No July. Imitation Amongst ExchangeRate Forecasters: Evidence from Survey Data. Michel Beine Agnès BénassyQuéré Hélène Colas


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1 No Juy Imiaion Amongs ExchangeRae Forecasers: Evidence from Survey Daa Miche Beine Agnès BénassyQuéré Héène Coas
2 Working Papers no Imiaion Amongs ExchangeRae Forecasers: Evidence from Survey Daa Miche Beine Agnès BénassyQuéré Héène Coas No Juy 2
3 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa TABLE OF CONTENTS SUMMARY...4 ABSTRACT...5 RÉSUMÉ...6 RÉSUMÉ COURT...7. INTRODUCTION DATA DESCRIPTION METHODOLOGY Causaiy wih he pane average Causaiy amongs individuas Herding and performance RESULTS Causaiy wih he pane average Causaiy amongs individuas Herding and performance CONCLUSION...22 REFERENCES...23 APPENDIX A...25 APPENDIX B...27 LIST OF WORKING PAPERS RELEASED BY CEPII
4 Working Papers no IMITATION AMONGST EXCHANGERATE FORECASTERS : EVIDENCE FROM SURVEY DATA SUMMARY A arge srand of he research on exchange raes and sock prices reaes he price dynamics o he ineracion of various ypes of agens (chariss vs fundamenaiss; informed vs uninformed, sophisicaed vs naive). The proporion of each ype of agens can move over ime depending on heir reaive performance, on a probabiisic conagion process, or on boh. Non inear price dynamics can be derived, incuding excess voaiiy, bubbes an chaos. Three kinds of herding can be disinguished (Bikhchandani & Sharma, 2000): informaionbased herding (where herding sems from he Bayesian exracion of informaion from he observed behavior of oher agens); repuaionbased herding (where imiaion is due o he uncerainy surrounding he reaive abiiy of invesmen managers); and compensaionbased herding (where herding is due o a compensaion scheme ha compares he performance of each invesor o a benchmark). Herding is found o be derimena since i reduces he informaion conen of prices, and because, being based on ie informaion, he prevaiing consensus is very fragie. The consequence is a price which can move far away from is fundamena vaue, which dispays high voaiiy and is subjec o specuaive bubbes. A hree ypes of herding can poeniay affec he foreign exchange marke. However, empirica evidence of herding so far has mainy concenraed on he sock marke, wih mixed resus. In his paper, we ry o bring some empirica evidence on he exisence of some imiaion behavior amongs professiona forecasers of he exchange rae. We use monhy survey daa from Consensus Economics of London concerning he Deuschemark, he euro and he yen agains he US doar over and Through Grangercausaiy ess, we firs sudy wheher forecasers are infuenced by he as pubished consensus (i.e. he as known average forecas), and conversey, wheher one or severa forecasers can be idenified as eader(s) of he forecasing communiy. We hen examine inerindividua causaiy reaionships, hrough a sepbysep mehodoogy invoving Grangercausaiy ess and SURE esimaions. This mehodoogy aows o ge rid of non robus reaionships and spurious causaiy. The resus aow o buid a ne eadership index for each forecaser ha can be compared wih his(her) performance over he period under consideraion. The resus show ha here are sequenia connecions beween exchangerae expecaions of individua forecasers. However, i is no possibe o idenify one guru eading more han four oher forecasers. Ineresingy, imiaion is no a specific feaure of shor run horizons, ahough individua eaders seem o be ess persuasive a 2 monhs han a 3 monhs. 4
5 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa The weak reaionship beween he performance of each individua and his/her ne eadership index ends o dismiss he hypohesis of a sequenia repuaionbased herding on he forex marke, which woud impy ha successfu forecasers become eaders, or ha high repuaion forecasers end o herd more. Imiaion hence woud fa raher on he compensaion and informaion ypes. Our resus emphasizing some imied evidence of herding are broady in ine wih he ieraure on herding behavior in sock marke recommendaions. However we ony dea here wih sequenia herding. Our monhy daa se is no we disposed o deec any nonsequenia herding (or sequenia herding a a higher frequency), since i is no possibe o disenange such herding from simuaneous reacions o forecasers o pubic news. In addiion, he ink beween forecass and foreign exchange posiions is far from cearcu. Neverheess, we beieve our resus can quesion sequenia herding of forecasers as one major cause of ong ived deviaions of he exchange rae from is fundamena vaue. ABSTRACT In his paper we assess he exen of herd behaviour in he major foreign exchange markes using monhy survey daa reaive concerning individua forecass for he DM (or euro) and he yen agains he US doar. We conduc Grangercausaiy ess and SURE esimaions over wo disinc periods ( and ) o anayze wheher forecasers where subjec o imiaion during hese periods. The resus aow o compue eadership and foowership indices. They show ha, ahough mos forecasers are conneced o ohers hrough eading or imiaion paerns, sequenia herding is no a prominen feaure of he marke, a eas a he monhy frequency. Moreover, here is no cear reaionship beween he degree of eadership and he performance of individuas. Hence, our resus cas doubs on sequenia herding of forecasers as one poenia major cause of ongived deviaions of he exchange rae from is fundamena vaue. JEL Cassificaion: Key Words: F3, F37 herding, exchangerae forecass, survey daa 5
