ABSTRACT. 1 Introduction

Transcription

1 LOTTERY STOCKS IN THE TAIWAN STOCK MARKET Chin-Shui Lo, Deparmen of Finance, Chang Jung Chrisian Universy, Taiwan(R.O.C.), No.396, Sec., Changrong Rd., Gueiren Dis., Tainan Cy 70, Taiwan (R.O.C.), Tel: Chiung-Hui Cheng, Graduae School Business and Operaions Managemen, Chang Jung Chrisian Universy, Taiwan(R.O.C.). No.396, Sec., Changrong Rd., Gueiren Dis., Tainan Cy 70, Taiwan (R.O.C.), Tel: ABSTRACT Many compare he sock marke o gambling. Invesors and gamblers may share common ras. This research invesigaes loery sock behavior in he Taiwan Sock Marke and finds marke capalizaions and earnings o be good predicors of loery socks. Gambling-induced co-movemens are significanly sronger for socks raded by individuals han hose raded by insuions. Consisen wh he findings of [2], our empirical resuls sugges ha individuals end o gamble during an economic downurn. However, loery socks were found o only weakly exacerbae marke volaily during up marke periods, whereas non-loery sock acs as a sabilizer for he marke during an up period. Keywords: Loery socks, gamble, volaily, skewness Inroducion Some have compared he sock marke o gambling, suggesing many commonalies beween gambling and sock invesmen. The survey of [7] revealed ha gamblers and invesors share five ras and differ on hree ras. [26] advanced he commonaly beween loery players and sock raders from he perspecives of overopimism, aspiraion, emoion, and enerainmen. Many invesors possess a risk-seeking propensy and wager on an uncerain invesmen oucome. The gamble of he remoe chance of a large gain may be more aracive and expeced for invesors by aking a large chance of a small loss. The gamble hab migh be deep rooed in he human psyche ([2]), be a radion of gambling in he Chinese New Year ([7]), a religious background wh a gambling propensy ([23]), or a endency o break-even ([28]). The rading volume of he Taiwan Sock Marke has been ranked welfh worldwide ([]) and share urnover is over hree imes ha of he developed marke ([6]), such ha high rading records migh be due o invesor preference of gambling-relaed socks. This sudy invesigaes loery sock behavior, which capures gambling characerisics and sheds ligh on heir effec in he Taiwan Sock Marke. [] proposed ha people who buy insurance policies simulaneously buy loery ickes, and are boh risk averse and risk aking. Based on he insurance-loery framework, [22] poss ha, wheher foolish or wise, people do paricipae in loeries, no only insurance.

2 Prospec heory poss ha value funcion describes why people have a risk-averse aude for gains and a risk-seeking menaly for losses. Sock rading is a negaive-sum game ([26]). [] advanced ha people rade sock or buy loery ickes because heir rades provide he likelihood of promoing from he working class social posion o he upper class. Invesors may be relucan o realize heir losses ([25]). [9] repored ha people gamble he game ha hey do no accep when hey are in he gain domain, bu wan a icke ou of loss when hey are in he loss domain. Gambling is a ge-rich-quick game ha aracs peoples o play. [2] conjecured ha invesors migh overweigh he low probabily even and prefer socks wh posive skewness. A loery icke represens a marginal cos ha renders a remoe chance of earning an exreme reurn ([6]). A parallelism can be advanced beween invesing in cerain ypes of socks and purchasing a loery icke. [7] indicaed hree requiremens of gambling: gambling ofen depends on luck, he sake can be los enirely, and a lucky be can resul in an excess reurn. However, in he sock marke, invesor gambling preferences for well-defined socks as a loery insrumen is unobserved or unavailable. No specific sock is likely o possess he paricular characerisics of loery ickes, paricularly he disproporional reward relaive o cos. For hese reasons, is difficul o invesigae he gambling-induced invesmen decision. In his vein, o indirecly idenify socks ha could be perceived as a gambling objec, [2] proposed hree ypical characerisics: low sock price, high idiosyncraic skewness, and high idiosyncraic volaily. The evidence provided by [8] for low sock price reveal ha invesors in low priced socks yield lower (even negaive) average reurns as he premium paid for he chance o earn an exreme reurn. Compared o high-priced socks, low-priced socks are more aracive o invesors wh gambling preference, who are searching for cheap bes. The findings of [6] show ha invesors in he Taiwan Sock Marke are willing o sacrifice average reurn for a remoe chance o earn an abnormal reurn when hey rade low-priced socks. Based on hese papers, low-priced sock serves o prime candidaes of gambling-ype socks, which are more aracive o gamble-preference invesors. Based on prospec heory, [2] proposed ha invesors may have a preference for socks wh posive skewness in he reurn disribuion. The model of [4] suggess ha invesor prefer skewness as an oucome of over-opimism abou he probabily of good saes. To address his issue, [4] provided evidences showing ha skewness of prize disribuions explains why risk-averse individuals may play he loery. [5] suggesed ha because he variance and skewness of be reurns are highly correlaed, beors migh appear o prefer variance when is skewness ha hey cove. When sock has high volaily, invesors migh believe in a greaer likelihood o realize previous exreme reurn evens again, even hough he re-occurrence of ha even is likely assigned a considerably lower probabily ([2]), while high reurn volaily likely emerges he dream of an exremely large payoff ([7]). Whin he se of low-priced socks, invesors are more likely o selec socks wh high idiosyncraic or sock-specific volaily. Among socks ha have low prices, high idiosyncraic skewness, and high volaily are more likely o be perceived as loeries.

