Earnings-consumption betas and stock valuation

Transcription

1 : Amecan J. nance and Accounn anns-consumpon beas and sock valuaon laude Beeon* École des scences de l admnsaon (SA Unvesé du Québec (TÉLUQ Québec Québec anada mal: claude.beeon@eluq.ca *oespondn auho Jean-ee Gueye and Komlan Sedzo École des scences de la eson (SG Unvesé du Québec à Monéal (UQÀM Monéal Québec anada mal: ueye.jean-pee@uqam.ca mal: sedzo.k@uqam.ca Absac: Ths pape neaes he lon-un covaance beween aeae consumpon and fm eanns no he sock valuaon pocess. Afe assumn ha fms adjus he dvdend paymens owad a ae dvdend payou ao we use he neempoal famewok of he consumpon capal asse pcn model (AM o exploe he effec of sysemac eanns sks on nnsc sock values. Ou man esuls show ha he equlbum pce of a sock s posvely elaed o s lon-un eanns owh ae and neavely elaed o s eanns-consumpon bea obaned fom s lon-un covaance beween eanns owh and aeae consumpon owh. Ths suess ha lon-un sk measued wh eanns affecs he heoecal value of a fm. Oveall ou wok suess ha he lon-un concep of sk usn accounn eanns epesens an appopae paamee fo esman he equy value of a fm. Keywods: Sock valuaon; Accounn bea; Ineempoal model; Lon-un sk; AM. Refeence o hs pape should be made as follows: Beeon. Gueye J-. and Sedzo K. (20X ʻanns-consumpon beas and sock valuaonʼ Amecan J. nance and Accounn Vol. XX No. X pp. XX-XX. Boaphcal noes: laude Beeon hd s an Assocae ofesso of nance a he Unvesy of Quebec (TÉLUQ anada. Hs eseach neess ae n dvdend polcy sock valuaon and neempoal models. He has publshed eseach papes n nenaonal pee-evewed jounals such as Jounal of conomcs and nance (Spne nance Reseach Lees (lseve Amecan Jounal of nance and Accounn (Indescence néco (Laval Unvesy and Inenaonal Jounal of conomcs and nance (Toono. D Beeon s he coespondn auho and can be conaced a: claude.beeon@eluq.ca

2 2 anns-consumpon beas and sock valuaon Jean-ee Gueye hd s an Assocae ofesso a he School of Manaemen Unvesy of Quebec n Moneal. He eceved hs h.d. fom Laval Unvesy anada. He has publshed seveal papes n efeeed scenfc jounals. Komlan Sedzo hd s a ofesso a he School of Manaemen of Unvesy of Quebec n Moneal (SG-UQAM. ofesso Sedzo has a boad ane of eseach neess encompassn such aeas as ovenance and pefomance evaluaon of fnancal and mcoced nsuons copoae fnance opmal pofolo allocaon alenave nvesmens ncludn hede funds eal esae and commody devaves and he applcaon of opeaonal eseach mehods n fnance. He has publshed numeous acles and ven pesenaons a vaous nenaonal confeences on hese opcs. Inoducon Accodn o Nekasov and Shoff (2009 measuemen of sk s pehaps he snlemos dffcul ask n valun a secuy. In addon accodn o he auhos f fm value s deemned by fundamenal vaables such as eanns hen would make sense o measue sk decly fom fundamenals. These pons of vew ae conssen wh consdeable eseach esablshn he empcal o heoecal elaon beween accounn vaables and make sk. o example Beave e al. (970 fnd a snfcan coelaon beween sandad make beas and accounn beas. Beave and Maneold (975 eveal a noewohy assocaon beween make and accounn beas as measued unde a vaey of specfcaons. Ismal and Km (989 confm po fndns abou he snfcan elaon beween make beas and eanns beas usn fou dffeen accounn eun vaables. 2 Kaels and Sackley (993 examne he sascal elaonshp beween make and accounn beas n he U.S. bankn ndusy. The esuls ndcae ha he accounn beas ae coelaed wh he make counepas a levels smla o ohe (non-bankn sudes. Bansk and Wahlen (2003 show ha accounn beas ae snfcanly posvely elaed o he pced sk pemums n unvaae eessons bu povde only lmed explanaoy powe. Nekasov and Shoff (2009 use he esdual ncome valuaon model o analycally deve a smple sk adjusmen ha equals he covaance beween a fm s eun on book equy (RO and economy-wde sk facos. Oveall he empcal esuls valdae he fundamenal accounn sk measues. In a ecen pape Da (2009 poposes a novel way o esmae sysemac sk usn exclusvely lon-un accounn eanns and aeae consumpon daa. Moe pecsely he auho poposes ha he covaance beween lon-un accounn eun and lon-un aeae consumpon epesens an appopae empcal measue of sk. Hs esuls show ha hs measue of sk explans 58% of he cossseconal vaaon n sk pema. If we add a duaon measue he model explans

