Psychological Barriers and Prices Behaviors. of Taiwan Futures Market

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1 Psychological Barriers and Prices Behaviors of Taiwan Fuures Marke Ming-Hsien Chen Deparmen of Finance, Naional Kaohsiung Firs Universiy of Science and Technology, Taiwan Vivian W. Tai Deparmen of Banking and Finance, Naional Chi Nan Universiy, Taiwan JEL Classificaion: D03, G4 Corresponding Auhor, Assisan Professor, Naional Kaohsiung Firs Universiy of Science and Technology, Adds: No., Jhuoyue, Rd., Nanzih Disric, Kaohsiung Ciy 8, Taiwan, Tel: ex. 407, Fax: Assisan Professor, Naional Chi Nan Universiy, Taiwan, No. Universiy Rd., Puli, Nanou 545, Taiwan, Tel: ex. 4636, Fax: (886)

2 Absrac This paper invesigaes wheher he exisence of psychological barriers in a variey of daily hree TAIFEX fuures price series. We use a number of saisical procedures and presens evidence of psychological barriers in prices. Our resuls show ha prices in round numbers ac as barriers wih imporan effecs on he condiional mean and variance of he fuures price series around psychological barriers. Keywords:Psychological Barriers; M-values; TAIFEX Fuures.

3 . Inroducion In pracice, recommendaions are usually appear, suggesed by securiies analyss, commercial research groups, even more financial correspondens and so on, o invesors who inend o adjus heir posiions on securiies, when he index has risen or fallen below a cerain level. Those recommended could deem ha an up or down rend of he index commence, when he index reaches or near in a specific number, moreover, could encourage invesors o opposiely rade in he specific index level as a reference basis, he price barrier. The price barrier means psychological barriers in erms of behavioral aspec. Lieraures reveal ha he phenomenon of psychological barriers in financial markes does exis. Tschoegl (998) poined ou ha all of he psychological barriers are assumed o be formed in inegers, bu no all inegers have a psychological barrier phenomenon. Amir and Ganzach (998) sudy he amendmen of earnings forecas from analyss and find he exisence of anchoring effec, since he adjusmen in analys earnings forecass are around he previously revealed values. McElroy and Dowd (007) observe characerisics of openness-o-experience, which means individuals end o make adjusmens when acceping new informaion and find ha anchoring effec posiively relaed o he openness-o-experience. In addiion, Bharai, Crain and Kaminski (008) shows daily prices in crude oil fuures are examined for evidence of clusering in he leas significan ineger digi and srongly indicae clusering in digi values around 9 coinciding wih periods of OPEC credibiliy. Aggarqal and Lucey (007) poined ou ha he concep of anchoring effec is closely relaed wih he psychological barrier, an anchoring effec. The effecs of psychological barriers can be explained by anchoring effec, which defines he phenomenon for hose who are unfamiliar wih or unsure of he siuaion will feel fear, herefore, usually rely on reference poin in he pas as a benchmark according o new informaion received. Kahneman and Tversky (98) poined ou ha when people have decision-making under uncerainy, individual characerisics play a very imporan role. Consisen wih he exisence of limied arbirage (Shleifer and Vishny, 997) and psychological aspecs of human informaion processing and decision-making, a number of behavioral biases have been shown o persis in asse price series (Hirshleifer, 00). For example, he conceps of anchoring and heurisic simplificaion in behavioral finance are closely relaed o he issue of psychological barriers. Anchoring (Slovic and Lichensein, 97) is he phenomenon whereby

