Time Varying Corporate Capital Stocks and the Cross. Section and Intertemporal Variation in Stock Returns

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1 Time Vaying Copoae Capial Socks and he Coss Secion and Ineempoal Vaiaion in Sock Reuns Jacob Sagi, Mahew Spiegel, and Masahio Waanabe * Novembe 8, 2008 We hank Thomas Chemmanu, session paicipans a he 2008 UNC-Duke Copoae Finance Confeence, and semina paicipans a Columbia Univesiy and Univesiy of Souh Caolina fo helpful commens. This is an exensively evised vesion of he pevious pape ciculaed unde he ile Equiy Issuance and Expeced Reuns: Theoy and New Evidence. We also hank Sugao Bhaachayya, Ines Chaieb, Takao Kobayashi, Nobuya Takezawa, Akiko Waanabe, session paicipans a he 2008 Euopean Finance Associaion Meeings, he 2008 Asian/Nippon Finance Associaion Meeings, and he 2008 Singapoe Inenaional Confeence on Finance, and semina paicipans a Hiosubashi Univesiy and Nomua Secuiies fo commens on ha vesion. Owen Gaduae School of Managemen, Vandebil Univesiy, 40 2s Ave S., Nashville, TN Phone: , fax: , Jacob.Sagi@owen.vandebil.edu. Yale School of Managemen, 35 Pospec See, New Haven, CT 065. Phone: (203) , fax: (203) , mahew.spiegel@yale.edu. *Jones Gaduae School of Managemen, Rice Univesiy - MS53, 600 Main S., Houson, TX Phone: (73) , fax: (73) , waanabe@ice.edu. JEL Classificaion: G2 Keywods: capial invesmen, poduciviy of capial, equiy issuance, expeced eun, ovelapping geneaions model, supply shocks, excessive volailiy.

2 Time Vaying Copoae Capial Socks and he Coss Secion and Ineempoal Vaiaion in Sock Reuns Absac This pape uses a geneal equilibium model o examine an economy in which fim manages seek o maximize hei individual fim s value hough he cosly adjusmen of hei capial sock in esponse o economic shocks. These economic shocks impac boh he numbe of capial unis each fim has and how poducive each uni is. The ulimae value of hese copoae asses is deemined by isk avese invesos ha ade in a compeiive muliple secuiy make. Because capial socks change slowly ove ime, he elaive eun o owning hem does as well. This geneaes boh coss secional and ineempoal eun paens in which economic shocks lead o lage euns, followed by wha appea o be long em abnomal euns in he ohe diecion.

3 Sock euns appea o display a numbe of long un coss secional and ineempoal paens. One of he mos sudied is pobably he endency fo euns o incease in a fim s book-o-make aio and decease in is size (Fama and Fench (992)). Bu hee ae ohes. Mash (982), Asquih and Mullins (986), Mikkelson and Pach (986), Jung, Kim and Sulz (996), and Bake and Wugle (2002) all find ha following a new equiy issue a sock s eun is lowe han one migh ohewise foecas. A he opposie end Ikenbey, Lakonishok, and Vemaelen (995) find ha afe a fim engages in shae epuchases i ends o have above nomal euns. The negaive elaionship beween ne equiy issuance and subsequen euns is fuhe confimed in boh he U.S. (Fama and Fench (2007) and Poniff and Woodgae (2008)) and inenaional (McLean, Poniff, and Waanabe (2008)) makes. Mos impoanly fo his pape, Timan, Wei and Xie (TWX, 2004) show ha he equiy issue and epuchase findings ae in fac ied o a fim s invesmens. Fims ha inves oday end o have lowe euns going fowad and visa vesa (also see Lyandes, Sun, and Zhang (2007) and Xing (2007)). The goal of his pape is o povide an explanaion fo his phenomenon in a acable geneal equilibium famewok and o geneae a numbe of new esable coss-secional pedicions. In he model boh fims and invesos play an acive ole in he deeminaion of equilibium pices and hus expeced euns. Fims ceae goods and sevices acoss a numbe of indusies by employing indusy specific capial ha vaies ove ime. One souce of his vaiaion comes fom employing individuals. These employees sell hei human capial o he fim which hen conves i o copoae capial. Anohe souce of vaiaion comes hough he diec puchase and sale of capial in he financial makes. Lyandes, Sun, and Zhang (2007) find ha an invesmen faco explains mos of he new issues puzzle, educing 75% o 80% of SEO and IPO undepefomance. Moivaed by he Q heoy, Xing (2007) shows ha an invesmen gowh faco does abou as well as he value faco, diving ou he value effec.

4 I is assumed ha if a fim adds o subacs fom is capial sock in his manne i is elaively less expensive o do so slowly. The demand side of he model comes fom isk advese invesos ha own shaes in he indusies and ade hem in a compeiive make. By using an ovelapping geneaions famewok based on Spiegel (998) and elaed o hose in Waanabe (2008), and Biais, Bossaes, and Spa (2008) he model is no only acable bu can easily be validaed agains eadily available daa souces. Anohe nice feaue of he model is ha he CAPM holds. Howeve, while i holds peiod-by-peiod he model is no saic. The eun an inveso can expec o ean by invesing in an indusy vaies ove ime as he fims vay hei capial levels. In paicula, he CAPM bea is a deceasing funcion of capial invesmen. One can hink of capial unis in his seing somewha moe conceely by consideing a fim such as Tyson Indusies which is in he pouly business. In hei case a capial uni would be a chicken fam and he cash flow would be he pofi pe fam (o somewha equivalenly he pice pe pound of chick poduced). In he model and ealiy, he numbe of fams Tyson has vaies ove ime as hei employees ae able o build and impove hem o a geae o lesse degee each peiod. A he same ime he pofis geneaed by each fam also vaies wih pouly and feed pices. In eacion o hese evens Tyson hen ceaes (o sells) addiional fams by employing financial capial. High capial values naually lead hem o add o hei capial base. Of couse, hey do so gadually as i ypically will no pay o speed up he ceaion of new fams oo much. Bu, as Tyson and hei compeios gadually change hei capial base hey also undo he economic shocks ha lead o he high capial values o begin wih. 3

