Overreaction and Underreaction : - Evidence for the Portuguese Stock Market -

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1 Overreacion and Underreacion : - Evidence for he Poruguese Sock Marke - João Vasco Soares* and Ana Paula Serra** March 2005 * Faculdade de Economia da Universidade do Poro ** (corresponding auhor) CEMPRE, Faculdade de Economia da Universidade do Poro, Rua Dr. Robero Frias, Poro, Porugal Tel: , Fax , 1

2 Overreacion and Underreacion : - Evidence for he Poruguese Sock Marke Absrac In he pas wo decades several sudies show and explain he occurrence of financial phenomena ha are conrary o he Efficien Markes Hypohesis (EMH) of Fama (1970). Among hem, he phenomena of overreacion and underreacion, inspired by cogniive psychology sudies, are one of he mos imporan challenges o marke efficiency, and helped o build he foundaions of Behavioral Finance. We invesigae he exisence of boh hese phenomena in he Poruguese Sock Marke and ry o conciliae heir simulaneous occurrence. We hus explore wheher Poruguese sock reurns are relaed o reurn pas performance for an exended sample (all socks lised in he main marke) and ime period (16 years). We sar by exploring he exisence of auocorrelaion in sock reurns: as in previous sudies we evaluae wheher here is negaive auocorrelaion in he long run, and posiive auocorrelaion in he shor run. We hen proceed in esing wheher hese phenomena sem from overreacion and underreacion by invesors. We use several differen esing mehodologies o evaluae he robusness of he resuls (conrolling for risk and non-risk facors) and assess he validiy of alernaive hypoheses ha have been pu forward o explain coninuaion and reversal paerns in reurns. Finally we examine our findings a he ligh of he predicions ha come ou of he heoreical behavioral models ha have been developed o explain momenum and reversal in reurns. Our resuls seem o be supporive of he overreacion hypohesis: here is negaive correlaion in sock reurns ha is robus o risk and non-risk conrols. Furher value sraegies show superior performance and his performance seems o be associaed wih exrapolaion of pas sales performance. As for he shor run reurn paern, we find weak evidence in suppor of momenum effecs ha persis afer conrolling for risk. The momenum effecs seem o be associaed wih an insufficien reacion o earnings announcemens surprises. The evidence we gaher for he Poruguese sock marke is consisen wih he resuls found in well researched, large, liquid developed markes. Alogeher he wo pieces of evidence (coninuaion followed by reversal in reurns) migh reflec he dynamic ineracion beween news wachers and momenum raders prediced by he behavioral model of Hong and Sein (1999). Keywords: Overreacion; Momenum; Underreacion; Behavioral Finance JEL: G1; G11 and G14 2

3 Overreacion and Underreacion : - Evidence for he Poruguese Sock Marke - 1. Inroducion In he pas wo decades several sudies highlighed he occurrence of financial phenomena quesioning he validiy of Efficien Markes Hypohesis (EMH) of Fama (1970). There is now exensive evidence ha i is possible o predic fuure reurns on he basis of pas reurns. Serial correlaion in reurns is conradicory evidence o he EMH (random walk) hypohesis and coupled wih anecdoal evidence of heurisic pracices by invesors, challenges he assumpion of raional price seing. Overeacion and undereacion behavior are among hose anomalous phenomena. Given ha he invesigaion of hese facs helps o undersand price formaion in he sock marke, i has araced he ineres of marke professionals and lead o he implemenaion of invesmen sraegies o explore hese anomalies. Mos previous sudies merely documen wo sylized facs in sock reurns: negaive auocorrelaion in he long run (over wo years) and posiive auocorrelaion in shor horizons (one monh up o 1 year). The firs piece of evidence is usually associaed o overreacion while he laer supposedly reflecs underreacion. The seminal works by De Bond and Thaler (1985 and 1987) and Jegadeesh and Timan (1993), respecively, for overreacion and underreacion, were he firs o show ha i was possible o conceive profiable sraegies on he basis of he observaion of pas reurns. De Bond and Thaler (1985 and 1987) showed ha socks ha have regisered he lowes reurns ( losers ) during he previous hree o five years did beer during he following hree o five years han hose ha previously had he highes posiive reurn 3

4 ( winners ). The main explanaion advanced by De Bond and Thaler for his negaive correlaion in reurns in he long run was he Overreacion Hypohesis, derived from he represenaiveness heurisic, as suggesed by Tversky and Kahneman (1974): invesors would overrae recen informaion, neglecing or aribuing less imporance o pas news, in heir prospecs revisions, based on heir judgmen assessmens of probabiliies. This would lead o excessive opimism over good news and exreme pessimism over bad news. Sock prices would deviae emporarily from heir inrinsic values, originaing in he medium-long erm a mean-revering effec. As for he posiive auocorrelaion in shor erm reurns, Jegadeesh and Timan (1993) showed ha a sraegy ha buy socks wih he highes posiive reurn in he previous 3 (o 12) monhs (winners) and sell hose wih he lowes reurns (losers) in ha same period, yielded significan abnormal reurns during he following 3 (o 12) monhs. They claim ha his momenum effec observed in reurns would reflec underreacion of invesors o recen informaion and would sem from he conservaism heurisic advanced by Edwards (1968): invesors would slowly adap o he arrival of recen news flowing ino he marke, gradually incorporaing heir expecaions ino prices. Chan, Jegadeesh and Lakonishok (1996) provide empirical suppor for his argumen: hey observe, in simulaneous, momenum in reurns and coninuaion in earnings surprises around earnings announcemen daes. Several alernaive heoreical models have been proposed o accoun for he occurrence of hese wo phenomena in andem. These are non-risk, behavioral models (see, for example, Barberis, Shleifer and Vishny (1998), Daniel, Hirshleifer and Subrahmanyan (1998) or Hong and Sein (1999)) ha conemplae differen frameworks in erms of he ype of agens and heir dynamic ineracion and focus on one paricular behavioral bias (biases of conservanism, excess confidence, self-aribuion or heurisic decision-making) o produce he empirically observed paerns in reurns (coninuaion followed by reversal). 4