4 individuals fixae on a recen number or a number which may be held ou o be imporan by informed commenaors. Drawing on he heurisics concep of Kahneman, Slovic, and Tversky (98) and on herding behavior of Avery and Zemsky (998) and Welch (000), Weserhoff (003) develops formal models of how raders cluser expecaions around round numbers. Oher researchers (e.g., Sonnemans, 003) noe a number of issues relaing o compeing hypoheses around why hese barriers migh a priori be expeced, and suggess ha in addiion o he anchoring approach an elemen of he phenomenon of odd-ending pricing may be imporan. Recen research by Shiller (000) noes ha in he absence of accurae agreemen on fundamenals many raders focus on he neares round number as a reasonable proxy for he fundamenal value. In erms of he limied memory, Siving and Winer (997) hink mos people lef he deepes memory of a few figures, such as: 4869, may only remember he 48 only. From lef o righ comparison, he resul of digial encoding is from lef o righ and in he limied ofen ignore he nex par of he memory manissa, hus direc comparison of wo numbers. For example, (, 5) and (8, ) are wo groups in he en-digi subracion numbers bu no he same, however he essence of he difference beween he wo groups are 6. Olsen (998) poined ou among he many diagnosic ools, he ineger poins in he financial news or securiies analyss commening on he mos frequenly menioned when referring o he so-called ineger poins in a paricular marke index, eg., 7500 poins or 8000 poins. Thus, his reference poins may reside in which some imporan informaion, as a index rises or falls, especially when he index fell below a paricular psychologically expeced levels. Ley and Varian (994) use he Dow Jones indusrial average index o es wheher here is he phenomenon of psychological barrier from 95 o 993. They conclude ha no evidence of significan psychological barrier exiss. Weserhoff (003) examine he behavior of exchange rae flucuaions in erms of anchoring effec and psychological barriers. They find he raders acively beween he exchange rae anchors for convergence. In addiion, Aggarwal and Lucey (007) prices in round numbers ac as barriers wih imporan The phenomenon of odd-ending pricing is he price of ending he se, such as: $ 99 or $ 00 o explore ways o increase sales, due o involve people psychological level, so in pracice he so-called "psychological pricing" (Mason and Mayer, 990). Fracional pricing sraegy ry o change consumers percepion in prices. Schindler (99) and Siving and Winer (997) view he price effec ino an image (image effecs) and level of effeciveness (level effecs), when an ineger for he manissa, on behalf of beer qualiy. Limied memory capaciy, from lef o righ comparison (lef o righ comparison) and close o ineger (round price down) and oher hree are he mos commonly discussed. Thomas and Morwiz (005) sudy ending 9 pricing sraegy and find ha when a price change in he far lef or he number of arge price, ending 9 on he price percepion have significan impac.

5 effecs on he condiional mean and variance of he gold price series around psychological barriers. Oher research (Michell and Izan, 006; Michell, 00) draws a disincion beween psychological barriers and clusering phenomena and disinguishes clusering, where paricular digis and levels appear more ofen, from psychological barriers, where rades are infrequen a or around a paricular cluser of prices. Thus, i is clarified ha he wo aspecs are relaed bu no synonymous. Clusering is a necessary, bu no a sufficien condiion, for a psychological barrier o be presen. Tschoegl (988) shows ha while all psychological barriers can be assumed o be round numbers, i is no he case ha all round numbers are psychological barriers. Using a number of saisical procedures o assess psychological barriers for four differen price daa series, TWSE index and hree neares fuures conracs, covering recen periods of one decade, his paper documens for he firs ime ha here indeed are significan changes in means and variances associaed wih cerain round number fuures prices ha are perceived as psychological barriers. Given he imporance of fuures, hese resuls should be of much ineres o policy-makers, scholars, and invesors. The paper conribues he lieraures ha we link he psychological barriers wih he anchoring effec and moreover, we provide he evidence of prospecive heory, proposed by Kahneman and Tverskey (979), by idenifying price behaviors of he barrier from a downwards and upwards direcion. This paper is srucured as follows. The nex secion shows he sample and relaed saisics, followed by a secion on oulining sraegies for esing psychological barriers. Secion 4 describes he resuls from a variey of ess and secion 5 concludes.. Sample Descripions We use he daily closing prices of sock index, Taiwan Sock Exchange Capializaion Weighed Sock (TWSE) Index, and hree neares fuures conracs Index Fuures (TX), Finance Secor Index Fuures (TF) and Elecronic Secor Fuures (TE) as our samples. The sample period is from January 4, 000 o December 3, 009, including,504 samples from he Taiwan Economic Journal (TEJ). Panel in Table shows he descripive saisics on TX, TE and TF fuures. Saisical characerisics of samples are similar. The mean of TX (TF, TE) is abou 6,46.5 (853.34, 8.8) wih a sandard deviaion,, (63.97, 76.4) and 3