3 . Beeon J-. Gueye and K. Sedzo 3 moe han 80%. Lkewse Da and Waachka (2009 consuc an analys eanns bea ha measues he covaance beween he cash flow nnovaon of an asse and hose of he make. They fnd evdence ha hs cash flow sk measue s pced n he coss-secon of expeced sock euns (see also Schluee and Seves 204. As Goyal (202 p. 29 menoned n hs asse pcn leaue evew Da s model s vey useful n explann euns. Also as Ball and Sadka (205 p. 5 poned ou sudes on sysemac eanns sk epesen a pomsn avenue fo fuhe eseach. In hs pape we consuc a sock valuaon model ha neaes he lon-un covaance beween eanns and aeae consumpon. Smlaly o Da s sudy ou sock valuaon model exends he mpoan concep of lon-un sk fs naed by Bansal and Yaon (2004 and Bansal e al. (2005. Bansal and Yaon (2004 eveal ha ha consumpon and dvdend owh aes nclude a small lon-un componen ha n conjuncon wh psen and Zn s (989 pefeences explans key asse make phenomena and esolves he equy pemum puzzle. Bansal e al. (2005 also show ha cash flow beas a measue of sk calculaed by he lon-un covaance beween dvdend owh and aeae consumpon owh accoun fo moe han 60% of he coss-seconal vaaon n sk pema. Accodn o Beele and ampbell (202 he lon-un sks model of Bansal and Yaon (2004 and Bansal e al. (2005 has aaced a ea deal of aenon wh mpoan subsequen wok by Hansen e al. (2008 Bansal e al. (2009 Bansal and Kku (20 and Bansal and Shalasovch (203 amon ohes. Alon hese lnes Beeon (203-A develops a heoecal sock valuaon model ha consdes he lon-un sensvy of dvdends o aeae consumpon and Beeon (203-B exends hs model o vaous economc facos. As lon e al. (204 noed he coec way o deemne he nnsc value of socks has occuped an enomous amoun of effo ove a lon peod of me. 3 Indeed follown he adonal models of Godon (962 Basu (977 and Ohlson (995 many ohe exenson models have been poposed o esmae he value of a sock. xamples nclude elham and Ohlson (999 aso and Veones (2003 Baksh and hen (2005 Don and Hshlefe (2005 Yee ( and Huley (203 n addon o Beeon (203-A 203-B. Neveheless none of hese above-menoned woks develop a heoecal sock valuaon model ha explcly neaes he lon-un covaance beween eanns owh and aeae consumpon owh decly no he nnsc value. In hs sense we can aue ha he movaon of he pesen pape comes fom he follown obsevaons: ( he success of he ecen concep of lon-un sk; (2 he empcal success of he lon-un covaance beween eanns and consumpon as

4 4 anns-consumpon beas and sock valuaon an appopae measue of sk; (3 he mpoance of sock valuaon n fnance; (4 he absence of a heoecal sock valuaon model ha explcly neaes he lonun eanns-consumpon covaance as a measue of sk. The developmen of ou model nvolves he follown seps. s we chaacese he hypohecal economy usn he neempoal equlbum famewok of he consumpon capal asse pcn model (AM of Rubnsen (976 Lucas (978 and Beeden (979. Then we show unde cean condons ha eanns and sock pces ae pefecly coneaed and ha andom fuue pces and eanns ae decly and sochascally elaed. Nex we demonsae ha a sock s eanns owh s posvely elaed o s lon-un covaance beween eanns and aeae consumpon. nally we solae he equlbum sock pce fom he above elaonshp. In hs manne we show ha he nnsc value of a sock s posvely elaed o s lon-un eanns owh ae and neavely elaed o s eannsconsumpon bea measued by he lon-un covaance beween he eanns owh ae of he sock and he lon-un owh ae of he aeae consumpon dvded by he lon-un owh ae of he aeae consumpon. Theeby he man conbuon of he model s o demonsae ha eannsconsumpon beas affec fm heoecal values. In addon ou wok suess ha he eanns-consumpon bea epesens an appopae measue of sk (on he lonun. Moeove suppos he use accounn vaables fo esman sk. Besdes eveals ha expeced eanns owh aes should be posvely elaed o sk n heoy. The emande of hs pape s oansed as follows. Secon 2 pesens he neempoal equlbum famewok. Secon 3 deves he nnsc value of a sock usn eanns and aeae consumpon. Secon 4 concludes. 2 The neempoal equlbum famewok ollown Beeon (203-B p. 87 and ohes befoe ou model s neempoal equlbum famewok consdes a hypohecal economy n whch he epesenave nveso maxmses he me-sepaable uly funcon: 4 s U ( ( s0