3 Risk aversion is he primary premise in finance heory. However, an undersanding of invesmen behavior is incomplee when risk seeking audes rooed in he minds of invesors are dismissed ([24). Research is increasingly concerned wh he effec of speculaive sock marke acivies. The Taiwan Sock Marke has been viewed as one of he mos volaile and speculaive developing markes. During he Lunar New Year, Taiwanese always gamble because gambling and winning means good luck for he whole year. An ineresing finding by [3] revealed ha buying loery ickes wh a large jackpo can subsue for sock rading in he Taiwan Sock Marke. 2 [] found ha he inroducion of legal loery in Taiwan reduced he TSE urnover by approximaely one-fourh. However, empirical evidence of he loery sock in his marke is scan. This research invesigaes he exisence and effec of loery sock on reurn and volaily on he Taiwan Sock Marke. Because of he loery-ype sock variance, here is approximaely a 30% probabily for a loery sock o move forward o anoher ype of sock. The evidence indicaes ha marke capalizaions and earnings per share are good predicaors of loery-ype socks. Gambling-induced co-movemens are also significanly sronger wh loery sock raded by individuals han ha of insuions. Consisen wh he findings of [2], our empirical resuls sugges ha individuals end o gamble during an economic downurn. Our findings also show ha loery socks could weakly drive marke volaily during up marke periods, whereas he non-loery sock acs as a sabilizer on he marke during an up marke period. The remainder of his research is organized as follows. The nex secion presens he daa and measures of loery sock. Secion 3 describes he findings of his research, and he final secion concludes his research. 2 Daa And Loery Index This research focuses on loery sock behavior in he Taiwan Sock Marke, an emerging marke, moivaed by he sudy of [2]. This work obained daily rading daa exraced from he Taiwan Economic Journal daabase (TEJ). The daa se includes common sock lised on he Taiwan Sock Exchange Corporaion from Ocober 986 o March 200. From his period, he number of lised firms increased from 30 in 986 o 763 in 20. To measure he index of loery socks, daily reurns are firs needed o esimae he idiosyncraic volaily and skewness. The quarerly volaily and skewness are he second and hird momen of residual reurns obained by fing a four-facor model o he daily sock reurns. The four facors are marke premium, size premium (small minus big), book-o-marke premium (high minus low), and momenum (winners minus losers). The quarerly idiosyncraic skewness and volaily are esimaed based on he model of [3]. The model is defined as follows: iv, is, ε, / ε,, (2) () where iv i, and i is, are idiosyncraic volaily and skewness, respecively. S() denoes he se of rading days from he firs day hrough he end of quarer, and le N ()

