usd in th thr forms of markt fficincy ar considrd nstd. Figur 1, blow, displays th thr information sts for markt fficincy. 13 Information such as annual rports, nws announcmnts and conomic data. 8

16 Figur 1 FIGURE 1- INFORMATION SETS FOR MARKET EFFICIENCY - SOURCE: FUNDAMENTALS OF INVESTMENTS, VALUATION AND MANAGEMENT P.229. iii) Th Pric Adjustmnt Procss Implicit in Efficint Markt Hypothsis Stock pric changs ar as a rsult of frqunt purchass and sal of shars. In an fficint markt, invstmnt dcisions ar basd on a dtrmination of a shar s fundamntal valu 14. According to th Efficint Markt Hypothsis any unxpctd firm-spcific nws announcmnt should rsult in an instantanous pric adjustmnt, whr th nw pric fully rflcts th availabl information, and hnc, its fundamntal valu. Unxpctd nws announcmnts might includ, for xampl, dividnd incras announcmnts. This typ of announcmnt is a positiv nws announcmnt 15 and should rsult in on of thr possibl pric adjustmnt procsss. Th thr possibl procsss ar as follows: 14. Fundamntal valu rfrs to th valu of a scurity which is intrinsic to or containd in th scurity itslf. It can b ascrtaind by calculating th prsnt valu of futur cash flows, discountd at th appropriat risk-fr rat. 15 Millr and Rock (1985) hypothsiz that invstors draw infrncs about implid changs in xpctd cash flows from corporat dividnd announcmnts, suggsting dividnd incrass rprsnt good nws for invstors. 9

17 Efficint Markt Raction: Th pric should immdiatly adjust to its nw fundamntal valu which rflcts all availabl information. Thr should not b a tndncy toward subsqunt changs. Dlayd Pric Raction: Th pric displays partial adjustmnt and thrfor trnds towards its fundamntal valu. Howvr a significant amount of tim lapss bfor it rflcts this nw information. Ovrraction and Corrction: Th pric initially ovrracts to th nw information, vntually corrcting to its intrinsic valu. Figur (2) provids an xampl of th thr ways in which prics can ract to positiv unxpctd nws. Figur 2 FIGURE 2- POSSIBLE MARKET PRICE REACTIONS TO A NEWS ANNOUNCEMENT- SOURCE: FUNDAMENTALS OF INVESTMENTS, VALUATION AND MANAGEMENT P229 10

18 iv) Markt Efficincy and th Momntum Effct Dspit dcads of rsarch, an xtnsiv body of rcnt financial litratur has producd vidnc on scurity rturns that sharply contrasts th traditional viw that scuritis ar rationally pricd to rflct all publicly availabl information. Ths findings confirm th prsnc of a markt anomaly known as th momntum ffct. Evidnc of th momntum ffct amount to th most controvrsial aspct of th dbat on stock markt fficincy. Two of th mor prvasiv phnomna associatd with th momntum ffct hav thus far bn idntifid. 1) Positiv short to mdium trm autocorrlation of rturns (short-trm momntum). 2) Ngativ autocorrlation of prior short-trm rturns (long-trm rvrsal). In fact, prominnt thortical modls in this ara such as Barbris, Shlifr and Vishny (1998), Danil, Hirshlifr and Subrahmanyam (1998) and Hong and Stin (1999) all trat short-trm momntum and long-trm rvrsals as insparabl phnomna. Th longr trm aspct of th momntum ffct, long trm rvrsals, was first documntd by D Bondt and Thalr (1985). Thy show that ovr 3- to 5-yar holding priods stocks that wr xtrm losrs ovr th initial 3 to 5 yars achiv highr rturns than stocks that prformd wll ovr th sam priod. Following D Bondt and Thalr, Jgadsh and Titman (1993) provid vidnc of shortr-trm, rturn continuations. That is, prior to th ngativ rturn corrlations documntd by D Bondt and Thalr (1985), xcss rturns tndd to xhibit positiv srial corrlations in th short to mdium horizon. Thy show that stocks that prform bst ovr a 3 to 12 month priod tnd to continu to prform wll ovr th subsqunt 3 to 12 months and stocks that prform th worst ovr a 3 to 12 month priod tnd to continu to prform poorly ovr th subsqunt 3 to 12 months. 11

