The Intraday Behavior of Information Misreaction across Investor Categories in the Taiwan Options Market

Transcription

1 The Inraday Behavior of Informaion Misreacion across Invesor Caegories in he Taiwan Opions Marke Chuang-Chang Chang a, Pei-Fang Hsieh b, Chih-Wei Tang c,yaw-huei Wang d a c Deparmen of Finance, Naional Cenral Universiy, No.300, Jhongda Road, Jhongli Ciy, Taoyuan Couny 32001, Taiwan b Deparmen of Quaniaive Finance, Naional Tsing Hua Universiy, No. 101, Secion 2, Kuang-Fu Road, Hsinchu 30013, Taiwan d Deparmen of Finance, Naional Taiwan Universiy, No.1, Secion 4, Roosevel Road, Taipei 10617, Taiwan This Version: Sepember 15, 2010 Absrac Following he analysis framework of Poeshman (2001), we use a unique daase including he complee hisory of all ransacions in he Taiwan opions marke o invesigae he paerns of invesor misreacion from he markewise observaions and he ransacions of four differen invesor caegories. Overall, invesors iniiae heir reacion o unexpeced informaion from shor-horizon opions and hen adjus heir posiions in long-horizon opions wih a cerain degree of delay because of he liquidiy concern. Boh of shor- and long-horizon reacions are insufficien. Alhough invesor misreacion ends o increase in he quaniy of previous similar unexpeced shocks, he misreacion o he curren unexpeced shocks sill dominaes he effec of increasing misreacion. The comparison for alernaive invesor caegories shows ha foreign insiuional invesors have he lowes degree of misreacion and insiuional invesors correc heir misreacion more promply. JEL classificaion: G14 Keywords: Opions; Misreacion; Sochasic volailiy; Insananeous variance; Invesors

2 1. Inroducion Invesor misreacion has been an accepable explanaion of sock marke anomalies such as shor- and mediae-horizon momenum and long-erm reversal. For example, Barberis e al. (1998), Daniel e al. (1998) and Hong and Sein (1999) heoreically presen ha invesors end o underreac in he shor horizon and overreac in he long horizon. In paricular, Barberis e al. (1998) argue ha he underreacion and overreacion are driven by conservaism and represenaiveness heurisic, respecively and he ineracion of invesors shor-horizon conservaism and long-horizon represenaive heurisic leads o increasing misreacion in he sock markes. 1 Namely, invesors end o underreac (overreac) o informaion ha follows a small (large) quaniy of similar informaion. 2 While here have already been many sudies of sock marke invesor misreacion, our undersanding on he misreacion in opions markes is sill quie lacking. Invesor misreacion should no be resriced o occur in sock markes. In an early aricle, Sein (1989) documens long-horizon overreacion in he S&P 100 index opions 1 The conservaism heory saes ha invesors cling oo srongly o prior beliefs and hus end o underreac o single piece of informaion, while he represenaiveness heurisic argumen shows ha invesors find paerns in informaion oo readily and hence overreac o mosly similar informaion. 2 A review of he sudies ha invesigae sock marke invesor misreacion is referred o Shleifer (2000). 1

3 marke by finding evidence ha he implied volailiy of long-horizon opions is higher han shor-horizon opions. Poeshman (2001) provides a comprehensive invesigaion for he S&P 500 index opions and finds ha invesors no only overreac o informaion on long-mauriy opions, bu also underreac o informaion on shor mauriy opions. In addiion, evidence is also provide o suppor he exisence of increasing misreacion in he opions marke. 3 Alhough previous sudies have documened he exisence of shor-horizon underreacion, long-horizon overreacion, and increasing misreacion in he US opions markes, wheher invesors have he same paerns of misreacion in a less maured marke is sill unanswerable. In addiion, all of hese sudies use daily daa and herefore impose a srong assumpion ha invesors aend o changes in informaion once per day. This assumpion may no be realisic especially when nowadays he informaion flow and he ease of rading have been incredibly boosed by modern echnology. Using daily daa could disallow us o look a invesors insan reacion when jus receiving informaion and a how invesors dynamically adjus 3 Furhermore, Cao e al. (2005) sudy S&P 500 index opions and long-daed S&P 500 LEAPS and find ha he underreacion lass for 3 rading days and ha he increasing misreacion reaches he peak afer four consecuive daily variance shocks wih he same sign. Based on he idenified misreacion paerns, opion rading sraegies are consruced and found o produce economically significan abnormal reurns in he range of 1% o 3% per day. 2

4 heir reacion aferwards. Our sudy ries o fill hese gaps by using a compee record of all ransacions in he Taiwan opions markes o invesigae he issues on invesor misreacion. Therefore, in addiion o providing more insighs for he invesigaed issues, our findings from he marke also have imporan implicaions for oher developing markes ha have similar characerisics such as a high urnover rae and a high paricipaion rae by individual invesors. 4 Our empirical invesigaion is implemened no only on he markewise base, bu also for he ransacions of four differen invesor caegories, domesic insiuional invesors, foreign insiuional invesors, individual invesors and marke makers. 5 Our empirical resuls include he following general findings. Firs, invesors iniiae heir reacion o unexpeced informaion from shor-horizon opions and hen adjus heir posiions in long-horizon opions wih a cerain degree of delay. Second, invesors underreac o he informaion on boh shor- and long-horizon opions wih he laer being more severe. Alhough hey ry o correc he misreacion aferwards, 4 According o he saisics published by he Tawin Sock Exchange, in 2005 individual invesors, domesic insiuional invesors and foreign invesors ake abou 68%, 13% and 17 % of he ransacions, respecively. The oal urnover rae for 2005 is abou % in he Taiwan sock marke. 5 Several sudies documen ha here exis some sophisicaed invesors ha can make profis in eiher he Taiwan sock or opions markes. See for example, Barber e al. (2007), Mahani and Poeshman (2008), Chang e al. (2009) and Bing e al. (2010). 3