4 denoe he number of rading days in quarer. Le ε d be he regression residual reurns using four facors, which include he Fama and French hree-facor model augmened wh a momenum facor MOM. Consisen wh he mehod of [22] [23], his work assigns all socks of lised firms each quarer o viginiles (semi-deciles) based on sock price, idiosyncraic volaily, and skewness (where is he lowes volaily and skewness groups, and he larges price group). The price, volaily, and skewness viginile assignmens are added quarerly for each sock o creae a loery score ranging from 3 o 60, which is hen scaled o range from 0 o applying (score 3)/(60 3) (abbreviaed as loery index in following). A higher loery index poss a sock ha is more aracive o invesors as an objec o gamble. This sudy idenifies socks ranked by he loery index in he lowes 30 h percenile as non-loery socks, and he highes 70 h percenile as loery socks. Socks ha do no belong o loery and non-loery socks are defined as oher socks Basic Saisics 3 Empirical Resuls Table repors he summary saisics for all variables, 4 he yearly average for all firms, and he average ime-series over he sample period, examined in his research. Loery socks are defined as having a higher average loery index, lower price, higher volaily, and skewness. On he conrary, he non-loery socks have a lower loery index, higher price, and lower volaily and skewness. On average, socks wh higher urnover, liabily, and book-o-marke raio are classified as loery socks. Table also presens non-loery socks as having higher marke capalizaions and earnings per share. Sales growh and reurns do no significanly differ beween loery and non-loery socks, and are highes in he caegory of oher socks. Table Basic saisics This able repors he mean quarerly characerisics of loery-ype socks during he hird season 986 o he firs season 20. We idenify socks ranked by he loery index as he lowes 30 h percenile as non-loery socks, and he highes 70 h percenile as loery socks. Socks ha do no belong o loery and non-loery socks are defined as oher socks. The index is he loery index. Sd is idiosyncraic volaily. Skew is idiosyncraic skewness. Price is sock price. We assign all socks of lised firms each quarer o viginiles (semi-deciles) by sock price, idiosyncraic volaily, and skewness (where one is he lowes volaily and skewness groups, and he larges price group). Value is he naural log of marke capalizaion. Turn is share urnover. Lib is liabily divided by asse. Eps is earnings per share. Sale is sales growh. Re is sock reurn. BV is book-o marker raio. P-value denoes he difference beween loery sock and non-loery sock. Index sd skew price size urn lib EPS sale re bv Non-loery Oher loery Loery sock p_value Transion Probabily Of Loery Socks

5 Loery socks are defined o capure hree characerisics of small price, high idiosyncraic volaily, and high skewness. Because of he variaions of he hree gambling-relaed characerisics, loery sock candidaes likely vary over he period. Table 2 indicaes he ransion probabily of hree caegory socks ranked by he loery index. If a sock is idenified as a loery sock in quarer, here is 60% probabily ha he sock is also a loery sock in quarer. The probabily of he loery sock moving o anoher sock is approximaely 30%, bu he probabily for a sock o jump from a loery sock o a non-loery is he lowes of approximaely 8%. The oppose is found in non-loery socks. For a non-loery sock in quarer, here are 0% and 38% probabilies o move forward from a loery sock o anoher sock in quarer. A 45% probabily exiss for anoher sock in quarer o say in he same caegory as oher socks in quarer. The nex secion evidences he ransion probabily of hree caegory loery socks and examines wha characerisics drive he ransion. Table 2 Transion probabily of loery sock This able repors he ransion of hree caegories of loery sock during he hird season 986 o he firs season 20. Loery, oher, and non-loery are loery sock, oher sock and non-loery sock, respecively. Loery (+) Oher (+) Non-loery (+) Loery () Oher () Non-loery () Predicors Of Loery Socks Wha feaures conribue o a sock being a candidae for a loery sock? Table shows differen characerisics beween loery and non-loery socks; however, he characerisics of sock-level fundamenals and marke facors migh be a predicor of he loery sock. To deermine which characerisics are sronger predicors of loery socks, his work applies he [0] cross-secional regression esimaes o es wha feaures migh predic loery socks. We examine he predicion using he following regression model: LOTs = Sd + Re urn + Skew + BM + Pr ice + Lib + MValue + Eps + Turn + Saleg (3) The dependen variable is he index of loery socks (LOTs) for sock i in quarer. The independen variables in he regression specificaion in quarer include () hree gambling-relaed characerisics: volaily (Sd), skewness (Skew), and price (Price); (2) four marke variables: naural log of firm marke capalizaion (MValue), share urnover (Turn), sock reurn (Reurn), and book-o-marke raio (BM); and (3) hree firm fundamenals: liabily-o-asse raio (Lib), earnings per share (Eps), and sales growh (Saleg). Boh he dependen variable and he independen variables have been sandardized (he mean is se o zero and he sandard deviaion is one). Firs, we run he quarerly cross-secional regression and hen compue he mean value of he coefficien and es he significance. Table 3 shows he empirical resuls. For he 98 quarers, we find ha 93 coefficiens on he price variable ou of 98 quarers significanly and