5 The purpose of his paper is o explore he exisence of hese reurn paerns for he Poruguese sock marke. Only a very few papers looked a he predicabiliy of Poruguese sock reurns on he basis of pas reurns. In paricular, Alves and Duque (1996) looked a he validiy of conrarian sock sraegies buil upon he findings of BT bu heir resuls for a small sample of Poruguese socks over he period of 1989 o 1994 were inconclusive. In his paper we hus explore wheher Poruguese sock reurns are relaed o reurn pas performance for an exended sample (all socks lised in he main marke) and ime period (16 years). We sar by exploring he exisence of serial correlaion in sock reurns: as in previous sudies we evaluae wheher here is negaive auocorrelaion in he long run, and posiive auocorrelaion in he shor run. We hen proceed in esing wheher hese phenomena sem from overreacion and underreacion by invesors. We use several differen esing mehodologies o evaluae he robusness of he resuls (conrolling for risk and non-risk facors) and assess he validiy of alernaive hypoheses ha have been pu forward o explain coninuaion and reversal paerns in reurns. Finally we examine our findings a he ligh of he predicions ha come ou of he heoreical behavioral models ha have been developed o explain momenum and reversal in reurns. Our main findings are he following. Our resuls seem o be supporive of he overreacion hypohesis: here is negaive correlaion in sock reurns ha is robus o risk and non-risk conrols. Furher value sraegies show superior performance and his performance seems o be associaed wih exrapolaion of pas sales performance. Ye mos of he resuls lack saisical significance. As for he shor run reurn paern, we find weak evidence in suppor of momenum effecs ha persiss afer conrolling for risk. The momenum effecs seem o be associaed wih an insufficien reacion o earnings announcemens surprises. The evidence we gaher for he Poruguese sock marke confirm he resuls found in well researched, large, liquid developed markes. 5

6 Alogeher, he simulaneous occurrence of he wo paerns in reurns (coninuaion followed by long horizon reversal) and he resuls from he addiional ess we run, seem o be consisen wih he model of Hong and Sein (1999) The paper proceeds as follows. Secion 2 provides a brief review of he relevan lieraure and secion 3 presens he daa and he ess we run. In secion 4 we show he empirical resuls and discuss he main findings. Secion 5 concludes. 2. Brief Lieraure Review 2.1 Overeacion The seminal works on overreacion were by De Bond and Thaler (BT) (1985 and 1987). Using a sample of socks lised on he NYSE, De Bond and Thaler (1985) analysed monhly reurns for he period beween 1926 and They showed ha socks ha have regisered he lowes reurns ( losers ) over he previous hree or five years (he observaion period) did beer during he following hree o five years (he es period) han hose ha previously had he highes posiive reurn ( winners ). This conrarian sraegy yielded an abnormal marke adjused reurn of 24.6% for he arbirage porfolio ( losers minus winners). These resuls of negaive serial correlaion for 36 monhs are inconsisen wih he weak form of he Efficien Markes Hypohesis of Fama (1970) and could be driven by excessive opimism as described above. During he las 15 years, several sudies came forward wih alernaive or complemenary explanaions for he successful performance of sraegies based upon he reversal effec in reurns, suggesing he observed abnormal reurns would resul, for example, from biases in compuing reurns or impropriae risk adjusmen. New refined mehodologies allowed esablishing he robusness of he findings in BT (1985). The more imporan conribuions were: 6

7 - Chan (1988): he auhor proposed a new mehod o measure he marke risk beyond CAPM, allowing ime-varying beas; - Zarowin (1989 and 1990): he auhor argued ha he resuls of De Bond and Thaler (1985, 1987) could be conaminaed by he Size-Effec and/or he January- Effec ; - Conrad and Kaul (1993): he auhors sugges correcing for microsrucure biases (bid-ask bounce) in he mehod employed for reurns calculaion, especially when long periods were analysed. In spie of hese and oher criicisms, he resuls obained by De Bond and Thaler (1985) for he US marke were confirmed for oher markes: Power, Lonie and Lonie (1991) and Campbell and Limmack (1997) presened similar evidence for he UK; Da Cosa (1994), for Brazil; Alonso and Rubio (1990), for Spain; and Mai (1995) for he French marke. Concurrenly, Lakonishok, Shleifer e Vishny (LSV) (1994) documened ha Value Sraegies were profiable and linked his resul wih he overreacion hypohesis as well. The auhors found ha socks which had performed well in he pas and were expeced o perform well in he fuure ( glamour socks) obained inferior reurns agains hose socks ha had had poor pas performance and were expeced o have a poor fuure performance (he value socks ). Using a sample of socks lised on he NYSE and AMEX, for he period beween 1963 and 1990, he auhors formed porfolios grouping he socks on he basis of BTM ( Book-o-Marke ), and measure he reurns of he firs decile ( glamour socks ) compared wih hose for he las decile ( value socks ) for a 60 monh-period afer he porfolio formaion. There are hree main resuls in Lakonishok e al. (1994). Firs, he reurn of he value porfolio ouperformed by 10%/11% a year he glamour porfolio (beween 8% and 9% on a size-adjused basis). Second, he superior performance of value socks could no be explained by risk. Finally, oher ess shed 7