5 bu he correcion is sill insufficien. Third, he misreacion o he curren unexpeced shocks sill dominaes he effec of increasing misreacion alhough invesors misreacion ends o increase in he quaniy of previous similar unexpeced shocks. We conjecure ha he inexisence of long-horizon overreacion is caused by he poor liquidiy of long-mauriy opions in he Taiwan opions marke. 6 Moreover, some findings are derived from he comparison among he ransacions of alernaive invesor caegories. Firs, foreign insiuional invesors have he lowes degree of misreacion. Second, domesic and foreign insiuional invesors correc heir misreacion more promply. The resuls in his paper are robus o differen sampling frequencies and also o difference measures for he quaniy of previous similar informaion. The remainder of his paper is organized as follows. Secion 2 describes he daa used for our empirical invesigaion. Secion 3 deails he empirical mehods employed in his sudy. Secion 4 illusraes he empirical resuls and some robusness ess. Finally, we conclude his sudy in Secion 5. 6 According o he saisics summarized from our daa, he near-monh conracs ake more han 90% of he ransacions. Invesors may herefore be relucan o rade heir informaion on he oher conracs wih poor liquidiy. 4

6 2. Daa Descripion The primary daase for our empirical invesigaion conains he complee record of ransacions of he opions wrien on he Taiwan Sock Exchange Capializaion Weighed Sock Index (hereafer TAIEX). The TAIEX opion conracs are raded in Taiwan Fuures Exchange (hereafer TAIFEX) wih he icker symbol TXO. Our daase is obained direcly from he TAIFEX and conains a highly deailed hisory of ransacions, such as he idenificaions of raders, he conrac characerisics and he ransacion conens. We also obain he complee record of ransacions of he TAIEX fuures from he TAIFEX. The moivaion o sudy he TAIEX opions is no only supplied by he availabiliy of a complee and sophisicaed daase, bu also furher enhanced by he fac ha he Taiwan marke shares several common characerisics wih oher developing markes, such as a high urnover rae and a high paricipaion rae by individual invesors. These characerisics are markedly differen from hose of he major opion markes in he US and Europe. Therefore, in addiion o providing more insighs for he invesigaed issues, our findings from he marke also have imporan implicaions for 5

7 oher developing markes. Our daase covers he rading daes from 2 January 2002 o 31 December 2005 and mauriy monhs from January 2002 o June Following some sandard daa- filering crieria employed by previous sudies such as Aï-Sahalia and Lo (1998) and Poeshman (2001), we exclude he conracs wih a ime o expiraion less han 6 calendar days due o he liquidiy concern or wih a Black-Scholes implied volailiy (hereafer BSIV) lower han 0 or higher han 0.7 o avoid exreme opion prices. Moreover, we exclude in-he-money (ITM) opions because in general hey are less acively raded and hus less informaive han heir corresponding ou-of-he-money (OTM) conracs. 7 We define shor-horizon opions as he mos nearby conracs and long-horizon ones as he conacs wih he oher mauriies. The risk free raes are proxied by he hree-monh deposi raes and obained from he websie of he Cenral Bank of Taiwan. Our inraday invesigaion is based on he rading inerval of five minue; in oal here are 59,640 rading inervals in our sample. 8 For each inerval, we selec all 7 Moneyness is defined as he raio of a srike price over he corresponding fuures price. 8 Some resuls from 15-, 30- and 60-minue and daily observaions are also provided laer for he robusness check. 6

8 qualified conacs raded wo minues before he ending imesamp. Whenever necessary in our analysis, we mach every conrac wih is corresponding fuures price from he daase of fuures ransacions. The summary saisics for our final sample are showed in Table 1. The number of observaions for call opions (6,047,083) is much larger han ha for pu opions (4,826,047). The averaged BSIVs for call and pu opions are 21.9% and 23.1%, respecively. The ime o mauriy and he moneyness range from 6 o 212 days and from o 1.62, respecively. < Table 1 is insered abou here > Since our daase allows us o idenify he ypes of raders for each ransacion, we classified he marke paricipans ino four main caegories, which are domesic insiuional invesors, foreign insiuional invesors, individual invesors and marke makers. We follow he same daa filering crieria menioned above o selec he observaions for each invesor caegory. Table 2 shows he summary saisics of our sample across invesor classificaions, which reveal he rading behavior of differen caegories of invesors. Obviously, foreign insiuional invesors rade more pu opions, while individual invesors rade more call opions. The ime o mauriy for 7

9 foreign insiuional invesors posiions on average is longes, while ha for domesic insiuional invesor s is shores. Obviously, he rading paern is differen across invesor caegories, which is likely due o disinc reacions o informaion. < Table 2 is insered abou here > 3. Empirical Mehods Following he analysis framework of Poeshman (2001), our invesigaion on invesors reacion o informaion is based on a sequence of insananeous variance ha represens he corresponding series of opion prices. Based on he decomposiion of he insananeous variance ino expeced and unexpeced componens, he measures for invesors misreacion are defined by he ineracion beween he changes in insananeous variance and he differences beween he variance changes from long- and shor-mauriy opions. Therefore, in his secion we deail how o generae he high-frequency series of insananeous volailiy and how o measure invesors misreacion o new informaion Esimaion of insananeous variance As he inclusion of sochasic volailiy, even wihou oher complicaed feaures like 8