6 posively associae wh loery socks. The higher he sock price index, he lower he sock price. The magnude of he mean coefficien on price is posive and significan a he % level. The evidence is consisen wh he definion of loery sock, and low-priced sock serves as a good candidae of loery sock. The resul is consisen wh he findings of [2]. The 79 coefficiens ou of 98 coefficiens on volaily are posive and significan a he 5% level. The mean of coefficiens on volaily is significan a he % level and heir sign is expeced, indicaing ha volaily also serves as a good characerisic o idenify a loery sock. Among he hree characerisics of loery socks, only seven of 98 quarers for he coefficien esimaes for skewness significanly and posively differ from zero a he 5% level and heir mean magnude is much smaller han he oher wo counerpars. The overall magnude of he coefficien on price is he larges among he hree characerisics of loery sock, and he small price is he cheapes wager o risk he gamble wh a small probabily of large gains. Our regression resuls sugges ha, for he coefficien esimaes of marke capalizaion, and 32 quarers of 98 quarers are significanly posive and negaive, respecively. The mean of coefficiens on marke capalizaion is negaive and saisically significan, suggesing ha small-cap socks are more likely o become loery sock in he fuure. From evidence provided in Table 3, only small-cap socks end o be a fuure candidae for loery sock. The oher hree marke variables have no capabily o predic loery sock. Among he hree firm fundamens, a sock wh high liabily implying high risk is more likely o serve as a fuure candidae of loery sock. Findings show a negaive mean coefficien for earnings per share and heir absolue magnude is approximaely riple ha of liabily, suggesing ha a firm wh high earnings is less likely o be a loery sock in he nex quarer. Table 3 Predicion of loery sock This able repors he predicion of loery sock during he hird season 986 o he firs season 20. LOTs is he loery index. The remaining variables are he same as Table. Mean is he average of he ime-series coefficien esimaes. Posive (negaive) is he number of posive (negaive) coefficiens esimaed quarerly. LOTs= Sd + Skew + Price + MValue + Turn + Lib + Eps + Saleg + Reurn + BM Sd Skew Price size urn Lib Eps Sale Re bv mean posive negaive p-value Because boh loery socks and heir explainable variables have been sandardized, is easy o compare he influence of each independen variable on he loery sock. In summary, among he hree firm fundamenals, he sronges saisical predicor for loery socks is earnings per share. The lower earnings a sock has, he more likely is o be a loery sock. However, marke capalizaion is he bes proxy of marke variables o predic loery sock. 3.4 Deerminans Of Reurn Co-Movemens In Loery Socks This sudy is moivaed by [2], who invesigaed wheher invesor gambling acivies

7 induce excess co-movemens in sock reurns. This subsecion examines he deerminans of reurn co-movemens wh loery socks. We firs compue he quarerly loery sock reurn co-movemen measures for each sock i by esimaing he following regression: Re R f = α + α RP + α SHM + α HML + α MOM + α LOTre + ε (4) The dependen variable is a daily risk premium for sock i in quarer. In addion o he four facor model of [5], he independen variables include he daily porfolio reurns of loery socks, which are idenified a he end of quarer. The main variable of ineres α from his regression is he reurn co-movemen measures for sock i relaed o he 5 porfolio reurns of loery socks. We esimae he bea α 5 quarerly using daily reurns where he reurn series used in he regression are sandardized so ha he co-movemen esimaes relaed o loery sock reurn indices can be compared wh oher independen variables ([22]). The findings of [22] sugges ha reurn co-movemens are sronger among socks ha have loery feaures and ha are locaed in regions where Caholicism is more prevalen. Individual invesors accouned for over 60% of he rading volume, whereas margin rades are only allowed for domesic individuals in Taiwanese marke. This sudy uses margin purchase raders as individual represenaives. To explore he preference of individual invesors oward loery sock, we employ he following regression specificaion o examine he reurn co-movemens of loery sock relaed o he chosen variable. The dependen variable, bea, comes from α5 in Eq. (4). LOTs denoes he index of loery sock. Ins (Ind) is he holdings of insuional invesors (individual margin raders). Remainders in he independen variables are he same of ha in regression (3). We run he following regression from he firs season of 997 o he firs season of 20, because he available daa ses conaining holdings of he insuional invesors begins from January 997. Bea = β LOTs 0 Saleg 5 0 Saleg MValue 6 Re urn LOTs Turn 2 7 * Ins BM Lib 2 3 LOTs Ins 8, 4 * Ind Eps Ind 9 (5) For oo many people, gambling is a simple form of enerainmen. Mos evidence suggess ha individual invesors prefer o gamble, whereas recen evidence indicaes ha gambling audes also influence insuional invesors ([22]). We apply regression (5) in he sock-level o examine reurn co-movemens wh loery sock. In he regression, he dependen variable is he co-movemen measure derived from regression (4) and we conrol for he direc effec of loery index and individual holdings (insuions), and firm fundamenals and marke variables in independen variables. Consisen wh he foregoing regression, we apply he [0] cross-secional regression esimaes o examine wha feaures migh commove wh loery socks. Boh he dependen variable and he independen variables are also sandardized. We are concerned wh he ineracion erms ( β 2 ) of loery sock (LOTs) and individual holdings (Ind); if individuals rade more loery sock, we expec β o be significanly posive. 2 Table 4 presens he resuls. The coefficien of he LOTs Ind ineracion erm in he

