Investor sentiment of lottery stock evidence from the Taiwan stock market

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1 Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 Yu-Min Wang (Taiwan) Chun-An Li (Taiwan) Chia-Fei Lin (Taiwan) Invesor senimen of loery sock evidence from he Taiwan sock marke Absrac This paper examines wheher loery feaures preference impacs reurns and volailiy of Taiwan lised sock. The work employs he idiosyncraic price and idiosyncraic volailiy (Kumar 9) which measure sock wih loery feaures. Our empirical resuls show ha in regions wih higher disracion affec he sock reurn more han low religion s. Moreover a rise or fall in invesor senimen does affec sock volailiy paricularly he bullish senimen. The paper showed ha he invesor senimen plays an imporan role for capuring he reurns and volailiy in he financial marke. Keywords: senimen loery sock gambling. JEL Classificaion: G1 G14. Inroducion Since he radiional financial heory canno illusrae he process of financial asse pricing many researchers have begun o examine he behavior of invesors. And he mos efficacious index measure of invesor senimen is currenly used wihin he financial markes. In he prior sudies on he effecs of invesor senimen here has ended o be a general focus on he relaionship beween invesors and he sock marke. Addiionally previous sudies have emphasized he poenial role of gambling in invesmen decisions (e.g. Shiller 1984; Shefrin and Saman ; Saman ; Barberis and Huang 8). The exan evidence from loery sudies indicaes ha he heavies loery players are poor young and relaively less educaed single men. Therefore our main conjecure is ha invesor senimen effec is differen in loery-ype socks. We hope his aricle can be provided o individual invesors as invesmen reference. We begin our ess wih he Taiwan sock marke and we employ measure of loery sock following Kumar (9); low sock price high idiosyncraic reurn volailiy and high idiosyncraic reurn skewness. From he Dorn e al. (9) we forgo he idiosyncraic skewness because many company characerisic variables are unavailable. The loery-ype socks have very low prices relaive o he highes poenial payoff hey have low negaive expeced reurns heir payoff is risky and hey have an exremely small probabiliy of a huge reward. Wih his moivaion we use he empirical definiion of loeryype socks o observe invesor senimen effec. The empirical resuls provide evidence of srong spillover effec beween he senimen and loery-ype sock. Yu-Min Wang Chun-An Li Chia-Fei Lin 1. Our paper would like o help clarify he channel by which invesor senimen influences sock prices. Baker and Wurgler (6) show invesor senimen disproporionaely affecs he prices of socks ha are small and exhibi exreme growh or disress which hey aribue o more subjecive valuaions and limis o arbirage. Kumar (9) shows ha loery-ype socks are overweighed in porfolio of reail invesors bu no in hose of insiuional invesors. Green and Hwang ( found ha i is he loery-like feaures of hese socks combined wih a sronger preference for skewness among cerain invesors ha leads o overpricing during periods of high invesor senimen. Overall our sudy would like o improve he relaion beween invesor senimen and financial marke ha adoping he concep of loery-ype socks. The remainder of his paper is organized as follows. Secion 1 presens a discussion of he daa source and he empirical model adoped for his sudy. The empirical resuls and he impac of invesor senimen are presened in secion wih he conclusions drawn from his sudy being presened in he final secion. 1. Daa and mehodology 1.1. Daa source. We use he daily closing price and oher variables of Taiwan lised company from he Taiwan Economics Journal (TEJ) daabase covering he period from 3 January 1 o 31 Ocober 1. Taiwan s sock marke is manly made up by domesic individual invesors who consiued abou 67.95% of marke volume in 1. And Chui and Wei (1998) found ha Taiwan marke has he larges sandard deviaion of monhly excess reurns among he Pacific-Basin emerging markes. Timan and Wei (1999) aribue his phenomenon probably o he invesor senimen. As shown above hese peculiar characerisics in Taiwan s sock marke enable us o es he prevalence of invesor s behavior. Form Kumar (9) hen we would measure 3