8 addiional ligh on he combined findings of JT and BT. In paricular, LSV examined he growh raes of fundamenal variables such as sales and cash flow change beween he period prior o porfolio formaion and he period afer ha. They found ha hose growh raes were superior for glamour socks before he formaion period, bu were inferior 2 o 5 years afer ha, suggesing ha invesors misakenly exrapolaed he growh raes of fundamenal values such as he sales, overreaced, and gradually proceeded he meanrevering, adjusing heir expecaions and pushing he prices back o he inrinsic values. 2.2 Underreacion Jegadeesh and Timan (JT) (1993) were he firs o refer he paern of underreacion in reurns. Using a sample of socks lised on he NYSE and AMEX, for he period beween 1965 and 1989, hey analysed several porfolios described as J-Monhs/K Monhs, ha included socks based on he reurn earned during he preceding J monhs and ha were held for K monhs. They showed ha a sraegy ha buy socks wih he highes posiive reurn in J monhs (winners), and sell hose wih he lowes reurns in ha same period (losers), yielded significan abnormal reurns during he following K monhs (here J and K are in muliples of 3, and no o exceed 12). For example, a 12x3 sraegy yielded an abnormal reurn of 1.49%/monh. The auhors paid special aenion o he case J=K=6, for which reurns were approximaely 1% per monh. Jegadeesh and Timan (1993) showed ha ha his excess reurn could no be explained in erms of CAPM risk - since he pos-ranking bea of he winner minus loser porfolio was negaive - or by ime varying risk, size, serial covariance or lead-lag effecs. Furher he auhors measured he differences in reurns for he winner and loser porfolio around he quarer earnings announcemen daes, and found ha, in he firs 6 monhs, winner socks had a beer 8

9 performance han loser socks 1. This resul is consisen wih Bernard (1992), ha showed average reurns around he quarer earnings announcemens are posiively significan, following posiive earnings surprises ( sandardized unexpeced earnings ) in he previous quarer. Bernard (1992) and Jegadeesh and Timan (1993) claim his evidence suppors he hypohesis of underreacion. Behavioural finance argues ha his behaviour could be led by conservaism as suggesed in Edwards (1968): conservaive invesors underweigh and slowly process he new informaion ha is herefore gradually incorporaed ino prices. Several empirical sudies challenged he under-reacion argumen for explaining he observed momenum effec in reurns and proposed a baery of alernaive hypoheses 2. The main compeing hypohesis is ha momenum would also occur as a resul of overreacion. The findings of Chan, Jegadeesh and Lakonishok (1996) are consisen wih underreacion by invesors, since hey observe, simulaneously, momenum and a coninuaion rend in earnings surprises around he announcemen daes. Ye more recen works have ried o demonsrae he presence of an overreacion paern in momenum, in line wih he model of Daniel, Hirshleifer and Subrahmanyam (1998). Cooper, Guierrez and Hameed (2003), considering he sae of he marke as a proxy for invesor senimen and for risk aversion, found ha he momenum profis only occurred when he marke was bullish, which could be in favour of he overreacion hypohesis. The raionale is ha invesors are overconfiden abou heir privae informaion and overreac o i. In up-markes his senimen, associaed wih self-aribuion bias, generaes high levels of overconfidence. The increase in overconfidence would generae momenum firs and only laer overreacion. Using an US 1 Jegadeesh and Timan (2001) re-examine he momenum sraegy for an exended period ( ) excluding NASDAQ socks. The momenum sraegy (holding winners, selling losers) generaes saisically abnormal reurns and is robus o CAPM and Fama and French (1993) risk-adjused reurns. 2 Rouwenhors (1999) explores wheher JT resuls are marke specific. He finds ha, jus like in he US, here is evidence of momenum effecs in inernaional maure and emerging sock markes and he momenum profis are of similar magniude. Several oher single counry sudies have produced consisen evidence since hen. 9

10 sample, for he period beween 1926 and 1985, hey found ha he momenum profis in posiive marke reurns were 0.93%, whereas in negaive marke reurns, here were losses of 0.37% and saisically insignifican. The resuls were also robus o he inroducion of CAPM and Fama and French (1993) hree-facor model. Similarly, Lee and Swaminahan (2000) examined he relaionship beween he momenum effec and urnover volume. The volume would proxy for he level of invesor ineres in a sock. On he basis of he original resuls of JT (1993), hey find ha he momenum premium is higher for high volume socks boh for he winner and he loser porfolios. A sraegy of buying high volume winners socks and selling high volume losers socks yielded superior reurns when compared wih he simple price momenum sraegy. 3. Mehodology and Daa 3.1 Daa We use daa gahered from Dahis, which is a daabase compiled by he Poruguese sock exchange and ha is he mos comprehensive daa se on Poruguese socks. We colleced firm-level daa (oal reurns and marke capializaion) for all socks lised on he Poruguese sock exchange. Empirical sudies sudying overreacion and underreacion require daa collecion for long periods of ime and for a high number of socks. The sample period runs from 1988 o 2003, summing a oal of 16 years. We consider all socks ha have raded in he marke during he sample period and no only hose rading a he end of he period in order o avoid survivorship bias. 3,4 For a given sock o be included in he 3 Up o 1994, Poruguese socks raded on wo exchanges: BVP - Bolsa de Valores do Poro and BVL - Bolsa de Valores de Lisboa. Afer 1994, he spo rades were concenraed on BVL while BVP kep he derivaives marke. In 2000, he wo exchanges merged ino BVLP - Bolsa de Valores de Lisboa e Poro. In 2002, Euronex ook over BVLP and Poruguese socks rade now on Euronex Lisbon. 4 In April 1991, he new Capial Markes law (Lei Sapaeiro) se up hree marke segmens in he Poruguese sock exchange. Regular firms, meeing all exchange requiremens (in erms of capial dispersion, marke capializaion, urnover and solvency), are lised on Mercado de Coações Oficiais (Marke wih Official 10

11 porfolio i mus have raded coninuously during all observaion period, and a leas once during he es period. Given ha he some Poruguese marke is quie illiquid, only socks ha have an average ransacion index superior o 80% were included. The oal number of socks is 82. We use monhly reurns and compue marke reurns as an equally weighed index of he consiuen socks in sample. 5 Excess reurns are compued relaive o risk-free raes Mehodology We sudy, separaely, he overreacion and he underreacion hypoheses. This procedure is due o he need of nea resuls for each paricular phenomenon. While some of he recen heoreical models expressed he concern o joinly evaluae he wo effecs, no empirical es has been proposed ye enabling ha join analysis. In any case, laer on, we will combine he resuls of he wo ses of ess, in order o ge a broad view of price formaion Overreacion Tess To es overreacion, we use wo differen ess. The firs es evaluaes he significance of negaive serial correlaion in he medium o long erm. Mean reversion in sock reurns will indicae overreacion, as long as i is robus o he conrol of oher facors, such as risk adjusmens. The second es assesses he profiabiliy of value sraegies. As in Lakonishok, Shleifer and Vishny (1994) we run furher ess of overreacion, in paricular direc ess of exrapolaion of news by invesors, as suggesed by Tversky and Kahneman (1974). Quoaions). Small and medium firms lis on Segundo Mercado (Second Marke). The firms ha do no mee he exchange requiremens are lised on Mercado Sem Coações (Marke Wihou Quoaions). 5 Similarly DeBond and Thaler (1980, 1985) use an equally weighed index. This weighing procedure is consisen wih he winner/loser porfolios in he overreacion and momenum ess. 6 We use -bill raes and governmen bond raes, respecively for shor and long erm reurns. When hese raes were no available we use erm deposi and savings raes. 11