8 regression is highly significan and posive, indicaing ha co-movemens are sronges for loery socks raded by margin purchase raders. However, observaions also show ha he coefficien ( β ) on he ineracion erm (LOTs Ins) of loery sock and insuions is also highly significan bu negaive, suggesing ha insuional invesors do no exhib a greaer appee for loery socks. The absolue magnude of he join effec of loery sock and individual rading is larger han ha of loery sock and insuional rading, implying ha he effec of a gambling-induced sock on excess co-movemens is significanly sronger on individuals han insuions. In summary, individuals exhib a greaer appee for loery payoffs han insuions, a resul consisen wh he findings of [22], who documened ha reurn co-movemens are sronger among socks ha have loery feaures and ha are locaed in regions where people are more prone o gamble. Conrary o he findings of [22], among he conrol variables shown on Table 4, loery sock reurns co-move posively wh marke capalizaion and negaively wh urnover. Table 4 Deerminans of reurn co-movemen wh loery sock This able repors he deerminans of reurn co-movemens wh loery sock esimaed by following he regression during he firs season 997 o he firs season 20. The dependen variable is bea measures esimaed by Eq. (4). Ins ( mar) is he holdings of margin purchase raders (insuions). Index is loery index. The remaining variables are he same as Table. Mean is he average of ime-series coefficien esimaes. Posive (negaive) is he number of posive (negaive) coefficiens esimaed quarerly. Bea = β 0 LOTs 5 0 Saleg Saleg MValue Re urn 6 LOTs Turn 2 * Ins 7 BM 2 3 Lib 8 LOTs Ins, 4 * Ind Eps 9 Ind index size urn lib eps sale re bv ins mar index* index* mean posive negaive p-value ins mar 3.5 Excess Reurn Of Loery Sock [9] proposed a hree-facor model o capure he paerns in sock reurns associaed wh risk premium (RP), size (SMB), and value versus growh (HML). Aemping o capure momenum reurns (MON), [5] proposed a four-facor model for sock reurns. Loery sock capures he compose characerisics of small price, high volaily, and high skewness, no associaed wh SMB, HML, and MOM. This sudy examines wheher empirical asse pricing models should capure he excess reurn of loery sock, in addion o he four-facor model. The leraure ([6]; [8]) found ha invesors are willing o sacrifice heir reurns in he amoun of a loery premium, in exchange for low sock price. This work consrucs a value-weighed porfolio reurn 5, he reurn difference beween loery sock and non-loery sock porfolios in quarer. The leraure suggesed ha firm-size may serve as a proxy variable for various unobserved firm characerisics. The curren sudy sors firms in each quarer ino five groups based on heir marke capalizaion a he end of he prior quarer. We hen invesigae wheher he model, which includes he excess reurn of loery sock in addion o he Carhar s RP, SMB, HML, and MOM facors, can explain he cross-secion