6 only TX is above he housand poins. Furhermore, he disribuions for TX and TE fuures conracs are skewness-o he-righ, whenever TF is lef-skewed which shows he rend of TF are over is average, TX and TE mosly volaile below he average, relaively. Kurosis of hree fuures shows differenly disribued which suppored by Jarque-Bera saisics. TX and TF are a low broad peak paern (play kurosis), bu TE has high kurosis (lepo kurosis). Panel shows he descripive saisics on TX, TE and TF fuures reurn process. On average, he mean of daily reurn in all hree fuures are negaive reurns, which he TF has he larges negaive value, while TE compensaes he smalles negaive premium. The skewness of hree fuures are negaive, indicaing is lef-skewed which shows he rend of TF are over is average. In he kurosis, all coefficiens are greaer han 3, implying a high kurosis disribuion which can be suppored by he Jarque-Bera saisics in % significance level. Roughly, he reurns on hree fuures seemly don follow a normal disribuion of daily reurns. Table. Descripive Saisics of TX, TF and TE Fuures Panel Mean Median Max. Min. Sd. Dev. Skewness Kurosis Jarque-Bera value Observaions TX TF TE Panel Mean Median Max. Min. Sd. Dev. Skewness Kurosis Jarque-Bera value Observaions TX -.7E TF -3.04E TE Sample period is from 4, Jan. 000 o 3, Dec We use log-reurn, hus, reurn could violaes he 7%, in erm of arihmeic measuremen. R = ln( P/ P ), in he sudy, 3. Mehodology We firsly invesigae ha here exiss abnormal movemen of fuures when facing a hundred and housand poins of he prices. Then we sudy wheher he firs and second momen of he fuures prices have significanly differen from hose far from he 00 or 000 ineger poins. In shor, his secion focus on he following issues, (a) he seing mehodology and ypes of ineger poins, (b) he meaning of M value and is measuremen, (c) es on he exisence of ineger poins, and (d) he effecs of barrier o reurns and volailiy on fuures prices. 4

7 3. Seing Mehodology and Type of Ineger Poins We follow he mehods showed by Burke (00) and Donaldson and Kim (993) o se he barrier poins of 00 and 000, applying o wo psychological impacs on invesors, one is he sric checkpoins and he oher is he region level. () Sric barrier a. Disance beween poins in he hundreds of checkpoins, he seing mehods, such as, K 00, K =,,3,... () For example, 00, 00,, 600, 600. b. Poin spacing of housands of poins, he se is shown as, K 000, K =,,3,... () For example, 3000, 4000, 5000,. () Region level We se he region levels o plus or minus 00 poins for index poins, for example: or 90-0 as a hundred barrier. Differen from sric checkpoins seing, region level allows us o find wheher invesors beforehand reflec heir behaviors on he fuures prices near around he 00 or 000 checkpoins. 3. M Values and Measuremens M is wo digial numbers, ranging from 00 o 99, and usually represens a poin, 00 as an imporan reference poin. When invesors have psychological barriers, M value appears abnormal in he viciniy of 00. The seings of M value are defined as follows. () Hundred, 00, barrier poins of he M value is se as, For deails see De Ceuser e al. (998). 5

8 [ ] [ ] mod 00 a M = P, (3) where P is he ineger par of P, [mod 00] is he wo digial inegers. a For examples, if he prices are and , M are 59 and 68, separaely. () Thousand, 000, barrier poins of he M value is se as, b (log p ) mod M = 00 0 mod 00, (4) b where M is he second and hird digi of he price in erms of housand measure and logarihms are o base 0. For example, if he prices are b and , M are 65 and 89, separaely. For an examinaion of barriers, we are ineresed in wheher he pair of digis brackeing he decimal poin displays a frequency ha is differen from oher pairs of digis. If here exis barriers a levels such as hese hen we would expec o see relaively fewer x00.xx digis for 00, and x00x.xx digis for 000 barrier poins han oherwise. The erm mod refers o he reducion modulo. These are known formally as M-values. Such frequencies would also depend on he execuion of sop and limi orders and could well deermine differen dynamics approaching he barrier from below or from above. 3.3 Mehodology of Idenifying Price Barrier Poins The hird issue of he paper invesigae wheher he abnormal disribuion of fuures prices exis, when he prices are near he barrier poins. The M value of he cumulaive number of poins will be compared wih non-ineger. We use he calculaed M values, coupled wih he poins es o find ou wheher he index level have an impac on invesor psychology. Regression model conains wo kinds of es poins, he firs es is called he value of he cumulaive number of es poins M (barrier proximiy), he second es is he barrier kurosis es (barrier hump). Regression model is as follows, () M value of he cumulaive number of es poins (barrier proximiy), f ( M) = α + βd + η M = 00, 0,..., 99, (5) 6

