Rational Expectation and Expected Stock Returns

Transcription

1 aional Expecaion and Expeced Sock eurns Chia-Cheng Ho Deparmen of Finance Naional Chung Cheng Universiy Chia-Yi Taiwan epublic of China Chien-Ting Lin* School of Commerce Universiy of Adelaide 233 Norh Terrace Adelaide SA 5005 Ausralia Tel: Fax: *Corresponding Auhor

2 aional Expecaion and Expeced Sock eurns Absrac The primary purpose of he sudy is neiher o resolve he dispue over he linkage beween he common risk facor and he documened characerisic nor o pursue he correc asses pricing model. Insead we examine wheher hese observed empirical regulariies are consisen wih he raional expecaions framework in which curren available informaion can help predic fuure sock reurns. The resuls indicae ha accouning-relaed aribues such as asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke and earnings-o-marke appear o have lile predicive power on fuure sock reurns. In conras he marke-relaed aribues such as firm size momenum sraegy rading volume and marke reurns are found o capure variaions in fuure sock reurns. 2

3 . Inroducion There is growing empirical evidence ha cross-secional variaions in sock reurns can be explained by cerain firm specific characerisics such as size (CAPT) book-o-marke (BE_ME) earnings-o-price (EA_ME) cash flow-o-price (CF_ME) and dividend yield (DV_ME). For example Banz (98) shows ha small firms earn significanly higher risk adjused reurns han large firms. Basu (983) also finds ha earnings-o-price capures variaion in average sock reurn afer conrolling firm size and bea. While Bhandari (988) documens ha average reurns are posiively relaed o he raio of deb o equiy. In an imporan series of papers Fama and French ( ) (henceforh FF) find ha size and book-o-marke play a more dominan role in explaining cross-secional differences in expeced reurns and subsume he apparen effecs of oher well known facors. In heir subsequen ess FF (993) adop he ime-series regression approach of Black e al. (972) and idenify hree common risk facors relaed o he average sock reurns; marke firm size (SMB small minus big) and book-o-marke (HML high minus low). They conclude ha size and book-o-marke equiy are proxies for sensiiviy o common risk facors in sock reurns. In addiion o firm specific characerisics numerous sudies have documened several paerns in average sock reurns. Mos noably Debond and Thaler (985) find ha pas losers end o become fuure winners. In line wih he finding ha sock reurns exhibi long-erm reversals Lakonishok a al. (994) (henceforh LSV) also show ha value socks (wih high book-o-marke earnings-o-price or cash flow-o-price) ouperform growh socks (wih low book-o-marke earnings-o-price or cash flow-o-price). While hese findings seem o sugges ha conrarian sraegies using pas reurns or firm characerisics could generae excess reurns in he long run Jagadeesh and Timan (993) find ha over a shor invesmen horizon of 3 o 2 monhs pas winners on average coninue o ouperform pas losers. Socks herefore appear o carry momenum in he shor run. 3

4 Alhough here is some consensus ha size and book-o-marke equiy facor in paricular are imporan in pricing socks a fundamenal disagreemen on he underlying reasons has emerged. FF argues ha higher reurns of high book-o-marke socks are due o higher sysemaic risk. LSV however explain ha higher reurns are caused by he overreacion of invesors. Tha is invesors are oo opimisic (pessimisic) o firms ha have performed well (poorly) in he pas. Daniel and Timan (997) indicae ha alhough high book-o-marke socks do srongly covary wih higher expeced reurns he covariance does no resul from compensaion for facor risk suggesed by FF (993) bu i raher reflecs he fac ha high book-o-marke socks end o have similar properies. For example hese socks migh be from he same indusry or hey migh be in relaed lines of businesses. The evidence suggess ha facor loadings do no explain he higher reurns of small or high book-o-marke socks once characerisics are aken ino accoun. In oher words i is he characerisics raher han facor loadings ha deermine expeced reurns. Furhermore from he marke microsrucure poin of view numerous sudies sugges ha rading volume is also an imporan source of cross-secional variaions in sock reurns. For example Simon e al. (998) repor ha socks experiencing unusually high rading volume over a day or a week end o experience large reurns over he subsequen monhs. More precisely a high-volume reurn premium seems o exis in sock prices. In oher relaed work Daer e al. (998) sugges ha urnover rae a proxy for rading volume and liquidiy may reduce he size impac of differen socks. They also provide evidence of negaive relaionships beween sock reurns and urnover rae. The primary purpose of he sudy is neiher o resolve he dispue over he linkage beween he common risk facors and he documened characerisics nor o pursue he correc asses pricing model. aher our focus is on wheher hese observed empirical regulariies are 4