5 . Beeon J-. Gueye and K. Sedzo 5 subjec o esouce consans whee ( s me dscoun faco (. s s s he aeae consumpon a me s he U( s an nceasn concave and devable funcon and 0 The soluon o hs poblem ven by he fs ode necessay condons can be used o show ha he pce of sock a me equals: U ( s D (2 s U ( whee D s s he dvdends of sock a me pemum epesens a devave of a funcon. 5 s ( s 2... and whee he The h-hand sde of quaon (2 coesponds o he pesen value of all fuue cash flows (dvdends whee he sochasc dscoun faco s equvalen o he neempoal manal ae of subsuon beween and ( : s U / U (. Wh hs noaon he equlbum pce of a sock becomes: ( s M s M s s M D. (3 Recusvely quaon (3 can be expessed fo a snle peod (beween and + n he follown manne (see ochane 2005 p. 27: whee M ( D ] (4 [ epesens he pce of sock a me + ven he avalable nfomaon a me. Moeove snce s nonzeo and s known wh he cuen nfomaon can hus be passed houh he condonal expecaon opeao and dvded on each sde o ndcae ha: [ M ( ] (5 whee s he ae of eun of sock beween me and + ( ( D /. In he same manne f hee s a sho-em skless asse we can we:

6 6 anns-consumpon beas and sock valuaon [ M ( ] (6 whee s he ae of eun of he skless asse beween me and +. quaons ( o (6 ae well known. In he follown secon we wll combne hese fundamenal equlbum condons wh eanns o oban a paccal nnsc value. 3 anns and sock pces Ths secon demonsaes ha he equlbum pce of a sock s a funcon of s expeced eanns owh ae oehe wh he covaance beween s eanns and aeae consumpon. We ben by assumn ha fms adjus he dvdend paymens owad a ae dvdend payou ao. We hen neae eanns no he fundamenal value of a lon-lved asse o eveal ha eanns and sock pces ae coneaed. Theeafe we deve he nnsc value of a sock usn (fs he quadac uly funcon (second he Taylo s expanson heoem (hd he nomal dsbuon and (fouh he lnea pocess fo eanns. 3. Quadac uly funcon The quadac uly funcon s commonly used n fnance (and economcs. As Huan and Lzenbee (988 p. 207 noed explc pcn fomulae can be deved by assumn ha he epesenave aen s uly funcon s quadac. In addon Huan and Lzenbee demonsaed ha he sk-eun elaonshp poposed by he canoncal AM can be easly deved usn hs smple uly funcon whch we also ulzed n subsecon 3.. Dvdend payou ao Smlaly o Baksh and hen (2005 and Don Hshlefe (2005 ou valuaon sock model focuses on eanns and bens by assumn ha dvdends elae o eanns accodn o: wh D d X (7 [ ] OV [ ] 0

7 . Beeon J-. Gueye and K. Sedzo 7 whee s he dvdend payou ao of sock ; s he eanns of sock a me ; and s he usual esdual andom em assocaed o quaon (7 fo sock a me ( s d s s X s The second lne of quaon (7 smply supposes ha he usual andom em ven he avalable nfomaon n me dsplays a zeo mean value and a zeo covaance wh any ohe andom vaables. As Don and Hshlefe (2005 menoned hs paameesaon s nsped by he classc suvey of Lnne (956 whch found ha fms adjus owad a ae dvdend ao. Theeby nean quaon (7 n quaon (3 ndcaes ha: M ( d X. (8 s The sandad assumpons eadn he esdual ems also ndcae ha: s M d X. (9 As befoe snce he eanns value of sock a me s known ven he avalable nfomaon a me hus be passed houh he condonal expecaon opeao of quaon (9 o exhb: X M d X / X (0a s X o f we assemble he elemens of he summaon em: whee vaable X H ] (0b [ H s defned n hs manne: H s M d X / X he noaon we can also expess quaon (0b n hs compac fom: X. To smplfy (0c whee [ H ]. Moeove f he sequence of vaables H ( = 0 2 s ndependen and dencally dsbued (..d. hen we can we:

8 8 anns-consumpon beas and sock valuaon X. ( Theefoe ven he avalable nfomaon a me quaon ( suess ha he fuue pce of he sock and he coespondn eanns ae sochascally elaed n he follown manne: X. (2 Inean quaons (7 ( and (2 no he snle peod expesson of he pce of an asse as fomulaed by quaon (4 allows us o we ha: X M ( X d X ] (3 [ and he sandad assumpon eadn he esdual em allows us o expess ha: Dvdn each sde of quaon (4 by Reaann also ndcaes ha: X M ( X d X ]. (4 [ X and ves afe smple manpulaons: [ M ( X / X d X / X ]. (5 [ M ( ( d ] (6 whee s he eanns owh ae of sock beween me and + ( X / X. quaon (6 pesens a pacula fom of he ule equaon expessed wh eanns. Takn he expecaon on each sde pems us o elease he ndex of he condonal opeao o eveals ha: [ M ( ( d ]. (7 In he same manne akn he expecaon on each of quaon (6 pems us o we:

9 . Beeon J-. Gueye and K. Sedzo 9 [ M ( ]. (8 quaon (7 mnus quaon (8 ves afe smples manpulaons he follown equaly: [ M {( ( d ( }]. (9 0 The mahemacal defnon of covaance ndcaes ha: om quaon (8 we have: OV [ M ( ( d ( ] M ] [( ( d ( ]. (20 [ [ M ] ( (2 and he basc popees of mahemacal covaance eveal afe smple manpulaons ha: OV [ M ]( d [ ]( d (. (22 Theefoe we can solae he expeced eanns owh ae of a sock o show ha equlbum condons pedcae ha: ] ( /( ( [ d OV M ]. (23 [ To e an explc pcn fomula we wll now make a sandad assumpon on he ndvdual uly funcon. Uly funcon We assume ha he uly funcon of he epesenave nveso s quadac whch 2 mples moe specfcally ha: U ( ( b / 2 wh b > 0 and < /b. Inean hs specfc uly funcon no quaon (23 shows ha: b [ ] ( OV d U( Usn aan he basc popees of covaance allows us o see ha:. (24

10 0 anns-consumpon beas and sock valuaon OV U b d ( ( ] [. (25 Mulplyn boh sdes of quaon (25 by and eaann ndcaes ha: OV U b d / ( ( ] [ (26a o f we pefe (known ha he covaance of a andom vaable wh a consan s equal o zeo: OV U b d ( ( ] [ (26b whee s he owh ae of aeae consumpon beween me and + ( /. Mulplyn on each sde by he vaance of he aeae consumpon owh ae ] [ 2 ves: ] [ ( ] [ ( ] [ 2 2 OV U b d. (27 Reaann allows us o see ha: d /( ( ] [ (28 whee ( / ] [ ( 2 U b ] [ ] / [ 2 OV. Snce all he follown values ( and ] [ 2 U b ae posve by consucon hen he paamee s also posve ( 0. The paamee can be vewed as an accounn consumpon bea. Moe pecsely epesens he sho-un eanns-consumpon bea of sock a me measued by he covaance beween he eanns owh ae of he sock and he aeae consumpon owh ae dvded by he vaance of he aeae consumpon

11 . Beeon J-. Gueye and K. Sedzo owh ae. I measues he sensvy of a company s eanns o aeae consumpon (eflecn economc acvy. quaon (28 epesens an equlbum condon fo one peod. I could be exended ove seveal peods o f we pefe n he lon un. Many peods In he lon un he elaonshp beween he company s eanns owh ae and s sensvy o aeae consumpon can be obaned by summn fom me zeo ( = 0 o me T- ( = T- ha s o say: T 0 T [ ] [( 0 /( d ] (29 o f we pefe by usn he basc popees of he summaon opeao: T 0 [ Mulplyn by he scala value whee w shows ha: T 0 T 0 [ T ] ( d ( 0 T 0 T. (30 0 on each sde of quaon (30 yelds: T ] ( d ( 0 T 0 T w (3 0 / wh 0 w. Dvdn by T on each sde of quaon (3 ( /( d (32 whee T / 0 T / 0 T 0 [ ] T T T / T 0 w. Hee he esmaos and epesen especvely he ahmec aveae of me values [ ] and whle can be vewed as he wehed aveae sensve coeffcens of me values ( = 2 3 T-.