19 Th vidnc implis that th combinations of a positiv rturn corrlation at short horizons and vntual man rvrsion at long horizons constitut th momntum ffct in its ntirty. Howvr, th availabl litratur has found mixd mpirical vidnc rgarding th momntum ffct, dpnding on xchang spcific variabls, such as stag of dvlopmnt, rlativ tim and frquncy of transactions. Th availabl litratur has yt to pinpoint th xact mchanism through which this anomaly taks plac. V) Algorithmic Trading Rcnt tchnological innovations hav rvolutionizd th way in which financial markts oprat. Ths advancs hav rsultd in trmndous changs in th structur of financial markts and hav an important baring on th procsss undrpinning scurity pricing and rturn dynamics. Two important intrconnctd tchnological changs hav bn associatd with this dvlopmnt. Firstly, computr tchnology has nabld invstors th ability to automat thir trading procsss and scondly, xchangs hav r-organizd thmslvs to th xtnt that mostly all markts ar now lctronically opratd. Th procss by which th scuritis trading bcam lctronic can b tracd as far back as th 1970s, whn, NASDAQ 16, prviously known as th National Association of Scuritis Dalrs (NASD) mbarkd on a computr assistd systm for automatd quotation in th Unitd Stats (Frund, 1989). This ld to th obsolscnc of physical trading floors, allowing for automatd lctronic trading systms to dominat. Information tchnology has progrssd to such a lvl that it can now b found at vry stag of th trading procss. A ky dvlopmnt stmming from ths advancs falls undr th rubric of algorithmic trading. Essntially, algorithmic trading is computr-dtrmind trading, utilizing supr computrs and complx algorithms that dirctly intrfac 16 National Association of Scuritis Dalrs Automatd Quotations. 12

20 with trading platforms at high spd, placing ordrs without immdiat human intrvntion. Thy mploy rlvant statistical and conomtric tchniqus via advancd computr and communication systms and ar capabl of anticipating and intrprting rlativly short-trm markt signals in ordr to implmnt profitabl trading stratgis 17. Consquntly, algorithmic trading has bcom a crucial comptitiv factor for capabl markt participants. A distinctiv sub catgory of algorithmic trading that has grown rcntly is known as high frquncy trading. Howvr, to dat, thr has not bn a unanimously accptd acadmic or rgulatory dfinition of high frquncy trading 18. According to Brogaard (2010), high frquncy trading is computr dtrmind trading whrby stocks ar bought and sold by an automatd algorithm at high spds and hld for a vry short priod, usually sconds or millisconds. Howvr sinc th typical proprtis of high frquncy trading could also dfin algorithmic trading, it bcoms xtrmly challnging to distinguish btwn th two. Adding to th complxity of th issu, som high frquncy trading stratgis ar sn to hav no spcial spd rquirmnt. (Tradworx 2010a). In ordr to lucidat th distinction btwn algorithmic trading and high frquncy trading w tak a mor gnral approach, by assuming that algorithmic trading is a hyponym including all its substs, including but not limitd to high frquncy trading. This viw is supportd by Abrgl, Bouchaud, Foucault, Lhall, and Rosnbaum (2012). This approach allows us to avoid th fals dichotomy oftn associatd with algorithmic trading and high frquncy trading. Th focus thn bcoms on th natur of th trading stratgis codd by th algorithms thmslvs. Thrfor, to summariz, algorithmic trading is dfind as computr-dtrmind trading, utilizing supr computrs and complx algorithms which dirctly intrfac 17 Brogaard (2010) posits that algorithmic tradrs gnrat gross trading profits of approximatly $2.8 billion annually and sharp ratios of about S Gombr, Arndt, Lutat and Uhl (2011), Appndix II- Acadmic and Rgulatory Dfinitions of Algorithmic Trading, pp