6 Working Papers no IMITATION ENTRE PRÉVISIONNISTES DES CHANGES : UNE ÉTUDE EMPIRIQUE SUR DONNÉES D'ENQUÊTES RÉSUMÉ Une par imporane de a recherche consacrée aux aux de change e aux cours boursiers reie a dynamique des prix à ineracion enre différens ypes d agens (charises conre fondamenaises, informés conre non informés, perfecionnés conre naïfs). La proporion de chaque ype d agens peu évouer au cours du emps en foncion des performances reaives, d un processus probabiisique de conagion, ou des deux. I en ressor une dynamique de prix non inéaire qui peu prendre a forme d une voaiié excessive, de bues spécuaives ou de chaos. On disingue rois formes de miméisme (voir Bikhchandani & Sharma, 2000): e miméisme «informaionne» (où imiaion provien de exracion bayésienne d informaion à parir du comporemen observé des aures agens) ; e miméisme «répuaionne» (dû à inceriude qui enoure es capaciés reaives des gesionnaires de fonds) ; e e miméisme fondé sur es modes de rémunéraion (dans eque a performance de chaque gesionnaire es comparée à une référence). Le miméisme es préjudiciabe car i rédui e conenu informaif des prix e parce que, à cause de ce faibe conenu informaif, e consensus es fragie. La conséquence es un prix qui peu s écarer rès oin de sa vaeur fondamenae, qui exhibe une fore voaiié e es suje aux bues spécuaives. Les rois ypes de miméisme peuven affecer e marché des changes. Cependan, es éudes empiriques sur e miméisme se son inéressées, jusqu à présen, essenieemen au marché boursier, e on donné des résuas miigés. Dans ce arice, nous enons d apporer queques éémens empiriques sur exisence de miméisme au sein des prévisionnises professionnes des aux de change. Nous uiisons es données d enquêes mensuees du Consensus Economics de Londres concernan e Deuschemark, euro e e yen par rappor au doar US sur es périodes e A aide de ess de causaié à a Granger, nous éudions d abord si es prévisionnises son infuencés par e dernier consensus pubié (c esàdire, a dernière prévision moyenne), e inversemen, si un ou pusieurs prévisionnises peuven êre idenifiés comme des eaders de a communaué des prévisionnises. Ensuie, nous examinons es reaions de causaié enre individus, à aide d une méhode pasàpas faisan appe à des ess de causaié à a Granger e à des esimaions SURE. Cee méhodoogie perme d éiminer es reaions de causaié non robuses ou ficives. Les résuas permeen de consruire, pour chaque individu, un indice de eadership ne, que on peu ensuie comparer avec sa performance au cours de a période. Les résuas monren qu i exise des reaions séqueniees enre es prévisions de aux de change des différens prévisionnises. Touefois, i n es pas possibe d idenifier un gourou 6
7 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa qui infuencerai pus de quare aures prévisionnises. De manière inéressane, imiaion n es pas apanage des horizons cours, même si es eaders semben êre moins persuasifs à 2 mois qu à 3 mois. Le faibe ien enre a performance de chaque individu e son indice de eadership ne end à infirmer hypohèse seon aquee i exiserai un miméisme «répuaionne» sur e marché des changes, ce qui impiquerai que es prévisionnises performans deviennen des eaders, ou que es prévisionnises jouissan d une bonne répuaion enden davanage au miméisme. L imiaion serai aors due aux modes de rémunéraion ou à a recherche d informaion. Nos résuas, qui meen en évidence peu de miméisme, son cohérens avec a iéraure sur imiaion enre anayses financiers. Cependan, nous nous inéressons ici seuemen au miméisme séquenie. Nos données mensuees ne son pas adapées pour éudier e miméisme non séquenie (ou e miméisme séquenie à pus haue fréquence), car i n es pas possibe de séparer ce ype de miméisme de a réacion simuanée des individus aux informaions pubiques nouvees. En oure, e ien enre es prévisions e es prises de posiion de change es oin d êre cair. Néanmoins, nous pensons que nos résuas son de naure à remere en cause e miméisme séquenie des prévisionnises comme une cause majeure des écars durabes des aux de change par rappor à eurs vaeurs fondamenaes. RÉSUMÉ COURT Dans ce ravai, nous éudions imporance des comporemens miméiques sur es principaux marchés des changes en uiisan des données d enquêes mensuees concernan es prévisions individuees sur e DM (ou euro) e e yen par rappor au doar US. Nous conduisons des ess de causaié à a Granger sur deux périodes disinces ( e ) pour anayser si es prévisionnises on éé sujes au miméisme duran ces périodes. Les résuas permeen de cacuer des indices de eadership e de «suivisme». Is monren que, même si a pupar des prévisionnises son reiés à d aures par des reaions d imiaion, e miméisme séquenie n es pas une caracérisique esseniee de cee communaué, au moins en fréquence mensuee. En oure, i n y a pas de ien ne enre e degré de eadership e a performance des individus. Par conséquen, nos résuas jeen un doue sur a responsabiié du miméisme séquenie dans es écars des aux de change par rappor à eurs vaeurs fondamenaes. Cassificaion JEL : Moscefs : F3, F37 miméisme, prévisions de aux de change, données d enquêes 7
8 Working Papers no IMITATION AMONGST EXCHANGERATE FORECASTERS : EVIDENCE FROM SURVEY DATA Miche Beine, Agnès BénassyQuéré and Héène Coas. INTRODUCTION A arge srand of he research concerning exchange raes and sock prices reaes he price dynamics o he ineracion of various ypes of agens (chariss vs fundamenaiss; informed vs uninformed, sophisicaed vs naive). The proporion of each ype of agens can move over ime depending on heir reaive performance (Franke & Froo, 986, de Grauwe e a., 993), on a probabiisic conagion process (Kirman, 993), or on boh (Lux, 995). Non inear dynamics can be derived, incuding excess voaiiy, bubbes an chaos (Shier, 984; Topo, 99; de Grauwe e a., 993; Lux, 998). Aernaivey, he con agion amongs marke agens can be nonsequenia as in Oréan (995) or Con & Bouchaud (2000), which eads o muipe equiibria and fa ais. Eary modes based on herd behavior assumed a significan share of he popuaion o deviae from perfec raionaiy, in he form of charism, noise rading or feedback rues (de Long e a., 990). However here has been subsania effor o raionaize herd behavior (see eary papers by