12 The reversal porfolios are consruced as in BT. Tess are run for a se of subperiods over he period sample. For each sub-period, we define an observaion period and a es period. Socks are ranked on he basis of is pas performance in he observaion period and assigned ino porfolios (winner, loser and arbirage porfolios). The winner porfolio includes he bes performing socks while he loser porfolio includes he wors performing socks. The arbirage porfolio measures he reurn difference beween he winner and he loser porfolios. All he hree porfolios are equally weighed a formaion and he consiuens socks wihin are held over he es period. Our sample period covers 15 years of monhly daa from 1988 o 2003 and we analyse 24 monh/24 monh sraegies. We hus have 7 non-overlapping observaion/es sub-periods 7. For each of hese periods and for each sock, we compue cumulaive marke-adjused log reurns (CAR) in he observaion period, given by: 1 24 CAR = µ. (1) i, i, µ i, is he marke-adjused reurn for sock i on monh compued as: µ (2) i, = R i, Rm, where R i, : log reurn for sock i on monh defined as log (P i, ) log (P i,o ). R m : marke reurn on monh, defined as an equally weighed average reurn of all socks in sample. Socks are sored in quiniles on he basis of hese CAR i. The winner porfolio includes he op quinile (P1) socks, i.e., he 20% bes performing socks. The loser porfolio includes he boom quinile (P5) socks, i.e., he 20% wors performing socks. For conrol purposes we also compue porfolios for he middle quiniles (P2, P3 and P4). 7 For he observaion periods, we have ; and so forh up o The corresponding es periods are ; and so forh up o

13 To evaluae he performance of hese porfolios, we compue he average CAR of he consiuen socks for periods in he fuure up o 24 monhs as: T N CAR p, z, T = ( 1/ N ) µ i, (3) = 1 i= 1 where p denoes he porfolio (W=winner, L=loser, A=arbirage), z refers o he subperiod es in analysis (I, II, III,..,VII) and T denoes he number of monhs he porfolio is held (T<=24). We hen calculae he grand mean (ACAR p ) for he seven sub-periods CAR p as: Z CARp, z, T ACAR p, T z= 1 = 7 (4) If here is negaive auocorrelaion in reurns, hen here is mean reversion: he loser porfolio makes posiive average es period excess reurns while he winner porfolio Shows negaive excess reurns, i.e. ACAR L >0 and ACAR W <0. As a resul, an arbirage sraegy (long losers, shor winners) beas he equally weighed index of all companies in sample, i.e. ACAR A =0. To assess he saisical significance of he ACAR reurns in he es period for he winner and he loser porfolio, we used a -saisic defined as: ACAR p, T p, T = (5) S / 7 p where S p is he esimaed variance for he mean marke-adjused reurns across firms (AR) assuming ime-series independence of monhly mean reurns. S p 2 ( AR p, AR p, T ) = x T (6) T 1 To assess he saisical significance of he ACAR reurns for he arbirage porfolio, we used a -saisic defined as: ( ACARL, T ACARW, T ) L W, T = (7) 2 2S / N 13

14 Given ha we use marke-adjused reurns i could be he case ha he paern observed in reurns reflecs improper risk conrol. Furher, several sudies have suggesed he need o conrol for oher risk and non-risk characerisics such as size, BTM (book-omarke) or bias in performance measuremen (due o ime-varying risk parameers, calendar effecs or bid-ask bounces). To assess he robusness of he negaive serial correlaion in reurns we conrol for he following risk and non-risk facors proposed in previous relaed lieraure: i) Sysemaic Risk Adjusmen (using CAPM) R p, R f, = α p + β p( Rm, R f, ) + ε p, (8) where R p, is an equally-weighed average reurn of all consiuen socks in porfolio p, R m, is defined as above and R f, is he risk-free rae for period 8. β p denoes porfolio p bea while α p measures he average abnormal reurn over he es period. To assess reversals we focus on he sign, magniude and significance of α p. If here is reversal in reurns hen α W <0 and α L >0. ii) Sysemaic Risk Adjusmen (Chan Mehod) R p, R f, = p, PF 1 D ) + α p, PT D + β p, PF( Rm, R f, ) + β p, D( Rm, R f, ) α ( D + ε (9) where R p,, R m,, R f,, β p and α p are defined as above. D equals 1 over he es period (PT) and 0 over he observaion period (PF). This es conrols for sysemaic risk as in i) bu allows for ime varying parameers. To assess reversals we now focus on he sign, magniude and significance of α p,pt. If here is reversal in reurns hen α W,PT <0, α L,PT >0 and herefore α A,PT =0. p, 8 We use weekly reurns o magnify sample size. 14