10 jumps, is he mos crucial sep in he developmen of lieraure in opion pricing models, we presume he underlying asse price follows Heson s (1993) sochasic volailiy model o generae insananeous variance. The model under he real-world measure is specified as follows: ds S ( S, V, ) d V dw (1) S dv k( V ) d V dw (2) V where k, θ and η are consan parameers. In he sysem, he ime price and insananeous variance of he underlying asse are respecively denoed by S and V and driven by he wo sandard Wiener processes wih incremens S dw and V dw ha have correlaion ρ. ( S, V, ) denoes he mean level of he underlying asse reurns. The marke price of variance risk is represened by λ. The risk-free ineres rae and he coninuously compounded dividend yield of he underlying asse are denoed by r and δ, respecively. For opion pricing, he risk-neural process of he model is obained as follows: ds S ( r ) d V dw (3) S dv k * ( * V ) d V dw (4) V 9

11 where k * * k and k /( k ). The correlaion beween S dw and V dw remains ρ. The resuling price of a call opion wih srike price X is derived as: C Se P Xe T rt 1 P 2 (5) where P 2 is he probabiliy for S T >X under he risk-neural Q measure and P 1 is he probabiliy for he same even under anoher measure, say Q *. The deails regarding he funcions P 1 and P 2 are referred o Heson (1993). The model is esimaed wih a wo-sage procedure from opion prices. Since he model describes he dynamic process of he underlying asse price, he parameers should no rely on he daa frequency. Therefore, in he firs sage we use he weekly closing prices of opions seleced on Wednesdays over our sample period and hen generae he esimaes of he risk-neural parameers, k *, θ *, η and ρ, by minimizing he sum of squared opion pricing errors. 9 Essenially, he prices for a spo opion and a fuures opion wih he same underlying asse, mauriy and srike price should be idenical if boh are European and he fuures conrac has he same expiraion dae as he opion conracs do. As a 9 In oal, he markewise sample for he firs-sage esimaion includes 198 observaions. Following Bakshi e al. (1997), we se he iniial value of he parameers as k 0 * =1.15, θ 0 * =0.04, η 0 =0.39 and ρ 0 =-0.64 for he esimaion. 10

12 resul, in order o avoid he challenge of deermining he underlying asse price and dividend yield separaely, we replace he underlying asse wih fuures conrac under he assumpion of spo-fuures pariy. The parameers are esimaed from our markewise sample as k * =1.13, θ * =0.12, η=0.65 and ρ= Taking he parameer esimaes as given, in he second sage we generae he high-frequency series of insananeous variance in which each observaion minimizes he cross-secional sum of squared pricing errors of opions a he corresponding imesamp. The series of insananeous variance is generaed no only on he markewise base, bu also from he ransacions of he four invesor caegories individually. Le {V }, =1, 2,, T be he high-frequency series of insananeous variance, where T is he oal number of observaions in our sample. Given ha he price dynamic of he underlying asse is correcly specified by he model, he change in insananeous variance from rading ime -1 o can be decomposed ino expeced and unexpeced pars, which are respecively denoed as Expeced V and Unexpeced V and formulaed as follows: 11

13 V Expeced V e k 1 (6) k ( 1 e ) V 1 V (7) Unexpeced Expeced ( V V 1) V where τ is he number of years for an observaion inerval. Given ha he price dynamic of he underlying asse follows Heson s (1993) model, he formula of Expeced V follows from he equaion (19) in Cox e al. (1985). The values of k and θ respecively follow from he relaionships of k * * k and k /( k ) wih he parameers k * and θ * esimaed in he firs sage. As suggesed by Poeshman * (2001), we assume ha he volailiy risk parameer k / Measures of misreacion As saed in Poeshman (2001), a variable called FarMisProj measures he exend o which he unexpeced change in insananeous variance from rading ime -1 o rading ime is overprojeced ino he far fuure. I is defined as: FarMisProj Unexpeced Long Shor sign( V )( V V ) (8) where Long V is he change in he insananeous variance from long-mauriy opions from rading ime -1 o and Shor V is he change in he insananeous 10 Poeshman (2001) also shows he robusness of alernaive seings such as λ=0 and λ=-k *. Basically, he resuls do no subsanially change. 12

14 variance from shor-mauriy opions from rading ime -1 o. While here is no reason for he price changes of opions wih differen mauriies o be he same, he price changes measured in insananeous variance should be exacly he same if he Heson s (1993) opion pricing model is appropriae. Inuiively, if he curren unexpeced change in insananeous variance is posiive (negaive), we would observe a posiive FarMisProj which means ha i is projeced oo much ino he far fuure when he curren change in insananeous variance from long mauriy opions is greaer (less) han hose from shor mauriy opions. According o he definiion of he FarMisProj variable, i is increasing in he exen o which he invesors misprojec he unexpeced changes in insananeous variance ino far fuure. Therefore, if invesors underreac o he unexpeced changes in insananeous variance, he FarMisProj variable would be decreasing in he magniude of he unexpeced change in insananeous variance and we can examine wheher he invesors have shor-horizon underreacion by invesigaing he Unexpeced relaionship beween FarMisProj and. V Sein (1989) reveals he invesors long-horizon overreacion by documening 13