5 Noice ha he wo evens ha move capial values: supply (numbe of fams in he above example) and pofi pe uni (pouly pices) also move sock pices. Since fims adjus hei capial bases in esponse o abnomally high o low capial values sock pices also move boh wih he iniial shock and he subsequen eacion by fims o ha shock. This hen leads o paens simila o hose in TWX as well as he pio lieaue on sock sales and epuchases. Tha is, high sock euns ae accompanied by an immediae incease in capial accumulaion. Afewads euns ae below nomal and capial accumulaion in he indusy apes off. Bu, as in TWX he eun phenomena ae ied o changes in copoae capial levels and no sock sales and epuchases pe se. We povide empiical evidence ha is consisen wih he above soy. Ou model implies ha he poduciviy of copoae capial and capial invesmen, o equivalenly he book-o-make aio, ae he key vaiables o deemine he coss-secional vaiaion in sock euns. We measue poduciviy by he aio of eanings pe uni capial o he cos of ceaing uni capial. We find ha he zeo invesmen pofolio ha goes long high-poduciviy gowh fims and sho low-poduciviy gowh fims eans a valueweighed aveage eun of 0.8% pe monh. The isk-adjused alpha fom he sandad fou faco model is 0.92% pe monh. Boh of hese numbes ae no only saisically significan (a he % level), bu also economically significan. This pape is no he fis o heoeically examine he elaionship beween sock euns and boh eal and financial copoae capial adjusmens. In esponse o he findings in he empiical lieaue on new shae issues a numbe of auhos have poposed behavioal explanaions in which manages ake advanage of ovevalued shaes o aise capial (Loughan, Rie, and Rydqvis (984), Rie (99), Loughan and 4

6 Rie (995), Rajan and Sevaes (997), Pagano, Panea, and Zingales (998), Bake and Wugle (2000) and Lowy (2003)). In conas, ecen models by Paso and Veonesi (2005) and Dima and Thako (2007) boh offe aional explanaions. Like Paso and Veonesi (2005) and Dima and Thako (2007) his pape also poposes a aional model ha geneaes eun seies simila o wha is seen in he daa. In Paso and Veonesi make condiions change exogenously ove ime along hee dimensions: expeced euns, aggegae pofiabiliy, and unceainy egading fuue pofiabiliy. This leads o a numbe of phenomena including IPO waves and pos-ipo euns ha ae lowe han one migh expec in a saic model. In Dima and Thako a fim s manages and he invesing public may no agee on he value associaed wih a new invesmen. When he divegence is lage fims finance wih deb, and when i is small wih equiy. Wha dives hei esul is ha a fim s sock value is likely o be highe when invesos and manages shae he same beliefs. Tha occus because when he beliefs ae simila he invesos hink i is less likely ha managemen will engage in waseful invesmen. This in un inceases he appeal of equiy financing as well bu i also means ha going fowad shaeholde euns ae likely o be lowe as he level of ageemen beween hem and managemen has nowhee o go bu down. This pape conibues o he above aicles by also seeking o explain he phenomena beween invesmen and euns documened in TWX. Anohe conibuion is o do so wihin a geneal equilibium famewok. Tha allows he model o examine no only ime vaiaion in euns, bu beas, coss secional paens, and he elaionship hese all bea o vaiables like indusy poduciviy. In he Paso and Veonesi (2005) pape make condiions ae exogenous and fims eac o hem, hee hey ae endogenous 5

7 and influenced by he fims. This ineplay allows he model o also make some pedicions egading how oveall capial invesmen impacs he fuue ajecoy of he economy. Also, whee Dima and Thako (2007) look a how heeogeneous beliefs influence euns in his aicle eveyone has idenical beliefs. Ohe elaed models ae hose by Bek, Geen and Naik (999) and Calson, Fishe, and Giammaino (2004, 2006). These auhos use eal opions models o examine how a fim s expeced eun will vay ove ime and focus on he elaionship beween a fim s book-o-make and size ha hey geneae. As hey show, i ends o induce paens ha look like hose found in Fama and Fench (992). The fims in his pape s model have a much simple invesmen poblem ye geneae simila book-o-make eun paens. Anohe diffeence is in he daa needed o cooboae each model s pedicions. Using commonly available daa souces i is ofen difficul o know whee and o wha degee eal opion values ae influencing a fim s cuen sock pice. In he model developed hee one only needs infomaion like he fim s cuen capial and invesmen levels. While ha does no make he model any moe o less likely o be igh i does make i easie o es and poenially efue. Finally, as boh Bek, Geen and Naik (999) and Calson, Fishe, and Giammaino (2004) acknowledge, hei models ae se up in a paial equilibium famewok wih eihe he picing kenel o he demand funcion exogenously given. In conas, ou model again is a geneal equilibium model in which pices equilibae supply and demand hough make cleaing. The pape is sucued as follows. Secion pesens he model. Secion 2 conains he analysis, followed by some empiical evidence in Secion 3. Secion 4 concludes. 6

8 . A Compeiive Model wih Capial Adjusmens. Seing Thee ae K poducion facos which he pape will also efe o as indusy secos. Each poducion faco is used by a coninuum of compeiive equiy value maximizing pice aking fims wih mass of uniy. Thee is a single isk fee bond ha pays pe peiod and seves as he numeaie wih a consan value of. The poducion facos evolve ove ime via: N = N + η + Y () whee N equals he K veco of poducion facos, he ime peiod. The η epesens he influence of human capial on he oal supply of copoae capial. In he model people ae bon wih a human capial endowmen which in aggegae equals η. Though hei employmen his human capial is hen conveed ino copoae capial and has he impac shown in (). Fom he pespecive of invesos η is a nomally disibued andom veco wih mean zeo and vaiance-covaiance maix Σ η. The Y em is a K veco of capial ceaed by fims in addiion o wha hey ge fom he amoun geneaed by hei employees in he nomal couse of hei business. 2 In each peiod he poducion facos pay a K dividend veco D ha evolves via: ( ) D = D + G D D + δ (2). 2 Ohe funcional foms wih vaious inepeaions ae clealy possible. Fo example, i is possible o change he assumpion ha employee capial conibuions have a mean of zeo by including a depeciaion componen o (). In he long un capial socks will hen adjus so ha depeciaion offses he aveage capial added by labo. 7