12 2 anns-consumpon beas and sock valuaon To pu dffeenly epesens he lon-un expeced eanns owh ae of sock ; whle epesens he lon-un eanns-consumpon bea of sock o moe smply he eanns-consumpon bea of sock. Reaann quaon (32 we can we: ( /( /( d (33 o f we pefe: /[( /( ] d. (34 A me = 0 quaon ( ndcaes ha: 0 / X 0 ; whee he h hand sde of he equaly coesponds o he cuen pce-eanns ao of sock. Theefoe we can we: /[( /( ] d X 0 / 0 (35 o afe manpulaons: d X 0 0. (36 In hs manne we can easly solae he equlbum pce of a sock o oban a smple fomula expessed wh accounn eanns. Ths may be wen as: 0 d X 0. (37 quaon (37 epesens ou man esul. I shows ha he equlbum pce of a sock depends on s cuen dsbued eanns expeced eanns owh and eanns-consumpon bea. Moe pecsely quaon (37 eveals ha he cuen equlbum pce of he sock s posvely elaed o s cuen dsbued eanns and s fuue eanns owh ae and neavely elaed o s eanns-consumpon bea obaned fom he lon-un covaance beween eanns and aeae consumpon. Because he elaonshp beween he pce of he sock and s eannsconsumpon bea s neave he las paamee s vewed as a hful measue of sk. 6 In hs sense he above sock pce expesson suppos he use of fundamenal vaables (as eanns fo esman sk.

13 . Beeon J-. Gueye and K. Sedzo 3 om quaon (37 deemnn he nnsc value of a sock eques he follown seps: ( esablshn he economc exoenous vaables (such as he ae of eun of he skless asse and he aeae consumpon owh ae (2 obsevn he sock s cuen eanns dsbuon and (3 esman he sock s expeced eanns owh ae and he sock s eanns-consumpon bea. If he sock exhbs no covaance wh aeae consumpon o no sk hen he deemnaon of s nnsc value s analoous o he classc consan owh model wh eanns. 7 Besdes f we accep ha he eanns-consumpon bea epesens a measue of sk hen quaon (32 suess ha a company s expeced eanns owh ae s posvely elaed o sk (n he lon un. Ths pon of vew s nuvely appealn. I s also conssen wh classc sudes on he assocaon beween accounn vaables and sk n s sandad fom. 8 Indeed f we accep ha owh n eanns ases fom he eun on new nvesmen and f we accep ha eun s posvely elaed o sk hen we mus accep ha he eanns owh ae s posvely elaed o sk. 9 Ou conbuon wh quaon (32 s o chaacese hs heoecal elaonshp wh a lon-un accounn sk measue. The esmaon of We can use he obsevable values of he make pofolo o faclae he esmaon of paamee. Indeed fom quaon (35 we can we: /[( m m /( ] dm X m0 / m 0 (38 whee he ndex m ndcaes he make. Thus afe smple manpulaons we have: [ ( /( d Y ]/ (39 m m m m whee Y / m X m0 m 0. The las value smply efes o he eanns-pce ao of he ene make whch coesponds o he nvese of he popula pce-eanns ao. 0 So f we esmae (fo example ha: ( he eanns-consumpon bea of he make s equal o (2 he skless asse equals 6% (3 he eanns owh ae of he make equals 5% (4 he make dsbuon ao equals 50% and (5 he make pce-eanns ao equals 5 hen we can popose ha paamee should be equal o 2.42% as shown below; [ 0.05 ( 0.06 /( 0.5/5]/.05 (.06 /( %.

14 4 anns-consumpon beas and sock valuaon A value of fo he eanns-consumpon bea of he make can be jusfed (fo paccal applcaons known ha he canoncal AM esablshes an equvalency beween make-dvdend and aeae-consumpon. In hs secon we used he quadac uly funcon fo he sake of smplcy. Howeve hs escve assumpon can be noed usn he Taylo sees expanson as we wll demonsae n he nex secon. 3.2 Taylo sees Accodn o Taylo s heoem we can evaluae he funcon pon a n ems of s devaves as follows: y f (x aound he 2 ( N N f ( a( x a f ( a( x a f ( x f ( a f ( a( x a.... 2! N! When N s equal o he Taylo sees appoxmaon ndcaes ha: f ( x f ( a f ( a( x a. Theefoe as Beeden e al. (989 p. 233 obseved an appoxmaon of he manal ae of subsuon (MRS can be obaned fom he fs-ode Taylo sees. Indeed aound we have: U U ( U ( (. (40 ( Inean quaon (40 no quaon (23 suess ha he expeced eanns owh of a sock appoaches he follown value: [ ] d U( U ( ( ( OV. (4 U( Usn he basc popees of mahemacal covaance and hen eaann ndcaes ha: ] d U ( ( U( OV [ [ Mulplyn by on each sde of quaon (42 shows ha: ]. (42