Oréan, 989, Scharfsein & Sein, 990, Banerjee, 995). Bikhchandani & Sharma (2000) cassify such raionaizaions ino hree groups: informaionbased herding (where herding sems from he Bayesian exracion of informaion from he observed behavior of oher agens); repuaionbased herding (where imiaion is due o he uncerainy surrounding he reaive abiiy of invesmen managers); and compensaionbased herding (where herding is due o a compensaion scheme ha compares he performance of each invesor o a benchmark). Herding is found o be derimena since i reduces he informaion conen of prices, and because, being based on ie informaion, he prevaiing consensus is very fragie. The consequence is a price which can move far away from is fundamena vaue, which dispays high voaiiy and gives rise o specuaive bubbes. Empirica evidence of herding so far has mainy concenraed on he sock marke (see Bikhchandani & Sharma, 2000, for a review). A firs group of sudies uses he porfoio composiion of fund managers, herding being defined as he propensiy o buy or se paricuar socks a he same ime, or as he endency of porfoio weighs o move in he same direcion. A second group ooks a herding amongs invesmen anayss and CADRE, Universiy of Lie 2, France and DULBEA. THEMA, Universiy of Paris X and CEPII, France. THEMA, Universiy of Paris X, France. 8
9 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa newseers. I sudies wheher he various anayss end o provide he same recommendaion a he same ime or wih shor deay (see Lakonishok e a., 992; Grinba e a., 993; Jaffe and Mahoney, 998), or wheher hey foow one weknown newseer (Graham, 999). On he whoe, hese empirica invesigaions provide ony mixed evidence of herding. They generay find ha herding is ess ikey for he mos raded socks and for he mos successfu anayss (ahough anayss wih high repuaion are more ikey o herd). A sraighforward inerpreaion of hese resus is ha (i) he proporion of privae informaion is higher for sma socks (eading o more informaionbased herding), (ii) a ow abiiy anays has greaer incenive o hide in he herd han a high abiiy anays (eading o more repuaionbased and more compensaionbased herding), and (iii) a high repuaion anays has more o ose by being wrong agains he benchmark, which eads o repuaionbased herding. A hree ypes of herding can poeniay affec he foreign exchange marke. In paricuar, Lyons (200) argues ha, ahough marke fundamenas cover macroeconomic variabes which are pubic knowedge, privae informaion does exis on his marke. Such privae informaion, which is conveyed by order fows, mainy concerns he way news concerning fundamenas are o be inerpreed. I is aso reaed o shorrun invenory consrains and risk aversion of marke deaers. Some macroeconomic announcemens and poicy acions such as cenra bank inervenions can aso conain privae informaion in he shor run. For insance, Peiers (997) and Dominguez (999) show how informaion concerning cenra bank inervenions spreads hrough he inerbank marke wihin a coupe of hours afer he ransacion has aken pace wih one or a sma number of eading banks. Simiary, D Souza (200) ess wheher cusomer rades incuding cenra bank inervenion conain shor run privae reevan informaion and wheher deaers uiize his informaion in a sraegic way. In his paper, we ry o bring some empirica evidence on he exisence of some imiaion behavior amongs professiona forecasers of he exchange rae. Hence, our approach is in ine wih hose sudies based on he recommendaions of invesmen anayss and newseers. In paricuar, i is no cear wheher he recommendaions are foowed by porfoio decisions: any herding found amongs forecasers wi no ransae ino herdbased price dynamics. Conversey, any evidence in favour of herding is ess ikey o be spurious amongs forecasers han amongs porfoio invesors because forecass do no inerac wih rading rues (such as soposs rues). In order o assess he exen of herd behavior, we use monhy survey daa from Consensus Economics of London concerning he Deuschemark, he euro and he yen agains he US doar over and Ahough exchange rae survey forecass can ofen be ouperformed by random wak predicions, hey coud generae posiive profis when used wih a reevan rading rue (Eio & Io, 999). Thus hey can be considered as meaningfu from a financia poin of view. Foowing Peiers (997), we carry ou Grangercausaiy ess o assess wheher one or severa forecasers ead ohers. We firs sudy Peiers however works on ickbyick quoes insead of monhy forecass. 9
10 Working Papers no wheher forecasers are infuenced by he as pubished consensus (i.e. he as known average forecas), and conversey, wheher one or severa forecasers can be idenified as eader(s) of he forecasing communiy. We hen examine individua causaiy reaionships, hrough a sepbysep mehodoogy ha aows o ge rid of non robus reaionships and of spurious causaiy. Causaiy resus aow o buid a ne eadership index for each forecaser ha can be compared wih his (her) performance over he period under consideraion. I is worh noing ha he Grangercausaiy mehodoogy ony accouns for sequenia herding. Nonsequenia herding can be very difficu o disenange from simiar reacions o pubic news. The paper is organized as foows. The daa se is briefy described in Secion 2. Secion 3 presens he mehodoogy. In Secion 4, he resus concerning he causaiy beween individua forecasers and he consensus forecas are commened. Secion 5 presens he resus for causaiy beween individuas. Secion 6 concudes. 