15 iii) Size Effec To conrol for size, we form wo porfolios wihin each p porfolio. Tha is socks are sored in quiniles on he basis of pas performance and for each quinile wo size porfolios are consruced above and below he quinile median marke capializaion. To assess reversals we now focus on he sign, magniude and significance of α p, PT. If here is reversal in reurns hen ACAR LB and ACAR LS >0 while ACAR WB and ACAR WS <0. iv) January Effec To conrol for he January effec, we compue average ACARs for every monh and compare January excess reurns wih hose observed for he oher 11 monhs. v) Three Facor Model Adjusmen Finally we conrol for risk using he Fama and French (1993) hree-facor model. R p, R f, = a p + p ( Rm, R f, ) + s p ( SMB ) + hp ( HML ) + e p, β (10) where SMB ( Small minus Big ) measures he size facor given by he differenial in reurns of wo porfolios conaining, respecively, all socks above and below he sample median marke capializaion. HML ( High minus Low ) measures he value/growh facor given by he differenial in reurns of wo porfolios conaining, respecively, all socks above and below he sample median book-o-marke. s P and h P are porfolio s p exposures o he SMB and HML facors. Lakonishok e al. (1994) use a differen approach o es overreacion. Porfolios are formed on he basis of fundamenals such as Book o Marke, Cash-Flow o Price and Earnings-Price raios. Higher (lower) raios would proxy bad (good) prospecs. If invesors form heir expecaions on he basis of recen news and if hey overreac, hen he longerm marke performance of socks ha invesors perceived as bad (good) would be meanrevering reflecing ha invesors were overly pessimisic (opimisic). Thus value socks (higher fundamenal raios) would perform well in he fuure while growh socks (lower 15

16 raios) would perform well. Value sraegies would hus inform on he exisence of overreacion by invesors if: a) value porfolios ouperform growh porfolios in he es period; b) his superior performance is risk-adjused; and c) i is possible o link hese resuls o news, in he sense ha hey reflec ha invesors exrapolae recen news o fuure prospecs as suggesed by Tversky and Kahneman (1974). As such, o prove overreacion we mus no only assess if value porfolios ouperform growh porfolios bu also evaluae risk-adjused performance and perform direc exrapolaion ess. We use hree years (36 monhs) of pas daa o form value and growh porfolios on he basis of BTM and Cash-Flow o Price (C/P). By combining he wo raios, we obain four quariles. Value (growh) socks belong o he op (boom) quarile wih he highes (lowes) BTM and C/P. Porfolios are hen held for hree years following formaion dae 9. We compue and assess he significance of CARs and ACARs as described above. To conrol for risk, we compare he (CAPM) beas of he value and he growh porfolios. To find ou wheher he performance of he wo sraegies was in fac driven by exrapolaion, we assess how variables such as Sales/Price, Earnings/Price, Dividend Yield and BTM compare, over differen periods in ime - -2 o agains o +3 for porfolios formed on he basis of BTM and C/P. Furher, we compare he geomeric annual growh raes of Cash Flows (ACG-average CF growh), Sales (ASG- average sales Growh) and Buy and Hold Reurns (RET- geomeric annual reurn) before and afer porfolio formaion. If here is exrapolaion, he growh (value) porfolio should observe higher (lower) marke raios a he ime porfolios are formed; high (low) ACG and ASG raes in he observaion period (2 years jus before formaion); and low (high) growh raes in he es period (3 years afer formaion). 9 We now use overlapping periods given ha porfolios are formed on he basis of fundamenal variables and no reurn informaion. We have eleven es periods: ; and so forh up o

17 3.2.2 Underreacion Tess We firs explore he exisence of posiive serial correlaion in reurns for shorperiods (horizons up o 12 monhs). The raionale is ha, if invesors ac wih conservaism or informaion disseminaion is gradual, prices do no correc immediaely, and herefore one should observe momenum in reurns. We analyse welve sraegies of J-monh x K-monh sraegies (J, K =3, 6, 12 monhs, where J denoes he observaion period and K he es holding period). For example, a 12-monh x 12-monh sraegy means forming a porfolio on he basis of he pas 12-monhs reurns ha is socks are ranked in quiniles on he basis of he reurns in he previous 12 monhs and porfolios are formed giving equal weigh o each of he socks wihin a quinile. These quinile porfolios are hen held for 12 monhs and heir reurn performance over he nex 12 monhs is analysed. The sraegy is repeaed each quarer/semeser/year. For example, for he six-monh/sixmonh sraegy we have 31 observaion periods and 31 es periods. For each of hese periods and for each sock, we compue he CARs in he observaion and es periods as described above. If here is momenum, socks ha performed well (badly) in he pas, will coninue o perform well (badly) in subsequen monhs. An arbirage porfolio long in socks wih good recen performance and shor in socks wih bad recen performance will hus earn non zero reurns. We analyse he performance of hese momenum sraegies relaive o heir expeced reurns given by he CAPM and he Fama and French (1993) hree facor model. For hese and oher robusness checks as well as for underreacion furher ess we focus on he 6-monh/6-monh sraegy 10. Ye evidence of momenum in sock reurns is a necessary bu no sufficien condiion o suppor underreacion. Two addiional condiions are required: 10 We selec his sraegy because i beer accommodaes risk-adjusmen ess given he sample size. 17

18 a) he momenum effec mus be linked o fundamenal firm-specific news. In oher words, we should observe a pos-earnings-announcemen drif, as a consequence of biased insufficien correcion or gradual informaion diffusion and, as such, slow adjusmen of prices o relevan news flowing ino he marke; b) he momenum effec should no be induced by iniial overreacion for shorerm periods, caused by excessive opimism and overvaluaion. a) Pos-Earnings Announcemen Drifs To es wheher he coninuaion paern in reurns reflecs underreacion, we analyse wheher he observed performance is associaed wih sock specific news. We focus on earnings news. If winner/loser socks regiser posiive/negaive earnings surprises i.e., repor good/bad news - and observe coninuaion in reurns, his is evidence in favour of he underreacion hypohesis. Prices adjus slowly o earnings surprises reflecing gradual disseminaion of he impac of his informaion or, alernaively, he insufficien reacion could be rooed in invesors conservanism. To es he pos-earnings announcemen drif, we use he same mehod as in Chan, Jegadeesh and Lakonishok (1996). We compare he rend in porfolios reurns, formed on he basis of pas reurns, wih he Sandardized Unexpeced Earnings (SUEs) associaed wih he mos recen announcemen previous o porfolio formaion and wih he following hree announcemens. To compue he SUE we use he mehod proposed by Bernard (1992): SUE is compued by aking he periodic earnings surprise and scaling i by he sandard deviaion. To compue he earnings surprise we compare he acual earnings wih he earnings forecas based on previous available earnings records. Thus, we only need observed earnings o compue he SUE. On a 6-monhly basis, SUE is given by: 18

