The Theory of Optimal Dividend Policy: An Intertemporal Approach and Empirical Evidences

Transcription

1 The Theoy of Opmal Dvdend Polcy: An Ineempoal Appoach and Empcal Evdences Mng-Jang Weng, Mn-Shann Tsa and Jyh-Ln Wu We popose a heoecal model of opmal dvdends based on mcofoundaon o nvesgae he elaonshps beween a fm s expeced seam of fuue ne eanngs and changes n sockholdes equy o he smoohng componen of he dvdend polcy. The sgnalng effecs of changes n equy and of dvdend polcy o he expecaons of he fuue ne eanng seam ae hen dscussed and esed. Empcal fndngs usng HP and C Bank s quaely daa n he pas decade povde obus suppo fo he heoecal pedcons of acual changes n sockholdes equy and o he smoohng componen of cash dvdends. JEL classfcaon: C; G3; G35 Key wods: dvdend smoohng, ne eanngs, sgnalng heoy, VAR Assocae Pofesso, Depamen of Appled Economcs, Naonal Unvesy of Kaohsung, Tawan. Coespondence addess: 7 Kaohsung Unvesy Rd., Nan-Tzu Ds., Kaohsung 8, Tawan. Phone: , Fax: , E-mal: mjweng@nuk.edu.w. Asssan Pofesso, Depamen of Bankng and Fnance, Naonal Ch Nan Unvesy, Tawan. E-mal: mssa@ncnu.edu.w Pofesso, Depamen of Economcs, Naonal Chung Cheng Unvesy, Tawan. E-mal: ecdjlw@ccunx.ccu.edu.w

2 Inoducon Dvdend polcy has been confusng o fnancal eseaches fo que a long me. Concepually, manages seem o pefe eanng eanngs n ode o educe fnancal coss of new nvesmen oppounes. Howeve, fms always declae dvdends, whch cause a educon n useful capal, bu hey smulaneously pay hghe coss o ssue new socks o bonds n he make o fund new nvesmens. Sgnalng heoy s commonly used o explan hese confusng aspecs of dvdend polcy. Snce manages possess che nfomaon of he fm s fuue eanngs han ousde nvesos, hen a fm wh a geneous dvdend polcy sgnalng bee busness pospecs wll usually pesen a hghe sock pce n he make. In addon, publc and/o fund manages may efe o he dvdend polcy o deemne he qualy of he company due o s nfomaon conens (Mlle and Rock, 985). The make pce wll hen pomply eac o a fm s dvdend decsons. Theefoe, a company wh hghe dvdends wll see a bee sock pce. Anohe useful vewpon of sgnalng heoy ndcaes ha a fm s announcemen of an ncease n dvdends wll cause a posve abnomal eun, snce may mply ha he manage s opmsc abou he fm s fuue eanngs. Mach and Meon (987) and Kao and Wu (994) poposed a aonal sgnalng model o nvesgae he nfomaon conens of dvdends. The model shows ha dvdends

3 ae smoohed accodng o he condons of he manage s expecaons of fuue eanngs. A numbe of sudes dd fnd evdence suppove of sgnalng heoy (Hggns, 987; Dvecha and Mose, 983; John and Wllams, 985; Mlle and Rock, Ba-osef and Huffman, 986). Empcal esuls suppo sgnalng heoy, bu he economec specfcaon s peplexng n he exsng leaue on dvdends. In addon, adonal sgnalng heoy only used dvdend smoohng o nvesgae he nfomaon conens and explan he phenomenon of dvdend declaaons, wheeas, s had o deemne f he dvdend polcy s opmal fo shaeholdes. The man pupose of hs pape s o complee he heoy of economc sense of dvdend polcy. We deduce a model of opmal dvdend polcy by ulzng an neempoal appoach. Ou model no only explans he dvdend saus as addessed n exsng sgnalng models, bu also ndcaes f he dvdend polcy s opmal. As n fnancal heoy, egadless of wha he fnancal decsons ae, he manage s pupose s always o maxmze he dvdend-based uly (o wealh) of shaeholdes. Snce dvdends ae he mos mpoan faco of wealh ansfeed fom a fm o shaeholdes, hen a dvdend polcy model needs o seously ake shaeholdes' uly no accoun. In ou specfcaon, he manage needs o desgn he dvdend polcy so as o maxmze he epesenave shaeholdes lfeme uly unde he neempoal escons of he fm s eques and eanngs. We hen show ha he 3

