Relationship between stock index and increments of stock market trading accounts

Transcription

1 Relaionship beween sock index and increens of sock arke rading accouns Zhenlong Zheng, Yangshu Liu Zhenlong Zheng, a professor fro Deparen of Finance, Xiaen Universiy, Xiaen, Fujian, 6005, China. E-ail: zlzheng@xu.edu.cn, el.: Yangshu Liu, a aser suden fro Deparen of Finance, Xiaen Universiy, Xiaen, Fujian, 6005,China. E-ail:Lajishu.suden@sina.co Absrac. In his paper, we pay aenion o he relaionship beween sock index and increens of rading accouns in A, B share arke and funds. We show ha here exiss bilaeral relaionship beween A, B index and heir rading accouns increens. However, Granger causaliy only exiss fro sock index o increens of funds accouns. Regressions show ha he invesors senien will be easily driven by he index in he sae direcion, which iply oenu sraegy in a very shor period. In coparison, when using weekly daa, only increens of funds accouns Granger cause he sock index. These uncover he differences beween fund anagers and sall invesors while invesing on sock arke. We also analyse he relaionship beween index volailiy and rading accouns volailiy. Keywords: sock index; increens of rading accouns; invesors senien ; oenu sraegy Inroducion According o efficien arke hypohesis(faa, 970[]),in a weak-for efficien arke, hisory of sock price can no help o anicipae fuure rend of sock price. So how sock arke perfors in he pas should no affec he rading accouns increens significanly. However, if he sock arke perforance has significan influence on daily or weekly rading accouns increens, we can conclude ha his arke is no weak-for efficien, and ay exis a phenoenon of herd behavior(shiller, 995[6]),which also esed o be exised in China (Jiang e al., 00[8]), or he sall invesors eploy soe sraegies on opening he rading accouns, say, oenu or conrarian. Considering shor sale is sill forbidden in China sock arke, increase of rading accouns increens iplicae capial inflow and sall invesors opiisic perspecives on fuure sock arke, which will probably resul in furher rise of index. So our sudy is oivaed by he curiosiy on he relaionship beween index and increens of rading accouns. There were soe

2 papers working on hese fields. Che(00)[9] and Zhu(000)[5] boh found a posiive relaionship beween he sock index and he increens of rading accouns in China sock arke. Che(00) [9]chose 04 daily daa sapling fro Augus s 000 o Deceber 9 h 000 and eployed a siple linear ie series regression o receive a coefficien which sugges a high correlaion beween he index and increens of rading accouns. Bu Che s approach was unsable since his daa ranged oo shor and did no consider he inerrelaion and affecion of lag effec. Zhu(000)[5] chose 9 onhly daa ranged fro January 999 o July 000 and also used a siple linear regression o receive a posiive correlaion which had alos a siilar proble wih Che(000)[9]. Zhan(00)[0] believed a high volailiy of China sock arke would lead o a high volailiy of accouns increens, bu he did no do epirical sudy on he relaionship of volailiy. Wih regard o rading sraegy, Jegadeesh and Tian(99)[4] firs noice he oenu effec in heir sudy on he reurn of winner and loser s porfolio. On he oher hand, DeBond and Thaler(985)[] find evidence on conrarian as hey exa he arke in a longer horizon. None have pay aenion on wheher he siilar effecs exis on he rading accouns, which igh be a very iporan quaniy o reveal he view of hose who are sill ouside he arke, especially in China, where shor selling is prohibied. Our priary conribuions are analyzing he relaionship beween Hushen 00 index, B index and increens of rading accouns in A, B share arke and funds arke hrough Granger causaliy es. Moreover, we find evidences ha he invesors in China are easily affeced by he recen perforance of index, which sugges ha here exiss a oenu effec on opening new rading accoun. We illusrae he econoics inuiion in deail, uncovering differen rading sraegies beween sall invesors and fund anagers. Firs of all, we find ha here exiss close relaionship beween A, B index and daily increens of rading accouns on A, B share arkes. Our epirical sudies show ha here exiss bivariae causaliy beween Hushen 00 index and daily increens of A share arke, which also exiss beween B index and daily increens of B share arke (Fig ). Bu causaliy disappears when we use weekly daa (Fig ). These consequences provide indirec evidences ha os of he sall invesors pursue oenu sraegies when invesing on A,B share arke because hey choose o creae new rading accouns iediaely afer sock index grows. Alhough i is no surprising ha he increens of rading accouns will affec sock index, since shor sale is prohibied in China sock arke, he ipacs of he new invesors on he sock index igh be plausible. Because capial flows no only coe fro he new incoer, hey also coe fro he forer invesors. As a resul, i is hard o judge wheher he forer invesors ay share he sae ideas wih he new incoers. So is i o heir invesen direcion. Secondly, here exiss a significan Granger causaliy fro Hushen00 o daily increens of funds rading accouns when our epirical sudies use daily daa (Fig ), bu his causaliy fade as we use weekly daa (Fig ), which is consisen wih he epirical resul on Hushen 00 index and increens of A share arke. This resul conveys ha he seniens of funds invesors are also significanly affeced by Hushen00 index. As index increases, sall invesors hold opiisic views on fuure, so hey will choose o inves on eiher sock arke or funds iediaely.