19 SUE i =[e is -E(e is )]/σ i (11) where e is and E(e is ) are he observed and expeced earnings relaive o he period jus before porfolio formaion. 11 σ i is he sandard deviaion of earnings over he previous wo years 12. Good/bad news are hen defined on he basis of he average SUEs (, +1, +2 and +3). Figure 1 in appendix illusraes he process. We perform an addiional es as suggesed by Chan, Jegadeesh and Lakonishok (1996). We form porfolios on he basis of pas earnings surprises and check wheher here is a coninuaion rend as observed in arbirage momenum porfolio reurns. If hese earnings sraegies (long in socks wih he highes SUEs and shor in socks wih he lowes SUEs) are profiable, his is evidence consisen wih underreacion. b) Iniial Overreacion To es he possibiliy of iniial overreacion, as he rue source of momenum, we used wo differen mehodologies. As in Cooper, Guierrez and Hameed (2003) work, we compare momenum ACARs for differen saes of he marke. If he momenum effec is more pronounced in bullish markes and inexisen or less impressive in bearish markes, i migh be in realiy driven by iniial overreacion. Moreover, if he momenum in up-markes vanishes up o 24 monhs, culminaing in a reversion, i consiues an addiional proof of excessive reacion by he invesors. Momenum would be he iniial oucome of overreacion ha would reverse in laer periods. The second es is he one suggesed by Lee and Swaminahan (2000). They form wo sub-samples, high volume vs. low volume, of winner and loser porfolios, respecively above and below median volume. If invesors overreac hen high volume winners and high volume losers should earn superior reurns in relaion o a simple price sraegy, reflecing ha 11 Expeced earnings are he observed for ha same semeser in he previous year. We assume earnings are announced wih a 2-3 monh delay relaive o he period hey refer o. To compue unexpeced earnings for a given semeser we hus need informaion on he previous -1 and -3 earnings records. 12 Hence, he SUEs were compued saring June

20 invesors are more enhusiasic over high volume socks. We briefly refer hese resuls in he nex secion bu ables are no shown for he sake of saving space. 4. Findings 4.1 Overreacion Long Term Reurn Reversal Table 1 presens he reurns for he five quinile porfolios (including he loser and winner porfolios) formed on he basis of he 24-monh pas reurns for holding periods up from 6 o 24 monhs. The firs column shows he pas performance of hese porfolios and he remaining columns show he average CARs for each holding period. Table A.1 in appendix shows he CARs for each of he seven es periods. Table 1 provides evidence in suppor of overreacion wihin he sample of Poruguese socks. Pas losers ouperform pas winners: he average abnormal reurn afer 24 monhs of he loser porfolio (ha los a -2.90% per monh over he pas 24 monhs) is 0.36% p.m. (ACAR of 8.62%), and of he winner porfolio (ha earn a 2.7% per monh over he pas 24 monhs before porfolio formaion) is -0.24% (ACAR of -5.64%). Any conrarian sraegy up o 24 monhs buying he boom quinile socks and selling he boom quinile socks earns posiive (bu no saisically significan) abnormal reurns. Afer 24 monhs he average cumulaive abnormal reurn is 14.26%. Resuls sugges ha he more posiive performance for he loser porfolio occurs in he firs 12 monhs afer porfolio formaion. As for he winner porfolio, he reversal occurs over he second year. Conrary o previous sudies we do no o find an asymmeric (sronger) effec for he loser porfolio. Finally, he resuls for he inermediae quiniles are mixed. The resuls in able A.1 show ha reversal holds over he sample period: he cumulaive abnormal reurns for he arbirage porfolio for 5 ou of he 7 es periods analysed are posiive. 20

21 Overall he resuls are consisen wih he lieraure bu lack saisically significan. Robusness Checks Table 2 shows he resuls when we adjus performance for marke risk (assuming he CAPM is valid). We underake ime series regressions of 104 weekly reurns before porfolio formaion for he loser, winner and arbirage porfolios o esimaes beas. We hen compue he Jensen alphas (for he 24-monh holding period) as he difference beween realized and expeced reurns. Loser socks have slighly higher CAPM marke beas han winner socks bu he difference is small (albei saisically significan) and canno explain he difference in performance oulined above 13. On he conrary, because over he sample period, marke reurns have been generally negaive, when we conrol for risk, he reversal is even sronger. The arbirage porfolio earns 16.5% agains he 14.3% repored wih no risk adjusmen. Table 3 shows he sysemaic risk adjusmen proposed by Chan (1988), allowing for ime varying alphas and beas. Loser socks are in fac riskier in he es period and winner socks are less risky (and he decrease is saisically significan) bu given he overall negaive reurns, he reversal in reurns does no vanish when we conrol for risk. We also examine he performance of hese porfolios conrolling for size. Table A.2 shows he average, median and sandard deviaion of he marke capializaion for he quinile porfolios formed above. The evidence is consisen wih Zarowin (1989): loser socks are in fac smaller han winner socks and his is rue on average and for each of he es periods. The marke capializaion of he median sock in he winner porfolio is around 250 million euros, 4.5 imes he marke cap of he median sock in he loser porfolio (47 million euros). While he loser socks are in fac he smaller firms in sample, he winner socks are amongs he larges bu he socks in quinile 3 and 4 seem o be of 13 -saisics (repored in parenheses) for aggregae esimaes (alphas and beas) in ables 2, 3, 6, 8 and 12 are ime-series averages of he periodic -saisics. Theses saisics do no denoe he saisical significance of he average esimaes. 21