2. DATA DESCRIPTION We use survey daa from Consensus Economics of London. Individua forecass from over 00 individuas and financia insiuions in he G7 capia ciies are coeced each monh for he exchange raes of he US doar agains he Deuschemark (he euro afer January 999), he Japanese yen and he pound Sering, a various horizons ranging from monh o 2 years. The survey is conduced on he firs Monday of each monh, and he resus are pubished before he 5 h of he corresponding monh. Imporany, a individua forecass are known before he nex forecas is made. Two periods are considered: from January 990 o December 994, and from January 996 o March 200. Ahough he daa source is he same for he wo periods, i is no possibe o connec he periods because a year of daa is missing beween periods and because here is a break in he forecasers fags. We concenrae on he, 3 and 2monh forecass for he yen and he Deuschemark (and euro) agains he US doar. The onemonh forecass are ony avaiabe for he second period, whie he 3 and 2monh horizons are avaiabe for boh periods. We dea wih missing daa by resricing he sampe in he foowing way. For he firs period, we seec he 25 respondens ha did no fai more han 4 imes (once a year on average) on each of he wo markes (JPY/USD and DEMEUR/USD) and on each horizon (3,2 monhs). Hence, he number of answers is generay very cose o 25 for each dae/currency/horizon. For he second period, given he high number of missing vaues, we seec hose forecasers ha did no fai more han 0 imes provided hey did no fai more han hree imes in a row. The number of forecasers ranges from 8 o 3 depending on he currency/horizon (Tabe ). Noe ha he forecasers wi no necessariy be he same across currencies and horizons for his second period, whereas hey are sricy he same for he firs period. Noe aso ha we consider he EUR/USD marke as he simpe coninuaion of he DEM/USD one. This simpificaion is made possibe by he fac ha we work on expeced percenage variaions of exchange raes (see beow). 0
11 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa The missing vaues for each individua are fied wih his/her as repored one for he same individua. 2 This procedure biases he resus agains herding in favor of a simpe auoregressive process for each individua forecas series. Hence any finding of imiaion wi appear more robus. Finay, we use he pane average expecaion cacuaed a each ime on he whoe pane (incuding hose individuas no incuded in he presen sudy) so ha each individua forecas canno have a significan mechanica impac on he pane average. Tabe : Number of forecasers seeced for each period/currency/horizon Horizon monh 3 monhs 2 monhs s period DMEUR/USD YEN/USD nd period DMEUR/USD YEN/USD Nomina exchange raes are we known o be non saionary, whereas here firs differences are generay saionary, a eas wihin OECD currencies. This is fuy confirmed for our daa by uni roo ess repored in Appendix A. Hence we work on he percenage of variaion expeced by each individua: ( S ) n( S ) si,, + h = n i,, + h () S + where i,, h sands for he expecaion of he exchange rae made a ime by individua i for ime +h. This quasidiffereniaed variabe is found o be saionary for mos individuas on amos a markes and forecas horizons. 3 In he foowing, we drop he horizon subscrip (+h) for he sake of simpiciy. The key feaures of he daa are repored in Tabe 2. On average, he US doar was expeced o appreciae agains boh he DM and, o a esser exen, agains he yen during he firs subperiod. This conrass wih he overa sabiiy of he USD/DM exchange rae and o he coninuous depreciaion of he USD agains he yen during his period. Over he second subperiod, a depreciaion of he USD was expeced agains he DMEUR and (a he 2 monh horizon) agains he yen, bu he USD appreciaed agains he DMEUR whereas i appreciaed and hen depreciaed agains he yen. On he whoe, hen, expecaions appear o be mean revering. The faiure of he pane o correcy predic 2 This is why we ony consider forecasers wih no more han hree missing vaues in a row. 3 We found more evidence of sochasic rend for he DEM(Euro)USD daa over he recen subperiod (see Tabe A2). We shoud neverheess be very carefu in acceping hese resus as sriking evidence of he presence of a uni roo in equaion () given he very ow power of ADF ess for sma sampes.
12 Working Papers no exchange raes is iusraed by he mean squared error of he average forecas which dispays he same order of magniude as he expecaion isef. No surprisingy, he error is arger he onger he horizon, which corresponds o arger exchange rae variaions. Finay, i is worh noing ha he dispersion of expecaions across he various forecasers is again of he same magniude as he mean forecas as we as he mean squared error; i is higher for he yen han for he DM. Tabe 2: Main feaures of he daa in % Mean expecaion of he pane () Mean squared error of he consensus (2) Mean dispersion across forecasers (3) M 3M 2M M 3M 2M M 3M 2M s period ( ) DMEUR/USD YEN/USD nd period ( ) DMEUR/USD YEN/USD () a posiive sign indicaes an expeced appreciaion of he USD. (2) T error T = / 2 2, where error is he percenage error of he pane average. T (3) sdev, where sdev is he sandard deviaion of expeced exchangerae T = variaions (in percenage) across forecasers a ime. 3. METHODOLOGY Two ypes of herding are successivey sudied. In he firs one, one or severa individuas are infuenced by he average forecas, or aernaivey one or severa individuas are eaders of he average. This firs ype of herding is diffuse in he sense ha each individua canno idenify he forecasers ha he/she foows or eads. The second ype of herding idenifies eaderfoower coupes. Hence his form of herding can be cassified as repuaionbased, whereas he firs ype can be of eiher ype defined in he inroducion. 3.. Causaiy wih he pane average For each currency, each horizon and each period, we esimae he foowing VAR mode, where s is he expecaion of he pane average and he opimum number of ags p is deermined using he Schwarz informaion crierion: 2