9 Hee G is a K K maix of consans epesening he speed a which asse payous mean eve, D a K veco of consans epesening he long un payou pe asse class, and he em δ is a K nomally disibued andom veco wih zeo mean and vaiancecovaiance maix Σ δ..2 Fims Each fim s oupu comes fom a single poducion faco. 3 Fim fk, (i.e., fim f using faco k) seeks o maximize is cuen equiy value as follows: 2 max ( n + fk, η + fk, yfk, ) p k, c k y fk, c2 k yfk, ηfk, pk,, y fk, 2 (3) whee p k, is he peiod make pice of a uni of capial associaed wih he k h poducion faco. The expession nfk, = nfk, + η fk, + yfk, is he dae- capial employed by fim fk. The human capial i employs o ceae addiional copoae capial is epesened by he η fk, em and y fk, is he new capial deployed beyond wha is ceaed by he employee base in he nomal couse of business. 4 Thus, he em η fk, pk, in (3) implies ha fims have o pay hei employees he full make value of he capial hey ceae. Implicily, his means boh sides of he labo make ae compeiive. By conas, y fk, coesponds o deployed capial ha ceaes posiive ne pesen value. The consans c k and c 2k epesen capial adjusmen coss fo he k h poducion faco. All fims in an indusy ae assumed o face he same coss c k and c 2k. 3 In pinciple, fims can poduce moe han a single ype of capial oupu. Assuming ha he cos of building o liquidaing capial is assessed a he fim level fo each poducion faco sepaaely, hee is no loss of genealiy in consideing fims ha specialize only in a single ype of oupu. 4 Thee is no physical limi o he amoun of new capial ha can be deployed. Also, o mainain acabiliy new capial is financed only hough he issuing (epuchase in he case of negaive deploymen) of equiy. One could also allow fo he use of iskless deb wihou any fundamenal change o he model s esuls. 8

10 Each of he c k ems epesen a diffeen aspec of he coss associaed wih ceaing poducive capial. The c k paamee capues he base line cos of consucing a uni of poducion. Fo example, conside a pouly poduce like Tyson. Fo i c k equals he cos of building a new chicken fam. This ulimaely depends on he pice of aw maeials like wood, wie, ucks, and he like and no he make value of Tyson s own asses. Thus, he fim can poenially pofi by building new fams when hei make value exceeds hei consucion value and by selling hem off when he evese is ue. The c 2k paamee capues he cos of inceasing he speed wih which asses ae ceaed o sold. Pesumably, ushing he consucion of a new chicken fam inceases is ulimae cos bu does allow he fim o geneae cash flows fom i ealie on. Naually, whehe a fim wishes o ush poducion of a new faciliy depends upon how much i expecs o ean on i. Diffeeniaing (3) wih espec o y fk,, ecalling ha he fims ake he pice veco as given, and hen solving fo y fk, yields fo each poducion faco a oal capial issuance of y fk, p c k, k =. (4) c 2k O, inegaing boh sides ove f and ecalling ha he oal mass is uniy, y k, p c k, k =, (5) c 2k whee yk, = yfk, df is he oal amoun of new capial deployed in faco k. Fo efeence, le Nk, = nfk, df and ηk, = ηfk, df. Wiing equaion (5) in veco fom: y C P 2 D C = ( ), (6) 9

11 whee C is he veco of linea coss wih he k h elemen c k, and C 2D is a K K maix wih he k h diagonal elemen equal o c 2k and zeos elsewhee hus: C 2D c = 0 c c 2K. (7).3 Populaion Invesos, like fims, ake pices as given. A coninuum of invesos wih uni mass is bon in peiod, consume and hen die in peiod +. Each inveso has a negaive exponenial uiliy funcion wih isk avesion paamee θ. The only endowmen an inveso begins life wih is his o he human capial. In hei fis peiod of life hey sell hei human capial o fims (ha conve i o copoae capial) and buy and sell secuiies o fund hei eiemen. Le X i, epesen he K pofolio of shae holdings of inveso i in peiod. Each shae is assumed o epesen one uni of a poducion faco. Le w i, be he wealh wih which inveso i is bon a dae. The assumpion ha people ae bon only wih human capial implies w i, equals he make value of ha capial. Fuhemoe, because invesos have negaive exponenial uiliy funcions and all of he andom vaiables ae nomally disibued he iniial allocaion of human capial does no impac he model s equilibium esuls. Thus, all ha is needed o poceed is knowledge ha in he aggegae he incoming human capial equals η and ha hose wih skills associaed wih indusy k will ean η k, pk,. 0

12 Based on he above discussion and leing R=+ an inveso s peiod + consumpion equals: ( ) X P + D RP + Rw (8) i, + + i, because i is assumed ha he o she sells he pofolio pio o deah. Again using he assumpion ha all of he andom vecos ae nomally disibued, and ha he invesos have negaive exponenial uiliies invesos maximize hei expeced uiliy by solving he following mean-vaiance poblem: max E i, ( ) i, va i, ( ) i,. X X P D RP Rw θ X P+ + D + RP + Rw i, 2 (9) This educes o, whee [ Q ] X E [ Q ] θ + i, + va =, (0) Q = P + D RP () is he excess payoff veco fom a uni posiion in each ype of capial, and [ ] va Q + is is vaiance-covaiance maix. Inegaing ove he coninuum of invesos and seing he make cleaing condiion N = Xi, di yields, [ Q ] N E [ Q ] θ + + va =. (2).4 Equilibium Invesos conjecue ha pices ae deemined via he following fomula: P = A + AN + A D (3) 0 2 whee A 0 is a K veco, while A and A 2 ae K K maices. Nex, updae he ime subscips in (3) o + and hen plug equaions (), (2) and (6) ino equaion (3) in

13 ode o solve fo P + in ems of he paamee values known a ime and he unknown + shocks: { δ } ( ) ( η ) ( ) P I AC A A N C C A D G D D + = 2D D Using (3), equaion (4) can be ewien as { ( η ) ( ) δ } P + = ( I AC 2D) P + A + C2DC + A2 G D D + +, (4) (5) implying ha he pice veco follows a VAR() pocess. Wih some algeba, use () and (5) o wie [ ] + ( 2 ) E Q = I AC D RI P ( I AC ) ( ) D AG D D AC DC D G( D D) (6) Similaly, va [ Q ] va ( I AC ) ( A A ) = η + δ + δ + 2D ( ) δ (( ) ) ' = ( I AC 2D) A A( I AC Ση 2D) + ( I AC 2D) A2 + I Σ I AC 2D A2 + I V. (7) To solve fo he equilibium values of he A s, eplace E [ Q + ] and [ ] va Q + in equaion (2) wih he coesponding ems in equaions (6) and (7). The coefficiens of N and D mus vanish sepaaely as well as hose ha do no muliply any ime vaying paamees. This yields fo he ems ha do no muliply eihe N o D, ( ) ( ) I AC RI A I AC AGD AC C + + GD= 2D 0 2D 2 2D 0, (8) while fo he ems muliplying N, 2