21 with trading platforms at high spd, placing ordrs without immdiat human intrvntion. It (algorithmic trading) mploys cutting dg mathmatical modls, adpt computational tchniqus and xtraordinary procssing powr via advancd computr and communication systms and is capabl of anticipating and intrprting rlativly short-trm markt signals in ordr to implmnt profitabl trading stratgis. VI) Th Evolution of Algorithmic Trading Dtailing th progrssion of algorithmic trading rquirs that algorithms b classifid into four gnrations. This is basd on th work of Almgrn (2009) and includs information from Johnson (2010) and Linwbr (2009) as wll as, Gombr, Arndt, Lutat and Uhl (2011). First gnration trading algorithms wr th rsult of a natural progrssion in basic ordr slicing. Thy involvd th ralization of spcific pr-dtrmind bnchmarks, such as th Tim Wightd Avrag Pric (TWAP) 19. Ths arly algorithms wr likly statically drivn and basd on spcific trading schduls. Howvr, du to th anticipatory natur of ths trading schduls, markt participants would oftn tak advantag of thir rgular trading pattrns. Scond gnration algorithms wr mor multifarious than thir prdcssors and sought to manag th trad-off btwn markt impact and timing risk. Th most prominnt scond gnration algorithms wr implmntation shortfall algorithms. Implmntation shortfall algorithms trid to rduc th markt impact of larg ordrs by considring th possibility of advrs pric ractions during th xcution procss (timing risk). In ordr to avoid this, ths algorithms prdtrmin an xcution plan basd on historical data, and split an ordr into 19 An xampl is givn by Gombr, Arndt, Lutat and Uhl (2011): TWAP algorithms divid a larg ordr into slics that ar snt to th markt in qually distributd tim intrvals. Bfor th xcution bgins, th siz of th slics as wll as th xcution priod is dfind. For xampl, th algorithm could b st to buy 12,000 shars within on hour in blocks of 2,000 shars, rsulting in 6 ordrs for 2,000 shars which ar snt to th markt vry 10 minuts. TWAP algorithms can vary thir ordr sizs and tim intrvals to prvnt dtction by othr markt participants. ( p. 24) 14

22 as many as ncssary but as fw as possibl sub ordrs. (Gombr, Arndt, Lutat & Uhl, 2011) Third gnration algorithms, oftn rfrrd to as adaptiv algorithms, follow a much mor sophisticatd approach. Instad of following a pr-dtrmind schdul, thy ar adaptiv in natur. Maning thy ar abl to r-valuat and chang thir xcution schdul with changing markt conditions. Th most rcnt dvlopmnt in th algorithmic trading domain concrns th so calld fourth gnration algorithm. Ths algorithms us incrasing lvls of mathmatical and conomtric sophistication and includ modls of markt forcasting, markt impact and markt risk. Thy hav accss to a wid varity of scuritis and drivativs and combin quantitat and non-quantitat mthods in ordr to forcast rlativly short-trm markt movmnts. Ths complx algorithms ar capabl of accumulating, stimating and utilizing colossal quantitis of information in ordr to dtct th kind of pattrns and vnts that tradrs look for thmslvs. Howvr thy do this for hundrds or thousands of scuritis simultanously at vry high spd. Most importantly, thy sk to xploit information byond th traditional data, including nws, pr-nws and othr forms of information. (Linwbr, 2009) Considring that contmporary rlvanc dmands a notric prspctiv, w focus primarily on ths so calld fourth gnration algorithms. VII) Algorithmic Trading and Financial Institutions In ordr to gnrat additional incom, larg financial institutions and invstmnt banks incrasingly mploy stat-of-th-art algorithmic and information tchnology as part of thir trading activitis 20. In fact incom from ths trading activitis is progrssivly rplacing rvnu from traditional activitis such as 20 Concptually, a financial institution s trading portfolio contains rlativly short trm -liquid assts, ranging from as short as on day to on yar. 15

