Overreact Analysis in the American Stock Market: A Fuzzy C-means Algorithm Approach

Transcription

1 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X Overreac Aalyss he Amerca Sock Marke: A Fuzzy C-meas Algorhm Approach Reao Aparecdo Aguar ad Robero Moura Sales Absrac I hs paper, emprcal ess, based o he fuzzy cluserg meas algorhm for he aalyss of overreaco ad uderreaco hypohess he Amerca sock marke are preseed. Such mehodology s srogly coeced wh wo heurscs of behavoral face heory: represeaveess heursc ad achorg heursc. The proposed mehodology s used o form porfolos hrough facal raos of publc compaes ad he resuls obaed are cosse wh he srog fluece of overreaco he Amerca sock marke. The aalyss s appled for socks from ol ad gas, exle ad, seel ad ro secors, wh facal dexes ragg from 999 o 007. Idex Terms - Behavoral Face, Fuzzy Cluserg Meas, Overreaco, Uderreaco. I. INTRODUCTION The developme of mehodologes o overreaco ad uderreaco aalyss he facal marke has bee objec of ese research. Geerally speakg, facal decsos am a maxmzg fuure prof ad, hs coex, he evoluo of he basc premses has gve brh o he appearace of clashg heores as, for sace, he heory of effce markes ad he heory of behavoral face []. Each of hese heores has bee srucured wh bass o he fudameal corbuos of a large umber of auhors. Noeheless, he fac ha each oe of hem coas s orgs works whch have bee awarded he Nobel rze for Ecoomcs, such beg he case of he porfolo heory proposed by H.M. Markowz [8], ad he heory of behavoral face proposed by D. Kahema ad V.. Smh [5], s udeably of he umos relevace. Ths s eough o gve a clear dea of he mporace of decso makg he ecoomc heory. Summg up, he Theory of he Effce Marke assumes ha he vesor s raoal, herefore lkely o avod rsk-akg. As a cosequece of hs hypohess, vesors' decsos are made wh bass o formao srogly suppored by sascs ad probables whch supposedly projec he fuure performace of he asses as well as of he facal marke as a whole. Dfferely, he Behavoral Theory uses models whch ake o accou facors of psychologcal aure whch ed o fluece he vesors decso makg; oher words, he vesors are o oally raoal ad her decsos are Mauscrp receved November 6, 00. Reao Aparecdo Aguar s wh he Cero Uversáro da FEI, Dep of Elecrcal Egeerg (e-mal: preraguar@fe.edu.br). Robero Moura Sales s wh he Escola olécca da US, Dep of Elecrcal Egeerg (e-mal: robero@lac.usp.br). affeced by her prefereces ad belefs, assocaed o heurscs ad rules of humb. Despe he clash of opos whch have promoed a ese debae volvg hese wo heores, he behavoral face has proved o be a adequae ool whe acklg several problems. I he area of asse prcg, for sace, has bee ulzed o erpre pheomea volvg he reur of asses, such as overreaco ad uderreaco from he marke o ews. Oe has leared a lo abou he behavor of vesors ad aalyss from he aalyss of formao abou he behavor of he facal marke. I corporae face, he behavoral approach has bee callg aeo o audes such as he excessve averso o rsk-akg as well as o excessve opmsm. The arge of he prese paper s he sudy of pheomea of overreaco ad uderreaco wha cocers he Amerca sock marke. Some of he papers whch focus o smlar problems he eraoal sock markes are: Referece [3] for he Amerca marke, Referece [6] for he Chese marke ad Referece [7] for he Brazla marke. Referece [] exames codos ha lead o overreaco ad uderereaco aalyss eargs forecass. These models have evdeced aomales (overreaco/uderreaco) he sock marke. The bod sll hardly vesgaed he leraure, as observed [9], bewee he heory of fuzzy ses, orgally proposed by. A. Zadeh 965 [], ad he heurscs of he heory of behavoral face s explored for he developmes here preseed. A mehodology s developed for he rag of a se of socks he Amerca marke wh bass o facal dexes of he correspodg frms. I s hus demosraed ha he proposed mehodology corporaes heursc flueces from he behavoral face heory. Emprcal ess for he overreaco ad uderreaco hypohess are preseed usg daa from 994 o 007 he Amerca marke. The mporace of pheomea of overreaco ad uderreaco les he fac ha decso makg overreaco jusfes he opo for he use of he sraegy amed corara sraegy whle uderreaco eds o jusfy he choce of he sraegy of momeum. II. MATHEMATICA BASIS The fuzzy se heory possesses as oe of s ma characerscs he fac of allowg he reame of lgusc varables, such as ho, very ho, hgh, low, advsable, o advsable, hghly rsky, ec. A fuzzy se s a se coag elemes ha have varyg membershp degrees he se ad such elemes are mapped 35