14 ( D ) I AC 2 RI A θ ( ) η ( ) ( ) ( ) δ (( ) ) I AC AΣ A I AC + I AC A + I Σ I AC A + I = (9) ' 2D 2D 2D 2 2D 2 0, and finally fo he ems muliplying D, ( D ) ( ) I AC A + I I G RA = (20) 2. Analysis 2. Seady Sae The economy is defined o be in a seady sae in peiod if fims do no acively seek o change hei capial sock and if he expeced change in he payou pe uni of capial is expeced o emain unchanged. This is a useful base case as i yields he model s pedicions egading uncondiional momens in he daa. Fom hee i is hen possible o see how vaious shocks o he sysem will impac esimaed euns, isk facos and ohe financial and economic vaiables of inees. Fim s do no acively change hei capial sock in peiod if Y equals a K veco of zeos and if dividends ae also expeced o emain unchanged implying E[D + ]=D. Fom equaion (6) he veco Y will equal zeo if and only if P = C. Similaly, asse payous ae expeced o emain unchanged if and only if D = D. The uncondiional expeced eun o an inveso fom holding a claim in one uni of copoae asse k equals E p p + d k, + k, k, k, + =, (2) pk, E 3

15 whee d k, epesens he k h elemen of he veco D. Employing he condiion ha p k, = c k and d, k = d in (5) and using he esul in (2) leads o he following poposiion: k Poposiion : If he economy is in seady sae hen dk E k, + =. (22) c Poposiion implies ha if a fim uses asse class k hen is sock s aveage eun will equal he long un aio of ha asse s abiliy o geneae cash flows pe uni o is uni ceaion cos, which we call poduciviy. Fuhe noe, he igh hand side of (22) can (a leas in pinciple) be calculaed wih daa commonly available. Fo a fim i should equal he long un aveage eanings divided by he pe peiod change in book value o simila measues of a fim s cash flow and poducive asses. Fim k s seady sae expeced euns in equaion (22) ae independen of isk o isk aiudes in he economy. The eason is ha he numbe of capial unis deployed adjuss o he poin a which invesos bea an opimal, o seady sae, level of isk. Essenially, N in equaion (2) adjuss o he poin whee i offses he em [ Q ] k θ va Book-o-Make in he Seady Sae Since c k is he cos of eplacing a uni of capial, when done as economically as possible, i should coespond somewha o a fim s pe uni of capial book value in indusy k as well. The fim s acual book value in his case would be c k n k,. In he long un he seady sae equiemen ha p k, = c k hus implies ha he long un book-omake aio and hus Tobin s q fo an indusy should equal. This esul will come ino play in he nex secion whee he impac of deviaions fom he seady sae ae examined and will esablish a value vesus gowh pemium in sock euns. 4

16 2.2 Seady Sae Disuped by a One Time Shock o Capial Imagine he economy is in is long un seady sae as of peiod and hee is a one ime shock o capial (η) o cash flows (D) in peiod. To simplify he noaion needed fo he analyses define he following vaiables: Pˆ P C, ( ) D D D = G D D + δ,and F I AC 2D. (23) Subacing C fom boh sides of (5) and making he above subsiuions yields: ( η 2 ) ˆ ˆ. P = F P + A + A D (24) Rolling (24) back and hen subsiuing ou P ˆ fo P poduces he equilibium pice veco ha invesos expec o occu going fowad: s = + η s + 2 s s= 0 P C F ( A A D ) (25) implying he impulse esponse τ peiods afe a ime supply shock is given by τ F A η. Similaly, he impulse esponse τ peiods afe a ime dividend change is given by F τ A2 D. Since F I AC as long as A is negaive definie equaion (25) implies 2D ha a capial o cash flow shock decays oughly a he ae of 0 F < < (in some maix nom) pe peiod. The nex poposiion says ha his will always occu in an economy wih a lage quadaic adjusmen cos ( C ). 2D Poposiion 2: As C 2D appoaches zeo, A ends o a negaive definie maix in an equilibium in which A is finie. Poof. See he Appendix fo he poof of his and all ohe poposiions. 5

17 In fac, i is saighfowad o confim ha he equilibia wih finie A convege o hose of Spiegel (998) as (20) simplifies o, C. Unde his assumpion 2D 0 C 2D equals he zeo maix and A ( I + G) + I G = 0 (26) 2 and hus A 2 equals ( I G)( I G) +. Nex (9) educes o, A + A Σ A + R I + G Σ I + G = 2 θ η ( ) δ( ) 0, (27) which can now be solved fo A, while using (8) hen yields R 0 = ( + ). A I G GD Assuming A is negaive definie, equaion (25) povides a numbe of empiical pedicions. A ime 0 suppose a shock ceaes a lage posiive pice move acoss socks. Equaion (25) shows ha his will hen be followed by a declining pice seies. Noe, his does no mean euns ae negaive as invesos coninue o eceive a cash flow seam fom he asses. Bu i does mean euns ae lowe han hey ae on aveage. Looking a euns, he implicaion is ha a lage eun in one diecion will lead o lowe fuue euns in he ohe. Also, noe wha his implies abou he elaionship beween capial expendiues and fuue euns. When an indusy capial uni feches a value above is long un equilibium value, fims in ha indusy incease hei holdings of i (see equaion (6)). Thus, if a shock geneaes a lage pice incease ha will in un geneae new invesmen by fims in he indusy. This will be followed by lowe equilibium euns fo invesos, lowe capial pices fo he indusy, and educed invesmen. The pocess coninues on like his unil he seady sae equilibium is esoed. 6

18 2.2. Book-o-Make and Expeced Reuns As discussed in Secion 2. fo indusy k he eplacemen cos fo a uni of capial, when done as economically as possible equals c k. Thus, in seady sae since p k, = c k one has ha he book-o-make aio should equal one. Bu sho un shocks will change ha. Fo example, if he cash flow (d k ) o a paicula ype of capial goes up so will he make value of ha asse. This will decease he book-o-make aio and induce capial accumulaion by fims in he indusy. If A is negaive definie hen he analysis in he pio secion implies a coss secional elaionship beween book-o-make and expeced euns. A shock ha deceases he book-o-make aio oday should be followed by fuue capial accumulaion and lowe han aveage expeced euns o shaeholdes. This will coninue unil he gowh sock sees is make-o-book (o equivalenly Tobin s q) eun o. The evese will be ue fo value socks. The above analysis povides a aionale fo he value-vesus-gowh eun elaionship ha is boh complemenay o and sepaae fom ha in eihe Bek, Geen and Naik (999) o Calson, Fishe and Giammaino (2004). In he pio models he pemium esuls fom fims aleing hei value hough he execise o expiaion of gowh opions. Hee he elaionship also comes fom capial changes in he undelying fims. Bu he fims in he model pesened hee do no execise an opion ha leads o he pice change, bu ahe eac o one by building new capial ha acually undoes he pice change. 5 5 I is woh noing ha while hee is consideable evidence fo a value pemium in sock euns hee is some quesion as o whehe o no i is concenaed pimaily in secuiies shunned by insiuional invesos. See Houge and Loughan (2006) and Phalippou (2007) fo evidence on his issue. 7