15 . Beeon J-. Gueye and K. Sedzo 5 ( ( [ ] U OV d U (. (43 Mulplyn by 2 [ ] on each sde of quaon (43 eveals ha: [ ] d 2 U ( ( [ U( [ ] OV 2 [ ] ]. (44 Reaann allows us o see ha: whee [ d ˆ ] ( /( (45 ˆ 2 [ ]( ( U( / U ( ˆ 2 [ ]( RRA wh RRA U / U(. ( Hee he em RRA epesens he elave sk aveson evaluaed a. Is value s necessaly posve because he second devave of he uly funcon mus be neave by consucon and he ohe values n he paamee mus be posve. As a esul s also posve ( ˆ 0 f we adm ha he vaance of a andom vaable and he sk-fee ae of eun ae eae han zeo jus as he paamee. ˆ Gven hs f we eplcae he devaon fom quaon (28 o quaon (32 we e (non he appoxmaon: ( /( d ˆ ˆ (46 T 0 whee ˆ ˆ / T T 0 T ˆ wˆ wˆ ˆ / ˆ. 0

16 6 anns-consumpon beas and sock valuaon Thus usn quaons (33 o (37 we can epoduce ou man esul concenn he equlbum pce of a sock. Tha s: ˆ ˆ 0 ˆ ˆ d X 0 (47 whee ˆ and ˆ ae smla o efe o he quadac assumpon. and deved pevously excep ha hey do no In he nex secon we wll ncease he model s obusness usn he usual nomal dsbuon whou any specfc uly funcon. 3.3 Nomal dsbuon Accodn o Sen s lemma: f vaable and vaable funcon s dffeenable and he expecaon of ochane 2005 p. 64: f (x x y ae bvaae nomal he s < hen (see f (x OV [ y f ( x] [ f ( x] OV [ y x ]. So f we suppose ha and X ae bvaae nomally dsbued hen fom quaon (23 we can we ha: U( [ ] ( OV (48 d U( s equvalen o he follown equaly: ] d ( [ U ( U ( ] OV [ [ ]. (49 Aan usn he basc popees of mahemacal covaance and hen eaann we e: U ( [ ( ] [ ] OV. (50 d U( Also mulplyn by 2 ] on each sde of quaon (50 ndcaes ha: [

17 . Beeon J-. Gueye and K. Sedzo 7 ( [ ] d [ U ( U ( 2 ] [ [ ] OV 2 [ ] ]. (5 Reaann one moe me allows us o see ha: [ ] ( /( d (52 2 whee ]( ( [ U( ]/ U(. [ As befoe we can easly pove ha he paamee Aan usn quaons (28 o (32 we can we: s posve ( 0. ( /( d (53 T 0 whee T / T 0 w T w /. 0 Theefoe usn quaons (33 o (37 we can expess: 0 d X 0. (54 whee and ae also smla o ˆ and ˆ deved pevously excep ha hey do no efe o an appoxmaon. In he follown secon we wll conclae he model s obusness usn a lnea assumpon. Beeden e al. (989 p. 233 Bansal e al. (2005 p. 644 and Beeon (203-B p. 86 nsped hs pocedue (wh eanns. 3.4 Lnea funcon We assume ha he elaonshp beween eanns and consumpon owh aes s eneaed by he follown lnea funcon: (55

18 8 anns-consumpon beas and sock valuaon wh ] OV [ ] 0 [ whee s he necep fo sock a me ; s (aan he eanns sensvy o consumpon fo sock a me ; and s he usual andom em fo sock a me +. Besdes we can easly pove ha he coeffcen of he eanns sensvy o consumpon (he bea expessed no he las equaon s equvalen o he paamee pesened pevously: 2 2 ]/ [ OV ]. [ Inean quaon (55 no quaon (23 ndcaes ha he expeced eanns owh of a sock equals: [ ] ( [ ] OV M. (56 d Usn he basc popees of covaance one moe me allows us o we: ] (57 [ ] ( OV [ M d Reaann also allows us o we: [ ] ( /( d (58 whee ( [ OV M ] and he paamee s posve ( 0 because he covaance beween M and s by consucon neave. Usn quaons (28 o (32 we e: ( /( d (59 whee T 0 T / T 0 w T w /. 0

19 . Beeon J-. Gueye and K. Sedzo 9 nally usn quaons (33 o (37 we have: 0 d X 0 (60 whee and ae also smla o and deved pevously excep ha hey come fom he eanns lnea pocess expessed by quaon (55. 4 oncluson ollown he adonal dscouned cash flow appoach many exenson models have been poposed o esmae he value of a sock. The pmay conbuon of hs pape s o develop a new sock valuaon model ha akes no accoun he lon-un covaance beween eanns and aeae consumpon. u dffeenly he pmay conbuon of hs heoecal pape s o develop a new sock valuaon model ha neaes he ecen concep of lon-un sk usn accounn vaables. 3 San fom he neempoal famewok of he AM we showed ha he equlbum pce of a sock s posvely elaed o s lon-un eanns owh ae and neavely elaed o s eanns-consumpon bea obaned fom s lon-un covaance beween eanns owh and aeae consumpon owh. In so don hs pape exends he ecen and pomsn concep of lon-un sk o accounn eanns. 4 In addon suppos he use of accounn vaables fo esman sk. Moeove demonsaes ha he elaonshp beween expeced eanns owh and sk s posve. Oveall offes a new ool fo sock valuaon (especally fo odnay socks. nally he neempoal equlbum famewok of ou model consdeed a hypohecal economy n whch he epesenave nveso maxmses a mesepaable uly funcon. o fuue eseach may be suable o see how we could enealze he uly funcon. Noes In eneal an accounn bea epesens he covaance beween he eanns of a company and he make eanns dvded by he vaance of he make eanns. Random eanns ( can be deflaed by cuen pces ( 0 book values (B 0 o eanns ( 0 usn he follown aos: / 0 /B 0 and / 0.