2 Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 loery feaures wih logarihmic price and idiosyncraic volailiy. We forgo he expeced idiosyncraic skewness because many firm characerisic variables are unavailable. Sock price is a measure a he end of he rading day. I use sock price as one of he defining of loery-ype socks he invesors would look for relaive cheap bes. Idiosyncraic volailiy is he sandard deviaion of residual reurns from a CAPM model of daily reurns. High idiosyncraic volailiy inflaes he percepion of he chance o realize high reurns hus aracing sock marke gamblers. Following Ang Hodrick Hodrick Xing and Zhang (6) i is defined as he sandard deviaion where 1 residual reurns are esimaed from he Fama and French (1993) hree-facor model. And hen we consider all Taiwan socks and assume ha socks in he lowes (highes) % sock price and he highes (lowes) % idiosyncraic volailiy are likely o be consruced a loery-ype sock or high religion loery socks (unloery-ype sock or low religion loery socks). The invesor senimen index was consruced by Wang e al. (6) and Simon and Wiggins (. In he sudy we adop hree proxies o measure he invesor senimen on he Taiwan sock marke. BS Buy-Sell Imbalance ( B ) ( ABS Margin lending on funds Margin Lending Raio () Margin lendingon securiies Volume 3 Turnover Raio %. (3) Shares Ousanding The firs senimen indicaor is buy-sell imbalance (B ). The B (S ) denoes he buy (sell) value of insiuional invesors on day. BS denoes B S and ABS is he average of B S wih B being posiive (negaive) when he invesor group buys (sells) more securiies han i sells (buys) on day. And he margin lending raio is anoher measure of spo marke senimen. If he marke becomes bullish hey would lend on funds more han lending on securiies. Turnover raio or liquidiy he raio of rading volume o he number of shares lised on he Taiwan Sock Exchange is a simple proxy for his concep and can be considered as an invesmen index. Baker and Sein (4) argue ha if shorselling is coslier han opening and closing long posiions irraional invesors are more likely o rade and hus add liquidiy. More generally Scheinkman and Xiong (3) recommend volume reveals underlying difference of opinion. Table 1 presens he descripive saisics abou excess reurn and he senimen daa. Following Table 1. Descripive saisics Ang Hodrick Hodrick Xing and Zhang (6) we divided all Taiwan socks ino five equal pars. And he paper assume ha socks in he lowes (highes) % sock price and he highes (lowes) % idiosyncraic volailiy are likely o be consruced a loeryype sock (unloery-ype sock). As repored in Panel A of Table 1 he high religion loery sock have 31 companies. The average price is 11 dollar/per share. And he low religion loery sock coss probably 3 dollar/per share i has 15 companies. This sudy shows ha low loery shares mosly well-known and radiional indusries socks in he Taiwan sock marke. In addiion he able shows all of indices being lepokuric and also displaying excess kurosis. I is necessary o adop he GARCH model for he disribuions which effecively encompasses he feaures of asymmery and fa ails. The asymmeric volailiy of invesor senimen is explained by he Glosen Jagannahan and Runkle GJR-GARCH model. Our sudy measures senimen and loery-ype socks a daily frequencies. Indices Mean Max. Min. Sd. dev. Skewness Kurosis Jarque-Bera a Panel A. High religion loery sock (31companies) Ri.1% 9.5% -8.43% *** Price *** S *** S *** S *** 4

3 Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 Table 1 (con.). Descripive saisics Indices Mean Max. Min. Sd. dev. Skewness Kurosis Jarque-Bera a Panel B. Low religion loery sock (15companies) Ri.77% 6.76% -7.86% *** Price *** S *** S *** S *** Noes: a The Jarque-Bera (JB) es concludes normaliy (or a criical value of 5%) and he series are lepokuric. *** Indicaes significance a he 1% level. 