22 similar size. Table 6 shows he resuls wih a wo way sor on he basis of he 24-monh pas reurns and median size, which gives 10 porfolios (5x2). The arbirage sraegies (SL- SW, BL-BW) shown involve now buying he {small loser, big loser} porfolio and selling he {small winner, big winner} porfolio. Negaive long erm serial correlaion does no seem o be driven by size. The wo arbirage sraegies earn posiive abnormal reurns even if we observe an asymmeric effec: he effec is much sronger for he small socks sraegy (21.49% agains 8.73% for he large socks). This resul reflecs ha while large or small losers rever, only small winners show ha reversal in reurns. When we looked a he differen es periods, resuls are no always consisen 14. In several periods we observe ha small losers coninue o perform badly over long periods and he same goes for small winners. We also examine wheher reurn reversals in and ouside he monh of January. Surprisingly, able 5 indicaes ha he reurn reversals occur mainly ouside he monh of January. In January, loser porfolios perform badly while winner porfolios are posiive performers. Finally we examine Fama and French (1993) hree-facor adjused reurns. To compue facor exposures we underake ime series regressions of 104 weekly reurns before porfolio formaion for he loser, winner and arbirage porfolios. Overall, he resuls in able 6 sugges ha he hree facors seem o be priced. The loser porfolio consiss of small and value socks (high-book value o marke) bu given ha he sample period covers a bear marke, he risk adjusmen performance coninues o show reversal in reurns and is hus magnified. The arbirage porfolio shows posiive average CARs of 31% (significan a 10% level). 14 Resuls are no repored here bu are available upon reques. 22

23 Conrarian Sraegies and Exrapolaion We use an alernaive approach o measure overreacion. Based on previous evidence, value sraegies, ha is conrarian sraegies ha buy socks ha have good fundamenal raios and sell socks ha have high fundamenal raios, are profiable. This would resul because invesors are overly opimisic abou good companies and overly pessimisic abou bad companies. Table 7 shows he average CAR up o 36 monhs for he value-growh quarile porfolios. Recall ha hese porfolios were formed by soring sample socks every year on he basis of wo fundamenal raios ha are proxies for value : book o marke (ha would inform abou good/bad companies) and cash flow-oprice (ha would inform abou good/bad prospecs for hose companies). The value (growh) porfolio includes he op (boom) quarile socks, i.e., socks wih high (low) BTM and high (low) C/P. The las row of able 7 shows he reurns earned by an arbirage sraegy ha buys value socks and sells growh socks. The arbirage sraegy gives average reurns of 22.93% afer 36 monhs. Ye hese resuls are no saisically significan. Table A.3 in appendix shows ha he posiive adjused reurns occur for all es periods excep and for hree periods, reurns are saisically significan a a 10% level. Growh sraegies show, as expeced, negaive reurns (he 36-monh CAR is %) and are in fac responsible for he posiive performance of he arbirage sraegy. The value porfolio gives posiive bu rivial reurns (he 36-monh CAR is 3.04%). This asymmeric effec is in conras wih previous sudies for oher markes ha show sronger posiive effecs due o he very posiive performance of value socks. When we compare he performance of he value (growh) porfolio before and afer formaion dae, we observe ha he value (growh) porfolio shows recen good (bad) pas performance as expeced. Ye reversal occurs only for growh socks. Table 7 shows ha he reversal sars in he firs year and coninues in he second and hird years. 23

24 Finally able 7 shows he aribues of he four quarile porfolios ranked on he basis of fundamenal price raios. We confirm ha value porfolios include he smalles socks while he value porfolio includes (ogeher wih quarile 2) he larges socks (on average, 10 imes larger). Ye as reversal occurs only for he growh porfolio one canno esablish ha he reurn observed is solely due o high ex ane risk associaed wih size. Table 8 shows CAPM risk-adjused reurns for all ess periods and on aggregae. We observe ha he negaive performance of he growh porfolio is robus (and consisen over ime). The resuls for he value porfolio are mixed. In any case beas are very similar for he wo porfolios. To inform wheher he negaive performance of he growh porfolio is associaed wih overly opimism we run he direc exrapolaion ess explained above. Table 9 conrass, for he wo porfolios, he average values for he fundamenal marke raios as well as he pas and fuure cash flows and sales growh raes and sock marke performance. The paern observed over ime for he sales growh indicaes ha he growh porfolio, ha iniially ouperforms he value porfolio, shows in he hree years ha follow similar growh raes as value socks. Ye he paern of CF growh raes is puzzling and reflecs he opposie. Overall hese resuls sugges ha he negaive performance of growh socks, revering pas posiive performance, could sem from overreacion and reflec a represenaiveness bias: invesors expec ha socks ha have aracive price-raios reflecing posiive recen sock price performance - show posiive sock performance in he fuure. Ye he resuls of he direc exrapolaion ess are mixed. 4.2 Underreacion Coninuaion in Reurns 24

25 Tables 10 and 11 show ha he several J x K sraegies (J, K=3, 6, 12 monhs) we analyse show posiive auocorrelaion in reurns. The arbirage sraegy 6 x 6 earns average monhly CARs of 1.11% (saisically insignifican). Buying recen good performers yields cumulaive 6-monh reurns of 2.27% (0.38%/monh) while selling recen losers yields 4.40% (0.73%/monh). For he inermediae porfolios resuls are inconclusive. The resuls are consisen wih he findings of Jegadeesh and Timan (1993, 2001) where momenum profi occurs up o horizons of around 12 monhs (for he 6x6 sraegy, in paricular, heir sraegy gives 0.95%). The momenum reurns are higher for a 12 x 3 sraegy (as in JT). The arbirage reurns are around 9% (2.9%/monh) The CARs for he arbirage porfolio peak a around 14% afer one year (i.e., an average of 1.17% a monh). These figures are mainly informaive given ha he resuls are no saisically significan. For he arbirage porfolios based on 6-monh pas performance, he CARs peak afer one year o 18 monhs; subsequen reurns are negaive: he wo-year CAR is 7.31%, i.e., 0.30% a monh agains an average monhly reurn of 0.80% for he one-year horizon. This resul is driven by he performance of he winner porfolio ha flips signs: he woyears CAR is -0.10% agains a 2.95% CAR afer one year. The resuls sugges ha he momenum effecs are sronger and las longer for he loser porfolio. This asymmery in resuls conrass wih previous resuls where he profiabiliy of he arbirage porfolio is mainly driven by he coninuaion in reurns observed for he winner porfolio. Robusness Checks Tables 12, 13 and 14 show risk adjused reurns. Table 12 shows coninuaion marke-adjused reurns. Bea esimaes for he loser porfolios han for winner porfolios. The resuling marke bea for he arbirage porfolio 25