20 20 anns-consumpon beas and sock valuaon 2. In he sudy Ismal and Km (989 use fou accounn vaables: ( ncome avalable o common equy; (2 ncome avalable o common equy plus depecaon; (3 ncome avalable o common equy plus depecaon and defeed axes; and (4 cash flows eneaed fom connun opeaons. 3 See hape 8 n lon e al. ( In hs documen he opeaos VAR and OV efe especvely o mahemacal expecaon vaance and covaance whee ndex mples ha we consde he avalable nfomaon a me. uhemoe he lde ( ndcaes a andom vaable. 5 See Rubnsen (976 o ochane (2005 hape. 6 quaon (28 demonsaes ha λ s posve (fo evey. As a esul paamee λ n quaon (37 s also posve. 7 See he consan owh model hape 8 n lon e al. ( On he posve elaonshp beween owh and sk see fo example he classc sudy of Beave e al. (970 and ohes. 9 See aan hape 8 n lon e al. ( The eanns-pce ao (eanns dvded by pce s somemes called he eanns-yeld. The second lne of quaon (55 assumes (as befoe ha he andom sandad em (Ɛ pesens a zeo mean value and a zeo coelaon value wh any ohe vaables. 2 If x y and e epesen eneal vaables and f y = a + bx + e whee OV(x e = 0 hen OV(x y = OV(x a + bx + e = OV(x xb. Theefoe: b = OV(x y/σ 2 (x. 3 Ohlson (995 elham and Ohlson (999 and Beeon (203-A fo example also pesen heoecal papes on sock valuaon ha offe dec paccal mplcaons. 4 Accodn o eson e al. (203 he lon-un sk model follown Bansal and Yaon (2004 has been a phenomenal success. Refeences Bansk. and Wahlen J.M. (2003 ʻResdual ncome sk nnsc values and shae pcesʼ The Accounn Revew Vol. 78 No. pp Baksh G. and hen Z. (2005 ʻSock valuaon n dynamc economesʼ Jounal of nancal Makes Vol. 8 No. 2 pp. -5. Ball R. and Sadka G. (205 ʻAeae eanns and why hey maeʼ Jounal of Accounn Leaue Vol. 34 No. pp Bansal R. Dma R.. and Kku D. (2009 ʻoneaon and consumpon sks n asse eunsʼ Revew of nancal Sudes Vol. 22 No. 3 pp