2 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X o a uverse of membershp values usg a fuco-heorec form, whch maps a uverse of objecs X oo he u erval [0,]. If a eleme x s a member of fuzzy se A, he hs mappg s gve by μ A ( x) [ 0, ] [4]. Accordg orgal dea of Zadeh [], a fuzzy se of he uverse of objecs X s defed as a fuco μ ha maps X o [0,], X. The resulg propery whe cosderg lgusc varables o characerze objecs s ha, sead of belogg or o o a cera se, as saed by he classc se heory, hese objecs wll have perece dexes assocaed wh dffere ses. A dealed preseao of he ma coceps of he fuzzy heory ca be foud [] ad [3]. ha s, [ 0,] Defo : e he se X { x x,..., } A = x m, C, C,..., C, subses of X ad real umbers 0 μ ( x j ), =,,..., j =,,..., m, such ha, for every j =,,..., m, oe has μ ( = x j ) =. Uder hese codos, μ ( x j ) s deoed membershp degree of he eleme x j wh respec o fuzzy subse C. The membershp degree may be udersood as a measure of he degree of affy, smlary or compably amog elemes. I he applcaos he Fuzzy Theory has bee employed a umber of areas such as Egeerg [5], Medce [6], as well as Ecoomcs [7]. Amog he echques for he groupg or classfcao of elemes subses of a gve se, he Fuzzy Cluserg Meas FCM algorhm has bee proved o be a effecve ool hose cases whch he feaures or arbues of he aalyzed elemes ca be represeed by a vecor of real umbers. I such cases, he FCM algorhm allows defyg clusers of elemes from a marx of dmeso p, beg he umber of elemes ad p he dmeso of he vecors of feaures of hese elemes [3]. As he specfc applcao of hs paper he aalyzed elemes are grouped subses oly, he preseao s specfed for hs case. Thus, le x, x,..., xm elemes of X ad cosder he problem of groupg hese elemes subses C e C. The FCM algorhm deermes he subses C ad C va he soluo of he followg problem. Gve he elemes x, x,..., xm, descrbed as vecors of dmeso p, deerme he vecors c ad c, also of dmeso p, ad μ ( x j ) 0 ad μ ( x j ) 0, j =,,..., m, such ha μ x ) + μ ( x ) =, j, m ad he fuco = j= ( j j =,..., m [ μ ( x j ) x j c ] s mmzed. The soluo of such opmzao problem s gve by []: c = m ( μ ( x j ) j= m j= ( μ ( x ) j x j =, () x j c μ ( x ) =, j =,,..., m () j = m k = k x c Vecors c are called ceers. If μ ( x ) > μ ( x ) oe says ha he eleme x s assocaed o C ad f μ ( x j ) > μ( x j ) he x j s assocaed o C. As oe ca well observe, he calculao of c, hrough (), depeds o μ ( x j ). These, o her ur, deped o c, accordg o (). The soluo ca be obaed eravely, by he algorhm amed FCM, whose seps are ex descrbed. Sep : Iae wh membershp degrees, such ha μ ( x j ) + μ( x j ) =, j =,,..., m ad μ ( x j ) 0 ad μ ( x j ) 0, j =,,..., m ; Sep : Calculae he ceers c ad c, by (); Sep 3: Recalculae he ew membershp degrees, va (), by ulzg he ceers obaed sep. Repea seps ad 3 ul he objecve fuco do o decrease, accordg o he assumed precso. I order o acheve he global mmum of square-error, dffere paros mus be chose such ha he fal paro resuls always he same []. III. BEHAVIORA FINANCE I he begg of he 70s, me whe he Theory of Effce Marke had aaed a hgh degree of fluece decso makg Ecoomcs, he search for he compreheso of abormales of behavor facal markes world over brough abou he perspecve of he cluso of coceps of sychology ad Socology he ecoomc aalyss, o such a exe ha Kaheema's paper [5], ad Smh [8], deserved o be awarded he Nobel rze of Ecoomcs 00. The elemes volved hs ew approach led o he elaborao