19 2.3 Ohe Limis of Inees Two ohe limis also yield simplified equilibium expessions and will pove useful fo developing he model s implicaions. The fis occus as invesos become moe and moe isk neual: θ 0. Fom equaion (9), hee ae wo possibiliies fo I AC RI A. Eihe i also ends o zeo o, alenaively, ( ) 2D 0 meaning ha A C > + 2D 0. The lae has he undesiable equilibium implicaion of upwad sloping demand cuves fo employed capial. Thus, he only economically sensible equilibium is one in which lim A 0. In un, his implies ha θ 0 lim A ( I G)( I G) θ Noice ha nea his limi A is negaive definie as A θv fom equaion (9). Thus, one has ye anohe se of sufficien condiions fo Poposiion 2 o hold wih egad o cash flow shocks. A second limi examined in his secion ha will pove useful occus as he vaiance of he cash flow shocks ends o zeo: Σ δ 0. In his case, equaion (9) becomes ( I AC D) RI A = θ ( I AC D) AΣη A ( I AC D) (28) One obvious soluion has A appoach 0 fom below, which in un implies lim A ( I G)( I G) Σδ Thus, one has he esul ha Poposiion 2 holds in his limi as well. One way o jusify concenaing on his equilibium is ha i holds if A has a powe seies soluion in θ. See he Appendix fo a poof. 8

20 2.3. Pice behavio in he limis θσ δ 0 and θσ δ As he isk fom δ becomes eihe vey small o lage elaive o he populaion s isk avesion he equilibium maix equaions appoach elaively simple limis. This addiional simpliciy hen makes i possible o geneae moe pecise implicaions fom he model. Poposiion 3: As he isk fom δ goes o zeo, θσδ 0, he equilibium pice goes o + ( + ) + Z ( I + G) ( I + G) GD + Z ( I G) GD Z ( C + GD) θσδ 0 P ( I + G) GD+ ( I + G) ( I G) D ( I + G) Z ( I G) D + Z C N, D (29) whee Z 0 epesens: 2 ( + ) 0 ( ) θ δ ( ) 2D Z = I + G Σ I + G C. In he opposie limi as he isk fom δ becomes vey lage, θσδ, he equilibium pices goes o θσδ P ( C GD) θσ C2 C2 I N ( I G) D. δ Σδ Σ D η D + (30) Wih a lile bi of addiional wok equaions (29) and (30) geneae a numbe of compaaive saics egading how pices move in esponse o vaious sae vaiables. Poposiion 4: Assume ha all maices ae diagonal and ha I-G is sicly posiive definie. Then in he limis θσ δ 0 and θσ δ, pk, / dk, > 0and pk, / nk, < 0. Moeove, lim θσδ 0 p d < lim p k, k, d θσδ k, k, and lim θσδ 0 p n > lim p k, k, n θσδ k, k,. The compaaive saics show ha because he laws of supply and demand hold wih egad o eal asses hey hen become efleced in sock pices as well. The esul ha 9

21 p / d > 0 saes ha he value of an asse inceases if he cash flow i geneaes k, k, inceases. On he ohe hand, pk, / nk, < 0 implies ha if he supply of an asse goes up hen is pice has o come down o clea he make. Reuning o he Tyson example he fis inequaliy saes ha if he pice of chickens inceases so will he value of each of hei fams. In conas, he second inequaliy shows ha if hee is an oveall incease in he numbe of such fams in he economy hen he value of each fam will decline. Coune inuiively, as he hid and fouh inequaliies show, while an economy wih a low cash flow isk (δ) shows less pice sensiiviy o cash flow shocks, i yields highe pice sensiiviy o asse supplies Pofis, Shape Raios, and appoximae expeced euns in he limis θσ δ 0 and θσ δ Assume ha all maices ae diagonal and ha I-G is sicly posiive definie. In he wo limis, we hen have ha and θσδ E [ Q+ ] D C RC2DY + ( I G)( D D), (3) θσδ 0 E [ Q ] D C C2DY ( I G) ( I G)( D D) (32) Thus excess pofis ae negaively elaed o capial issuance, Y, and posiively elaed o deviaions of capial payou fom he uncondiional. Moeove, boh sensiiviies ae moe ponounced when cash flow isk (δ) o isk avesion is high. The Shape Raio fo each indusy can be calculaed as 20

22 SR k E[ qk, + ]. = (33) SD [ q ] k, + By wiing VAR [ Q+ ] = ( F R) ZC2D, and aking he limis, one concludes ha θ SR k θ { D C RC2 Y ( I G)( D D) } Σδ D + k c σ + σ k2 η, k δ, k, (34) and SR k θσδ 0 { D C C2DY+ ( I + G) ( I G)( D D) } R ( I + G) σ δ, k k k. (35) As wih he excess pofis, he Shape Raio is negaively elaed o capial issuance, Y, and posiively elaed o deviaions of capial payou fom he uncondiional. Hee oo, boh sensiiviies ae moe ponounced when isk o isk avesion is high. By wiing pk, = c2 kyk, + c k, and dividing he excess pofi of indusy k by he pice of a uni of indusy k s capial, we can obain fom equaions (3) and (32) ha he excess eun on indusy k s shaes is d c y + ( g )( d d ) θσδ e k 2 k k, k k, k E k, +, c2 kyk, + c k (36) and d 0 k + ( gk)( dk, dk) θσδ e + gk E k, +, c y + c 2 k k, k (37) Fo small shocks away fom he seady sae, one can linealy appoximae hese wo equaions in he shocks as 2