9 f ( M ) means he cumulaive frequency of M values, D is a dummy variable. When he prices reach on he sric barrier or near he region barrier, D is, oherwise D is 0. η is he residual erm. Barrier seing in he sudy is consruced as, sric barrier: M = 00, region barrier: () M > 95, or M< 05, () M > 90, or M< 0. Donaldson and Kim (993) find ha he M values a 00 of U.S. Dow Jones Indusrial Average (DJIA), he cumulaive numbers are lower relaive o oher M values, bu Bahng (003) show M values a 00 of Indonesia's Jakara Composie Index are higher han non-barrier price regions. In our works, we assume ha β is 0, when here is no prices barrier effecs, oherwiseβ may be negaive or posiive values. () Barrier hump esing, f( M) = α+ ϕm+ γm + ε M = 00, 0,..., 99, (6) where f (M) is he cumulaive frequency of M values and ε is he residual erm. In equaion (6), we are concerned wih kurosis disribuion of M values and es wheher here are unusually barrier hump effecs. If he effec doesn exis, M value should be a uniform disribuion (γ is zero); he oher hand, if he effec exiss, he disribuion of M value is no disribued a uniform form and γis significanly differen from zero. 3.4 Effecs of Barrier o Reurns and Volailiy on Fuures Prices. The barrier, defaul reference price, is generally regarded as a resisance or a suppor price level in erms of invesor s psychology. In his subsecion, we use GARCH (p, q) model o invesigae he effecs of barrier o reurns and volailiy on fuures prices. The model is as follows, Y = Xb+ ε, ε Ω ~ N(0, σ ) (7) σ = α + 0 q i= α ε i i p + i= β σ i i (8) 7

10 In order o observe he behavior of index reurns on or near he barrier, we define four regimes around barriers: BU for he 5 day prior o he fuures price reaching a barrier from below, bu before i breaches he barrier, AU for he 5 day afer reaching he barrier from below, BD and AD for he 5 day before and afer breaching he barrier in a downwards direcion. Bollerslev and Wrigh (00) poined ou ha he GARCH (,) model can successfully esimae and predic beer han oher more complex or condiional variance ones. Therefore, we use GARCH (,) model o observe he behavior of index reurns on or near he barrier. R = β + β BD + β 3 AD + β 4BU + β 5 AU + ε, ~ N(0, h ) ε, (9) h = α + α BD + α 3 AD + α 4BU + α 5 AU + α 6h + α 7ε + η, (0) BU where R = ln( P/ P ), represen he log-reurn of fuures prices. BD, AD, and AU ake he value for he days noed, and zero oherwise. 4. Empirical Resuls Resuls for he barrier proximiy for he M value of hundred 00 and housand 000 are shown in Tables, respecively. I is clear ha we can rejec he no sric barriers hypohesis for he 000 s digis in TX series, bu no for he 00 s digis. Barriers in he daily TX series appear from his es o exis a levels such as 4000, 5000 ec bu no a levels such as 400, 500 ec. Barriers in TF and TE, however, also no seem o exis sric or region barrier. There being some evidence of barriers a all forms of specificaions (sric and region) we concenrae hereafer on he srices formulaion of barriers. Poins in he ineger digis of a hundred poins are sudied on all fuures. In he case of sric barrier, he coefficien of TF is negaive, indicaing TF fuures has lower frequency on or around hundred barrier as well as he case of TX in housand sric barrier. Table Barrier proximiy es Panel A. Hundred poins sric barrier Region Barrier 90-0 Region Barrier β P-value β P-value β P-value TX *** TF *