23 dposit taking and lnding 21. Institutional invstors utiliz advancd algorithms in ordr to conduct, for xampl, basic position trading and risk arbitrag. With position trading, institutions buy larg blocks of scuritis on th xpctation of a favorabl pric mov. Whil risk arbitrag ntails, purchasing blocks of scuritis in anticipation of som information rlas. Institutions that ngag in algorithmic trading us advancd computr programs to accss and procss vast amounts of data in ordr to succssfully initiat th abov trads. Also by utilizing algorithms thy ar abl to trad larg quantitis gradually ovr tim, thrby minimizing markt impact and implmntation costs (Saundrs & M. Corntt, 2011). VIII) Algorithmic Trading and th Momntum Effct Acadmic rsarch concrning th impact of algorithmic trading is still in its infancy and, as such, paprs documnting its association with spcific markt anomalis such as th momntum ffct rmain, rlativly unxplord. Howvr, that bing said, a rcnt papr by Frank Zhang (2010) quats to, prhaps, th closst work documnting this association. A short summary of th findings will b discussd blow. By using a sampl that contains all stocks covrd by th Cntr for Rsarch in Scurity Prics (CRSP) and th Thompson Rutrs Institutional Holdings databas btwn th 1st quartr of 1985 and th 2nd quartr of 2009, Zhang (2010), attmptd to xamin algorithmic trading s association with both pric volatility and th markt s ability to incorporat fundamntal nws into stock prics. 21 This rsults in financial institutions having to manag a growing arnings uncrtainty (markt risk). 16

24 As algorithmic trading is not dirctly obsrvabl, Zhang (2010) proposd a novl way of stimating it, that is, by quating it to all th trading activitis not includd in th 13f databas. Th rasoning bhind this approach is as follows. Th Unitd Stats Scuritis and Exchang Commission (SEC) rquir institutions with ovr $100 million in Assts undr Managmnt (AUM) to rport thir long trm holdings in th 13f quartrly rport of quity holdings. Ths institutions includ hdg funds, invstmnt companis, pnsion funds, insuranc companis, univrsity ndowmnts, banks and many othr typs of profssional invstmnt advisors. Crucially short positions ar not rquird to b disclosd and thus xcludd from th rport. Thus by masuring trading volum rlativ to institutional portfolio changs in quartrly 13f filings, Zhang (2010) was abl to captur trading frquncis gratr than thos of long trm traditional invstors (Scuritis and Exchang Commission, 2013). Ovrall, th vidnc indicatd that algorithmic trading incrass stock volatility. Th positiv corrlation btwn algorithmic trading and stock pric volatility is strongr for stocks in th invstabl univrs, strongr for stocks with high institutional holdings, and strongr during priods of high markt uncrtainty (Zhang, 2010, p. 24) Howvr, th rason that his rsarch quats to, prhaps, th closst work documnting th association btwn algorithmic trading, th momntum ffct is sn in th scond aspct of his invstigation, namly algorithmic trading s association with th markts ability to incorporat fundamntal nws into stock prics. By using analysts arnings rvisions and.arnings surpriss to proxy for fundamntal nws, Zhang dtrmind that algorithmic trading dtracts for th markts ability to incorporat nws into prics, whrby, prics tndd to ovrshoot thir fundamntal valus, rsulting in thir rgrssion in subsqunt priods. Intrstingly this algorithmic trading-rlatd pric raction and subsqunt rvrsal is consistnt with th momntum ffct documntd in financial markts. 17