4 opmal dvdend polcy depends on he manage s expecaon of fuue ne eanngs, oppouny coss of he company s endowed eques, nees aes, and shaeholdes uly paamee,.e., he me pefeence. Snce he manage s expecaon of fuue ne eanngs as saed n hose sgnalng models s one of he facos nfluencng opmal dvdend polcy, he man mplcaon of adonal sgnalng models can be adequaely deved and nepeed by ou model. Howeve hee ae some dffeences beween ou model and adonal sgnalng heoy. In adonal sgnalng heoy, he age dvdend s smoohed accodng o he condons of he manage s expecaon of fuue eanngs. In ou model, he opmal dvdend polcy depends on he expecaon of fuue ne eanngs nsead, and ou heoy also consdes he equed euns (oppouny coss) of he nal equy nvesmen. Tha s, f a fm expecs posve fuue eanngs, bu hey wll be less han he equed payoff on he nal equy, hen should lowe s dvdend snce has a negave fuue ne eanng. Ths may explan why a fm mgh possess posve fuue eanngs, bu sll declae a lowe dvdend and have a lowe sock pce n he make. In addon, ou model ndcaes ha he opmal dvdend polcy wll be geae (o less) han he smoohed dvdend accodng o f he me pefeence of shaeholdes s less (o geae) han he nees ae, whch means sockholdes ae mpaen (o paen) abou ecevng a cash dvdend f he ousde 4

5 nvesmen envonmen s ho (o cold). Snce ou opmal dvdend polcy s based upon maxmzaon of shaeholdes' uly, we can fuhe es f a fm s manage has eally made opmal dvdend decsons ove me by lookng a he empcal dvdend saeges. We hen vefy he heoecal fndngs wh an empcal sudy of HP (Hewle-Packad) and C Bank. The economec eamens of empcal ess of he pesen-value model, ognally developed by Campbell (987) and Campbell and Shlle (987), allow us o map he heoy-oened pedcons o he acual changes n equy. Ths pape s oganzed as follows. In secon, we pesen he heoy of he neempoal appoach o dvdend smoohng, followed by a bef noducon o economec pocedues n esng he pesen-value model n secon 3. In secon 4, he VAR (veco auoegesson) esmaon of he model s pesened usng HP and C Bank s quaely daa ove 99Q-Q, due o he avalably of he daa esouces. In secon 5, conclusons ae summazed. The Model We exend he neempoal model o decsons of opmal dvdend polcy n copoae fnance. The neempoal appoach was fs poposed n he 98s by Bue (98), Sachs (98), Svensson and Razn (983), and Obsfeld (986), and 5

6 has been well appled o seveal aeas of nenaonal fnancal eseach, such as capal mobly, consumpon smoohng, and he valdy and susanably of heoecal foecass of acual cuen accouns (e.g., Sheffn and Woo, 99; Oo, 99; Ghosh, 995a; Ghosh and Osy, 995; Cashn and McDemo, 998; Begn and Sheffn, ). The mehod has also been appled o sudes of bond pces (Campbell and Shlle) and n dealng wh ax smoohng/govenmen defcs (Huang and Ln, 993; Ghosh, 995b). The scenao of ou model s pesened below. Consde a epesenave fm n whch a change n he fm s equy can be nepeed as eanngs mnus dvdends,.e., as eaned eanngs n peod. The eaned eanngs hus ae defned as eanngs afe axes and deb mnus dvdends. The manage s facng an neempoal equy consan, n pe capa ems, as follows, S S S S D RE () whee S denoes he equy a he begnnng of me ; s he make sk-fee nees ae; s he fm s ne eanngs (.e., eanngs afe axes, deb, and equy nees dung peod ); D s he cash dvdend o be deemned and dsbued pe shae a he end of me ; and RE s he fm s eaned eanngs. Theefoe, S can be vewed as he equed eanngs,.e., he so-called oppouny cos, of a 6

7 fm wh an nal collecon of nvesmen. can hen also be nepeed as S he excess eanngs fom. S Now, he manage has o deemne how much of a cash dvdend pe shae should be poposed o he boad of decos so as o fulfll sockholdes expecaons. Theefoe, we assume hee exss an nfnely-lved epesenave sockholde whose lfeme uly, U, known o he manage, a me s gven by, U E β ( D ) u, () whee u(), he nsananeous pefeence, s assumed o epesen nceasng and concave n cash dvdends, D,.e., u () >, u <. β, he subjecve dscoun () faco whch anges fom o, means ha ules ae valued lowe, he lae hey ae eceved. E ndcaes he expecaon of a aonal sockholde based on all nfomaon avalable o dae. Tha s, he manage consdes no only shaeholdes myopc sasfacon abou he nvesmen euns, bu also he long-un comfo of dvdend flow; n ohe wods, he fm s pospecs of fuue developmen ae consdeed as well. Heen, we fuhe assume ha nfomaon on ne eanngs,, ae exogenously gven o he manage when makng a decson abou he cash dvdend (see Nakamua and Nakamua, 985). Fowad eaon of equaon () wh he ansvesaly 7

8 condon held gves us, p p S S D D ) ( E ) ( E, (3) whee and ae defned as he pemanen dvdend and pemanen ne eanngs (analogous o Nakamua and Nakamua), especvely. Equaon (3) hus saes ha he expeced dscouned seam of he dvdend, o he pemanen dvdend, mus equal he expeced sum of he dscouned fuue ne eanngs (.e., pemanen ne eanngs) plus equed eanngs (.e., nal nees clams on eques). The opmzaon poblem faced by a fm s manage now s o maxmze n equaon (), subjec o he neempoal equy consan of equaon (). Wh no Ponz game p D p U assumpon and a CRRA (consan elave sk aveson) fom of he uly funcon,.e., ( ),, > σ σ σ D D u whee s he elascy of neempoal subsuon, uns ou ha he opmal dvdend polcy necessaly follows σ : [ ] p p D S S D θ θ θ ) ( E, (4) σ β σ θ ) ( ) ( 8