23 θσδ e dk dk c2k ( gk) E k, + ( + ) y, k + ( dk, dk), ck ck c k c k seady sae pa (38) and θσδ 0 e dk dk c2k ( gk) E k, + yk, + ( dk, dk), ck c k c k + gk ck seady sae pa (39) In each case, he deviaion fom seady sae expeced euns ae negaively elaed o capial issuance, Y, and posiively elaed o deviaions of capial payou fom he uncondiional mean. As wih he excess pofis and Shape Raios, he sensiiviies ae moe ponounced when isk o isk avesion is high. 2.4 Coss-secional euns 2.4. The book-o-make effec Equaion (6) saes ha he make value of a uni of capial is inceasing in Y. Holding he payou pe uni of capial consan, equaions (38) and (39) indicae ha expeced euns ae deceasing in he pe-uni make pice of capial. Because a fim in ou model is an aggegae of unis of capial, a high book-o-make aio fo fim k in ou model coesponds o a (elaively) low value of p k,, and heefoe (elaively) high expeced euns. Fo insance, he coss-secional dispesion coesponding o his book-o-make c2 effec fom equaion (38) will be oughly of he ode of σ η, whee he ba signifies a c coss-secional aveage. This allows one o esimae he ode of magniude of he capial adjusmen coss, C 2D, o he obseved book-o-make effec. 22

24 2.4.2 Eanings momenum Benad and Thomas (989) demonsae he pesence of eanings momenum: fims ha announce high (lowe) eanings exhibi posiive (negaive) abnomal euns elaive o hei pe-announcemen isk-adjusmen. This can be inepeed as a change in isk subsequen o he announcemen o ha makes inadequaely adjus fo he impac of eanings announcemens. Equaions (38) and (39) indicae ha fims whose payous incease will have an ex-pos highe expeced eun, consisen wih he pos-eanings dif of Benad and Thomas (989). 2.5 Capial Invesmen and Expeced Reun Geneally in a model wih a downwad sloping demand cuve a negaive supply shock inceases he cuen pice. In he cuen model, his is addiionally associaed wih an obsevable change in capial invesmen in he same diecion as he pice change. When an asse s value is high companies can pofi by ceaing moe of i. Howeve, inuiively, his should hen lead o lowe fuue sock euns as capial accumulaion by he indusy esuls in a gadual educion of ha paicula asse s make value. Theefoe, one expecs o see a negaive elaion beween fuue expeced sock euns and capial invesmen. To fomally analyze he above scenaio define fim k s excess eun as q e = k, + k,, p (40) + k, 23

25 whee q k,+ is he k h elemen of Q +. Thoughou he es of he pape assume ha he pice and supply of capial ae posiive. 6 The nex poposiion asses ha he expeced excess eun deceases wih capial invesmen as long as he quadaic adjusmen cos is sufficienly lage, as assumed in Poposiion 2. Poposiion 5: As C a fim s expeced excess eun deceases wih capial 2D 0 invesmen caused by supply shocks: E[ ] e k, + lim < 0. C2 D 0 yk, (4) Noice ha he esul in Poposiion 5 looks like ha found in he daa by TWX and he elaed lieaue on new sock issuances and epuchases. Fims issue o eie secuiies o buy o sell capial in esponse o shocks in he eal economy ha also impac sock pices. Bu, as indusies ale hei capial socks hey also cause he value of hei capial o move in he opposie diecion which also impacs hei sock s value. As Poposiion 5 shows he esul is a negaive elaionship beween capial changes and sock euns. 2.6 Capial Invesmen and CAPM Bea Since he model s andom vaiables ae nomally disibued and since he sock make is assumed o be compeiive and ficionless he CAPM mus hold. To veify his ewie he equilibium condiion in equaion (2) as E[ Q ] = θ cov ( Q, Q ), (42) + + M, + 6 While boh he pice and supply ae nomally disibued in ou model, one can abiaily educe he pobabiliy of hei assuming negaive values. The disibuion of he aio of nomals is called he Fielle disibuion and is applicaion is abundanly found in he saisics lieaue. 24

26 whee Q M,+ Q + N + is he excess payoff on he make pofolio. Pe-muliply he o obain M, + M, + N E[ Q ] = θ va( Q ). (43) Dividing hese wo expessions side by side and eaanging, we have cov ( Q+, QM, + ) E [ Q + ] = E[ QM, + ]. (44) va ( Q ) M, + Define he veco of excess euns and he excess make eun as = Q P, e + + Q = Q e M, + M, + M, + ' PM, + P+ N+, (45) whee denoes he elemenwise division opeao, and ewie equaion (44) in ems of excess euns: e e cov ( +, M, + ) e e ] = E[ M, ] E[ M, ]. e + β (46) va ( ) e E [ + + M, + Hee, he veco of beas can be wien as cov (, ) NP β = = ( ) i. (47) e e + M, + VN P e va ( M, + ) NVN Is k h elemen is β k, evn = i = (48) e [, ] k NP E k + e, pk, NVN E[ M, + ] whee e k is he choice veco wih in is k h elemen and 0 elsewhee. Since a fim s expeced eun deceases wih supply-induced capial invesmen as long as he quadaic adjusmen cos is sufficienly lage (see Poposiion 5), we expec ha he CAPM bea 25

27 will also decease. The nex poposiion shows ha his is ue in a lage economy wih independen indusies: Poposiion 6: Conside a lage economy wih independen indusies (i.e. V and A ae diagonal). As C, a fim s CAPM bea deceases wih capial invesmen caused by 2D 0 a supply shock: β k, lim < 0. C2 D 0, y K k, (49) Inuiively, he assumpion of coss-secional independence ensues ha he supply shock does no cause make wide pice movemen. Theefoe, in a lage economy he fim k shock only affecs is own pice and has a negligible effec on he expeced make eun. Thus, he esul on he expeced eun in Poposiion 5 anslaes ino he bea. Impoanly, his esul suggess modeling he CAPM bea as a (deceasing) funcion of capial invesmen in an empiical asse picing es. 2.7 Numeical illusaion The analyic esuls in he peceding secions povide a qualiaive sense ha he model can be consisen wih a numbe of sylized facs in he lieaue. In ode o illusae his bee we choose a se of paamees highlighing he coss-secional effecs. Ou inenion is no o pefom a full scale calibaion o indusy daa and coss-secional momens a his sage (as is done, fo insance, in Calson, Fishe, and Giammaino, 2004). We conside he case of en iid indusies, whee Σ δ, Σ η, and G ae popoional o he ideniy maix. We focus on en indusies so ha we can focus on he equivalen of 26