25 Zhang s articl provids valuabl insight into th dynamic rlationship btwn algorithmic trading, th momntum ffct and stock markt fficincy. Howvr, th undrlying thortical mchanism bhind this rlationship rmains unknown, incrasing th ncssity for furthr invstigation. 1.4) Problm Statmnt Th momntum ffct and thus rturn prdictability has dominatd discussions on markt fficincy, yt no clar rasons or causs of th phnomna hav bn stablishd. Th initial prcption fails to tak into account th trmndous changs that hav takn plac in financial markts, consquntly, nglcting th rol playd by algorithmic trading in this complx dynamic rlation. Sub Problm Th vidnc put forward by Zhang (2010) indicats that algorithmic trading can potntially gnrat th momntum ffct vidnt in th rsarch, howvr, du to algorithmic trading s rlativly rcnt mrgnc, th litratur is yt to produc a thortical modl that xamins this rlation dirctly. 1.5) Rsarch Objctivs This rsarch intnds to invstigat th rlationship btwn algorithmic trading, th momntum ffct and stock markt fficincy by focusing, formost, on th impact algorithmic trading has on scurity pricing and rturn dynamics. Mor spcifically, algorithmic trading s association with short-run momntum and subsqunt long-trm rvrsal. Sub Aims To analyz from th litratur, th thortical mchanism through which, algorithmic trading can possibly gnrat th momntum ffct. Propos a thortical modl that is bttr suitd to dscrib th world of algorithmic trading. 18

26 Produc a rprsntativ modl, incorporating faturs that fit wll with th stylizd facts about algorithmic trading, in ordr to ascrtain whthr, thortically, algorithmic trading can gnrat th momntum ffct. 1.6) Rsarch Qustions Can algorithmic trading potntially gnrat th momntum ffct? If algorithmic trading can gnrat th momntum ffct, what is th undrlying mchanism? Can this mchanism b modlld by a rprsntativ agnt mod? 1.7) Significanc of th Study Th aim of this papr is to mak a contribution to th rsarch on markt fficincy and its associatd anomaly, th momntum ffct, by studying th impact of algorithmic trading on scurity pricing and rturn dynamics. Th main focus will b on U.S. quity markts. Primary invstigations into th Efficint Markt Hypothsis yild xtnsiv support for markt fficincy. Howvr, it is important to not that th majority of ths studis wr conductd bfor th advnt of algorithmic trading. Adding to this, thr has bn a growing body of mpirical litratur of lat which dos not support th fficint markt hypothsis. Could an analysis of algorithmic trading b a catalyst for th furthr growth of such contradictory vidnc? Prvious studis on th rlationship btwn markt fficincy and th momntum ffct hav bn limitd by thir xclusion of nw dvlopmnts such as algorithmic trading in thir analysis. Thus, thr is a nd for furthr invstigation that is consistnt with th currnt stat of th capital markt. 19

27 Du to algorithmic trading s rlativly rcnt mrgnc, this papr sms to b on of th first to dirctly invstigat whthr, thortically, algorithmic trading can gnrat th momntum ffct. Evaluating th rlationship btwn algorithmic trading and its rlativ ffcts on markt fficincy is of intrst to both invstmnt practitionrs and financial acadmics. In addition, th finding of th study is xpctd to assist policymakrs undrstand th rlativ impact algorithmic trading has had on financial markts in th U.S., thus allowing thm to gaug th rlativ risks associatd with it, in ordr to mak informd policy dcisions. 1.8) Structur of th Rsarch I. Chaptr 2 prsnts a rviw of th prvious works on markt fficincy, th momntum ffct and algorithmic trading, as wll as considring th thortical links btwn ths thr factors. II. Chaptr 3 provids an ovrviw of th rsarch dsign and mthodology utilizd in this study to ascrtain th ffcts of algorithmic trading on markt fficincy. Th conomtric mthodology is also discussd in this chaptr. III. Chaptr 4 prsnts a thortical modl IV. Chaptr 5 rports th rsults of th study. IV. Chaptr 6 provids th conclusion of th study and rcommndations for furthr rsarch. 20