15 ha he prices of long mauriy opions are oo high. If he overreacion exiss, we would expec a posiive relaionship beween he level of insananeous variance and he difference beween he changes in insananeous variance from long-mauriy opions and hose from shor-mauriy opions. Therefore, V can serve as Long Shor V a measure o explore he issue of long-horizon overreacion. 4. Empirical Resuls Differen from previous sudies, we use inraday, raher han daily, daa o invesigae informaion misreacion. Poenially we can provide more insighs on he issue of invesors misreacion paricular when we are having very powerful echnology o help rading and hus raders can rade on heir informaion promply. We firs look a wheher here exiss any inraday paern for he FarMisProj variable in he Taiwan opions markes and hen es for he exisence of shor-horizon underreacion, long-horizon overreacion and increasing misreacion, respecively. Some robusness analyses are provided finally The inraday paerns of invesors misreacion o new informaion Afer generaing he five-minue series of markewise FarMisProj, we calculae he 14

16 averages of he variable levels for each inraday inerval. Figure 1 shows he inraday paern of he variable across observaion inervals. Differen from he findings of previous sudies using daily daa for he US markes, we find ha all of he inraday averages of he variable are negaive. While we also find he exisence of invesor misreacion o he curren unexpeced informaion in he high-frequency daa, invesors projec he unexpeced changes in insananeous variance relaively more ino shor-mauriy opions han ino long-mauriy opions. Wheher he signs of unexpeced changes in insananeous variance are posiive or negaive, he reacions in insananeous variance from shor-mauriy opions are larger han hose from long-mauriy opions. This finding from high-frequency daa may reveal ha invesors usually rade shor-mauriy opions firs when hey receive unexpeced informaion since in he Taiwan opions markes nearby conacs are much more liquid han he ohers. 11 Hence, he insan adjusmens from long-mauriy opions are always relaively smaller and i may ake ime for long-mauriy opions o be adjused comparably. 11 In almos all of he opions markes around he world, nearby conracs are usually mos liquid. However, he difference beween he liquidiy of nearby and non-nearby conracs in he Taiwan opions marke is exremely large. This huge difference in liquidiy could make he prices of non-nearby conracs insensiive o informaion flow. 15

17 In addiion o he negaive FarMisProj, we also find ha he magniude of he misreacion is paricularly high when he marke is open (8:45-9:15) and during he noon ime (12:00-12:30). For he larger misreacion during he open ime, we conjecure ha i is due o he relaively higher level of informaion asymmery caused by he long non-rading overnigh period. For he larger misreacion during he noon ime, i may be owing o he relaively higher level of informaion asymmery caused by some paricipans absence for lunch for a while. < Figure 1 is insered abou here > 4.2. Shor-horizon underreacion Inraday daa is paricularly ideal for he invesigaion on shor-horizon misreacion. We can explore no only how invesors insanly reac o unexpeced shocks, bu also how invesors adjus heir reacion aferwards. If invesors underreac o he unexpeced changes in insananeous variance, he FarMisProj variable would be decreasing in he magniude of he unexpeced change in insananeous variance. Therefore, a regression es for he relaionship beween FarMisProj and can ascerain wheher he shor-horizon underreacion o informaion Unexpeced V 16

18 exiss in he Taiwan opions marke. The model is specified as: FarMisProj 6 i 0 Unexpeced i 3 Unexpeced V D V (9) i j 1 j j, where FarMisProj and Unexpeced V are defined in Equaions (8) and (7), respecively. In addiion o he conemporaneous relaionship beween he wo variables, we furher consider he ime invesors may spend o fully reac o he unexpeced shock and he frequenly found auocorrelaion in inraday financial ime series by adding he absolue value of he unexpeced changes in insananeous variance in previous 30 minues ino he model. As shown in Figure 1, he FarMisProj variable shows a paricular inraday paern wih a higher absolue value during he open and noon inervals. Moreover, many sudies ha invesigae he inraday paerns of financial variables ofen find some paricular paerns for he close ime. Therefore, in he model we also conrol for he inraday effec by including hree dummy variables, D 1, D 2 and D 3, which are equal o 1 for he open, noon and close inervals, respecively and 0 oherwise. To adjus for serial correlaion and heeroskedasiciy, we use he Newey-Wes robus sandard errors in our empirical regressions. 17

19 The regression resuls from he markewise observaions and he ransacions of he four invesor classificaions are shown in Table 3. Consisen wih previous sudies using daily daa, we also find srong evidence for he exisence of shor-horizon underreacion and his finding is valid across invesor caegories since all he esimaes of β 0 are negaively significan a he 1% of significance level. For all samples excep he marke makers ransacions, some of he esimaes for lagged absolue insananeous variances urn o posiive alhough hey may no be saisically significan. I seems ha invesors ry o correc heir underreacion, bu according o he size of he coefficiens, he correcion is obviously insufficien. Moreover, his insufficien adjusmen can also be suppored by he significanly negaive coefficien in he model using daily observaions. 12 When furher comparing he resuls among he four invesor caegories, we find ha he magniude of he underreacion for foreign insiuional invesors are smalles as he value of he β 0 esimae is jus half of hose for he oher invesor caegories. This finding may signal ha foreign insiuional invesors are he mos sophisicaed invesors in he Taiwan opions markes, which is consisen heir superior 12 The resuls are shown in he secion of robusness analysis. 18

20 profi-making abiliy and informaion advanage found in previous sudies. According o he size and significance of he esimaes of he dummy coefficiens, i seems ha he higher magniude of he markewise FarMisProj during he open and noon inervals mainly comes from individual invesors ransacions. Alhough he esimae of γ 2 for individual invesors is marginally insignifican a he 10% of significance level, he size of he esimae value is much larger han hose for he oher invesor classificaions. We conjecure ha i is due o less aenion paid o he marke by individual invesors when he marke is close and during he lunch ime. Consisen wih our previous discussion wih Figure 1, here is no paricular paern of misreacion during he close ime as all esimaes of γ 3 are saisically insignifican. <Table 3 is insered abou here > 4.3. Long-horizon overreacion Using daily daa, Sein (1989) and Poeshman (2001) presen he evidence of long-horizon overreacion in he OEX and SPX opions markes, respecively. However, using he daily observaion frequency may no be able o allow us o see invesors insan reacion when hey receive unexpeced shocks and wha we can see 19