9 whee D denoes he opmal pah fo he cash dvdend, and θ eflecs he dvdend-lng effec. Equaon (4) ndcaes ha he opmal cash dvdend o be dsbued s popoonal o he pemanen ne eanngs,.e., he pemanen seam of expeced ne eanngs, plus s equed euns. Ths dffes fom adonal sgnalng heoy n wo ways. Fs, even hough equaon (4) s analogous o Kao and Wu s elaon beween he age dvdend and pemanen eanngs, he age dvdend s smoohed accodng o he condons of he manage s expecaon of fuue eanngs; howeve, n ou heoy, he opmal dvdend polcy depends on he expecaon of fuue ne eanngs nsead. Second, equaon (4) also consdes he oppouny cos of nal equy holdngs. Tha s, even convenonal sgnalng models ely on a smla agumen of pemanen eanngs, bu lack consdeaon of he equed euns fom he peexsng sock of equy. Ths mples ha a fm should lowe s dvdends even hough expecs posve fuue eanngs ha ae less han he equed payoff on he nal equy. Moeove, fom θ, we know ha f β ( ρ), whee ρ s he sockholde s ae of me pefeence, hs ( ) mples θ, whch n un saes ha he dscepancy beween he objecve make ae of nees,, and subjecve ae of me pefeence,, deemnes whehe ρ he fm s manage chooses a paen of pe capa cash dvdends whch ls owads he pesen p p ( θ < D ) o he fuue ( > ) > D θ D < D. If θ,.e., 9

10 D p D, hee s no lng componen o he dvdend, meanng ha he dvdend s smoohed. In ohe wods, D wll be geae (o less) han he smoohed dvdend, D θ, as θ < (>),.e., as ρ > (<), whch means ha he sockholdes ae mpaen (o paen) abou acqung he cash dvdend. Combnng equaons () and (3) gves us S S p p S ) ( D D ) (5) ( Equaon (5) shows ha changes n equy esul fom wo componens. The fs s he dvdend-smoohng move, whch sablzes dvdends n he face of shocks o ne eanngs, ha s, he epesenave sockholde egads changes n equy as a buffe o smooh dvdends n he face of shocks o he ne eanng seam. The second componen s he dvdend-lng move, wheeby he manage ls he dvdend owads he pesen o fuue, dependng on he elave magnudes of shaeholdes subjecve dscoun ae and he make objecve nees ae. In ode o emove he dvdend-lng effec, we hen defne he assocaed opmal change n equy unde dvdend smoohng as: S S θd p. (6) Then, wh some manpulaon 3 we end up wh S E ( ), (7)

11 whee. Equaon (7) expesses changes n equy as he negave sum of he dscouned pesen value of expeced fuue changes n ne eanngs. Ths mples ha a fm wll gan n equy only f expecs s flow of ne eanngs o fall n he fuue, whch means ha a aonal manage wll save fo a any day (.e., lowe he cash dvdend) when expecng he fm s pospecve pofs o declne, and vce vesa. The nuon behnd equaon (7) s que saghfowad. A fm s manage wll popose a sngy dvdend polcy (.e., ean moe eanngs now) f he/she foesees ha he fm s ne eanngs wll wosen n he fuue. Ths esuls n an ncease n he equy, whch gves us a useful applcaon o sgnalng heoy. Once a fm s equy nceases (.e., s savng moe eanngs n s own pocke), he make wll hen ake as a sgnal, o wanng, o pedc ha he fm may pof less n he fuue, and vce vesa. Theefoe, he opmal smoohed dvdend,.e., whou he lng effec, can be easly shown o be θ D S E. (8) ( ) Ths means ha he cuen opmal smoohed dvdend depends no only on boh he equed and excess eanngs n hs peod bu also on expecaons of fuue pefomance of excess eanngs. Moe pecsely, a aonal fm should no make s dvdend polcy only by lookng a s cuen eanngs. Theefoe, he opmal smoohed dvdend should even be negave when expecng a declnng ne eanng

12 seam, alhough some posve ne eanngs and equed eanngs exs. Economec Pocedues n Esmang he Opmal Dvdend Flow Fom equaon (7), we know ha he cuen change n equy seves as a good pedco of he fuue ncome seam of ne eanngs. Theefoe, n dscussng whehe o no he change n equy s opmal, we can also jusfy a fm s dvdend polcy ove me. In ode o esmae hs opmal change n equy, we hen ulze echnques developed by Campbell o fs esmae an unesced p-h ode of VAR n and S as follows, ( L) b( L) ( ) ( ) v L d L S v a o Z ΦZ V, (9) S c x p ( L) x j L j j, x a, b, c, d and L s he lag opeao, whee S s he acual dvdend-smoohng componen of he change n equy as n equaon (6) 4. Fo smplcy, we assume ha p fo lae devaon of economec pocedues fo he pesen-value model, bu wll poceed o choose an opmal p-h ode of VAR wh some cea when pefomng he empcal sudy. v and v ae dsubances wh condonal means of zeo; and Z [ S ]' and Φ ae he anson maces of he p-h ode VAR. We can now dscuss he mplcaons of equaon (9) fo he VAR sysem. One mplcaon s ha S mus