28 CHAPTER 2: LITERATURE REVIEW 2.1) Introduction This sction provids a rviw of th prvious works on markt fficincy, th momntum ffct and algorithmic trading, as wll as considring thir thortical links. 2.2) Rviw of th Currnt Litratur Concrning th Efficint Markt Hypothsis According to Eugn F. Fama (1970): Th primary rol of th capital markt is allocation of ownrship of th conomy s capital stock. In gnral trms th idal is a markt in which prics provid accurat signals for rsourc allocation: That is, a markt in which firms can mak production -invstmnt dcisions, and invstors can choos among th scuritis that rprsnt ownrship of firms activitis undr th assumption that scurity prics at any tim fully rflct all availabl information. A markt in which prics always fully rflct availabl information is calld fficint. (p. 383). Th qustion, as to what th phras fully rflct mans, thus ariss. Its ambiguity rsults in a situation whr it lacks th ability to b mpirically tstabl. In ordr to crat a situation in which it is tstabl, thr is a nd for gratr spcification rgarding th pric formation procss. In dtrmining what is mant by th phras fully rflct, on could argu that markt quilibrium can b statd in trms of xpctd rturns, whrby, conditional on a spcific informational st, th quilibrium xpctd rturn is a function of its risk (Fama, 1970). Gnrally xpctd rturn thoris can b dscribd algbraically as follows: E(p j,t+1 θ t ) = [1 + E(r j,t+1 θ t )] p jt, 21

29 Whr: E = xpctd valu oprator p jt, = pric of scurity j at tim t p j,t+1 = pric of scurity j at tim t + 1 r j,t+1 = prcntag rturn at tim t + 1 θ t = th st of fully rflctd information in th pric at tim t Whr; p j,t+1 and r j,t+1 ar random variabls at tim t. Th spcific chosn xpctd rturn thory would dtrmin E(r j,t+1 θ t ), th valu of th xpctd rturn in quilibrium, on th basis of th information st θ t.th quation implis that th information in θ t is fully utilizd in dtrmining quilibrium xpctd rturns, thrfor θ t if fully rflctd in th formation of th pric p jt,. By assuming that conditions of markt quilibrium can b statd in trms of xpctd rturns and that quilibrium rturns ar formd on th basis of information in θ t has major mpirical implications: thy rul out th possibility of trading systms basd only on information in θ t that hav xpctd profits or rturns in xcss of quilibrium xpctd profits or rturns (Fama, 1970, p. 385). Th abov modl of markt fficincy is oftn rfrrd to as th xpctd rturn or fair gam modl. Howvr, th fair gam modl mrly says that conditions of markt quilibrium can b statd in trms of xpctd rturns, and it has littl to say about th stochastic procss gnrating rturns (Fama, 1970). Thrfor, th random walk modl, whr th squnc of past rturns is of no consqunc in dtrmining distributions of futur rturns, should b viwd as an xtnsion of th xpctd rturn modl. It crats a mor dtaild statmnt about th spcific conomic nvironmnt. Thr ar many variations of th random walk modl 22, but formally it is dfind as follows: 22 S pag 7 of this papr. 22

30 F(r j,t+1 θ t ) = F(r j,t+1 ), Whr futur pric changs ar indpndnt and idntically distributd. In his papr on stock pric bhavior, Eugn Fama (1970) rviwd th thortical and mpirical litratur on th fficint markts modl. His primary objctiv was to crat a clar, up-to-dat pictur of th work conductd thus far. His work stablishd th first cohrnt summary of th diffrnt aspcts of markt fficincy; in so doing, Fama (1970) cratd a formal sparation and catgorization of information substs into wak, smi-strong and strong form tsts of markt fficincy. Aftr thorough invstigation th argumnt was mad that thr was minimal (if any) vidnc against th strong form tst and no vidnc against th wak and smi-strong form tsts. Evidnc against th strong form tsts wr disrgardd bcaus, at th tim, thr was no indication of monopolistic accss to information bing a prvalnt issu among invstors. Intrstingly, th currnt qustions surrounding algorithmic tradr s accss to mor sophisticatd information sms to crat an atmosphr in which to contst th abov finding. Ar th abov rsults still applicabl, or could thy simply b a product of th tim instad of dscribing fundamntal rsults? At th tim, th majority of vidnc smd consistnt with th Efficint Markt Hypothsis. Any rsults indicating quity rturn prdictability wr summarily found insignificant, and prics wr viwd as following a random walk. Support for th Random Walk Hypothsis was vidnt from th rsults of Osborn (1959) and Cootnr (1964) whn tsting th hypothsis using historical data. Similarly, th srial corrlation tsts of Moor (1962) also smd to indicat vidnc in support of th modl. In th studis, succssiv pric changs displayd srial corrlation cofficints that wr xtrmly clos to zro, thus ruling out chang dpndncy. A plthora of subsqunt studis mrgd as a rsult of th strong support for th Efficint Markt Hypothsis. A common thm was to invstigat quity pric ractions to unxpctd nws announcmnts (Ball & Brown, 1968). Th rsults 23