28 coss-secional deciles when calculaing eun momens. Each peiod coesponds o a yea. Wihou loss of genealiy, we nomalize he seady-sae book value of capial o be. The isk fee ae is chosen o be R =.0, consisen wih he ealized eal ae of eun ove he pas half cenuy, while D is chosen o be 0.09, so ha he seady sae ae of eun is 8% pe yea. We se he volailiy of payoffs and poduciviy shocks o be σ δ = σ η = 8% and he ae of payoff mean-evesion is g = 0.5 (whee G = gi). The emaining paamees ae chosen o help aive a easonable magniudes fo he sylized coss-secional momens. Specifically, we se θ = 2 and C 2 = 6. These paamees compleely deemine he model. The coefficien, a, solves a degee-five polynomial, which unde ou paamee specificaion has a unique negaive eal oo a ; given ha a negaive eal value fo a is he only sensible economic soluion, his means ha his paicula paamee specificaion is no complicaed by he pesence of muliple equilibia. The emaining coefficiens in he equaion elaing pice o quaniy and payoffs ae a 0 =.84, and a 2 = In he seady sae, he size of an indusy is solved by seing he pice o C and he payoff o D, yielding.73 unis of capial. The sandad deviaion of he pice of a uni of capial is The ae of mean-evesion of he pice, is F = We simulae 0,000 yeas of he economy assuming ha i is iniially a he seady sae. Thee was no insance in which he pice fell below 0.5 o ose above.6. The aveage diffeence beween he indusy wih he highes pice pe uni capial and ha wih he lowes pice pe uni capial is 0.38, implying a diffeence of abou 6% in he amoun of equiy issued beween he indusy wih he highes gowh (i.e., posiive y ) and ha wih he lowes gowh. Below is a plo of he pice pe uni capial in indusy 5 27

29 afe a bun-in peiod of 000 yeas; his is beside a plo of he coesponding expeced excess euns fo he same indusy ove he same peiod. As explained ealie, when he pice of capial is high expeced euns ae low, and vice vesa. The model also poduces he familia un-ups peceding majo issuance evens, and which ae subsequenly followed by declining euns. An insance of his is ploed below. 28

30 The figue illusaes he aveage euns 5 yeas befoe and five yeas afe a majo invesmen made by he leading invesing indusy (i.e., he even is said o ake place wheneve he leading indusy makes an invesmen of y>5%). While he gaph plos acual euns (and no cumulaive abnomal euns, CARs), i should be clea ha he expec euns pio o he even ae highe han he expeced euns following he even, hus using a make model o adjus fo isk will esul in he obseved paens in CARs. We calculae he make capial of each indusy by muliplying is dae pice pe uni capial by he size of he indusy. We calculae he make-o-book aio of an indusy o be is pice pe uni capial. By soing he indusies wih espec o size, make-o-book, invesmen, and eanings, we can calculae he vaious asse picing momens, epoed below: Pofolio Aveage Excess Reuns SMB.0% HML 5.4% Low Invesmen 3.3% High Invesmen 2.% High Payoffs 0.8% Low Payoffs 0.4% The SMB euns ae he aveage diffeence beween he annual expeced euns of he smalles indusy (in make value) and he lages indusy a dae. We use expeced euns ahe han ealized euns o impove he powe of he es (and because we can calculae hese in ou model). We only use he lae half of he simulaed sample (using he fis half makes a negligible diffeence given he numbe of significan digis we keep). The HML euns ae he aveage diffeence beween he annual expeced euns 29

31 of he highes book-o-make indusy and he lowes book-o-make indusy a dae. Boh he SMB and HML euns ae consisen wih sylized coss-secional evidence in magniude and sign. The Low Invesmen pofolio euns epo he diffeence beween he lowes y indusy expeced euns a dae and he uncondiional expeced euns (iid in ou paameeizaion, and equal o 9%). The High Invesmen pofolio euns ae similaly calculaed. Boh ae consisen wih he obseved issuance puzzle. The payoff pofolios epo a simila aveage fo he indusy ha happens o pos he highes (esp. lowes) change in payoffs beween daes - and. These lae esuls ae consisen wih he eanings momenum phenomenon obseved by Benad and Thomas (989). 3. Evidence The esuls in Secion 2.2. and Poposiion imply ha he book-o-make aio in he sho un and he poduciviy in he seady sae ae he key vaiables o deemine he coss-secional vaiaion in expeced euns. We now examine his poin empiically. Consisen wih he model s implicaion, we will find ha aveage euns incease wih he poxies of hese wo quaniies. 3. Daa and Mehodology We obain accouning vaiables fom he Compusa annual file. d k in Equaion (22) can be measued by he long un aveage eanings pe uni capial. We compue his as he aio of Opeaing Income Befoe Depeciaion (Compusa Xpessfeed daa iem OIBDP, FTP daa iem 3) o lagged Popey Plan and Equipmen - Toal (Goss) 30

32 (PPEGT, daa 7). c k in he denominao of ha equaion measues he cos of ceaing uni capial, o he pe peiod change in he book value of a fim s poducive asses. To avoid division by zeo, we employ he goss (ahe han ne) gowh ae of PPEGT (daa 7). Given by he aio of hese wo quaniies, ou poxy fo a fim s poduciviy, PROD, a he end of fiscal yea effecively equals OIBDP / PPEGT OIBDP PROD PPEGT PPEGT PPEGT = =. (50) / The consucion of he book-o-make aio (BM) follows Fama and Fench (993). Based on he fim chaaceisics a he end of fiscal yea, we fom pofolios in June of calenda yea and measue value-weighed monhly euns fom July hough nex June. The consevaive six-monh lag accouns fo possible delay in he disseminaion of accouning infomaion and follows he usual pacice. The monhly euns and vaiables necessay o compue make capializaion ae fom he Cene fo Reseach in Secuiy Pices (CRSP), which ae mached o he Compusa daa by he CRSP-Compusa Meged Daabase. We use only odinay common shaes (CRSP Shae Code 0 o ) of fims in non-financial indusies (one digi SIC code no equal o 6), because invesmen of financial fims may be vey diffeen in naue fom ha of non-financial fims. We use only NYSE fims (CRSP Exchange Code ) o compue beakpoins fo anking, bu include NYSE, AMEX, and NASDAQ fims (CRSP Exchange Code, 2, and 3) in pofolio fomaion. Ou final sample uns fom July 968 hough Decembe