13 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa si, = ci + s = c j + Ρ a s = Ρ 2 b = s i, i, + + Ρ = Ρ 2 b s = a s + u i, + u (2) We hen proceed o wo Granger causaiy ess: Tes : H 0 : b b = K = b 0 agains H : / b 0 (Grangercausaiy from pane average o individua i) = 2 p = Tes 2: H 0 : b b = K = b 0 agains H : / b 2 0 (Grangercausaiy from = 2 p = individua i o pane average) If H 0 is rejeced in boh ess (no Granger causaiy), or if i is no rejeced in boh ess (doube Granger causaiy), we concude ha here is no causaiy beween i and he pane average. If ony one nu is rejeced, we concude o a oneway causaiy, from average o i (resp from i o average) in case H 0 is rejeced in he firs (resp second) es. In order o improve he robusness of he causaiy ess, we successivey use a Fisher es and a ikeihood raio es. For insance, in he case of he causaiy from he pane average o individua i, he Fisher es compares he sum of squared residuas of he firs equaion of (2) (denoed RSS) wih he sum of squared residuas of he same equaion excuding (=,, p) (denoed RSS0): s S ( RSS RSS0) / p = RSS/( T 2p ) (3) Under H 0, S foows a F(p,T2p) disribuion. We compemen he Fisher es wih a ikeihood raio es, aking advanage of he VAR specificaion. Like he Fisher es, he ikeihood raio es is based on he comparison of he esimaes of he firs equaion of (2) wih and wihou (=,, p): S s [ og Ω Ω ] 2 =T og 0 where Ω is he esimaed variancecovariance marix of he residuas from OLS esimaion of he firs equaion of (2) and Ω 0 is esimaed variancecovariance marix of he residuas from OLS esimaion of he firs equaion of (2) in which (=,, p) is 2 excuded. Under H 0, he S 2 saisic foows a χ ( nn2 p) disribuion where n is he dimension of si, and n 2 is he dimension of s (n =n 2 = here). We rejec H 0 if and ony if boh mehods ead o he same concusion and he causa b j i (j=,2) coefficiens are posiive. 3 s (4)
14 Working Papers no Causaiy amongs individuas For each currency, each horizon and each period, we proceed in 4 seps, using boh es saisics: Sep For each coupe (i,j) of individuas ( j i < ), we esimae he foowing VAR mode, where he opimum number of ags p is deermined using he Schwarz informaion crierion: = = Ρ = Ρ = Ρ = Ρ = j j i j j i j i i i u s a s b c s u s b s a c s,, 2, 2,,,,, (5) We hen proceed he same way as in secion 3.. Sep 2 Suppose wo differen forecasers j and j are found eaders of he same individua i in Sep. We es for he robusness of each causaiy reaionship by inroducing he firs ag of he expecaion of say j in he VAR mode for he (i,j) coupe: = = Ρ = Ρ = Ρ = Ρ = j j j i j j i j j i i i v s c s a s b c s v s c s b s a c s, ', 2, 2, 2,, ',,,, (6) We hen proceed o he same Grangercausaiy ess beween i and j han in sep. This aows o reduce he number of causaiy reaionships found in Sep. Sep 2 is ieraed uni a causaiy reaionships are found robus o he incusion of he agged expecaion of oher eaders of he same individua as a conro variabe. Finay, causa reaionships wih significany negaive coefficiens are removed. Sep 3 So far, he esimaion procedure has negeced he possibe reaionships across equaions. Of course, common shocks, ahough mosy unobservabe, affec he way forecasers buid heir exchange rae expecaions. We accoun for spurious herding semming from common shocks by reesimaing a equaions which incude a causa reaionship amongs individuas using he SURE mehodoogy. The vaues of he correaions across equaions sugges ha, on average, he error erms are significany and posiivey correaed: for boh
15 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa currencies and a a horizons, he correaions are mos of he ime posiive, wih a significan par of hese correaions we above Accouning for common shocks resus in a sigh decrease in he number of causa reaionships. Sep 4 For each individua (i = o N), a eadership index (L i ) is defined as he number of individuas he(she) eads as obained in Sep 3. Simiary, a foowership index (F i ) is derived as he number of forecasers which exer some eadership on he corresponding individua. Finay, he ne eadership index (I i ) is he simpe difference beween he eadership and he foowership index for each individua: I i = L F, i = o N i i The ne eadership index heoreicay ranges from (N) o +(N), where N is he oa number of forecasers Herding and performance I has someimes been shown in he ieraure ha successfu sock anayss are ess ikey o herd han ow abiiy anayss (Graham, 999). Symmericay, eaders can be viewed as informed forecasers who shoud dispay higher accuracy han foowers. Hence we ry o reae he ne eadership index of each anays o his(her) persona performance over he period. Three aernaive measures of performance are used which we borrow from Eio and Io (200). The firs measure of performance is based on he roo mean squared error of he forecass, normaized for he performance of he random wak, which makes he performances comparabe no ony across individuas, bu aso across horizons and currencies: PERF RMSE 0, i =, RMSEi wih = ( ) / 2 2 T T RMSE 0 s + h and RMSEi = ( si,, + h s+ h ) T = T = / 2 2 RMSE 0 is he roo mean squared error of he naive mode (based on a random wak), wih s + h sanding for he exchangerae variaion beween and +h. RMSE i is he roo mean squared error of individua i. Hence, a high abiiy forecaser shoud dispay high vaue of PERF,i. 4 The resus are avaiabe upon reques. 5