3 And we pay aenion o anoher ineresing consequence ha daily increens of funds accouns provide no help o predic index (Fig ). I ay be caused by differen rading sraegies beween sall invesors and fund anagers. Alhough sall invesors creae new funds accouns when sock index rise, heir fund anagers are no likely o inves on he sock arke a once. Bu funds will affec he sock index in a longer horizon, he effec which we esed wih weekly daa is significan lagged for ~4 weeks, and i ay be consisen wih he anagers sraegies on revising porfolios wih a uch larger aoun of capials han which owned by sall invesors. Moreover, we wan o esiae in deail how invesors seniens are affeced by he index. Thus, besides Granger Causaliy es, we regress he increens of rading accouns direcly on he sock index. I shows ha he seniens of hose who have no paricipaed in he arke will be influenced iediaely by he sock index in a surprisingly shor period. And he resul also iplicaes slighly differences beween he characerisic of sall invesors iediaely invesing on sock arkes and heir counerpars invesing on funds (Fig ).A las, we analyse B index wih Granger causaliy es and variance decoposiion o find ou how uch he increens of B share rading accouns will affec B index (Fig 4). The reason why we choose B share arke is ha B share arke is less liquid han A share arke, and os inforaion will efficienly affec A share arke ore iediaely han B share arke. So we suppose A index as an agen of inforaion, and increens of B share rading accouns as an agen of capials enering ino B share arke, and use A index as a conrol variable. The epirical resuls, including Granger causaliy es (Fig 4) and variance decoposiion, boh show ha A index and increens of B share rading accouns have significan effec on B index (Fig 4). Epirical sudy We do epirical sudy o provide evidence for our forer discussion, and we ainly eploy Granger causaliy es and Variance decoposiion inroduced as followed.. Granger causaliy es Granger (969)[] proposed a odel o es he bivariae dynaic relaionship beween wo variables, which is expressed as Y = αiy i + βix i + u () i= i= ' In equaion (), Y and X represen X = wo λiy variables, i + θix i + and u here ay exis causaliy beween i= i= he. If β, β, β, β are significan differen fro 0,hen X Granger cause Y. If θ, θ are significan differen fro 0,hen Y Granger cause X. If boh β, β, β, β and θ, θ are significan differen fro 0,hen here exiss bilaeral relaionship