of he heory amed Theory of Behavoral Face. Accordg o he behavoral heory, dvduals make decsos guded by heurscs, or praccal rules, hkg a way whch devaes from he sasc rules. Several heurscs fluece decso makg. I parcular, he heurscs of represeaveess ad achorg [9], are drecly relaed o he heory of fuzzy ses, he way s see hs paper. Brefly speakg, he heursc of represeaveess s assocaed wh he smlary bewee he cosdered elemes. I he sequece, s preseed a classcal example, whch decso makg s srogly flueced by descrpve peces of formao, eve whe he probably of occurrece s kow, ha s, dvduals prefer o value descrpve formao sead of cosderg he probably of occurrece of he fac. I hs classcal example of he leraure some dvduals are asked o guess wha he occupao of a perso chose radomly a group of e people, kowg ha egh people he group are ruck drvers ad wo ohers are accouas. I he frs case he e people are dressed he same maer 36

3 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X ad, afer oe of hese e havg bee chose amog hem, he majory of he parcpas, relyg o he kow probably, decded ha hs perso would be a ruck drver. I he secod case, however, a eleme of ambguy was added, ha s, he e people were dfferely dressed, ad a dvdual wearg a su, glasses ad carryg a brefcase was chose. I hs case, he majory of parcpas defed hs perso as beg a accoua, eve hough he probably of hs dvdual beg a ruck drver was greaer ha he probably kow beforehad of hs beg a broker [7]. I hs example, he ma wearg a su, glasses ad carryg a brefcase has more smlary wh he se of accouas ad, herefore, less smlary wh he se of ruck drvers Expermes of hs kd sreghe he hypohess ha a mehod whch makes use of fuzzy ses s more adequae o shape decso makg uder codos of ambguy ha sasc mehods [0]. I he coex of decso makg Ecoomcs, dvduals uder he fluece of he heursc of represeaveess ed o produce exreme predcos, or overreaco [], whch former losers ed o be wers he fuure ad vce-versa [9]. I oher words, he sock marke overreaco maas ha a gve sock decreases (creases) oo far prce as a cosequece of rece bad (good) ews assocaed wh he sock. Thus, raders who are o sure abou he rsc value of a sock wll be oo opmsc abou s value whe he frm s wg ad oo pessmsc whe s losg [0]. I he fuzzy se heory he smlary s drecly relaed o he membershp degree, whch s a more suable ool o descrbe such characersc ha sasc mehods [0]. The heursc of achorg esablshes ha people ofe base hemselves o elemes or codos of referece order o make decsos. The heursc of achorg, dfferely from he heursc of represeaveess, leads o excessve moderao decso makg, hus causg he uderreaco pheomeo, whch former wers ed o be fuure wers, ad former losers ed o be fuure losers [9]. The heursc of achorg s assocaed wh coservave decso makg, causg people o ress quck chages her belefs he presece of ew formao. A experme coduced [7] shows he fluece of he achorg heursc he decso of a dvdual. I hs experme, wo sude groups mus esmae he value of a expresso fve secods: for group ad for group. Alhough he correc aswer o he wo sequeces s 40.30, he average esmae obaed for he sequece was 5, whle he average esmae obaed by he group (descedg sequece) was.50. Ths occurs because he descedg sequece he frs seps of mulplcao (from lef o rgh) produce a umber greaer ha he case of he ascedg sequece. I erms of he heory of fuzzy ses, a decso based o hs heursc s focused o he eleme of sroger referece he se, ha s, he eleme of oal membershp μ ( x) = [9]. Accordg o wha has bee meoed formerly, he Theory of Behavoral Face corporaes elemes whch are dffere from hose cosdered he Theory of Effce Marke []. Ths fac has allowed he developme of some ew models order o expla possble abormales he facal marke, ad such abormales whe explcable wh he help of classcal ools has foud sasfacory explaaos he Theory of Behavoral Face []. Some models relaed o he heurscs of represeaveess ad achorage are: A model of he vesor's seme has bee proposed [3]. Ths