11 TE * Panel B. Thousand poins sric barrier Region Barrier 90-0 Region Barrier β p-value β p-value β p-value TX The able shows he resuls of a regression, f( M) = α + βd+ η, where he dependen variable is he frequency of appearance of individual modulo values and D is a dummy variable ha akes he value in he presence of a barrier. Sric barrier akes he value a he zero modulo poin, barrier akes he value if he modulo is in he inerval, and 90-0 barrier akes he value if he modulo is in he inerval. The daa in he 00 s digis column examine barrier behavior a he level of hundreds, ha in 000 s digis ha a he level of housands. p-value gives he marginal significance of he coefficiens agains a null of zero. Table 3 shows he resuls of he barrier hump es bu here is lile evidence here of a persisen barrier. In hundred barriers, he coefficien of TE is posiive indicaing more frequen on or around he barriers. TF has significanly negaive coefficien in hundred barriers, as he similar resul in barrier proximiy es. As for he TX, empirical resuls show TX has no barrier effecs no maer in hundred or in housand poins which conradics wih he resuls in sric barrier es show in Table 3. In sake of robusness, we show more accrue evidence in laer of GARCH model es. Table 3. Barrier hump es Hundred poins Thousand poins γ p-value γ p-value TX E E TF -5.50E-07 ** TE.790E The able shows he resuls of a regression, f( M ) = α + ϕm+ γm + ε, where he dependen variable is he frequency of appearance of individual modulo values and M is he frequency of appearance of individual modulo values. p-value gives he marginal significance of he coefficiens agains a null of zero. Psychological barriers are generally aken as offering suppor or resisance o series. The saisical inerpreaion of his is ha he dynamics of he reurns series around and in he viciniy of hese barriers should differ from ha elsewhere. We do no impose exogenous assumpions regarding he impac of being in he barrier region. Insead, wha is of ineres is he issue of he differenial effec on he reurn and volailiy from being in he region of he barrier, and wheher he barrier is being approached from above (owards a hypohesized suppor barrier) or below (owards a presumed resisance barrier). The resuls are shown in Table 4, which uses a GARCH (,) analysis of he reurns shown in equaion (9) and (0). We do no include an 9

12 ARCH-in-Mean erm or AR/MA erms in he daa based on recen research (Lucey and Tully, 006). Again, we expec ha in he absence of barriers he coefficiens on he indicaor variables in he mean equaion would be insignificanly differen from zero. A number of poins are eviden from he resuls presened in he wo ables, Tables 5 and 6. For a number of he barrier regions, he mean coefficiens have changed in sign, magniude, and significance. Few of he mean coefficiens are now significan. While here is evidence of limied mean effecs around barriers, here are clear, consisen, and srong indicaors of significan variance effecs around barriers. This is paricularly eviden in he index series, where all values are significan. The variance indicaor afer a downward movemen hrough a barrier is in all cases negaive, indicaing ha he marke calms having fallen hrough a barrier. Consisen wih his is he fac ha in all cases he indicor before a downward movemen is posiive, indicaing increased marke volailiy. This, in all cases a he % level, is he only variance indicaor ha is significan across all series. Moreover, when he fuures prices break down he presupposed round poins, he invesors suffer losses; oherwise, when he fuures prices rise up he presupposed round poins, he invesors gain losses. From he absolue values of coefficiens beween U and D, he resuls are consisen wih he prospec heory predics. Finally, in all case, expec for AD, he volailiy increase when he presupposed round poins are broken. For fuures reurns, i is acceped ha volailiy is greaer in bear condiions (see Campbell & Henschel, 99) and ha here are leverage effecs exis. The similar resuls can be found in Table 5 which is in he barrier in housand poins for TWSE Index and TX fuures. Table 4. GARCH analysis: Barrier in hundred poins for fuures price series TX TF TE Coefficiens p-value Coefficiens p-value Coefficiens p-value Panel A: mean equaion β ** β (BD) *** β 3 (AD) *** *** *** β 4 (BU) *** *** β (AU) *** *** *** Panel B: condiional volailiy equaion α -4.9E E-06 *** E-06 *** α (BD).35E-05 *** E-05 *** E-05 **