31 typically showd that stock prics adjustd somwhat instantanously to th vnt, an infrnc that is in lin with th Efficint Markt Hypothsis. Th growing availability of intraday data in th 80s and 90s allowd rsarchrs to tst informational ffcts on stock prics within minuts (Gosnll, Kown, & Pinkrton, 1996).Howvr, this priod also witnssd th intllctual dominanc of th Efficint Markt Hypothsis bcoming far lss univrsal. Many financial conomists and statisticians bgan to bliv that stock prics ar at last partially prdictabl. Paprs bgan to uncovr mpirical vidnc pointing to stock rturn prdictability. For xampl, Kim and Stambaugh (1986) found stock prics can b prdictd using crtain forcast tchniqus basd on crtain prdtrmind variabls. In addition, Lo and MacKinlay (1999) rjct th Random Walk Hypothsis aftr finding svral statistically significant short-trm srial corrlations. A positiv srial corrlation in this contxt would b viwd as vidnc of short-trm momntum. This crats an opportunity for invstors to arn xcss rturns through an invstmnt stratgy of buying aftr priods with positiv rturns and slling aftr priods of ngativ rturns. 2.3) Rviw of th Currnt Litratur Concrning th Momntum Effct Dspit dcads of rsarch, an xtnsiv body of rcnt financial litratur has producd vidnc on scurity rturns that sharply contrasts th traditional viw that scuritis ar rationally pricd to rflct all publicly availabl information. Ths findings confirm th prsnc of a markt anomaly known as th momntum ffct. Evidnc of th momntum ffct amount to th most controvrsial aspct of th dbat on stock markt fficincy. Th prvasiv anomalous rturns associatd with th momntum ffct ar dscribd as bing anomalous bcaus thy cannot b xplaind by th capital asst pricing modl (CAPM) of Sharp (1964) and Lintr (1965). 24

32 Two of th mor prvasiv phnomna associatd with th momntum ffct hav thus far bn idntifid. 1) Positiv short to mdium trm autocorrlation of rturns (short-trm momntum). 2) Ngativ autocorrlation of prior short-trm rturns (long-trm rvrsal). In fact, prominnt thortical modls in this ara such as Barbris, Shlifr and Vishny (1998), Danil, Hirshlifr and Subrahmanyam (1998) and Hong and Stin (1999) all trat short-trm momntum and long-trm rvrsals as insparabl phnomna. Th longr-trm aspct of th momntum ffct, long trm rvrsals, was first documntd by D Bondt and Thalr (1985). Thy show that ovr 3 to 5 yar holding priods stocks that wr xtrm losrs ovr th initial 3 to 5 yars achiv highr rturns than stocks that prformd wll ovr th sam priod. Following D Bondt and Thalrs, Jgadsh and Titman (1993) provid vidnc of shortr-trm rturn continuations. That is, prior to th ngativ rturn corrlations documntd by D Bondt and Thalr (1985), xcss rturns tndd to xhibit positiv srial corrlations in th short to mdium horizon. Thy show that stocks that prform bst ovr a 3 to 12 month priod tnd to continu to prform wll ovr th subsqunt 3 to 12 months and stocks that prform th worst ovr a 3 to 12 month priod tnd to continu to prform poorly ovr th subsqunt 3 to 12 months. Th vidnc implis that th combinations of a positiv rturn corrlation at short horizons and vntual man rvrsion at long horizons constitut th momntum ffct in its ntirty. Subsquntly invstigating th momntum ffct in stock markts bcam a worldwid phnomnon (Kang, Liu & Ni, 2002; Hong, L & Swaminathan, 2003 ; Snyman 2011). Evidnc to dat sms to indicat that, in trms of countris, th momntum ffct is shown to b strongr in th dvlopd markts, than in 25