13 negavely Gange-causes,.e., b <, accodng o he dscusson and equaon (7). The sgnalng effec can hus be esed. Then he -peod-ahead expecaon on Z s smply ( Z ) Φ Z E. ( ) [ ] E ( Z ) [ ] Φ Z Theefoe, E. The nfne sum n equaon (7) s hus 5 S [ ] Φ I Φ S [ ] Γ Γ S, () S whee I s a ( ) deny max, and vaables wh he ha-lke ccumflex ndcae esmaes. Ŝ s ou model s pedcon of he change n equy 6 ha wll be compaed o he acual dvdend-smoohng componen of he change n equy, S, n equaon (6). Theefoe, o evaluae he pefomance of he VAR model of equaon (9), we need o oban he esmaed coeffcen max Φ, hen plug no equaon () o calculae Γ Γ ] and es he hypohess [ ] [ ]. If [ S Γ Γ S we accep he hypohess ha ou model s pedcon of he change n equy s equal o he acual opmal change n equy, S, hen we can conclude ha he fm has an opmal dvdend polcy ove me. Moeove, boh he heoy-based model 3

14 pedcon of smoohed dvdend and he acual smoohed dvdend can hen be compued. Fnally, we may compae he sandad devaons of pedced and acual (dvdend-smoohng) changes n sockholdes equy and smoohed dvdend as well o quanfy he flexbly of equy movemens and dvdend polcy, especvely. Empcal Evdence Quaely daa fom 99Q o Q fo boh HP and C Bank wee used o jusfy he heoecal model s pedcon of he changes n equy o he acual sees. All daa ae fom COMPUTSTAT and ae expessed n pe capa ems,.e., pe shae. The sample peods chosen ae based on he avalably of nfomaon n COMPUTSTAT as nepeed n secon. An aveaged annual make nees ae of 5%,.e.,.5% quaely, was calculaed usng US dscoun aes ove he nvesgaon peod fom he Inenaonal Fnancal Sascs (IFS). Fuhe deals on he consucon of all sees ae specfed wheneve needed n he followng dscusson. The fs sep n he analyss s o vefy f S and D ae nonsaonay,.e., I(), and conegaed. Table I shows un-oo es sascs fo seveal sees whch ae used n he esmaon pocedue. Nex, we have o oban an esmae of θ n equaon (6) n ode o consuc he (saonay) dvdend-smoohng componen 4

15 of he change n sockholdes equy by emovng he non-saonay componen of he acual sees assocaed wh dvdend lng. Fom Table I, S and he sees boh exhb saonay a he 5% and D % sgnfcance levels fo HP, especvely; neveheless, hese wo sees ae nonsaonay fo C Bank a he 5% sgnfcance level. The OLS (odnay leas squaes) egesson can hen gve an effcen esmae of he lng effec fo HP; on he ohe hand, he conegaed elaonshp beween S and D fo C Bank, heefoe, was esmaed usng Phllps and Hansen s (99) FM (fully modfed) coecon mehod; he esuls ae abulaed n Table II. The advanage of he FM pocedue (ove use of OLS) s ha hypohess ess based on he FM egesson ae asympocally nomal when vaables encouneed nonsaonay. Thus we can fomally es f θ o jusfy he exsence of dvdend-lng effecs. In Table II, he OLS esmae of he dvdend-lng effec fo HP,.848, s no sgnfcanly dffeen fom uny; howeve, he smple es of θ s ejeced a he % sgnfcance level fo C Bank (θ 4.46 ), whch means ha hee exss no dvdend lng effec fo HP, bu C Bank s dvdend dsbuon may l owads he fuue. The LC es sasc of Hansen (99) fo he null hypohess of conegaon beween S and fo C Bank s.849, whch confms ha conegaon does exs n C Bank. Moeove, Hansen s sably ess of he consan paamee n C Bank s FM conegang egesson, FM D θ OLS 5

16 show he conssen nfeence wh LC es; he mean-f and sup-f ess fo he null of sable θ enfoce ha he conegaed elaonshp beween S and D s faly sable fo C Bank. In ohe wods, HP has dsbued adequae cash dvdends of s pemanen seam of ne eanngs o s shaeholdes. On he conay, C Bank s dvdend polcy has been oo consevave ove me, n ha has dsbued smalle cash dvdends of s pemanen flow of ne eanngs o s shaeholdes han should have due o s pecepon of bleak pospecs. These evens may have esuled fom he hsocal oulook of HP whch has been confden abou he bus of e-busness and h-ech nduses snce 99s, whle, a he same me, C Bank was on he bnk of collapse n 99 due o he fall of he eal esae make and o loans o oubled Lan Amecan naons whch soued. The esmaon esuls shown above sugges a spuous long un elaonshp beween S and fo HP, heefoe, s acual dvdend-smoohng D componen of he changes n equy s jus he dffeence beween hem. Howeve, C Bank s esuls enable us o ake he esduals fom he FM conegang egesson of S on D as he acual dvdend-smoohng componen of he changes n equy. Havng he acual dvdend-smoohng componen of he changes n equy and he ne eanng seam sees fo boh fms n hand 7, we ae able o un he VAR esmaon descbed n he pevous secon, excep ha he VAR eques ha saonay vaables be used. Founaely, as epoed n Table I, boh he dffeences n neempoal ne eanngs,, and acual changes n equy, S, ae saonay a leas a he 5% sgnfcance levels fo HP and C Bank, especvely; heefoe, hey ae qualfed fo use n geneal VAR esmaons. 6