1.. The GJR-GARCH model for he loery-ype sock of invesor senimen. To analyze he effecs of invesor senimen in he Taiwan sock marke we propose a GJR-GARCH(1 model and we hen model invesor senimen as follows: r h (4) ( 4 1 h I 1 ) h 3 (5) N( h ) (6) ~ where is he spillover effecs of he reurns which explains how invesor senimen affec reurns in he spo marke; and i is he error erm which follows normal disribuion. Equaion (5) is he variaion equaion where ( I 1 = 1 if 1 and () I 1 = if 1 > ; we expec o measure he bad news causing he volailiy effec. In general when senimen in he spo marke is higher his can raise he overall level of confidence in he financial marke. Thus in he presen sudy we expec o find a significanly posiive coefficien on invesor senimen in he loery or unloery sock. We use ( ) o measure he volailiy of invesor senimen and Var( ) as he second momen measure of noise rader risk. Since he mean of he change in senimen is close o zero he variance of he change in senimen can be approximaed by ( ). The coefficien of 4 capures he senimen effec of he magniude of he shifs in he loery or non-loery sock marke on volailiy formaion wihin he fuures marke. The above models all describe he same period The asymmeric volailiy of invesor senimen for he loery-ype sock. Wih a rise or fall in invesor senimen here will be corresponding flucuaions in he sock marke; his is because such flucuaions allow invesors o avoid risk more easily and hereby increase heir profis. An examinaion of his opic has already been underaken by Lee e al. (); we also include his opic in our discussion. r h (7) h 1 1 h 3 4( ) D -1 5( ) (1 D - I (8) N( h ) (9) ~ D 1 in equaion (8) is a dummy variable where ( D 1 = if 1 ; and () D 1 = 1 if 1 >. The coefficiens ( 4 5 ) in he condiional volailiy equaion capure he effecs on volailiy from he magniude of he shifs in senimen.. Empirical resuls and analysis For he high religion loery sock and low religion loery sock we esimae a base model ha includes senimen as an explanaory variable in he mean and condiional volailiy equaions. The esimaed coefficiens of he GJR-GARCH models are repored in Table. The major findings are summarized below. Firs we find ha invesor senimen is an imporan facor in explaining reurns and changes in condiional volailiy. In he mean equaion for each of he wo religion sock indices a shif in senimen has a significan posiive impac a 1% level on sock reurn. For example an increase of 1 percenage poin in high religion loery sock senimen is associaed 3 wih 1.1 percenage poin increase in sock reurns. We also find ha he magniude of he percenage change in senimen has a significan impac on he formaion of condiion volailiy paricularly on he urnover raion. Bullish shifs in senimen in he curren period resul in saisically significan posiive in he volailiy of sock reurns. The magniude of he percenage change N senimen does appear o lead o alike revisions in volailiy. However he magniude of he change in senimen causes he larger revisions in volailiy for he high religion loery sock. 5

4 Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 Table. Invesor senimen spillover effecs Panel A: High religion loery sock Panel B: Low religion loery sock Variables (.1993).1 (.83).1 (.)*** (.9)***.1498 (.16)***.499 (.78)***.5994 (.435)*** -3.5*1-7 (5.86*1-8)***.68 (.17)*** -.48 (.6)*.7768 (.4)***.197 (.5)***.99 (.)***.3 (.6).8811 (.19)***.15 (.16)*** Noe: The resuls are based upon he following model: R.14 ( (.4) 1.8 (.8***.878 (.68)***.144 (.8)***.197 (.35)***.88 (.6)***.913 (.45)*** h.711 (.159)***.14 (.36).3 (.)***.9 (.3***.948 (.5)***.68 (.34)**.8879 (.)*** -4.14*1-7 (.*1-8 )***.8 (.158)***. (.38).3158 (.34)***.991 (.3)***.91 (.5)***.174 (.34)***.888 (.)*** -. (.3).467 (.154)***.76 (.37)**.799 (.1***.117 (.38)***.137 (.9)***.171 (.39)***.864 (.5)***.419 (.37)*** h 1 I 3h 4 ( ~ N( h ) where he equaion for h is he condiional variance of residuals. measures he fuures marke reurns associaed wih daily shifs in senimens. is he error erm. I 1 is he dummy variable o measure bad news or good news. measures he bad news (or good news) causing he volailiy effec. ( 1 ) measures he volailiy of invesor senimen. The figures in parenheses are sandard errors; * indicaes significance a he 1% level; ** indicaes significance a he 5% level; and *** indicaes significance a he 1% level. Wih a rise or fall in invesor senimen wihin he sock marke we expec o find differen volailiy effecs being discernible. As shown in Table 3 a rise or fall in invesor senimen does affec sock volailiy paricularly he bullish senimen. The regression resuls for high religion loery sock are repored in Panel A of Table 3. Srikingly he senimen coefficien esimaes are all posiive and saisically significan a he 1% level. The resuls from variance regressions indicae ha he 4 are all posiive and saisically significan a 1% level. This suggess ha an increase in senimen of good news wih a subsequen increase in sock reurns. From he 5 Panel B of Table 3 repors he same resuls as Panel A of Table 3. However i appears he sronger effec in he high religion loery sock han low religion loery sock. Table 3. Invesor senimen asymmeric spillover effecs Panel A: High religion loery sock Panel B: Low religion loery sock Variables (.173)*** -.67 (.5).14 (.)