4 beween X and Y, or hey are boh affeced by anoher variable Z. If β, β, β, β and θ, θ boh are insignifican saisically, hen here exiss no causaliy beween X and Y.. Variance decoposiion Sis(980)[7] provided a ehod o analyse variance of VAR odel, which is expressed as Equaion () is a VAR (Vecor Auo regression) Z = [ Y, X ]', e = [ ε ε ]' y, x Z = A + AZ + e () 0 i i i= Z EZ = e + Ae + A e A e () n + n + n + n + n + n + Equaion () gives n-period forecas errors of Z Y EY = φ (0) ε +... φ ( n ) ε + φ (0) ε +... φ ( n ) ε (4) + n + n y+ n y+ x+ n x+ σ ( n) = σ [ φ (0) + φ () +... φ ( n ) ] + σ [ φ (0) + φ () +... φ ( n ) ] (5) y y x Fro equaion (4) and (5), we can find ha σ () is equal o a weighed su of σ and σ y n y x. Epirical resul Liiing by daa on increens of rading accouns, our daa spans fro May 8 h in 006 o Jan h in 008, conaining 44 observaions. In his period, China sock arke obviously presens a bull arke. Hushen00 index rise fro 8.44 poin o poin, and a he sae ies A share rading accouns, B share rading accouns and funds accouns have increased by 57.6%, 44.97% and 85.09% respecively. We give he epirical resuls lagged 8 periods. There are a leas wo suppored reasons: Firsly, SIC and HQ es show ha we should choose odel which lag less han 8 periods; Secondly, wih daily daa, 8-period lag can already cover he lag effec in las one and a half week, while, wih weekly daa, we can es our hypohesis in abou las wo onhs. So even if we can find saisically significan influences for ore han 8-period lag, i is no convinced ha, for shor horizon invesors, heir seniens will be affeced heavier by he index ore han week before han he index jus in las week, which is uch ore scepical in weekly es. Wha s ore we find heir coefficiens significances deflae quickly along wih lag periods afer he peak value. Due o hese wo reasons enioned above, we only give 8-period lag resuls. However, we acually do epirical sudies on ore han 8-period lags and do no find significan differences.

5 Fig repors daily relaionship beween index and increens of rading accouns. x A represens logarih growh of daily increens of rading accoun on A share arke. x B represens logarih growh of daily increens of rading accouns on B share arke. x F represens logarih growh of daily increens of funds rading accouns. r A00 denoes daily logarih reurn of Hushen00 index. r B represens daily logarih reurn of B index. And he nubers in Fig are probabiliies ha we can no deny H 0 of Granger causaliy es (H 0 is he original hypohesis ha he independen variable X provides no help o predic dependen variable Y). Fig : Daily relaionship beween index and increens of rading accouns Fig shows us ha index has a significan ipac on invesors rading accouns including A,B share and funds rading accouns, while he increens of A,B share rading accouns affec A,B index significanly on soe lags. Differen fro sall invesors rading accouns, increens of funds accouns do no have a significan ipac on he index. This resuls show ha index can easily affec invesors seniens, and sall invesors ay ake a oenu sraegy in shor periods. In coparison, fund anagers adop oally differen sraegies fro sall invesors. The x reason ha one-period lag of F is significan ay be caused by opiisic psychological influence fro new funds. x Fig repors weekly relaionships beween index and increens of rading accouns. AW represens logarih growh of weekly increens of rading accoun on A share arke. x BW represens logarih growh of weekly increens of rading accoun on B share arke. x FW represens logarih growh of weekly increens of funds rading accoun r denoes weekly A 00 W log reurn of Hushen00 index. r BW represens weekly log reurn of B index. And he nubers in Fig are also probabiliies we can no deny H0 of Granger causaliy es (H0 is he original hypohesis ha he independen variable X provides no help o predic.

6 Fig : Weekly relaionship beween index and increens of rading accouns Fro Fig, we can find he weekly relaionship beween index and increens of rading accouns are very weak. Index changes in his week do no affec invesors seniens in nex week, which is reasonable ha invesors seniens can only be affeced by he neares rading days. And Fig also ells us ha increens of sall invesors do no ipac he index on a longer horizon. However, increens of funds accouns will significanly affec index in he nex ~4 weeks. These resuls provide cues on fund anagers rading sraegies ha hey consruc heir porfolios in longer periods coparing wih sall invesors. The phenoena ay be caused by he wo facs: Firsly, fund anagers should anage grea volues of oneys and hey us consider he liquidiy when consrucing heir porfolios. Secondly, fund anagers pursue differen sraegies fro sall invesors, such as conrarian sraegy or index replicaion sraegy. Fig repors how sock index will affec invesors seniens in deail. The variables are he sae as above, and ra ( i), rb ( i) represen he ih lag of logarih reurn of A and B index respecively. The lag ers are chosen according o Schwarz Inforaion Crierion. NA eans ha he corresponding lag er is no chosen according o SIC. Fig : Regression of increen of sock arke rading accoun on he sock index