17 Anohe poblem n pefomng VAR s he choce of an opmal lag ode; we efeed o Akake s Infomaon Ceon (AIC), and he Schwaz Bayesan Ceon (SBC) o selec he opmal lag lengh fo he VAR esmaon. Table III ndcaes que conssen selecon of he VAR() model usng AIC and SBC fo boh HP and C Bank. We heefoe epo he fs-ode VAR sascal esuls and daw conclusons based on hem. A summay of VAR esuls s gven n Table IV. The especve sandad eo coeffcens of he VAR esmaons ae epoed n paenheses. Fs, he sgnalng effec dscussed n he pevous secon eques a negave b n he Φ max (efe o equaon (9)). The VAR esmaes of b ae and fo HP and C Bank, especvely, whch ae negavely sgnfcan a he % sgnfcance level, and boh ae conssen wh ou model s pedcon of he sgnalng effec. Tha s, he null hypohess ha S negavely Gange-causes canno be ejeced, whch mples ha f a fm makes a consevave cash dvdend pe shae hs me due o pessmsc expecaon abou s fuue, wll ean moe eanngs and esul n a hghe level of equy now,.e., S >. The make, hen, wll ake as a wanng sgnal ha hs fm may pof less fom s busness n he fuue, and vce vesa. Ths n un geneaes he pefec f of expeced changes n equy o he acual sees (Fg. ) and close pedcons of expeced smoohed dvdends o acual ones (Fg. ) fo boh HP and C Bank. Moeove, he fomal ess by he Wald sascs 8 epoed n Table V fo he escon of [ ] [ ] can no be ejeced a he 5% sgnfcance level fo boh HP and C Bank whch conclude he ousandng pefomance of ou heoecal modelng and empcal sudes. Γ Γ S Fnally, n Table V, he esmaed coeffcen max, Γ Γ [ S ], fo boh HP and 7

18 C Bank ae que close o [ ]. Ths has been confmed by he Wald sascs fo he fomal es of he coeffcen escons mpled by he pesen-value elaonshp,.e., equaon (), whch says ha boh fms VAR esmaon acks he dynamc behavo of he changes n equy pecsely. The coelaon beween he acual and pedced sees of changes n equy eaches.9999 and.999 fo HP and C Bank, especvely. Ths s que obvous fom Fg.. We hen compued he ao of he vaance of S o ha of S. The acual changes n equy fo HP wee abou % of volaly elave o he sees geneaed fom he heoecal model esmaon. In ohe wods, hs says ha he acual changes n sockholdes equy mgh have flucuaed moe han hey wee supposed o dung he me peod beng nvesgaed. Noneheless, he volaly almos pefecly fed he case of C Bank. Fnally, coelaons beween he acual and pedced smoohed dvdends ead.9748 and.9996 fo HP and C Bank, especvely. Ths can also be confmed by he pefec fness shown n Fg.. The aos of he vaance of acual smoohed dvdends o ha of model s pedcon ae.998 fo HP and.33 fo C Bank, whch mples ha boh fms have mplemened opmally flexble polces egadng smoohed dvdends ove me. Conclusons The man pupose of hs pape was o develop a heoy of dvdend smoohng by ulzng an neempoal appoach and hen o jusfy he heoecal pedcon usng HP and C Bank s quaely daa fom 99Q o Q. In secon, we povded a heoy of dvdend smoohng based on he mcofoundaon of a epesenave agen model. The model hen poduced que 8

19 plausble esuls specfyng he elaon beween he opmal dvdends and pemanen ne eanngs, and s an mpoan applcaon of sgnalng heoy. In ode o judge f he heoecal mplcaons of he heoy of dvdend smoohng ae obus, secons 3 gave a full dscusson of economec pocedues fo esng he heoecal fndngs. In secon 4, he empcal esmaon was mplemened usng HP and C Bank s quaely daa n a fs-ode VAR. Fom he empcal fndngs fo boh HP and C Bank, we showed ha he heoy s fully paccal. Ou heoy-based VAR esmaon of dvdend smoohng povded a sascally confden pedcon of he dynamc behavo of he acual changes n sockholdes equy and he smoohng componen of cash dvdends. 9

20 Table I: Phllps-Peon Tess fo Un Roos HP C Bank S D S Noe: The second and hd columns epo he un oo ess fo HP and C Bank, especvely. s he equy; s he make sk-fee nees ae; S s he fm s ne eanngs; D s he cash dvdend. The Newey-Wes auomac uncaon lag selecon fo Phllps-Peon (PP) equals Inege{4(T/) /9 }3, whee Inege{} s he Gauss funcon, and T s he numbe of obsevaon. Nehe consan no me end s ncluded n he PP esng egesson. and means es sasc sgnfcan a he 5%, and % sgnfcance levels, especvely. MacKnnon ccal values fo ejecon of hypohess of a un oo a he 5%, and % sgnfcance levels ae -.95, and -.63, especvely. Ths able ndcaes ha S, D and exhb saonay fo HP, hen OLS egesson s used n geneang Table II. On he ohe hand, S, D and exhb nonsaonay fo C Bank, heefoe, he FM (fully modfed) coecon mehod s used n poducng Table II.