21 from daily daa is jus he oucome resuled from some correcions made by invesors. If he long-horizon overreacion exiss, we would expec a posiive relaionship beween he level of insananeous variance and he difference beween he changes in insananeous variance from long-mauriy opions and hose from shor-mauriy opions. Therefore, a regression model of regressing V on V can serve as Long Shor V an channel o explore he issue of long-horizon overreacion. Wih he same concerns on including lagged insananeous variance and dummy variables for he model used o es for shor-horizon underreacion, he regression model for he long-horizon overreacion is specified as follow: V Long V Shor 6 i 0 i 3 V D V (10) i j 1 j j, where Long V is he insananeous variance implied from long-mauriy opions, Shor V is he insananeous variance implied from shor-mauriy opions, V is he insananeous variance for he corresponding rade inerval, and D 1, D 2 and D 3 have idenical definiions o hose in Equaion (9). We also use he Newey-Wes robus sandard errors o adjus for serial correlaion and heeroskedasiciy. Using inraday daa, we run he regression model no only for he markewise 20

22 observaions, bu also for he four invesor caegories individually. In general, he long-horizon overreacion is no presen in he Taiwan opions marke. As shown in Table 4, here is srong evidence agains he hypohesis of insan long-horizon overreacion since all of he β 0 esimaes are negaively significan a he 1% of significance level. This finding is consisen wih our previous discussion in Secion 4.1. When invesors receive unexpeced shocks, heir insan reacions on long-horizon opions are relaively insufficien since shor-horizon conracs are ofen much more liquid. However, for all samples excep foreign insiuional invesors, almos all of he coefficiens of lagged insananeous variance are posiive and many of hem are saisically significan. I may indicae ha hose invesors adjus heir percepion on long-horizon opions afer hey finish heir rading aciviies on shor-horizon conracs, bu his adjusmen is sill insufficien since all of he coefficiens of lagged insananeous variance are much smaller han hose of concurren variance and he coefficien of insananeous variance is sill significanly negaive even when we use daily daa. 13 When furher comparing he resuls among differen invesor classificaions, we 13 The resuls are shown in he secion of robusness analysis. 21

23 find ha he absolue value of β 0 esimae for foreign insiuional invesors are much smaller han hose for he oher invesor classificaions. I indicaes ha foreign insiuional invesors are relaively more raional alhough he insan reacion on long-mauriy conracs is also insufficien. Moreover, all of he esimaes of lagged insananeous variance for foreign insiuional invesors are also negaively significan a he 5% of significance level. I may reveal ha foreign insiuional invesors do no delay heir informaion projecion on long-mauriy opions. By conras, all of he esimaes of lagged insananeous variance for individual invesors are posiively significan a 5% of significance level. I reveals ha individual invesors are relaively more irraional and delay heir reacion o unexpeced shocks on long-mauriy conracs mos severely. Since in he Taiwan opions marke individual invesors ake he larges proporion of oal rading volume, he markewise findings are similar o hose from individual invesors ransacions. Moreover, we find no consisen and significan inraday paern for he difference beween he insananeous variance from long-horizon and shor-mauriy opions. <Table 4 is insered abou here > 22

24 Differen from he findings for he US opions markes, here is no long-horizon overreacion in he Taiwan opions marke. Insead, compared o he reacion on shor-mauriy opions, he reacion on long-mauriy opions is far more insufficien. We conjecure ha his insufficien reacion on long-mauriy opions is caused by he poor liquidiy of non-nearby opion conracs. During our sample period, he nearby conracs ake more han 90% of he oal ransacions in he Taiwan opion markes. Therefore, when receiving unexpeced shocks, invesors usually projec heir reacion o highly liquid nearby conracs insanly. More sophisicaed invesors may simply choose no ge involved oo much in non-nearby conracs, while less sophisicaed invesors may sill wan o adjus heir posiions in long-mauriy opions aferwards. As a resul, invesors reacion on long-mauriy opions is far more insufficien han ha on shor-mauriy opions, alhough he shor-horizon underreacion is sill exisen Increasing misreacion Barberis e al. (1998) reconcile shor-horizon overreacion and long-horizon underreacion in he sock marke by providing evidence ha invesors end o 23

25 underreac o informaion ha is preceded by a small quaniy of similar informaion and overreac o informaion ha is preceded by a large quaniy of similar informaion. In oher words, invesors misreacion o informaion is increasing in he quaniy of previous similar informaion. Invesigaing wheher he exen o which invesors misprojec he unexpeced componen of a curren change in insananeous variance ino he far fuure is an increasing funcion of he quaniy of previous similar unexpeced changes in insananeous variance, Poeshman (2001) designs a sysem of regression models wih daily daa o suppor he exisence of increasing misreacion in he SPX opions markes. The quaniy of previous similar unexpeced changes in insananeous variance is measured by he w QPrevSim variable defined as: QPrevSim w w Unexpeced Unexpeced sign( V ) sign( V ) (11) i 1 i where Unexpeced V is he unexpeced change in insananeous variance defined in Equaion (7). If he curren unexpeced change in insananeous variance is posiive (negaive), he variable value is equal o he number of posiive (negaive) minus he number of negaive (posiive) unexpeced changes in he insananeous variance over he previous w rading periods. 24