16 Working Papers no The second measure of individua performance is based on a rading rue ha consiss in buying one doar on he spo marke when he doar is forecased higher han is forward rae, and o se one doar if i is forecased ower. The normaized performance of individua i over he period is hen: PERF 2, i = BEN i BEN o wih BEN = T ( s f ) SIGN ( f ) 0 = + h, + h, + h and BEN = T ( s f ) SIGN ( s f ) i = + h, + h i,, + h, + h SIGN ( x) is equa o if x > 0 and if x < 0. BEN 0 is he benefi ha woud obain a naive forecaser who expecs no change in he exchange rae and hence buys doar on he spo marke whenever he forward rae of he doar is ower han he spo rae ( f = f s 0 ). BEN i is he benefi of individua i if he(she) bes on his(her) own, + h, + h < forecas (assuming risk neuraiy). The hird measure of performance is he abiiy of each individua o forecas he direcion of exchangerae change: C PERF 3, i = 00 T i i where C i sands for he number of correc predicions of he direcion and T i is he oa number of forecass of individua i. This hird measure of performance shoud exceed 0.5 for a successfu forecaser. 4. RESULTS As described above, we firs es for Granger causaiy beween he pane average and each individua, and hen es for causaiy across individuas. 4.. Causaiy wih he pane average The causaiy reaionships from individuas owards he pane average are repored in Tabe 3, whereas Tabe 4 repors he reaionships from he pane average owards he individuas. Noe ha he resus for he second period are ess reiabe han hose for he firs period due o he ower number of individuas. Three main commens are in order. Firs, here are ofen more causaiy reaionships a he 2 monh horizon han a he 3 monh horizon: diffuse herding of individuas (where individua forecasers ead or foow he average) is no specific o shor horizons. 6
17 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa Second, individua forecass for he yen/doar exchange rae seem o have been ed by he pane average over he firs period, whereas a few individuas seem o have ed he pane average over he second period. Third, i is no possibe o idenify any eader of he pane average which woud be he same for each currency and each horizon, ahough A6 is a eader in 3 cases ou of 4. Vice versa, here is no pure foower, bu A2 and A9 are ceary ed for he yen, A2 is ed for he 3 monh horizon, A and A25 are ead for he 2 monh horizon. Noe ha he same individua can ead he average on a paricuar currency/horizon whie being a foower for he same currency bu a differen horizon (for exampe, A7). Tabe 3: Causaiy owards he pane average Horizon monh 3 monhs 2 monhs s period DMEUR/USD  A5, A7 (8%) A3, A5, A6 (2%) YEN/USD  A3, A6, A6 (2%) A6 (4%) 2nd period DMEUR/USD B8 (2.5%) B2 (8.3%) None (0%) YEN/USD B6, B8, B5, B7 (40%) Source : economeric esimaions. Percenage of eaders under parenheses. None (0%) B2, B8, B, B7, B9 (38.5%) Tabe 4: Causaiy from he pane average Horizon monh 3 monhs 2 monhs s period DMEUR/USD  A2 (4%) A7, A, A8, YEN/USD  A2, A2, A7, A9, A24 (20%) A25 (6%) A, A2, A3, A7, A8, A, A3, A4, A6, A9, A2, A25 (48%) 2nd period DMEUR/USD B5, B7 (25%) B4, B6 (6.7%) None (0%) YEN/USD B2 (0%) None (0%) None (0%) Source: Economeric esimaions. Percenage of foowers under parenheses. 7
18 Working Papers no Causaiy amongs individuas Our economeric procedure is quie discriminaive as he number of causaiy reaionships fas dramaicay from Sep o Sep 3. Tabe 5 presens he eadership, foowership and ne eadership indexes as obained from Sep 4 for he firs period. The abe deais he resus for each currency/horizon as we as he sum of ne eadership indices across currencies/horizons for each individua (as row) and he number of causaiy reaionships for each currency/horizon (as coumn). The resus for he second period are no repored since no causaiy reaionship remains afer Sep 3. This feaure can be reaed o he sma number of forecasers over his period (8 o 3 depending on he currency/horizon, compared o 25 individuas in he firs period) or o an evouion of he foreign exchange marke. Tabe 5 deserves he foowing commens. Mos individuas are invoved in a causaiy reaionship a eas for one currency/horizon. Indeed, ony A3 seems o be independen from a oher forecasers. A5 appears aso independen for he yen as we as for he DM a 2 monhs, bu he/she eads hree individuas for he DM a 3 monhs. Three individuas (A9, A20, A23) seem o form independen expecaions for he DM bu no for he yen, whie hree individuas (A, A25, A24) are in he opposie siuaion. Foowership indices range from 0 o 2: foowers appear o foow one or wo individuas ony. Conversey, eadership indices range from 0 o 4: eaders can ead as much as 4 individuas. Ahough subsania, given he number of individuas invoved in forecass, his number is far from denoing a srong prominence of a few eaders in he marke. Leaders are more prominen a he 3 monh han a 2 monh horizon: a 3 monhs, A4 and A7, for insance, ead 3 or 4 individuas (depending on he currency) bu do no foow any; a 2 monhs, A8, A20 and A22 are prominen eaders and prominen foowers for he yen. However he oa number of causaiy reaionships is comparabe for boh horizons, which confirms he resus obained wih he pane average. On he whoe, he main eaders appear o be A5, A7, A2, A20 and A23, he main foowers being A9, A6, A8 and A9. 8
19 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa Tabe 5: Leadership, foowership and ne eadership indices A A2 A3 A4 A5 A6 A7 A8 A9 A0 A A2 A3 A4 A5 A6 A7 A8 A9 A20 A2 A22 A23 A24 A25 SUM DM 3 monhs eadership foowership ne eadership monhs eadership foowership ne eadership YEN 3 monhs eadership foowership ne eadership monhs eadership foowership ne eadership TOTAL NET Source: economeric esimaes and auhors cacuaions. 9
20 Working Papers no Herding and performance The performance of he 25 individuas is poed in Figure wih he hree measures of performance averaged over he four currency/horizon combinaions. Srikingy, he forecasers dispay very poor performances: heir roo mean square errors are arger han hose of he naive mode (PERF < ); hese resus are consisen wih hose found by Eio and Io (999); furhermore, heir ne gain from he rading rue is generay ower han wha hey woud have obained foowing he naive mode (PERF2 < 0), and hey generay do worse in predicing he direcion of change of he exchange rae han if hey had jus fipped a coin (PERF3 < 50%). In fac, here is a high correaion beween he hree measures of performance: he correaion over he whoe sampe (no averaged) is 42% beween PERF and PERF2, 67% beween PERF and PERF3 and 56% beween PERF2 and PERF3; he correaion on average measures is even higher: 66%, 67% and 92% respecivey. To assess he significance of hese poor performances, we performed severa saisica ess. Firs, we esed wheher he difference beween he performance of each individua and ha of a naive forecaser wih respec of he wo firs measures, i.e. he RMSE and he ne gains drawn from impemening he rading rue, are significany differen from zero. The resus are repored in Tabes B o B4 in he Appendix B. Second, we esed wheher he abiiy of each forecaser o predic he direcion of he change in he exchange rae is significany differen from 0.5 (Tabes B5B6). As a whoe, he saisica ess confirm ha on average, hese forecasers dispay very poor performances. For boh currencies and forecas horizons, we find a o of cases in which he RMSE of individua forecass are significany higher han he RMSE of he naive forecaser. 