33 3.2 Resul 3.2. One dimensional so on PROD Table shows he chaaceisics, excess euns, and isk-adjused alphas of decile pofolios soed by PROD. The second column ells us ha fims in he lowes PROD decile incu losses on aveage. The make capializaion (SIZE) ends o incease, and BM o decease, wih PROD, bu he elaions ae no monoone. In fac, we will see vaiaions in BM wihin a given PROD quinile, and vice vesa, when pofolios ae double soed by hese quaniies in he nex subsecion. The able also indicaes ha hee ae elaively a lage numbe of fims (N) in he op and boom deciles; his implies ha many NASDAQ fims fall in hese wo exeme PROD deciles, and ha he poin esimaes of SIZE and BM may no popely epesen he chaaceisics of fims in hose deciles. To he exen of such vaiaion in chaaceisics, he excess eun (EXRET) may no exhibi a linea elaionship wih PROD. This appeas o be he case in he column fo EXRET, fom which one migh incoecly conclude ha he undepefomance of low PROD fims pimaily comes fom he lowes PROD decile only. To accoun fo he poenial loadings on isk facos, we compue alpha fom a ime seies egession of each excess pofolio eun on he excess make eun and he size, value, and momenum facos. 7 The esimaed fou-faco alpha (ALPHA) inceases wih PROD moe monoonically, and ends o be negaive fo low poduciviy fims and posiive fo high poduciviy fims. While he zeo-invesmen pofolio ha goes long he highes 7 The fou facos ae MKTRF, SMB, HML, and MOM, especively, downloaded fom Kenneh Fench s web sie. We hank him fo making hese seies available. 32

34 poduciviy fims and sho he lowes poduciviy fims eans a significan, albei only modeae, aveage eun of 0.36% pe monh, is isk-adjused alpha is 0.56% pe monh and is significan a he % level. This demonsaes ha, consisen wih Poposiion, fims wih highe poduciviy ean highe expeced euns and ha his poduciviy pemium canno be explained by exising isk facos. Anohe way o conol fo exising piced facos is o fuhe so fims by he chaaceisics o which he isk facos ae coelaed. This is he subjec of he nex wo subsecions Two dimensional so on BM and PROD Table 2 pesens he chaaceisics of 25 pofolios fomed as he coss secion of PROD and BM quiniles. Panel A indicaes ha aveage fims in he lowes PROD quinile again incu losses. Excep fo his quinile (and pehaps he highes-prod fouh-lages BM pofolio), he level of poduciviy is conolled faily well by he independen double so. Panel B epos he aveage size in million dollas. Fims in he lowes PROD quinile end o be small, especially fo gowh fims. If his has any implicaion on ou esul, he size effec will wok agains us; if high poduciviy fims end o be lage in size, we would expec hem o ean low aveage euns, ahe han high euns implied by Poposiion. Panel C demonsaes ha he independen double so conols fo he book-o-make aio quie well, as hee is lile vaiaion in BM along he columns. The numbe of socks in Panel D assues us ha each pofolio is well populaed on aveage. Panel E deseves aenion. Excess eun geneally inceases in PROD conolling fo BM. The poduciviy spead, given by he eun on a zeo-invesmen pofolio ha goes long he highes poduciviy fims and sho he lowes poduciviy fims wihin a BM quinile, monoonically deceases wih he level of BM. The long-sho pofolio 33

35 yields 0.8% pe monh among he gowh fims, which is significan a he % level. On he ohe hand, he value spead is songes among low poduciviy fims, yielding.05% pe monh. Ineesingly, he value spead monoonically deceases wih he level of PROD. The wo numbes shown above ae quie high. A legiimae concen is ha hese speads may paially eflec he ewad fo beaing known isks. The fou-faco alphas in Panel F conol fo his possibiliy. As anicipaed, he value spead is significanly educed afe aking ino accoun he loadings on he value and ohe facos. Howeve, he poduciviy spead baely changes o even inceases fo gowh socks upon isk adjusmen; he fou-faco alpha of he zeo-invesmen poduciviy pofolio is 0.92% among gowh fims. This magniude of alpha is no only saisically significan (a he % level), bu also economically significan. The alpha deceases monoonically wih BM. Fo conceeness, he nex subsecion fuhe conols fo size Thee dimensional so on Size, BM and PROD Table 3 epos he chaaceisics of 27 pofolios fomed as he coss secion of SIZE, BM, and PROD eciles. Fo simpliciy, we focus on he lowes and highes poduciviy eciles as we ae ineesed in he poduciviy spead. Panel A shows he make capializaion of he nine SIZE-BM eciles a he lowes and highes poduciviy levels. Again, if hee is any bias esuling fom size, i will wok agains us because he highes poduciviy fims end o be lage han lowes poduciviy fims, heeby educing he poduciviy spead. Similaly, he book-o-make aio in Panel B appeas o be well conolled. Panel C confims ha he poduciviy spead is highes among small o mid gowh fims, yielding 0.72% o 0.76% pe monh, boh significan a %. These speads baely change wih isk adjusmen; he fou-faco alphas in Panel D fo he 34

36 coesponding pofolios ae 0.68% and 0.6% pe monh, especively. Indeed, he alpha fo he lages gowh pofolio is also significan a he 5% level, yielding 0.49% pe monh. Oveall, he empiical esul pesened in his secion is consisen wih Poposiion, which says ha high poduciviy fims should ean high euns. This poduciviy effec canno be explained by exising isk facos. 4. Conclusion Tadiionally he asse picing lieaue has aken he se of copoae asses as given and hen asked wha he equilibium euns should be o hose ha hold hem. Recenly a numbe of papes have begun o look a he poblem when copoae asses change ove ime. Aicles by Spiegel (998), Waanabe (2008), Biais, Bossaes, and Spa (2008), Paso and Veonesi (2005), Dima and Thako (2007), Bek, Geen and Naik (999), and Calson, Fishe, and Giammaino (2004, 2006) all fall ino his caegoy. This pape seeks o add o his lieaue a geneal equilibium view of he poblem. Rahe han ake he picing kenel as given o he movemen in asse supplies boh ae unde he populaion s conol o a leas some degee. In his pape asse pices ae endogenously deemined peiod by peiod via make cleaing condiions. A he same ime copoae capial socks ae impaced by boh andom flucuaions and fims as hey seek o add and subac fom hei capial base in esponse o make condiions. The end esul is a acable model ha yields a numbe of empiical pedicions many of which ae consisen wih he daa. Among hese ae he following: 35

37 Sock euns should be posiively coelaed wih a poxy fo poduciviy of capial, such as he eanings yield on a fim s capial sock. Lage euns (pice moves) in one diecion will be followed by a decaying seies in he opposie diecion. Capial expendiues will be negaively coelaed wih fuue euns. Since he CAPM holds, peiod-by-peiod in he model, he above elaionships egading euns also hold fo peiod-by-peiod beas. This, howeve, also implies ha empiical models ha do no allow beas wih ime ends will be incoecly specified. In paicula, he CAPM bea should be modeled as a deceasing funcion of capial invesmen. We plan o calibae ou model and empiically examine hese pedicions in fuue wok. 36

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