21 . Beeon J-. Gueye and K. Sedzo 2 Bansal R. Dma R.. and Lundblad. (2005 ʻonsumpon dvdends and he coss-secon of equy eunsʼ The Jounal of nance Vol. 60 No. 4 pp Bansal R. and Kku D. (20 ʻoneaon and lon-un asse allocaonʼ Jounal of Busness and conomc Sascs Vol. 29 No. pp Bansal R. and Shalasovch I. (203 ʻA lon-un sks explanaon of pedcably puzzles n bond and cuency makesʼ The Revew of nancal Sudes Vol. 26 No. pp Bansal R. and Yaon A. (2004 ʻRsks fo he lon un: A poenal esoluon of asse pcn puzzlesʼ The Jounal of nance Vol. 59 No. 4 pp Basu S. (977 ʻInvesmen pefomance of common sock n elaon o he pce eanns aos: a es of effcen make hypohessʼ The Jounal of nance Vol. 32 No. 3 pp Beave W. Kele. and Scholes M. (970 ʻThe assocaon beween make deemned and accounn deemned sk measuesʼ The Accounn Revew Vol. 45 No. 4 pp Beave W. and Maneold J. (975 ʻThe assocaon beween make-deemned and accounndeemned measues of sysemac sk: some fuhe evdenceʼ Jounal of nancal and Quanave Analyss Vol. 0 No. 2 pp Beele J. and ampbell J. (202 ʻThe lon-un sks model and aeae asse pces: an empcal assessmenʼ cal nance Revew Vol. No. pp Beeon. (203-A ʻDvdend owh sock valuaon and lon-un skʼ Jounal of conomcs and nance Vol. 37 No. 4 pp Beeon. (203-B ʻDvdend sensvy o economc facos sock valuaon and lon-un skʼ nance Reseach Lees Vol. No. 3 pp Beeden D.T. (979 ʻAn neempoal asse pcn model wh sochasc consumpon and nvesmen oppounesʼ Jounal of nancal conomcs Vol. 7 No. 3 pp Beeden D.T. Gbbons M.R. and Lzenbee R.H. (989 ʻmpcal ess of he consumponoened AMʼ The Jounal of nance Vol. 44 No. 2 pp ochane J.H. (2005 Asse cn. nceon Unvesy ess nceon N.J. Da Z. (2009 ʻash flow consumpon sk and he coss-secon of sock eunsʼ The Jounal of nance Vol. 64 No. 2 pp Da Z. and Waachka M.. (2009 ʻasflow sk sysemac eanns evsons and he coss-secon of sock eunsʼ Jounal of nancal conomcs Vol. 94 No. 2 pp Don M. and Hshlefe D. (2005 ʻA enealzed eanns-based sock valuaon modelʼ The Manchese School Vol. 73 No. 9 pp. -3. lon. Gube M. Bown S.J. and Goezmann W.N. (204 Moden ofolo Theoy and Invesmen Analyss. Wley 9 h don NewYok N.Y. (752 p.. psen L. and Zn S. (989 ʻSubsuon sk aveson and he empoal behavo of consumpon and asse euns: A heoecal famewokʼ conomeca Vol. 57 No. 4 pp elham G.A. and Ohlson J.A. (999 ʻResdual eanns valuaon wh sk and sochasc nees aesʼ The Accounn Revew Vol. 74 No. 2 pp eson W. Nallaeddy S. and Xe B. (203 ʻThe ou-of-sample pefomance of lon-un sk modelsʼ Jounal of nancal conomcs Vol. 07 No. 3 pp Godon M. (962 The Invesmen nancn and Valuaon of he copoaon. Iwn Homewood Ill (256 p..

22 22 anns-consumpon beas and sock valuaon Goyal A. (202 ʻmpcal coss-seconal asse pcn: a suveyʼ nancal Makes and ofolo Manaemen Vol. 26 No. pp Hansen L.. Heaon J.. and L N. (2008 ʻonsumpon skes back?: Measun lon-un skʼ Jounal of olcal conomy Vol. 6 No. 2 pp Huan. and Lzenbee R.H. (988 oundaons fo fnancal economcs. lseve Scence ublshn New Yok N.Y. Huley J.W. (203 ʻalculan fs momens and confdence nevals fo enealzed sochasc dvdend dscoun modelsʼ Jounal of Mahemacal nance Vol. 3 No. 2 pp Ismal B.. and Km M.K. (989 ʻOn he assocaon of cash flow vaables wh make sk: fuhe evdenceʼ The Accounn Revew Vol. 64 No. pp Kaels G.V. and Sackley W.H. (993 ʻThe elaonshp beween make and accounn beas fo commecal banksʼ Revew of nancal conomcs Vol. 2 No. 2 pp Lnne J. (956 ʻDsbuon of ncomes of copoaons amon dvdends eaned eanns and axesʼ Amecan conomc Revew Vol. 76 No. 2 pp Lucas R.. (978 ʻAsse pces n an exchane economyʼ conomeca Vol. 46 No.6 pp Nekasov A. and Shoff.K. (2009 ʻundamenals-based sk measuemen n valuaonʼ The Accounn Revew Vol. 84 No. 6 pp Ohlson J.A. (995 ʻanns book values and dvdends n equy valuaonʼ onempoay Accounn Reseach Vol. No. 2 pp aso L. and Veones. (2003 ʻSock valuaon and leann abou pofablyʼ The Jounal of nance Vol. 58 No. 5 pp Rubnsen M. (976 ʻThe valuaon of uncean ncome seams and he pcn of oponsʼ The Bell Jounal of conomcs Vol. 7 No. 2 pp Schluee T. and Seves S. (204 ʻDeemnans of make bea: he mpacs of fm-specfc accounn fues and make condonsʼ Revew of Quanave nance and Accounn Vol. 42 No. 3 pp Yee K.K. (2008 ʻA Bayesan famewok fo combnn valuaon esmaesʼ Revew of Quanave nance and Accounn Vol. 30 No. 3 pp Yee K.K. (200 ʻombnn fundamenal measues fo sock seleconʼ In Handbook of Quanave nance and Rsk Manaemen pp Spne New Yok N.Y.