13 α 3 (AD) -4.E E E α (BU).03E-05 *** E-05 *** E-05 * α (AU) 7.85E-06 ** E E α *** *** *** α *** *** *** Table shows he resuls of a GARCH esimaion of he form, R = β + β BD + β AD + β BU + β AU + ε ; ε ~ N(0, h ); h = α+ αbd + α3ad + α4bu + α5au + α6h + α 7 ε + η. AU, BU, AD and BD are dummy variables. BD and AD for he 5 days before and afer breaching he barrier in a downwards direcion; BU is for he 5 days prior o he gold price reaching a barrier from below, bu before i breaches he barrier, and AU for he 5 days afer he barrier from below,. Thus hese ake he value for he days noed, and zero oherwise. p-value gives he marginal significance of he coefficiens agains a null of zero. Table 5. GARCH analysis: Barrier in housand poins for TWSE Index and TX fuures price series Panel A: mean equaio n TWSE Index Coefficiens p-value Coefficiens TX p-value β ** β (BD) *** β (AD) *** * β (BU). 9E-03 ** β (AU) *** Panel B: condiional vo lailiy equaion α.36e-06 *** E-06 *** α (BD).36E-05 *** E-05 *** α (AD) 4.3E E α (BU) E-05 *** E-06 *** α (AU) -.04E E α 0.98 *** *** α *** *** Table shows he resuls of a GARCH esimaion of he form, R = β + β BD + β AD + β BU + β AU + ε ; ε ~ N(0, h ); h = α+ αbd + α3ad + α4bu + α5au + α6h + α7ε + η. AU, BU, AD and BD are dummy variables. BD and AD for he 5 days before and afer breaching he barrier in a downwards direcion; BU is for he 5 days prior o he gold price reaching a barrier from below, bu before i breaches he barrier, and AU for he 5 days afer he barrier from below,. Thus hese ake he value for he days noed, and zero oherwise. MA is he moving average parameer and GARCH he GARCH parameer in he variance equaion. p-value gives he marginal significance of he coefficiens agains a null of zero. Thus hese ake he value for he days noed, and zero oherwise. p-value gives he marginal significance of he coefficiens agains a null of zero. 5. Conclusion

14 This aricle aemps o invesigae round numbers effecs, he psychological impac on invesors, and he behavior of fuures near or on he barrier poins. The effecs of psychological barriers can be explained by anchoring effec, herefore, usually rely on reference poin in he pas as a benchmark according o new informaion received, o reduce he uncerainy in mind. Prior lieraure documens psychological barrier, a suppor or resisance level, and sress on he imporance of round numbers in equiy, bond, foreign exchange and gold markes. Despie he imporance of psychological elemens in he securiy markes, here is no prior research on hese phenomena in TAIFEX fuures marke. Using a number of saisical procedures, his paper examines for he firs ime mean and volailiy effecs around psychological barriers in he Taiwan s fuures marke. Moreover, in erms of frequency and ime series ess, we find ha TX fuures has sric barrier in hundred poins bu no in housand ones. TF conacs have significanly negaive coefficien in hundred barriers, however, TE does no show any psychological barriers effecs. In addiion, differences experience in invesors could lead o differen cogniive. Our resuls suppor Barber and Odean s (999) viewpoin ha decision making on invesmen could exis cogniive biases in erms of ha differen invesors have differen indices and psychological barriers, when making decisions independenly. Thus some fuures have he round number effecs in psychological barriers, bu some do no. Finally, volailiy indicaor afer a downward movemen hrough a barrier is in all cases negaive, indicaing ha he marke 'calms' having fallen hrough a barrier. Consisen wih his is he fac ha in all cases he indicor before a downward movemen is posiive, indicaing increased marke volailiy. When he fuures prices break down he presupposed round poins, he invesors suffer losses; oherwise, when he fuures prices rise up he presupposed round poins, he invesors gain losses. Our resuls are consisen wih he prospec heory predics. Reference Aggarwal, R., and B. Lucey, (007), Psychological Barriers in Gold Prices?, Review of Financial Economics 6, Amir, E., and Y. Ganzach, (998), Overreacion and Underreacion in Analyss Forecass, Journal of Economic Behavior and Organizaion 37,