model s based o behavoral devaos as a cosequece of he already meoed heurscs, leadg vesor o eher uderreac or overreac o he avalable formao. Dael, Hrshlefer ad Subrahmayam's model [4], ams a coclag he emprcal facs of overreaco ad uderreaco. Accordg o hese auhors, he vesors wh o formao do o prese behavoral devaos, whle he vesors who possess formao are flueced by wo facors of devao: overcofdece, whch s assocaed o he heursc of represeaveess ad excessve value arbued o her percepos, whch s assocaed wh he heursc of achorg. I [3], based o he accumulao of mohly reurs he Amerca sock marke, evdeces of overreaco assocaed o he heursc of represeaveess he prces of asses are preseed. To sreghe he overreaco ad uderreaco hypoheses he sock marke, he ex seco a ew mehodology for aalyss of overreaco ad uderreaco s preseed. IV METHODOOGY FOR EMIRICA TESTS OF UNDERREACTION AND OVERREACTION I hs seco, he mehodology employed for he developme of a ew aalyss of overreaco ad uderreaco s roduced. Ths mehodology compreheds wo seps: paer recogo ad sock rag. The daa or feaures of he socks ulzed by he model are facal dexes of ope frms, cludg some reur dexes relaed o sock evaluao, profably ad deb. These dexes have bee colleced every rmeser from he Ecoomaca daa base [4], bewee he 4 h rmeser/994 ad he rmeser/007. The relao bewee hese raos ad he facal reur of he socks s a heme whch s hghly dscussed he leraure [5]. For he developme of hs paper several ses of facal raos relaed o markeably, profably, debedess ad socks rag have bee esed, grouped dffere ways. The raos here seleced ad effecvely adoped, whch have produced he bes resuls, are dvded o: rofably raos: e prof marg, reur o e worh, reur o asses [6]; Deb rao: deb o equy [6]; Marke dcaors: prce o book value of equy, prce o earg per share [5]. 37

4 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X The wo seps of he proposed model are ex descrbed. Sep : hs sep, amed paer recogo, he Fuzzy Cluserg Meas algorhm classfes he socks of a gve group. Ths aalyss has bee based o daa he perod bewee he 4 h rmeser/999 ad he rmeser/004. I each rmeser, he FCM algorhm was appled o he paer marx p, whch each le correspods o oe frm of he group ad each colum correspods o he facal dexes assocaed o he frms. Two clusers have bee obaed ad he average facal reur ha each cluser produces a he ed of he rmeser + s calculaed accordg o (3). I he sep of he FCM algorhm was used o ge he wer ceers ad he loser ceers each rmeser. + = = + r l (3) where s he value of sock a he ed of rmeser, + s he value of he sock a he ed of perod + ad s he umber of socks classfed. The cluser wh larger average facal reur s called wer cluser ad he oe wh smaller average facal reur s called loser cluser. Each group s represeed by vecor of facal raos calculaed eravely usg () ad (3) ul he objecve fuco s mmzed. I hs sese, accordg o he defo of he achorg heursc, whch he esmaes are formed from a al value o produce he fal aswer, he deermao of hese vecors of facal raos may be see as based o he achorg heursc. I hs sep, he classfcao of he groups as wer or loser has bee possble oly a he ed of he rmeser +, ha s, he classfcao s a poseror. Sep : he am of hs sep s o classfy, a he ed of rmeser, he cluser of socks wh performace supposedly wer or loser a he ed of rmeser +. Thus, dfferely from sep, he am s o se a classfcao a pror. For hs secod sep he clusers formed by he ceers of he s rmesers, rmesers, rmesers ad 4 h rmesers from 999 o 004 are cosdered separaely. The, he FCM algorhm s appled aga order o defy a wer ceer ad a loser ceer for each se of s rmesers, rmesers, rmesers ad 4 h rmesers. I he classfcao of a sock a he begg of a parcular rmeser, s eough o calculae he membershp degrees relaed o he wer ad he loser ceers correspodg o ha rmeser. For each rmeser, he group of promsg socks wll be called wer porfolo ad he group of o-promsg socks wll be called loser porfolo. For he umercal resuls, he classfcao