21 Table II: Esmaon fo Cash-Dvdend lng Effecs ( θ ) HP (OLS) C Bank (FM OLS) θ ( value fo H : θ ).848(-.35) 4.46 (7.895) LC es N/A.849 Mean-F N/A.3845 Sup-F N/A.9486 Noe: and means es sasc sgnfcan a he 5%, and % sgnfcance levels, especvely. The second ow s he es esul fo he null of θ. θ s he dvdend lng effec and s esmaed fom followng equaon: S θ D ε The OLS esmae of θ can sgnfcanly ejec θ fo HP (.848 ). Howeve, he null of θ s ejeced by he FM esmaon a he % sgnfcance level fo C Bank ( 4.46 ). Theefoe, hee exss no dvdend lng effec fo HP, bu C Bank s dvdend dsbuon may l owads he fuue. The hd o ffh ows ae he conegaon es esuls beween S and fo C Bank. LC es s based on Hansen (99) fo D θ FM H: a conegaed elaonshp (5% and % ccal values ae.575 and.898, especvely). Mean-F and Sup-F ae based on Hansen (99) as well fo H : conegang veco s sable (5% and % ccal values fo Mean-F ae 4.57, 6.78, and Sup-F ae.4, 6., especvely). Nehe consan no me end s ncluded n FM esmaon. The LC es sasc s.849, whch means he θ OLS conegaon does exs beween S and D fo C Bank. The mean-f and sup-f ess confm ha hs conegang elaonshp s sable.

22 Table III: Deemnaon of Opmal Lag Lengh n VAR Esmaon HP C Bank Lag AIC SBC AIC SBC Noe: : ndcaes he mnmum value of AIC o SBC amongs all lag lenghs. We efeed o Akake s Infomaon Ceon (AIC), and he Schwaz Bayesan Ceon (SBC) o selec he opmal lag lengh fo he VAR esmaon. Ths able ndcaes que conssen selecon of he VAR() model usng AIC and SBC fo boh HP and C Bank.

23 Table IV: VAR Resuls fo HP and C Bank HP C Bank S S.53 (.58) (.37).437 (.4) (.69) S.43 (.58).7569 (.36).96 (.5). (.8) Noe: s he change of equy n heoy; s he change of fm s ne S eanngs. VAR() model s used fo boh HP and C Bank, S a c b d S v v. Sandad eos ae n paenheses, (), unde esmaes., and mean ha es sascs ae sgnfcan a he %, 5%, and % sgnfcance levels, especvely. Nehe consan no me end s ncluded n VAR esmaon. The VAR esmaes of b ae and fo HP and C Bank, especvely, whch ae boh negavely sgnfcan a he % sgnfcance level. Then he null hypohess ha S negavely Gange-causes canno be ejeced fo boh fms, whch s conssen wh ou model pedcon of he sgnalng effec. The make, hen, wll ake oday s S as a wanng sgnal of he fm s fuue pof pospec on,.e., f S > (<), fms may pof less (moe) n he fuue. 3

24 Table V: Ohe Sascs fo he Pesen-Value Models HP C Bank Γ Γ ] [.64.94] [ ] [ S Wald[d.f.].3667[].673[] Coelaon(, Ŝ ) S Coelaon(θ D,θ D ) Va Va ( S ) Va ( S ).8.4 ( θ D ) Va ( θ D ) Noe: Γ Γ ] s he coeffcen max n equaon (), [ S Ŝ Γ Γ SS. The null hypohess fo he fomal es of he heoy s [ Γ Γ S ] [ ]. Wald es sascs fo he null ae epoed n he hd ow, whch show he null can no be ejeced a he 5% sgnfcance level fo boh HP and C Bank, whee χ degees of feedom ae n [ ]. Theefoe, we conclude ha ou heoecal modelng and empcal sudes pefom que successfully. Coelaons beween acual and pedced sees of changes n equy ae shown n he fouh ow, and each.9999 and.999 fo HP and C Bank, especvely. The aos of he vaance of S o ha of S ae epoed n he sxh ow and ndcae he 4