7 Fig ells he consequence of hree linear regressions on daily daa. Fro he able, we can find he invesors seniens will be significanly affeced by he perforance of he las days and ha day when hey open he rading accouns. The posiive and significan coefficiens deonsrae ha sall invesors will end o open new rading accouns when he sock index rise, and vice versa if he sock index fall down. The sligh differences beween consequence of regressions on invesors direcly invesing on A,B sock arke and hose who inves on funds announce ha invesors planned o ener ino A,B sock arke are influenced uch easier by he exree shor ers perforance, which are no ore han wo days in he able; heir counerpars who inves on funds ay reac o he index in few days lag, which igh be ore conservaive. We also ipose siilar regressions on he weekly daa, and all he paraeers are insignifican wih a very low level of R-square. The resul proves our discussion indirecly ha he senien of invesors only be affeced in a very shor period. Fig 4 repors how B share rading accouns and A index will affec B index in Shanghai sock exchange. r AS represens logarih reurn of A index in Shanghai sock exchange. Oher variables are he sae as above. Fig 4: Explain B index by increens of B share rading accouns and A index Fig 4 shows ha increens of B share rading accouns and A index in Shanghai sock exchange will significanly affec B index in Shanghai sock exchange, which is proved boh by Granger causaliy es and variance decoposiion. Bu in deail, we find ha wih variance decoposiion increens of B share rading accouns and A index in Shanghai sock exchange provide only a os 5% explanaion o B index in Shanghai sock exchange. And he par of explanaion does no increase significan even we add ore lags. This resul shows ha due o arke pariion, B index and A index face differen risk, and wheher B share arke will incor-

8 porae ino A share arke ay be a os iporan cause. Anoher possible reason is ha new invesors on B sock arke have less influence han he forer ones, as hey igh be araced only by he reurns of B index while lack he knowledge of risk in B sock arke.. Conclusions Afer sudying on he relaionship beween A,B index, increens of rading accouns in A,B and funds arkes, we receive hree iporan conclusions. Firs of all, here exiss bilaeral relaionship beween A, B index and heir rading accouns increens. Index significanly affecs invesors seniens, especially in a very shor period. This evidence denoes ha hose who incline o inves direcly on A,B share arke are likely o pursue oenu sraegy o creae new rading accouns. And invesors invesing on funds pursue a siilar sraegy on opening he rading accouns, alhough hey igh be a lile ore conservaive. Generally speaking, all sall invesors incline o pursue oenu sraegy o creae new rading accouns, Secondly, Hushen00 index Granger causes daily increens of funds accouns. However, weekly increens of funds accouns Granger cause Hushen00 index. These iplicae he differen rading sraegies beween sall invesors and fund anagers. Sall invesors are very likely o consruc heir porfolios as soon as hey creae new rading accouns, bu fund anagers revise heir porfolios in he nex ~4 weeks afer receiving hose funds fro heir cliens. Thirdly, alhough A index and increens of B share arke rading accouns affec B index significanly, increens of B share arke rading accouns can provide no ore han 8% explanaion o volailiy of B index. References. De Bond W. F. M. and Thaler R., "Does he Sock Marke overreac?"[j], The Journal of Finance 40(985) Faa, E. F., Efficien Capial Markes: A Review of Theory and Epirical Work, The Journal of Finance 5(970) Granger, C. W. J., Invesigaing Causal Relaions by Econoeric Models and Cross-specral Mehods, Econoerica 7(969) Jegadeesh,N., Tian, S. Reurns o buying winner and selling loser: Iplicaion for sock arke efficiency, The Journal of Finance,vol XLVIII, No.(99) Mach, Ke Zhu, Correlaion beween index and increens of rading accouns on Shanghai and Shenzhen sock exchange, Shanghai Invesen (000) Shiller, R. J., Conversaion, Inforaion, and Herd Behavior, The Aerican Econoic Review85(995) Sis, C. A. Macroeconoic and Realiy, Econoerica 48(980) Xuelei Jiang, Min Chen, Guofu Wu, The ARCH Model and is Epirical Analysis of Herding Behavior on he Chinese Sock Marke, Maheaics in Pracice and Theory (00) 56-6.

9 9. Xuan Che, Sudy on he quaniive relaionship beween sock arke and increens of rading accouns, Saisics Science & Pracice (00) Yubo Zhan, Relaionship beween Invesors of Chinese Sock Marke and Vibraion of Sock Marke, Journal of Chongqing Insiuion of Coence (00) 4-4.