26 is negaive bu very close o zero. 15 In shor, he observed posiive auocorrelaion in reurns canno be explained on he basis of marke risk. Afer conrolling for marke risk, reurns for he arbirage porfolio are slighly lower (3.79% agains he 6.66% unadjused CARs). Previous evidence (see, for example, JT (1993), Liu,Srong and Xu, 1999 and Fama, 1996) suggess ha loser porfolios include mainly smaller socks. Table A.4 in appendix shows he average marke capializaion for he porfolios ranked on he basis of he previous 6-monh reurn performance. In fac, on average, and for every porfolio formaion period, he loser porfolio shows he lowes average marke capializaion. The winner porfolio, and Quiniles 3 and 4 share he larger socks. The profiabiliy of momenum sraegies could resul, evenually, from holding long smaller socks. If ha is rue he momenum should only observed for ha sub-sample of socks. To conrol for ha bias, we examine porfolio reurns wih sub-samples sraified by size: we formed wo porfolios wihin each winner/looser porfolios. Table 13 shows hese resuls. The evidence suggess ha he momenum profis occur boh for small and large socks and he momenum effecs are even sronger for he laer. Finally able 14 shows Fama and French (1993) hree-facor model s adjused reurns. The loser porfolio is loaded on smaller, high book-o-marke socks relaive o he winner porfolio. The adjused CARs for he arbirage porfolio are now only 2.66% (agains he unadjused 6.66%). In sum, risk-adjused CARs are smaller bu he arbirage porfolio posiive reurns do no vanish. The loser porfolio includes, as suggesed in previous sudies, smaller high BTM socks bu conrolling for hese characerisics does no eliminae momenum profis. 15 We do show here he periodic beas o save space. Those resuls show an ineresing feaure: he beas for he winner and loser porfolios change over ime. When he marke is bearish he laer is riskier while he former is less risky. Ye, when he marke is bullish, he beas of he winner porfolios are larger. 26

27 Furher, we find no evidence ha momenum is confined o smaller socks, for which informaion diffusion is likely o be slow. Momenum and Pos Earnings Announcemens Drif Tables 15 and 16 indicae ha here seems o be a relaion beween he drif observed in reurns and he arrival of fundamenal informaion. Table 15 conrass, for each of quinile porfolios ranked on he previous 6-monh reurns he average CARs, heir fundamenal aribues and he observed SUEs. Panel A of able 15 repeas he resuls shown in able 11; Panel B shows he fundamenal characerisics referred before (size and BTM); and Panel C shows he SUEs for he announcemen around porfolio formaion dae and for he 3 following announcemens. Panel C shows ha he loser (winner) porfolio has negaive (posiive) sandardised unexpeced earnings. Furher he loser porfolio has he more negaive SUEs and his is rue for he four announcemens analysed. Similarly he winner porfolio has posiive sandardised unexpeced earnings and hese are he more posiive SUEs observed in all he quiniles excep for he firs announcemen. Comparing Panels A and C, we observe ha he coninuaion in reurns seems o follow coninuaion in earnings surprises. In oher words, successive earnings surprises are refleced in momenum in reurns: he loser porfolio shows consisen negaive earnings for he period up o 2 years afer porfolio formaion suggesing a U shape forma, reflecing he earnings drif is ransiory. The same paern is observed for he CARs over he 24-monh period following porfolio formaion dae. The paern is similar for he winner porfolio bu he reversion in earnings surprises seems o occur afer one year. Again he paern seems o be mimicked by he CARs. To explore wheher his relaion beween earnings and prices is or no spurious, we pariion socks ino ranked quinile porfolios based on he SUEs and evaluae he profiabiliy of hese earnings momenum sraegies. Table 16 shows he resuls. Panels A, B and C conain he same informaion described for able 15. Panel A shows ha he 27

28 lowes SUE porfolio consiss of smaller and value socks and shows negaive CARs ha are sronger for he firs 18 monhs; he highes SUE porfolio shows posiive reurns. The resuling arbirage porfolio (Highes SUE-Lowes SUE) generaes CARS of 4.43%, 5.79% and 9.53%, respecively afer 6, 12 and 18 monhs. These figures are well below he ones presened for he reurn momenum porfolios bu seem o sugges ha invesors lose/make money afer invesing in socks ha repor unexpeced negaive/posiive earnings. Resuls in able 16 sugges hus ha companies ha announce negaive/posiive earnings coninue o so over a period of ime. Ye invesors do no seem o acknowledge his behaviour and reac wih conservanism o bad/good news and only gradually updae heir own earnings esimaes. Hence, he reurns mimic he coninuaion rend in SUEs. Iniial Overreacion Finally, o es he possibiliy of iniial overreacion, we performed he ess oulined in he mehodology secion (sae of he marke; volume). The resuls, no repored here, are mixed and do no confirm ha he iniial posiive correlaion is due o overconfidence. 4.3 Discussion of main findings Several models have been proposed o accoun for he observed paerns in reurns (coninuaion followed by reversal). Among hese are he models proposed by Daniel, Hirshleifer and Subrahmanyan (1998) and by Hong and Sein (1999). In he Daniel, Hirshleifer and Subrahmanyan (1998) model invesors handle public informaion (for example, earnings) in an asymmeric way. Overconfiden invesors abou heir own privae informaion aribue a posiive earnings announcemen o heir skills (self-aribuion bias) and push prices up. As such, one would observe price momenum effecs ogeher wih he pos-earnings announcemen drif. Invesors forecasing an opposie rend in earnings growh may no reac iniially bu will reverse heir beliefs afer a 28

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