26 Using daily daa acually imposes an assumpion ha marke paricipans reac o informaion changes once a day. In his sudy, we use inraday daa o ry o capure he poenial ha marke paricipans aend o informaion changes much more frequenly. Following he analysis framework of Poeshman (2001), he regression model is specified as: FarMisProj w 3 QPrevSim i i Di 1, Unexpeced V V QPrevSim w (12) where D 1, D 2 and D 3 have idenical definiions o hose in Equaion (9) and are used Unexpeced o conrol for he inraday paern in he FarMisProj variable, V and V are respecively used o conrol for he impac of long- and shor-horizon misreacion discussed previously. Wih several ses of consrains on some paricular parameers, we also run hree alernaive models for he markewise observaions and he ransacions of he four invesor classificaions. The parameer consrains for hese hree models are deailed as follows: Model 1: Base model: 0. Model 2: Conrolling for he impac of long-horizon misreacion: 0. Model 3: Conrolling for he impac of shor-horizon misreacion: 0. 25

27 We refer Model 4 o he full model specified in Equaion (12), which conrols for impac of boh misreacions. To adjus for serial correlaion and heeroskedasiciy, we also use he Newey-Wes robus sandard errors in our empirical analysis. Following he same crieria for he inclusion of lagged informaion in he invesigaions on shor-horizon underreacion and long-horizon overreacion, we selec a racking window of 30 minues for he calculaion of he w QPrevSim variable, i.e. w=6. The esimaion resuls of he four alernaive models from markewise observaions are shown in Table 5. The esimaes of β coefficiens are posiively significan a he 1% of significance level for all window sizes in Models 1 and 2. I indicaes ha invesors misreacion o informaion increases in he quaniy of similar unexpeced changes in insananeous variance even hough i is conrolled for he impac of he overall level of insananeous variance. However, he resul is no robus o conrolling for he size of he magniude of he curren unexpeced changes in insananeous variance. The esimaes of β coefficiens in Models 3 and 4 urn o insignifican, while he esimaes of δ coefficiens are sill negaively significan a he 1% of significance level. This resul indicaes ha he effec of shor-horizon 26

28 underreacion dominaes he effec of increasing misreacion alhough he laer does exis in erms of markewise ransacions. Namely, compared wih previous similar informaion, he curren unexpeced shock is he mos influenial facor o drive invesors reacion. <Table 5 is insered abou here > The esimaion resuls of he four alernaive models for he four invesor caegories are shown in Tables As shown in Panels C and D, he findings for individual invesors and marke makers are similar o hose from markewise observaions. These wo ypes of invesors end o increase heir misreacion when receiving more similar unexpeced informaion, bu he effec of misreacion o he curren informaion is sill more influenial han o previous similar informaion. Therefore, afer conrolling for he effec of he shor-horizon underreacion in Models 3 and 4, he effec of increasing misreacion almos disappears. The esimaion resuls for domesic and foreign insiuional invesors are shown in Panels A and B, respecively. The esimaes of β coefficiens in Model 1 where we 14 As he esimaion resuls of γ 1, γ 2, γ 3 and θ are similar o hose from markewise observaions and similar across invesor classificaions, hey are no repored in Table 6 o avoid providing redundan informaion. Noneheless, hey are available upon reques. 27

29 conrol for he inraday effec only are also posiively significan a he 1% of significance level for almos all window sizes. Essenially, hese wo ypes of invesors misreacion o unexpeced informaion also increase in he quaniy of similar unexpeced informaion. However, afer conrolling he impac of he unexpeced shocks in Models 3 and 4, he esimaes of β coefficiens become no jus negaive bu also significan a 5% of significance level for all window sizes. I means ha hese wo ypes of invesors acually learn from previous unexpeced shocks o lower he levels of heir misreacion alhough heir rading behavior is sill dominaed by he shor-horizon underreacion. Moreover, for foreign insiuional invesors, he phenomenon of increasing misreacion vanishes afer we conrol for he impac of he level of curren insananeous variance, bu wihou conrolling for he impac of shor-horizon underreacion. <Table 6 is insered abou here > 4.5. Robusness analyses The main resuls of our empirical invesigaion are based on he observaion frequency of 5 minues. To check he robusness of our resuls, we also implemen he 28

30 ess of shor-horizon underreacion and long-horizon overreacion for he observaions wih alernaive sampling frequencies such as 15, 30 and 60 minues and one day. The size and significance of he coefficien esimaes are very similar across sampling frequencies. The resuls from daily markewise observaions are shown in Table 7. Poeshman (2001) also suggess an alernaive variable o measure he quaniy of previous similar shocks, which is denoed as QPrevSim 2 w and defined as: QPrevSim 2w w Unexpeced sign ( V ) V. (13) i 1 Unexpeced i This measure modifies w QPrevSim by aking ino accoun boh he sign and magniude of previous unexpeced changes in insananeous variance. We also run he ess for increasing misreacion wih his modified measure. The new resuls are in general consisen wih heir corresponding ones discussed previously. 5. Concluding Remarks Using a unique daase ha conains he complee record of ransacions in he Taiwan opions marke, his paper examines opions marke invesors reacion o he informaion conained in inraday changes in insananeous variance under he 29