***.5 (.56)***.153 (.3)*** -.77 (.9)***.8741 (.***.5*1-7 (8.15*1-8)*** -4.79*1-8 (6.8*1-8).695 (.17*** -.5 (.6)**.7911 (.5***.178 (.48)***.886 (.19)*** -.1 (.6).8893 (.17)***.465 (.35)*** (.*** -.44 (.149).83 (.3)*** 1.66 (.84)***.679 (.63)***.118 (.7)***.11 (.33)***.894 (.5)***.769 (.117)*** (.54)***.78 (.159)***.18 (.36).3 (.)***.93 (.3***.951 (.6)***.4 (.34).889 (.)*** -3.5*1-7 (3.11*1-8)*** -6.11*1-7 (3.33*1-8)*** -.6 (.15).119 (.13).3536 (.45)*** (.149)***.97 (.55)*** (.75)*.4667 (.199)*** -.16 (.6)*** -.14 (.13)***.377 (.154)**.94 (.36)***.818 (.11***.116 (.36)***.11 (.9)***.171 (.38)***.867 (.5)***.118 (.*** (-.353)*** Noe: The model incorporae he effec of changes in invesor senimen as measured by. Dummy variable D 1 and (1 D are used o indicae he direcion of changes oward more bullish and bearish senimen respecively. 1h h 1 I 3h 4( D 5( (1 D ).In addiional 4 and 5 capure he effec of he magniude of shifs in senimen on he volailiy. ** and *** denoe significance a 5% and 1% level. The numbers in parenheses are sandard errors. 6

5 Given he above resuls he change in senimen ends o be more significan in high religion loery sock han he low religion loery socks. These resuls indicae ha he magniude of he loery premium is incremenally affeced by he gambling propery. Conclusion This aricle examines he invesor senimen impac of loery sock in Taiwan. We firs separaed wo loery socks high religion and low religion sock. In doing so i exends he radiional analysis o examine wheher loery sock has increased sock reurns by considering he issue of volailiy and asymmeric. Reference Invesmen Managemen and Financial Innovaions Volume 9 Issue 1 We use religion as a proxy for loery sock and examine wheher loery sock affecs sock reurns. We focus on Taiwan lised company which he exising lieraure has suggesed he role of gambling as loery sock. Our resuls indicae ha in regions wih higher disracion affec he sock reurn more han low religion s. Furhermore he asymmeric models capure he momenum effecs. The models ha furher allow vary wih invesor senimen can ofen capure he impac of good news and bad news on volailiy. Overall he evidence suggess ha invesor senimen plays an imporan role for capuring he sock reurns especially obvious in he loery sock. 1. Ang A. R.J. Hodrick Y. Xing and X. Zhang (6). The cross-secion of volailiy and expeced reurns Journal of Finance 61 pp Baker M. and J.C. Sein (4). Marke Liquidiy as a Senimen Indicaor Journal of Financial Markes 7 pp Baker Malcolm and Jeffrey Wurgler (6). Invesor Senimen and he Cross-Secion of Sock Reurns Journal of Financial 61 pp Barberis Nicholas and Ming Huang (8). Sock as Loeries: The implicaion of Probabiliy weighing for securiy prices American Economic Review forhcoming. 5. Dorn Daniel and Paul Sengmueller (9). Trading as Enerainmen Managemen Science forhcoming. 6. Fama E.F. and K.R. French (1993). Common risk facors in he reurns on socks and bonds Journal of Financial Economics 48 pp Green T.C. and B.H. Hwang (9). IPO as Loeries: Expeced Skewness and Firs-day reurns Working paper Available a SSRN. 8. Kumar A. (9). Who gambles in he sock marke? Journal of Finance forhcoming. 9. Lee W.Y. C.X. Jiang and D.C. Indro (). Sock Marke Volailiy Excess Reurns and he Role of Invesor Senimen Journal of Banking and Finance 6 pp Scheinkamn Jose and Wei Xiong (3). Overconfidence and speculaive bubbles Journal of Poliical Economy 111 pp Shefrin H. and M. Saman (). Behavioral Porfolio Theory Journal of Financial and Quaniaive Analysis 35 () pp Shiller R.J. (1998). Human Behavior and he Efficiency of he Financial Sysem in J. Taylor and M. Woodford (eds.) Handbook of Macroeconomics NBER Working Paper No Simon David P. and Wiggins Roy A. (. S&P fuures reurns and conrary senimen indicaors Journal of Fuures Marke 1 (5) pp Saman M. (). Loery players/ sock raders Financial Analyss Journal 58 pp Wang C. (. Invesor Senimen and Reurn Predicabiliy in Agriculural Fuures Markes Journal of Fuures Markes 1 ( pp Wang Y.H. A. Keswani and S.J. Taylor (6). The Relaionships beween Senimen Reurns and Volailiy Inernaional Journal of Forecasing pp