of socks was made he perod bewee he 4 h rmeser/004 ad he 4 h rmeser/007. The asses are classfed each group wh a degree of smlary whch s calculaed by equao 3. The degree of smlary s so much greaer he shorer he dsace bewee he ceer vecor ad he raos vecor of he asse. I hs sese, here s a evde lk bewee he proposed mehodology for classfcao ad he represeaveess heursc, whch s based o he degree of smlary ha a objec A belogs o class B. 38 The pheomea of overreaco ad uderreaco have bee largely vesgaed hrough emprcal research [3], [6]. The procedure for he emprcal ess of such hypohess alog wh he ess of sasc sgfcace preseed hs paper are smlar o hose preseed [3]. Frsly, by usg he wer ad he loser ceers, socks are classfed. Thus, wer ad loser porfolos for each rmeser are formed. Nex, he correspodg resdual reur s calculaed for each week of he rmeser +, accordg o (4), (5) ad (6), for he wer porfolo. M +, j r +, j r + j RR =, (4) + = = + r l (5) IM IM +, j r +, j = l (6) IM where RR +, j s he resdual reur for he porfolo he week j of he rmeser +, r +, j s he reur for he M porfolo he week j of he rmeser +, r +, j s he reur assocaed wh he marke dex he week j of he rmeser +, +, j s he value of he sock, of he porfolo a he ed of he week j of he rmeser +, s he value of he sock of he porfolo a he ed of rmeser, IM +, j s he marke dex a he ed of week j of he rmeser +, IM s he marke dex a he ed of rmeser ad s he umber of socks he porfolo. Smlar calculaos are performed for he loser porfolo. From he resdual reurs correspodg o he weeks of each rmeser, he average resdual reurs of he wer porfolo ARR ad of he loser porfolo ARR are calculaed from he s rmeser/005 up o he 4 h rmeser/007. The hypohess of overreaco says ha ARR - ARR < 0 [7]. I order o evaluae wheher he dfferece bewee average resdual reurs each rmeser s meagful, a es of sasc- s performed. The ull hypohess o be esed s H 0 : ARR ARR = 0, agas he alerave hypohess of overreaco H A : ARR - ARR < 0. Smlarly, he alerave hypohess for uderreaco s H A : ARR ARR > 0. Furhermore, are calculaed, accordg o (7) ad (8), he cumulave ARR ( CARR ) for he wer porfolo ad cumulave CARR for he loser porfolo from s ARR ( ) rmesers of 005 o 4 h rmesers of 007 for vesgae he flueces of overreaco ad uderreaco durg he perod cosdered. = CARR ARR (7) = CARR ARR (8)

5 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X V. THE AMERICAN STOCK MARKET A CASE STUDY I hs seco he mehodology proposed seco IV s ulzed o form porfolos ad, ex, ess for he hypohess of overreaco ad uderreaco are performed. The marke dex adoped s he S& 500 dex ad he daa from socks of he ol ad gas secor, exle secor ad seel ad ro secor are cosdered he perod ragg from 999 o 007. I sep of he algorhm daa from he 4 h rmeser/999 o he rmeser/004 are used o ge he wer ad he loser ceers ad he sep daa from he 4 h rmeser/004 o he 4 h rmeser/007 are used o form wer ad loser porfolos. As a example of he obaed resuls, Fg. he graphs of he resdual reurs for he wer porfolo () ad for he loser porfolo () obaed a he ed of he s rmeser of 007, as well as he dfferece bewee hem durg each week of he rmeser of 007 for he ol ad gas secor are preseed. Resdual Reur quarer Fgure. eekly Resdual Reurs Ol ad Gás Secor I hs case, evdeces of overreaco are obvous. By calculag he average resdual reurs for he wer ad loser porfolos for hs quarer, oe ca observe ha he loser porfolo ouperform approxmaely 8.06% he average resdual reur of he wer porfolo, meagful a he level of 5% (sasc :-7.989). Table I shows he resuls of hs aalyss for every quarer of 005, 006 ad 007 for socks of he ol ad gas secor. Oe ca oce ha he majory of quarers here are sascally meagful evdeces of overreaco. Furhermore, he CARR = 6, 464 from loser porfolo ouperform he CARR =0, 975 from wer porfolo 5,489%, afer welve quarers (hree years), supporg he overreaco hypohess for he ol ad gas secor. I able II ad able III are preseed he resuls of hs procedure