15 Avery, C., and P. Zemsky, (998), Mulidimensional Uncerainy and Herd Behavior in Financial Markes, American Economic Review 88, Bahng, B., (003), Do Psychological Barriers Exis in he Sock Price Indices? Evidence from Asia s Emerging Markes, Inernaional Area Review 6, Barber, B., and T. Odean, (999), The Courage of Misguided Convicions, Financial Analyss Journal 55, Bharai, R., S., Crain, and V. Kaminski, (008), OPEC Credibiliy and Clusering in Crude Oil Prices, working paper. Bollerslev, T., and J. Wrigh, (00), High-Frequency Daa, Frequency Domain Inference, And Volailiy Forecasing, Review of Economics and Saisics 83, Burke, S., (00), Barriers in US Benchmark Bonds, Universiy of Briish Columbia Working Paper. Campbell, J., and L. Henschel, (99), No News is Good News: An Asymmeric Model of Changing Volailiy in Sock Reurns, Journal of Financial Economics 3, De Ceuser, M., Dhaene, G., and T. Schaeman, (998), On he Hypohesis of Psychological Barriers in Sock Markes and Benford s Law, Journal of Empirical Finance 5, Donaldson, R., and H. Y. Kim, (993), Price Barriers in he Dow Jones Indusrial Average, Journal of Financial and Quaniaive Analysis 8, Hirshleifer, D., (00), Invesor Psychology and Asse Pricing, Journal of Finance 56, Kahneman, D., Slovic, P., and A. Tversky, (98), Judgmen under Uncerainy: Heurisics and Biases, New York, Cambridge Universiy Press. Kahneman, D., and A. Tversky, (979), Prospec Theory: An Analysis of Decision under Risk, Economerica 47, Kahneman, D., and A. Tversky, (98), The Framing of Decisions and he Psychology of Choice, Science, Ley, E., and H. Varian, (994), Are There Psychological Barriers in he Dow Jones Index? Applied Financial Economics 4,

16 Lucey, B., and E. Tully, (006), Seasonaliy, Risk and Reurn in Daily COMEX Gold and Silver Daa, Applied Financial Economics 6, Mason, J., and M. Mayer, (990), Modern Reailing: Theory and Pracice, BPI /Irwin, Homewood, IL. McElroy, T., and K. Dowd, (007), Acion Orienaion, Consisency and Feelings of Regre, Judgmen and Decision Making, Michell, J., (00), Clusering and Psychological Barriers: The imporance of Numbers, Journal of Fuures Markes, Michell, J., and I.H.Y., Izan, (006), Clusering and Psychological Barriers in Exchange Raes, Journal of Inernaional Financial Markes, Insiuions and Money 6, Olsen, R., (998), Behavioral Finance and is Implicaions for Sock-Price Volailiy, Financial Analyss Journal 54, 0-8. Schindler, R., (99), Symbolic Meanings of a Price Ending, Advances in Consumer Research 8, Shiller, R., (000), Irraional exuberance. Princeon, Princeon Universiy Press. Shleifer, A., and R. Vishny, (997), The Limis of Arbirage, Journal of Finance 5, Slovic, P., and S. Lichensein, (97), Comparison of Bayesian and Regression Approaches o he Sudy of Informaion Processing in Judgmen, Organizaional Behavior and Human Performance 6, Sonnemans, J., (003), Price Clusering and Naural Resisance Poins in he Duch Sock Marke, Tinbergen Insiue working paper. Siving, M., and R. Winer, (997), An Empirical Analysis of Price Endings wih Scanner Daa, Journal of Consumer Research 4, Thomas, M., and V. Morwiz, (005), Penny Wise and Pound Foolish: The Lef-Digi Effec in Price Cogniion, Journal of Consumer Research 3, Tschoegl, A., (988), The Source and Consequences of Sop Orders: A Conjecure, Managerial and Decision Economics 9, Welch, I., (000), Herding Among Securiy Analyss, Journal of Financial Economics 58,

17 Weserhoff, F., (003), Anchoring and Psychological Barriers in Foreign Exchange Markes, Journal of Behavioral Finance 4,

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