25 acual changes n equy fo HP wee abou % of volaly elave o he sees geneaed fom he heoecal model esmaon. Ths says ha he acual changes n sockholdes equy mgh have flucuaed moe han hey wee supposed o dung he me peod beng nvesgaed. Noneheless, he volaly almos pefecly fed he case of C Bank. Fnally, coelaons beween he acual and pedced smoohed dvdends ae shown n he ffh ow and ead.9748 and.9996 fo HP and C Bank, especvely. The aos of he vaance of acual and pedced smoohed dvdends ae shown n he sevenh ow, whch ae.998 fo HP and.33 fo C Bank. I says ha boh fms have mplemened opmally flexble polces egadng smoohed dvdends ove me. 5

26 Fgue : HP and C Bank s Acual and Pedced Changes of Equy (pe shae) HP's acual and pedced Changes of Equy.3. Changes of Equy Q3 93Q Acual sees Pedced sees 93Q3 94Q 94Q3 95Q 95Q3 C Bank's acual and pedced Changes of Equy 96Q 96Q3 97Q 97Q3 98Q 98Q3 99Q 99Q3 Q Q3 Q Q3 Q. Changes of Equy Q3 93Q Acual sees Pedced sees 93Q3 94Q 94Q3 95Q 95Q3 96Q 96Q3 97Q 97Q3 98Q 98Q3 99Q 99Q3 Q Q3 Q Q3 Q Noe: Ths n un follows he empcal sudes nepeed above and geneaes he pefec f of expeced changes n equy o he acual sees fo boh HP and C Bank. We showed ha he heoy s fully paccal. 6

27 Fgue : HP and C Bank s Acual and Pedced Smoohed-Dvdend (pe shae) HP's acual and pedced Smoohed Dvdend...8 Acual sees Pedced sees Smoohed Dvdend Q3 93Q 93Q3 94Q 94Q3 95Q 95Q3 96Q 96Q3 97Q C Bank's acual and pedced Smoohed Dvdend 97Q3 98Q 98Q3 99Q 99Q3 Q Q3 Q Q3 Q Smoohed Dvdend Q3 93Q Acual sees Pedced sees 93Q3 94Q 94Q3 95Q 95Q3 96Q 96Q3 97Q 97Q3 98Q 98Q3 99Q 99Q3 Q Q3 Q Q3 Noe: Ths also follows fom he empcal pefomance saed above, and heefoe geneaes he close pedcons of expeced smoohed dvdends o acual ones fo boh HP and C Bank. We concluded ha he heoy s fully paccal. Q 7

28 Mahemacal Appendx Devaon of equaon (7): Fom he defnon of ha p, F F F F E ) ( E p whee F denoes he fowad opeao, Equaon (6) can hen be ewen as,,,..., F ) ( E F F F F p D S S θ ) ( E ) ( E. (7) Devaon of equaon (): Fom equaon (7) and he fac ha, we hen have, ( ) [ ] Z Φ E [ ] Φ ) ( ) E( ) ( Z S [ ] [ ] Φ Φ Φ ) ( S I Z [ ] S S Γ Γ, whee [ ] [ ] Φ Φ I Γ Γ S.() 8

29 Refeences Ba-osef, Sasson and Lucy Huffman (986), The nfomaon Conen of Dvdend: a Sgnalng Appoach, Jounal of Fnancal and Quanave Analyss,, Begn Paul R. and Seven M. Sheffn (), Inees Raes, Exchange Raes and Pesen Value Models of he Cuen Accoun, The Economc Jounal,, Bue, Wllem H. (98), Tme Pefeence and Inenaonal Lendng and Boowng n an Ovelappng Geneaons Model, Jounal of Polcal Economy, 89, Campbell, John. (987), Does Savng Ancpae Declnng Labo Income? an Alenave Tes of he Pemanen Income Hypohess, Economeca, 6, Campbell, John. and Robe J. Shlle (987), Conegaon and Tess of Pesen Value Models, Jounal of Polcal Economy, 95:5, Cashn, Paul and John C. McDemo (998), Ae Ausala s Cuen Accoun Defcs Excessve? The Economc Recod, 74, Chen, Chung and Chunch Wu (999), The Dynamcs of Dvdends, Eanngs and Pces: Evdence and Implcaons fo Dvdend Smoohng and Sgnalng, Jounal of Empcal Fnance, 6, DeAngelo, Hay, L. DeAngelo and Douglas J. Sknne (996), Revesal of Foune Dvdend Sgnalng and he Dsappeaance of Susaned Eanngs Gowh, 9

30 Jounal of Fnancal Economcs, 4, Dvecha Ash R. and Dale Mose (983), Make Responses o Dvdend Inceases and Changes n Payou Raos, Jounal of Fnancal and Quanave Analyss, 8, Ghosh, Ash R. (995a), Inenaonal Capal Mobly amongs he Majo Indusalzed Counes: oo Lle o oo Much? The Economc Jounal, 5, 7-8. Ghosh, Ash R. (995b), Ineempoal Tax-Smoohng and he Govenmen Budge Suplus: Canada and he Uned Saes, Jounal of Money, Ced and Bankng, 7:4, Ghosh, Ash R. and Johahan D. Osy (995), The Cuen Accoun n Developng Counes: a Pespecve fom he Consumpon-Smoohng Appoach, Wold Bank Economc Revew, 9, Hansen, Buce E. (99), Tess fo Paamee Insably n Regessons wh I() Pocesses, Jounal of Busness and Economc Sascs,, Hggns, Robe C. (97), The Copoae Dvdend-Savng Decson, Jounal of Fnancal and Quanave Analyss, 7, Huang, Chao H. and Kenneh S. Ln (993), Defcs, Govenmen Expendues and Tax Smoohng n he Uned Saes: , Jounal of Moneay Economcs, 3, John, Kose and Joseph Wllams (985), Dvdends, Dluon, and Taxes: A Sgnalng Equlbum, The Jounal of Fnance, 4,