5 In no case, we find a significany negaive difference. Basicay, hese poor performances are confirmed by he difference in he ne gains: in genera, he gains of individuas are ower han he gains of he naive forecaser, wih some significan differences especiay over he recen period. In genera, he abiiy o forecas he direcion in he change is ower han wising a coin, ahough a coupe of forecasers achieve good performances on he YENUSD marke. There is a sighy negaive reaionship beween performance and ne eadership: over he whoe sampe (no averaged), he correaion beween ne eadership and performance is 7% for PERF, 7% for PERF2 and 9% for PERF3; he corresponding correaions on average measures of eadership and performance are 33%, 6% and 9%. This resu is inconsisen wih he view ha successfu agens are ess ikey o herd (Graham, 999). On he conrary, ne foowers seem o be more successfu. Aernaivey, successfu individuas end o heard more, which woud be consisen wih repuaionbase herding (successfu forecasers have more o ose). 5 The resus are sriking especiay for he DM over he second period : a he 3 monhs horizon, a forecasers do worse han he naive one. 20
21 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa Figure : Three measures of individua performance a. Invered roo mean squared error reaive o he naive mode (PERF),00 0,90 0,80 0,70 0,60 A6 A6 A24 A3 A5 A A8 A8 A3 A4 A20 A25 A9 A7 A5 A A9 A2 A7 A2 A2 A23 A4 A0 A22 2b. Ne benefi from rading rue reaive o he naive mode (PERF2),50,00 0,50 0,000,50 ,00 ,502,002,50 A6 A3 A5 A4 A A23 A24 A3 A A9 A2 A8 A8 A0 A7 A25 A20 A2 A2 A6 A5 A7 A22 A9 A4 c. Percenage of correc predicions of direcion of change (PERF3) A6 A4 A3 A5 A A3 A24 A A20 A25 A23 A7 A8 A2 A8 A9 A5 A7 A0 A6 A2 A2 A22 A9 A4 Source : Auhors cacuaions on Consensus Forecas Daa. 2
22 Working Papers no However i can be argued ha successfuness shoud precede he behavior of forecasers in erms of eadership or foowership. To acke his probem, we cacuae he correaion beween he ne eadership index (cacuaed over he period) and he performance of each individua during he firs year of he sampe. The correaion is hen much ess negaive and someimes even posiive (see Tabe 6). On he whoe, here seems o be some independence beween successfuness in 990 and he ne eadership index over he period. Tabe 6: Correaion beween eadership and performance (in %) PERF PERF2 PERF Non averaged vaues Average over currencies and horizons CONCLUSION The resus provided in he paper show ha here are sequenia connecions beween exchangerae expecaions of individua forecasers. However, i is no possibe o idenify one guru eading more han four oher forecasers. Ineresingy, imiaion is no a specific feaure of shor run horizons, ahough individua eaders seem o be ess persuasive a 2 monhs han a 3 monhs. The weak reaionship beween he performance of each individua and his/her ne eadership index ends o dismiss he hypohesis of a sequenia repuaionbased herding on he FOREX marke, which woud impy ha successfu forecasers become eaders, or ha high repuaion forecasers end o herd more. Imiaion hence woud fa raher on he compensaion and informaion ypes. Our resus emphasizing some imied evidence of herding are broady in ine wih he ieraure on herding behavior in sock marke recommendaions. However we ony dea here wih sequenia herding. Our monhy daa se is no we disposed o deec any nonsequenia herding (or sequenia herding a a higher frequency), since i is no possibe o disenange such herding from simuaneous reacions o forecasers o pubic news. In addiion, he ink beween forecass and foreign exchange posiions is far from cearcu. Neverheess, we beieve our resus can quesion sequenia herding of forecasers as one major cause of ong ived deviaions of he exchange rae from is fundamena vaue. 22
23 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa REFERENCES Bikhchandani, S. & Sharma, S. (2000), Herd behavior and financia markes: a review, IMF working paper 00/48. Con, R. & Bouchaud, J.Ph. (2000), Herd behavior and aggregae fucuaions in financia markes, Macroeconomic Dynamics, 4 (2), De Grauwe, P., Dewacher, H. & Embrechs, M. (993), Exchange Tae Theory: Chaoic Modes of Foreign Exchange Markes, Backwe, Oxford UK and Cambridge USA. Dominguez, K.M. (999), The Marke Microsrucure of Cenra Bank Inervenion, NBER Working Paper no D Souza, C. (200), A Marke Microsrucure Anaysis of FX inervenion in Canada, Bank of Canada Working Paper. Eio, G. & Io, T. (999), Heerogeneous Expecaions and Tess of Efficiency in he Yen/Doar Forward Exchange Rae Marke, Journa of Moneary Economics, 43, Graham, J.R. (999), Herding among invesmen newseers: heory and evidence, The Journa of Finance, LIV (), Franke, J.A. & Froo, K. (986), The doar as a specuaive bubbe: a ae of fundamenaiss and chariss, NBER working paper 854, March. Kirman, A. (993), Ans, raionaiy and recruimen, Quarery Journa of Economics, 08, Lesourne, J. (992), The Economics of Order and Disorder, Oxford: Oxford Universiy Press. Lux, Th. (995), Herd behaviour, bubbes and crashes, The Economic Journa, 05, Lux, Th. (998), The socioeconomic dynamics of specuaive markes: ineracing agens, chaos and he fa ais of reurn disribuion, Journa of Economic Behavior and Organizaion, 33,