9 reurns. All variables of he dependen variable and independen variables are sandardized. The parameer esimaes and es saisics are obained from he ime series of quarerly cross-secional regression esimaes as in [0]. The p-value for esing he significance of each coefficien is he p-value corresponding o he -saisic calculaed from he mean of he coefficien divided by s sandard error. Table 5 Excess reurn of loery sock This able repors he excess reurn of loery sock during he firs season 997 o he firs season 20. The dependen variable is he value-weighed porfolio reurn sored by marke capalizaion. RP is risk premium. SMB is value premium (small minus big). HML is value versus growh (high minus low). MOM is momenum reurns. LOT-NONLOT is he reurn difference beween porfolios of loery and non-loery sock. coe. is coefficien. Marke capalizaion RP SMB HML MOM LOT-NONLOT small high coe p-value coe p-value coe p-value coe p-value coe p-value Table 5 presens he empirical resuls. In addion o RP, SMB, and HML, we find ha he coefficiens on loery sock excess reurn are posive and significan a he 5% level among he five group socks classified by marke capalizaions. The absolue value of he coefficien of loery sock excess reurn is larges among he five explaining facors, while he momenum facor loses influence on he five group porfolio reurns. Loery sock excess reurn monoonically decreases wh marke capalizaion ranked by marke capalizaion of firms a he end of he prior quarer. The resul suggess ha he excess reurn of loery sock capures some characerisics no relaed o RP, SMB, HML, and MON. To check he robusness of he effec of excess reurn of loery sock on five sizes of porfolio reurns, we also consruc he equally weighed excess reurn of loery sock and find a very similar paern using his alernaive measure. 3.6 Do Individual Invesors Prefer Loery Sock During An Economic Downurn? Many researches assume ha noise raders do no rade based on firm fundamenals, bu in a herd-like manner. Individuals are generally considered as less informed han insuional invesors, and margin purchases examined in his paper may be viewed as imperfecly informed speculaive invesors ([27]). During an economic downurn, invesors migh become frusraed and pessimisic and more willing o allocae more wealh o gamble-relaed socks, which migh provide a possible fuure forune. If individual invesors wh srong gambling preferences discover he small possibily of a very large reurn, hey migh be

10 willing o allocae a larger porfolio of loery socks o eliminae povery, even hough loery socks are expeced o underperform. This work invesigaes he ime variaion in he aggregae demand for loery socks by esimaing he following ime-series regression model: EBSI = Mb + α2ms+ α3exp+ α4mp+ α5uemp+ α6pe+ α7 α Rp+ ε (6) The dependen variable (EBSI) in he regression (6) is he excess buy-sell imbalance of loery socks raded by margin purchase raders in a given quarer. EBSI is he buy-sell imbalance of a loery sock porfolio minus he buy-sell imbalance of a porfolio ha conains he oher wo caegories of socks (non-loery and oher socks). EBSI measures individual invesor preference oward loery socks relaed o he change oward he oher wo caegories of socks 6. The independen variables in he regression include he following macroeconomic variables ha may vary significanly over he business cycle: moneary aggregae (Mb), monoring indicaors (Ms), increased rae of expor (Exp), indusrial producion index (Mpi), unemploymen rae (Uemp), price-o-earnings raio (Pe), and hree monh defaul risk premium 7. All variables included in he regression are sandardized. The available daases reveal he holding of margin purchase raders used as proxy individuals, saring from he firs season 99; his sudy deec wheher individual invesors prefer loery sock during an economic downurn from he firs season 99 o he firs season 20. Table 6 Macroeconomic condion and loery sock demand This able repors he excess reurn of loery sock during he firs season 99 o he firs season 20. The dependen variable is EBSI. EBSI is he buy-sell imbalance of a porfolio of loery socks minus he buy-sell imbalance of a porfolio ha conains he wo caegories of socks (non-loery and oher socks). Mb is moneary aggregae. Ms is monoring indicaors. Exp is he increase rae of expor. Mpi is he indusrial producion index. Uemp is he unemploymen rae. Pe is he price-o-earnings raio. rp3m is he 3-monh defaul risk premium. coefficien low upper MB ligh expor MPI Uemp pe rp3m Table 6 repors he effec of economic downurn on individual invesor rading behavior. Only he coefficien on unemploymen rae is significan and posive a he 5% level, unlike he cases of oher independen variables. Our resuls are consisen wh he findings of [2]. The empirical resuls sugges ha individuals end o gamble during an economic downurn, implying ha hey are willing o risk earning a small chance of a huge gain a he expense of margin cos when hey are in economic sress. Loery-ype socks provide opions o