for all rmesers from 005 o 007 he case of socks of exle ad seel ad ro secors, respecvely. TABE I. AVERAGE RESIDUA RETURNS AND TEST-T FOR THE ETRO/ETROCHEMICA SECTOR STATISTICAY MEANINGFU AT THE EVE OF (*) 5% AND (**) 0%. Trmeser/ V ARR year ARR Tes- s rm/005 9,66 4,058 * rm/005, 0,46 rm/005-3,968 -,9 ** 4 h rm/005 4,594,55 * s rm/006-5,970 -,580 * rm/006-0,338-0,438 rm/006 0,705 0,74 4 h rm/006-6,083-5,48 * s rm/007-5,80 -,55 * rm/007-8,455-7,989 * rm/007 0,07 0,0 4 h rm/007 -,557 -,654 ** TABE II. AVERAGE RESIDUA RETURNS AND TEST-T FOR THE TEXTIE SECTOR STATISTICAY MEANINGFU AT THE EVE OF (*) 5% AND (**) 0%. Trmeser/ V ARR year ARR Tes- s rm/005 3,89,50 rm/005 -,586-0,68 rm/005-3,930-4,645 * 4 h rm/005 7,533,437 * s rm/006,698,039 rm/006 0,9 0, rm/006-5,446 -,488 * 4 h rm/006 -,59-0,7 s rm/007 4,054,85 ** rm/007 9,98, ** rm/007-6,98 -,096 4 h rm/007-4,037 -,693 * TABE III. AVERAGE RESIDUA RETURNS AND TEST-T FOR THE STEE AND IRON SECTOR STATISTICAY MEANINGFU AT THE EVE OF (*) 5% AND (**) 0%. Trmeser/ V ARR year ARR Tes- s rm/005-0,4-0,090 rm/005-30,580 -,954 ** rm/005,867 0,50 4 h rm/005-6,596 -,595 s rm/006-4,009-0,530 39

6 Ieraoal Joural of Trade, Ecoomcs ad Face, Vol., No.4, December, X rm/006-8,789-4,05 * rm/006 6,746,54 * 4 h rm/006 5,905,367 s rm/007 -,834-0,640 rm/007 4,534,369 * rm/007 5,66,43 * 4 h rm/007-0,368 -,654 * The same procedure has bee adoped for socks he exle secor ad seel ad ro secor ad he obaed resuls are preseed able II ad able III, respecvely. I hs case, flucuaos bewee overreaco ad uderreaco, sascally meagful, are observed. Though, he CARR = 48,664 from loser porfolo ouperform he CARR = 0,789 from wer porfolo 7.875% for he ro ad seel secor ad, CARR =, 80 from loser porfolo ouperform he CARR = 4, 637 from wer porfolo 6.87% for he exle secor afer welve quarers (hree years), dcag a srog fluece of overreaco seel ad ro secor ad exle secor. VI. CONCUSION I hs paper a mehodology based he Fuzzy Cluserg Meas Algorhm for socks rag s proposed ad a procedure for emprcal ess of overreaco ad uderreaco he sock marke s preseed. The proposed mehodology s based o he Fuzzy Ses Theory, whch o s ur s closely relaed o he Theory of Behavoral Face. To form he porfolos, he proposed mehodology ulzes facal raos of publc compaes. Numercal resuls are preseed whe applyg he proposed mehodology o he Amerca sock marke. Three ses of socks are cosdered hs case: socks of he ol ad gas secor, socks of he seel ad ro secor ad socks of he exle secor. The ol ad gas secor preses sascally meagful evdeces of overreaco whle he porfolos formed by socks of he exle secor ad socks of he seel ad ro secor prese flucuaos bewee overreaco ad uderreaco, sascally meagful. Therefore, afer welve quarers (hree years), he loser porfolo resuls a abormal prof wh regard o wer porfolo for all he secors cosdered. The resuls obaed are cosse wh he overreaco hypohess he Amerca sock marke ad cofrm he fdgs [3]. These facs, added o he exsg bod bewee fuzzy ses ad he Theory of Behavoral Face po, hus, o he fluece of he heursc of represeaveess he behavor of he Amerca sock marke ad s cosse wh he srog fluece of he overreaco he marke. The mporace of pheomeo of overreaco ad uderreaco les he fac ha decso makg overreaco jusfes he opo for he use of he sraegy amed corara sraegy whle uderreaco eds o jusfy he choce of he sraegy of momeum. I he case of 330 he momeum sraegy, pas wers are bough ad pas losers are shored ad, he corara sraegy, pas wers are shored ad pas losers are bough. The resuls obaed suggess hus ha abormal profs could be obaed wh a sysemac applcao of he corara sraegy he cosdered Amerca sock marke ad shows ha a vesor could oba abormal profs wh he shor of he wer porfolo ad he buy of he loser porfolo. REFERENCES [] E. Amr.; Y. Gazach. Overreaco ad Uderreaco Aalyss Forecass. Joural of Ecoomc Behavor & Orgazao, v. 37, p , 998.) [] J. C. 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