33 th mrging markts 23. This sms to suggst that stock markt dvlopmnt plays an important rol in th momntum ffct ) Possibl Explanations for th Momntum Effct Fama (1998) idntifid profitabl momntum stratgis as th on outstanding anomaly in modrn financ. On of th prmir xplanations for this anomaly rvolvs around invstor psychology and blongs to a fild of study aptly namd bhavioral financ. Bhavioral financ sks to bttr undrstand how motions and cognitiv rrors influnc invstors in th dcision-making procss. As prviously statd th momntum ffct ncompasss two intrconnctd phnomna. That is both short-trm momntum and long-trm rvrsals. Howvr modls consistnt with both ths ffcts ar rlativly scarc. Som bhavioral modls ar abl to xplain short-trm momntum but not longtrm rvrsals (Brk, Grn & Naik, 1999; Holdn & Subrahmanyam, 2002; Makarov & Rytchkov, 2012.) Othr modls can justify long-trm rvrsals but not short-trm momntum. For xampl, Wang (1993) prsnts a dynamic asst-pricing modl undr th assumption that invstor s possss diffrnt information rgarding th xpctd futur growth rat of rturns. By diffrntiating btwn informd and uninformd invstors, h dtrmins that information asymmtry among markt participants can rsult in highr pric volatility and ngativ autocorrlation in rturns. His discovry of an association btwn information asymmtry and ngativ auto corrlations provids significant insight into th possibl procss undrlying th rvrsal aspct of th momntum ffct. Wang (1993) attributs th ngativ srial corrlation to th man rvrsion in th undrlying variabls that affct xpctd xcss rturns. H assums that information asymmtry nhancs this ngativ corrlation whn uninformd participants only larn about ths stat variabls from ralizd rturns, thus incrasing xpctd futur rturns dpndnc on past rturns. (S also Lwlln & Shankn, 2002 and Fama & Frnch, 2008). 23 (Rouwnhorst, 1998; Griffin, Ji, & Martin, 2003; Muga & Santamaria, 2007.) 26

34 Howvr, rgarding th momntum ffct in its ntirty, thr ar a small numbr of modls consistnt with both ths phnomna. Two of th most notabl xcptions ar th positiv fdback modl of D Long, Shlifr, Summrs, and Waldmann (1990) and th invstor ovrconfidnc hypothsis of Danil, Hirshlifr and Subrahmanyam (1998). a) Th Positiv Fdback Modl D Long, Shlifr, Summrs, and Waldmann (1990) in thir study of invstor bhavior, prsnt an mpirically significant argumnt against th standard prcption that rational spculators stabiliz asst prics. Thir analysis posits that in th prsnc of positiv fdback tradrs 24, th actions of rational spculators can dstabiliz prics. Thy argu that whn thr ar numrous fdback tradrs in a spcific markt, actions of rational spculators xaggrat pric trnds. An xampl of this is givn by D Long t al. (1990). Accordingly, whn a rational spculator rcivs good nws, thy rcogniz that subsqunt trading on this information will rsult in a pric incras, which would incntiviz fdback tradrs to purchas th shars. In anticipation of such a raction, informd invstors buy mor today, and so thy driv prics up today mor than is implid by th fundamntal nws vnt. Tomorrow, th uninformd invstors buy in rspons to th prior pric incras and thus kp prics abov thir fundamntals, vn as rational invstors sll out thir positions and stabiliz prics. Thir modl gnrats a positiv corrlation of stock rturns at short horizons, as positiv fdback tradrs rspond to past pric incrass by flowing into th markt, and ngativ corrlations of stock rturns at long horizons, as prics vntually rturn to thir fundamntal (D Long t al,1990,p.381). Thus, thir modl is abl to gnrat th momntum ffct in its ntirty. 24 For xampl, invstors that purchas scuritis whn prics ris and sll whn prics fall. S D Long t al. (1990). 27

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