11 individual invesors wh he opporuny o enrich heir life in a declining marke. 3.7 The Effec Of Loery Sock On Marke Reurns And Volaily A common belief is ha invesing in he sock marke is more like gambling. If gambling was widely acceped and speculaion in he sock marke emerged, heir sysemaic shifs could be associaed wh higher volaily and lower average reurn. Tha is, loery socks raded sysemically by invesors migh influence sock marke reurns and volaily. The rading raionale of he speculaor, who buys an asse a a lower price and sells a a higher price, may sabilize he marke ([2]). On he conrary, posive feedback raders, who migh be irraional speculaors, will drive marke volaily. The evidence of [6] shows ha speculaive rading acivy hrough day rading increases inraday price volaily and exacerbaes such volaily if he price rises on a paricular day. [8] found no desabilizing effec of speculaion in he pos-world War II period or in he period prior o he 929 crash, only a relaion beween speculaion and volaily during This sudy focuses on he effec of loery sock, viewed as speculaive objecs, and non-loery sock on marke reurn and volaily. Table 7 Loery sock effec on marke reurn and volaily This able repors he loery sock effec on marke reurn and volaily during he hird season 986 o he firs season 20. Lore and nonlore are value-weighed loery and non-loery sock porfolio reurns quarerly, respecively. mr is marke reurn. urn is urnover. r= α + α lore + α nonlore + α log( h ) + ε ln( h ) = β 0 0 ( ε 2 h ) 2 3 [ ε h ] ln( h ) urn rlore nonlore 3 variable coefficien prob. coefficien prob. Mean 4 5 equaion α lore nonlore log h Variance equaion β ε / h ε / h ln h urn lore nonlore (mr>0)*lore (mr<0)*lore (mr>0)*nonlore (mr<0)*nonlore

12 To examine furher he effec of loery and non-loery sock reurns on marke reurns and volaily, he curren sudy consrucs quarerly value-weighed loery and non-loery sock porfolio reurns. A large volume of leraure has emerged on modeling and predicing volaily in financial markes because accurae volaily forecass of financial asses are crucial inpus for derivaives pricing. This work uses he ime-varying condional variance of reurn as he proxy for marke volaily and applies he EGARCH (,) process wh GARCH-in-mean o esimae marke volaily in his research. For no decomposing marke reurns ino posive and negaive, Table 7 shows ha value-weighed loery and non-loery reurns are significanly and posively associaed wh marke reurns in he mean equaion. No evidence suppors ha loery sock reurns could resul in marke volaily, or he desabilizing effec of loery sock on marke volaily. However, findings show ha non-loery sock reurns have a negaive effec on marke volaily in he condional variance equaion. As we furher decompose marke reurns ino up and down marke reurns, we find ha loery sock reurns could weakly exacerbae marke volaily during up marke periods. Our evidence does no compleely suppor irraional roles of loery sock, while he negaive effec of non-loery sock reurns on marke volaily is found during he up marke. Based on hese empirical resuls, he evidence suggess a sabilizing effec of non-loery sock on marke volaily. 4 Conclusion The sock marke has ofen been compared o gambling. This sudy invesigaes loery sock in he Taiwan Sock Marke and finds marke capalizaions and earnings negaively relaed o loery socks. The effec of gambling-induced sock on excess co-movemens is significanly sronger on individuals han on insuions. Consisen wh he findings of [2], our empirical resuls sugges ha individuals end o gamble during an economic downurn. Furher decomposion of marke reurns ino up and down marke reurns found ha loery sock reurns could weakly exacerbae marke volaily during up marke periods. The negaive effec of non-loery sock reurns on marke volaily is only found during an up marke, indicaing ha non-loery socks have a sabilizing effec on he marke. Insuional invesors increase he holdings of socks and loery sock favored only by individual invesors, and we will like o see he weak effec of loery sock on marke volaily. Reference [] Barber, B., Lee, Y.T., Liu, Y.J., Odean, T. Jus How Much do Individual Invesors Lose by Trading? Review of Financial Sudies, 2009, 22, [2] Barberis, N. & Huang, M. Socks as Loeries: The Implicaions of Probabily Weighing for Secury Prices, American Economic Review, 2008, 98, [3] Boyer, B., Mon, T. & Vorkink, K. Expeced Idiosyncraic Skewness, Review of Financial Sudies, 200, 23, [4] Brunnermeier, M. K., Gollier, C. & Parker, J. A. Opimal Beliefs, Asse Prices, and he Preference for Skewed Reurns, American Economic Review, 2007, 97, [5] Carhar, M. M. On Persisence in Muual Fund Performance, Journal of Finance, 997, 52,