24 Working Papers no Lyons, R.K. 200, The Microsrucure Approach o Exchange Raes, Cambridge: MIT Press. Oréan, A. Mimeic conagion and specuaive bubbes, Theory and Decision, 27, Peiers, P. (997), Informed raders, inervenion and price eadership: a deeper view of he microsrucure of he foreign exchange marke, The Journa of Finance, LII (4), Scharfsein, D.S. & Sein, J.C. (990), Herd behavior and invesmen, American Economic Review, 80 (3), Topo, R. (99), Bubbes and voaiiy of sock prices: effec of mimeic conagion, Economic Journa 0,
25 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa APPENDIX A: UNIT ROOT TESTS Tabe A: Uni roo es for s i,, + h : DM s period 2 nd period Individuas monh 3 monhs 2 monhs monh 3 monhs 2 monhs A *** 3.95*** A * *** 4.70*** .2 A *** 2.27** A *** A *** 4.74*** .93* 3.90*** .2 A * *** .3 A ** .90* A *** 3.0*** .68* A * 2.40** 2.84*** 3.80*** .5 A ** .68* 4.02*** 6.74*** .37 A ** A *** 4.7*** 2.8** 7.33*** .5 A ** 4.33***   A *** 3.0*** A * 5.24*** 6.5*** .59 A *** 3.6*** A *** .65* * A *** A *** 2.86*** A *** 3.03*** A *** 2.52** 4.6*** 4.55*** 4.53*** A *** A *** .84* 3.29*** 5.45*** .89* A *** 3.47*** 4.72*** 7.39*** .50 A *** Proporion of I() 2% 20% 8.3% 8.3% 83.3% Noes: ADF ess ; number of ags needed o conro for he presence of seria correaion ; seria correaion a order 4 assessed hrough a LM es wih significance eve of 5%.***,**, * denoe significance respecivey a he, 5 and 0% nomina eves. Proporion of I() gives he proporion of concusions in favor of non saionary variabes using a 0% significance eve. 25
26 Working Papers no Tabe A2: Uni roo es for s i,, + h : YEN s period 2 nd period Individuas monh 3 monhs 2 monhs monh 3 monhs 2 monhs A *** .77* A *** .67* 4.42*** 3.73*** 3.36*** A *** 2.86*** A *** 3.85*** A *** 2.7* 3.20*** 3.37*** 3.92*** A *** 3.58*** 4.6*** 4.0*** .93* A *** 2.55** A *** .92* 4.73*** 3.79*** 2.79*** A ** .63* 4.87*** 4.92*** 3.73*** A *** *** 4.9*** 2.28** A ** A *** 4.29*** 6.6*** 5.4*** 3.96*** A *** 4.89*** *** A ** 4.28*** *** A ** .79* 5.0*** *** A *** 3.0*** A *** 2.56** 4.23*** * A *** 2.39** A *** 2.20** A *** 3.44*** A *** 3.29*** 6.27*** 3.26*** .88* A *** *** A *** .6* 4.44*** 2.40** 3.24*** A *** 3.82*** 7.35*** 4.49*** 4.74*** A *** .69*** Proporion of I() Noes: see Tabe A. 0 2%
27 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa APPENDIX B: STATISTICAL TESTS OF FORECASTERS PERFORMANCES Tabe B: Significance of RMSE differenia beween each individua he naive forecaser: DM s period 2 nd period Individuas 3 monhs 2 monhs 3 monhs 2 monhs A 0.004** A ** 0.047* A *** A ** ** 0.02** A ** *** ** A ** 0.060** A *** A *** 0.009* *** 0.099*** A *** *** *** A *** ** 0.054** A 0.000*** * A *** A *** ** 0.046*** A A * 0.006*** 0.060*** A * A ** *** *** A * A ** * ** A *** 0.009***   A ** A ** 0.055**   A *** *   A A Consensus * ** 0.05** Noes: The abe repors he coefficien of a regression of he RMSE differenia beween individua i and he naive forecaser on a consan ; he sandard error used o evauae he significance of his coefficien is correced wih a NeweyWes esimaor ; he number of ags is se as h where h is he forecas horizon. ***,**,* denoe significance respecivey a he,5 and 0% nomina eves. 27
28 Working Papers no Tabe B2: Significance of RMSE differenia beween each individua and he naive forecaser :YEN s period 2 nd period Individuas 3 monhs 2 monhs 3 monhs 2 monhs A 0.004** A ** A *** A ** 0.024*** ** A ** ** A *** 0.007* A *** A *** *** *** A *** 0.032**** A *** 0.075** A 0.000*** 0.080** A *** 0.066***   A ** * 0.00*** A *** *   A ** 0.0*** 0.007* * A A *** 0.080** 0.005** *** A * A *** A ** A *** *   A *** 0.096** ** A *** A **   A ** 0.034**   Consensus ** ** Noes: See Tabe B. 28
29 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa Tabe B3: Significance of he ne gain differenia beween each individua and he naive forecaser: DM Individuas s period 2 nd period 3 monhs 2 monhs 3 monhs 2 monhs A A * 0.05** A A * ** ** A * * *** A ** A * A * * ** *** A ** *** A * *** A * A A ** 0.43*** A A *** *** A A * *** *** A A * ** A **   A A A * A A Consensus * *** Noes : The abe repors he coefficien of a regression of he ne gain differenia beween individua i and he naive forecaser on a consan. The ne gain is cacuaed using he rading rue presened in Secion 3.3. The sandard errors used o evauae he significance of his coefficien is correced wih a NeweyWes esimaor ; he number of ags is se as h where h is he forecas horizon. ***,**, * denoe significance respecivey a he, 5 and 0% nomina eves. 29
30 Working Papers no Tabe B4: Significance of he ne gain differenia beween each individua and he naive forecaser: YEN s period 2 nd period Individuas 3 monhs 2 monhs 3 monhs 2 monhs A A * A A A ** A * A A ** A A A A A * ** A A ** 0.06 A **   A *** * A A * A A * A A ** A A Consensus Noes: See Tabe B3. 30
31 Imiaion Amongs ExchangeRae Forecasers : Evidence form Survey Daa Tabe B5: Abiiy of individuas o forecas exchangerae direcion: DEM/USD s period 2 nd period Individuas 3 monhs 2 monhs 3 monhs 2 monhs A *   A2 0.40* ** A A4 0.3*** ** A *** A *** A7 0.34** A *** A9 0.4* *** 0.23*** A * 0.25*** A A A *** A ** A * 0.25*** A A ** 0.3*** 0.7*** A **   A ** A ** 0.37**   A2 0.38** 0.4*   A * 0.40*   A *** A A Consensus 0.38** * 0.33*** Noes: The abe repors he proporion of correc direcions of change prediced by individua i, and is significance from 0.5, using a sudenized version of he signes saisic (see Diebod & Mariano, 995).***,**, * denoe significance respecivey a he, 5 and 0% nomina eves. 3
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