31 Kao, Chhwa and Chunch Wu (994), Raonal Expecaons, Infomaon Sgnalng and Dvdend Adjusmen o Pemanen Eanngs, The Revew of Economcs and Sascs, 76, 49-5 Mash, Tey A. and Robe Meon (987), Dvdend Behavo fo he Aggegae Sock Make, Jounal of Busness, 6, -4. Mlle, Meon H. and Fanco Modglan (96), Dvdend Polcy, Gowh and he Valuaon of Shaes, Jounal of Busness, 34, Mlle, Meon H. and Kevn Rock (985), Dvdend Polcy unde Asymmec Infomaon, The Jounal of Fnance, 4, 3-5. Nakamua, Alce and Masao Nakamua (985), Raonal Expecaons and he Fm s Dvdend Behavo, The Revew of Economcs and Sascs, 67, Obsfeld, Mauce (986), Capal Mobly n he Wold Economy: Theoy and Measuemen, Canege Rochese Confeence Sees, 4, O Connell, Sephen A. and Sephen P. Zeldes (988), Raonal Ponz Games, Inenaonal Economc Revew, 9, Oo, Glenn (99), Tesng a Pesen-Value Model of he Cuen Accoun: Evdence fom US and Canadan Tme Sees, Jounal of Inenaonal Money and Fnance,, Phllps, Pee C.B. and Buce E. Hansen (99), Sascal Infeence n Insumenal Vaables Regesson wh I() Pocesses, Revew of Economc Sudes, 57,

32 Sachs, Jeffey D. (98), The Cuen Accoun and Macoeconomc Adjusmen n he 97s, Bookngs Papes on Economc Acvy, 9, Sheffn, Seven M. and Wng T. Woo (99), Pesen Value Tess of an Ineempoal Model of he Cuen Accoun, Jounal of Inenaonal Economcs, 9, Svensson, Las E.O. and Assaf Razn (983), The Tems of Tade and he Cuen Accoun: he Habege-Lausen-Mezle Effec, Jounal of Polcal Economy, 9,

33 Foonoes: Assocae Pofesso, Depamen of Appled Economcs, Naonal Unvesy of Kaohsung, Tawan. Coespondence addess: 7 Kaohsung Unvesy Rd., Nan-Tzu Ds., Kaohsung 8, Tawan. Phone: , Fax: , E-mal: mjweng@nuk.edu.w. Asssan Pofesso, Depamen of Bankng and Fnance, Naonal Ch Nan Unvesy, Tawan. E-mal: mssa@ncnu.edu.w Pofesso, Depamen of Economcs, Naonal Chung Cheng Unvesy, Tawan. E-mal: ecdjlw@ccunx.ccu.edu.w The ably of any busness o oll ove s deb pepeually bngs o mnd he nooous Boson fnance Chales Ponz who used o pay exoban nees o lendes ou of an eve-expandng pool of deposs, whou eve nvesng one penny. M. Ponz was ndced n Fedeal Cou n Novembe 9, and hs bank evenually collapsed. The sockholde s efusal o fnance a Ponz game means ha he wll demand ha he ne pesen value of hs equy poson o be zeo,.e., full epaymen of hs nvesmen. O Connell and Zeldes (988) offe a heoecal sudy of Ponz games. As we maxmze equaon () subjec o equaon (), Bellman s fomula gves us Eule s equaon. Then subsuon of he CRRA fom of he uly funcon esuls n equaon (4). 3 Please efe o he mahemacal appendx. 4 We defne as he opmal change of equy unde dvdend smoohng n S equaon (6). In assocaon wh he empcal sudes, we vew he acual change n equy (dvdend-smoohng componen) as hs opmal change. 5 Please efe o he mahemacal appendx. 6 If he consan em and me end ae added o ou empcal sudes of VAR esmaon, he above fomula has o be modfed as: 33

34 [ ] [ ] ( ) [ ] [ ] [ ] [ ] Φ Φ Φ Φ Φ Φ Φ Φ Φ B I I I I I B A I B A I Z I S ) ( ) ( Â B S S S S, whee and ae esmaed VAR coeffcen maces of consan em and me end, especvely. 7 As saed n Oo, follows fom equaon (5) ha n he seady sae,. In ou analyss, f we subsue and wh he means of and sees, especvely, he make nees ae mpled by he model s seady-sae escon s mplausbly lage and even negave fo HP. Theefoe, we follow Oo s mehodology o eplace and by he devaons fom especve means n empcal sudes. 8 Please efe o Campbell and Shlle (987) fo moe deals n mplemenng hs es. 34