13 [6] Chen, M. H., Chen, S. J., Yen, M. F. & Shen, Y. C. Loery Premium in he Taiwan Sock Marke, Asia Pacific Managemen Review, 2008, 3(2), [7] Doran, J. S., Jiang, D. & Peerson, D. R. Gambling Preference and he New Year Effec of Asses wh Loery Feaures, Review of Finance, forhcoming. [8] Downs, T.W. & Wen, Q. Is here a Loery Premium in he Sock Marke? Journal of Porfolio Managemen, 200, 28, 2-9. [9] Fama, E. F. & French, K. R. Common Risk Facors in he Reurns on Socks and Bonds. Journal of Financial Economics, 993, 33, [0] Fama E. & MacBeh J. Risk, Reurn, and Equilibrium: Empirical Tess, 973, Journal of Polical Economy, 8(3), [] Friedman, M. & Sayage, L. J. The Uily Analysis of Choices Involving Risk, Journal of Polical Economy, 948, 56(4), [2] Friedman, M. J. Essays in posive economics, 953, Chicago Universy, Chicago press. [3] Gao, X & Lin, T. C. Do Individual Invesors Trade Socks as Gambling? Evidence from Repeaed Naural Experimens, 20, working paper. [4] Garre, T. A. & Sobel, R. S. Gamblers Favor Skewness, No Risk: Furher Evidence from Uned Saes Loery Games, Economics Leers, 999, 63(), [5] Golec, J. & Tamarkin, M. Beors Love Skewness, no Risk, a he Horse Track. Journal of Polical Economy, 998, 06, [6] Hsin, C. W., Guo, W. C., Tseng, S. S. & Luo, W. C. The Impac of Speculaive Trading on Sock Reurn Volaily: The Evidence from Taiwan, Global Finance Journal, 2003, 4(3), [7] Jadlow, J. W. & Mowen, J. C. Comparing he Tras of Sock Marke Invesors and Gamblers, The Journal of Behavioral Finance, 200,, [8] Jones, J. D., Mulherin, J. H. & Tman, S. Speculaive Trading and Sock Marke Volaily, 990, working paper. [9] Kahneman, D. & Tversky, A. Prospec Theory: An Anialysis of Decision Making under Risk, Economerica, 979, 47(2), [20] Kumar, A. & Lee, C. M. C. Reail Invesor Senimen and Reurn Comovemens, Journal of Finance, 2006, 6, [2] Kumar, A. Who Gambles in he Sock Marke? The Journal of Finance, 2009, 44, [22] Kumar, A., Page, J. & Spal, O. Gambling and Comovemens, 20a, Working Paper. [23] Kumar, A., Page, J. & Spal, O. Religious Beliefs, Gambling Audes, and Financial Marke Oucomes, Journal of Financial Economics, 20b,02(3), [24] Markowz, H. M. The 'Two-Bea' Trap, Journal of Porfolio Managemen, 984, (), [25] Odean, T. Are Invesors Relucan o Realize heir Losses. Journal of Finance, 998, 53(5), [26] Saman, M. Loery Players/Sock Traders, Financial Analyss Journal, 2002, 58(), 4-2. [27] Sein, J. C. Informaional Exernalies and Welfare-reducing Speculaion, Journal of polical Economy, 987, 95, [28] Thaler, R. N. & Johnson, E. J. Gambling wh he House Money and Trying o Break Even: The Effec of Prior Oucomes on Risky Choice, Managemen Scinence, 990, 36, Gamblers and invesors share five ras: maerial needs, compeiveness, supersion, financial conservaism (negaive), and numeracy. They are differen on hree ras: presen-ime orienaion, emoional insabily, and impulsiveness.

14 2 The Public Welfare loery has been debued since s incepion in 2002 in Taiwan. 3 Kumar (2008) chose he 30 and 50 percenile o idenify loery socks. 4 For each variable, s ime-series average over he sample period is calculaed and esed for significance, using a sandard -es in he following form : a( rˆ) i = rˆ i ( σ (ˆ) ri / n), i=,2,3,n. where rˆ is he average of he i quarer-by-quarer variable σ ( rˆ i ) is he sandard quarerly deviaion of variable and n is he oal number of quarers. 5 The resuls are persisen when we consruc equal-weighed porfolio reurns. 6 According o he work of Kumar and Lee (2006), he buy-sell imbalance (BSI) of he loery sock n (non-loery and oher socks) porfolio in given quarer is defined as BSI= 00 ( i = BSI i ) / n, where j= ij ij j= d d BSI = ( ( B S )) /(( ( B + S ))). d is he number of days in a given quarer, B ij is he buy volume (measured in i ij ij dollars) for sock i on day j in quarer, S ij is he sell volume for sock i on day j in quarer, and n is he number of socks in loery sock (non-loery and oher socks) porfolio. 7 Three-monh defaul risk premium denoes he ineres rae of a commercial paper of 90 days minus he hree-monh erm depos ineres rae.