31 assumpion ha he sochasic volailiy opion pricing model is appropriae. The empirical invesigaion is implemened no only for he markewise observaions, bu also for he ransacions of four differen classificaions of invesors individually. This paper provides evidence o suppor he following general findings. Firs, invesors iniiae heir reacion o unexpeced informaion from shor-horizon opions and hen adjus heir posiions in long-horizon opions wih a cerain degree of delay. Second, invesors underreac o he informaion on boh shor- and long-horizon opions wih he laer being more severe. Alhough hey ry o correc he misreacion, bu he correcion is sill insufficien. Third, he misreacion o he curren unexpeced shocks sill dominaes he effec of increasing misreacion alhough invesors misreacion ends o increase in he quaniy of previous similar unexpeced shocks. This paper also provides some findings from he comparison among he ransacions of alernaive invesor caegories. Firs, foreign insiuional invesors have he lowes degree of shor-horizon underreacion. Moreover, insiuional invesors correc heir misreacion more promply. The resuls in his paper are robus o differen sampling frequencies and also o 30

32 difference measures for he quaniy of previous similar informaion. Using high-frequency daa relaxes he assumpion ha invesors reac o informaion changes once a day and invesigaing he Taiwan marke enhances our knowledge abou invesors misreacion o informaion in a less maured marke. Therefore, he findings in his paper provide no only furher undersanding on he paerns of invesor misreacion, bu also more insighs on how invesors reac o informaion change and how o correc he reacion. In addiion, his paper also provides some ineresing findings on he comparison of misreacion paerns across alernaive caegories. 31

33 References Aï-Sahalia, Y., and Lo, A.W., 1998, Nonparameric esimaion of sae-price densiies implici in financial asse prices, Journal of Finance 53, Barber, B.M., Lee, Y.T., Liu, Y.J., and Odean, T., Jus how much do individual invesors lose by rading? Review of Financial Sudies 22, Berberis, N., Shleifer, A., and Vishny, R., A model of invesor senimen, Journal of Financial Economics 49, Bing, H., Lee, Y.T., and Liu, Y.J., Invesor rading behavior and performance: Evidence from Taiwan sock index opions, Working paper, Universiy of Texas a Ausin. Cao, C., Li, H., and Yu, F., Is invesor misreacion economically significan? Evidence from shor- and long-erm S&P 500 index opions, Journal of Fuures Markes 25, Chang, C.C., Hsieh, P.F., Lai, H.N., Do informed opion invesors predic sock reurns? Evidence from he Taiwan Sock Exchange, Journal of Banking and Finance 33, Cox, J.C., Ingersoll, J.E., and Ross, S.A., A heory of he erm srucure of ineres raes, Economerica 53, Daniel, K.D., Hirshleifer, D., and Subrahmanyam, A., Invesor psychology an securiy marke under- and overreacions, Journal of Finance 52, Heson, S.L., A closed-form soluion for opions wih sochasic volailiy wih applicaions o bond and currency opions, Review of Financial Sudies 6, Hong, H., and Sein, J.C., A unified heory of underreacion, momenum rading and overreacion in asse markes, Journal of Finance 54, Mahani, R.S., and Poeshman, Overreacion o sock marke news and misevaluaion of sock prices by unsophisicaed invesors: Evidence from he opion marke, Journal of Empirical Finance 15, Poeshman, A.M, Underreacion, overreacion, and increasing misreacion o informaion in he opions marke, Journal of Finance 56, Sein, J., Overreacions in he opions marke, Journal of Finance 44,

34 Figure 1 The Inraday Paern of Invesors Misreacion This figure exhibis he averages of he FarMisProj variable levels for each inraday inerval. The variable is defined as Unexpeced Long Shor FarMisProj sign( V )( V V ) Unexpeced where V is he unexpeced componen of change in he insananeous variance, Long V is he change in he insananeous variance from long mauriy opions and Shor V is he change in he insananeous variance from shor mauriy opions from rading ime -1 o. The sample period covers from January 2, 2002 o December 31,

35 Table 1 Summary saisics of he enire sample This able consiss of he summary saisics of our final sample for he inraday observaions of he opions wrien on he Taiwan Sock Exchange Capializaion Weighed Sock Index. The sample period covers from January 2, 2002 o December 31, The sample excludes he conracs wih a ime o expiraion less han 6 calendar days, wih a Black-Scholes implied volailiy lower han 0 or higher han 0.7, or wih a moneyness of in-he-money. Moneyness is defined as he raio of a srike price over he corresponding fuures price. The risk free raes are proxied by he average hree-monh deposi raes and obained from he websie of he Cenral Bank of Taiwan. Perceniles Variables Obs. Mean S.D. Min 1% 10% 50% 90% 99% Max Panel A: Calls Price (NT$) B-S implied vol Time o mauriy Srike price Risk-free rae Moneyness Panel B: Pus Price (NT$) B-S implied vol Time o mauriy Srike price Risk-free rae Moneyness

36 Table 2 Summary saisics across invesor caegories This able consiss of he summary saisics of our final sample for he inraday observaions of he opions wrien on he Taiwan Sock Exchange Capializaion Weighed Sock Index by four invesor caegories, which are domesic insiuional invesors, foreign insiuional invesors, individual invesors and marke makers. The sample period covers from January 2, 2002 o December 31, The sample excludes he conracs wih a ime o expiraion less han 6 calendar days, wih a Black-Scholes implied volailiy lower han 0 or higher han 0.7, or wih a moneyness of in-he-money. Moneyness is defined as he raio of a srike price over he corresponding fuures price. The risk free raes are proxied by he average hree-monh deposi raes and obained from he websie of he Cenral Bank of Taiwan. Types of Invesors Variables Domesic Insiuional Invesors Foreign Insiuional Invesors Individual Invesors Marke Makers Panel A: Calls Obervaions Price (NT$) mean S.D B-S implied vol mean S.D Time o mauriy mean S.D Srike price mean S.D Risk-free rae mean S.D Moneyness mean S.D Panel B: Pus Obervaions Price (NT$) mean S.D B-S implied vol mean S.D Time o mauriy mean S.D Srike price mean S.D Risk-free rae mean S.D Moneyness mean S.D

37 This able presens he esimaion resuls for he regression specified as Table 3 Tess for inraday shor-horizon underreacion FarMisProj 6 i 0 V i Unexpeced i 3 D j 1 j j, V Unexpeced Unexpeced where FarMisProj and V are defined in Equaions (8) and (7), respecively. D 1, D 2 and D 3 are dummy variables, which are equal o 1 for he open, noon and close inervals, respecively and 0 oherwise. The sample period covers from January 2, 2002 o December 31, The regression model is esimaed from he markewise observaions and he four invesor classificaions. The coefficiens and -saisics are repored. The -saisics are calculaed using he Newey-Wes robus sandard errors. ***, ** and * denoe he significance a he 1%, 5% and 10% levels, respecively. Marke Domesic Insiuional Foreign Insiuional Invesors Invesors Individual Invesors Marke Makers Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. α *** *** *** *** *** β *** *** *** *** *** β * β * *** β β * β * * β γ * * *** γ ** γ Adj. R % 47.88% 13.99% 35.98% 40.49% 36

38 Table 4 Tess for inraday long-horizon overreacion This able presens he esimaion resuls for he regression specified as Long Shor 6 3 V V i 0 iv i j 1 j D j, V where Long V is he insananeous variance implied from long mauriy opions, Shor V is he insananeous variance implied from shor mauriy opions, V is he insananeous variance for he corresponding rade inerval, and D 1, D 2 and D 3 are dummy variables, which are equal o 1 for he open, noon and close inervals, respecively and 0 oherwise. The sample period covers from January 2, 2002 o December 31, The regression model is esimaed from he markewise observaions and he four invesor classificaions. The coefficiens and -saisics are repored. The -saisics are calculaed using he Newey-Wes robus sandard errors. ***, ** and * denoe he significance a he 1%, 5% and 10% levels, respecively. Marke Domesic Insiuional Foreign Insiuional Invesors Invesors Individual Invesors Marke Makers Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. Coeff. -Sa. α *** *** *** *** β *** *** *** *** *** β *** *** *** * β * * *** *** β *** ** *** *** ** β *** *** *** β *** ** β *** ** *** γ ** γ γ * Adj. R % 60.38% 42.40% 40.48% 56.28% 37

39 Table 5 Tess for increasing misreacion from markewise observaions This able presens he esimaion resuls o examine he exisence of increasing misreacion from markewise observaions. The full model referred o Model 4 is specified as: FarMisProj QPrevSim D QPrevSim V V w 3 i 1 i i, w Unexpeced where D 1, D 2 and D 3 are used o conrol for he inraday paern in he FarMisProj variable, V is used o conrol for he impac of he curren level of insananeous variance, and Unexpeced w V is used o conrol for he impac of underreacion or overreacion. QPrevSim measures he quaniy of previous similar unexpeced changes in insananeous variance variable defined as: w Unexpeced w ) i 1 QPrevSim sign ( V sign( V ). Unexpeced i Wih several ses of consrains on some paricular parameers, we also run he following hree alernaive models: Model 1: Base model: 0. Model 2: Conrolling for he impac of insananeous variance: 0. Model 3: Conrolling for he impac of misreacion: 0. The sample period covers from January 2, 2002 o December 31, The regression models are esimaed from he markewise observaions. The coefficiens and -saisics are repored. The -saisics are calculaed using he Newey-Wes robus sandard errors. ***, ** and * denoe he significance a he 1%, 5% and 10% levels, respecively. Model Window size Panel A: β (7.33) *** (7.18) *** (4.77) *** (5.55) *** (4.20) *** (4.51) *** (6.89) *** (6.90) *** (4.31) *** (5.08) *** (3.80) *** (3.85) *** (-1.45) (-0.41) (-1.36) (-0.52) (-1.01) (-0.60) (-1.36) (-0.32) (-1.33) (-0.49) (-0.98) (-0.62) Panel B: γ (-0.29) (-1.62) (0.03) (-0.85) (-0.44) (-0.44) (-0.35) (-1.52) (0.18) (-0.83) (-0.36) (-0.26) (0.20) (-0.65) (0.51) (0.11) (0.13) (0.14) (0.18) (-0.65) (0.52) (0.09) (0.14) (0.16) Panel C: γ (1.87)* (1.16) (1.38) (0.47) (0.40) (0.05) (2.18)** (1.03) (1.28) (0.30) (0.04) (-0.36) (0.96) (0.73) (0.76) (0.30) (-0.15) (-0.24) (1.04) (0.72) (0.75) (0.28) (-0.20) (-0.32) Panel D: γ (-1.43) (-1.23) (-0.48) (-0.60) (0.10) (-0.64) (-1.19) (-1.05) (-0.18) (-0.46) (0.06) (-0.47) (-0.34) (-0.73) (0.03) (-0.17) (0.20) (0.04) (-0.40) (-0.71) (0.07) (-0.15) (0.19) (0.06) Panel E: θ (-51.16) *** (-51.15) *** (-51.14) *** (-51.13) *** (-51.13) *** (-51.14) *** (-9.17) *** (-9.18) *** (-9.18) *** (-9.18) *** (-9.18) *** (-9.20) *** Panel F: δ ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** ( ) *** 38