5 consisen wih he raional expecaions framework in which curren available informaion can help predic fuure sock reurns. In paricular we would like o see which regulariies are more powerful on ha regard when hey are pu ogeher. Since we have no idea on he rue asse generaing process we conduc he sudy based on previously documened empirical regulariies wihou resoring o a so-called asse pricing model. Our paper is organized as follows. In he nex secion we describe he daa he hypohesized aribues and our mehodology. We also discuss why we use daily observaions insead of adoping daa a a specific ime poin when forming porfolios. We hen presen he empirical resuls in secion 3 and conclude he paper in he las secion. 2. Mehodology 2. Daa The sample in his sudy includes all New York Sock Exchange (NYSE) American Sock Exchange Sock Exchange (AMEX) and Naional Associaion of Securiies Dealers Auomaed Quoaion (NASDAQ) firms from he Cener for esearch in Securiy Prices (CSP) and COMPUSTAT from July 962 o Dec Daily sock reurns and he financial saemen iems are obained from CSP and COMPUSTAT respecively. We exclude financial firms in our sample since hese high leveraged firms may associae wih higher financial disress. Preferred socks and ADs are also excluded in our sample. From he daa we consruc he following aribues ha have been hypohesized o explain expeced reurns: Size (CAPT) book-o-marke (BE_ME) earnings-o-marke (EA_ME) cash flow-o-marke (CF_ME) dividends-o-marke (DV_ME) momenum sraegy (MOMT) conrarian sraegy (CONT) leverage (AT_ME) and rading volume (TDV). To be included in he sample a he end of a given monh a firm is required o mee he 5

6 following crieria: () i mus have complee daily observaions of he following variables for he pas 2-monh period: asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke earnings-o-marke size and rading volume; (2) i mus have complee daily reurns for he pas 5-year period. We use a 5-year period o implemen he conrarian sraegy while he momenum sraegy will be esed using reurn daa of boh -monh and 2-monh periods. A he end of he monh he qualified socks are ranked respecively by he average of each of hese firm-relaed aribues for he specified period. Across each of he firm-relaed aribues he socks are hen sraified ino quinile and decile porfolios according o heir ranks of he aribue based on he breakpoins of he rank values of NYSE firms. 2.2 The aional Expecaion Approach Suppose ha he sock reurn has he following linear relaion wih an observed firm-relaed aribue: i F = a + bai + ε i () Now we rank he aribue so ha A B and A S respecively represen he bigges and he smalles aribues across all firms a ime. B F = a + bab + ε B (2) S F = a + bas + ε S (3) For each of he five accouning-relaed aribues such as asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke and earnings-o-marke only hose socks wih a posiive average of he aribued are ranked and assigned o a porfolio according o he ranked value. 6

7 7 These wo equaions imply ha ) ( ] [ ] [ ) ( ) ( = = + S B S B S B S B A A b E E ε ε (4) If we believe ha higher expeced reurns are o compensae for higher risk hen ( ) S B A A can proxy for he expeced risk premium induced by he observed firm-relaed aribue. We can hen define he sensiiviy of firm s i' risk premium o he aribue-relaed risk premium as follows: ) ( ) ( = S B S B F i Var Cov β (5) The sensiiviy measure can be rewrien in he following form: ) ( ) ( ) ( ) ( ) ( ) ( = + = = S S B B S S B B i i S B S B i i S B S B F i ba ba Var ba ba ba Cov Var ba Cov Var Cov ε ε ε ε ε ε β (6) I follows ha firm s i' aribue i A can be viewed as a proxy for sensiiviy o he risk premium relaed o he aribue. On he oher hand due o he presence of ) ( S B ε ε he difference in realized reurns ) ( S B can only serve as a noisy proxy for he expeced risk premium induced by he observed firm-relaed aribue. Alhough each firm's error erm is orhogonal o he aribue conemporaneous error erms across various firms migh sill co-vary

8 srongly due possibly o he misspecificaion of he model and/or possibly o he occurrence of significan unexpeced news common o hese firms. Therefore forming porfolios based on he rank of he aribue can fix hough no compleely resolve he problem. Despie is limiaion we will follow he convenion in he lieraure o find he aribue-relaed risk premium. To ensure ha he accouning informaion is available o invesors before hey pu money ino he equiies we follow he reamen in FF (992). The annual accouning measure is used o miigae he seasonal effec. We impose a 6-monh delay in he announcemen of he accouning number o he public. The 6-monh gap beween he fiscal yearend and he announcemen ime would avoid look-ahead bias proposed by Banz and Breen (986). Previous sudies usually use he measure of an aribue a a specific ime poin (e.g. he end of December or June) o form hese porfolios and adjus he porfolios annually. Since he ime poin is no randomly deermined he observed aribue could possibly suffer seasonal and cyclical paerns such as he January effec and he window dressing phenomenon. Insead we form he porfolios based on daily observaions of he aribue over a pas period o smooh ou he unwaned effec. A he end of each monh we rank he qualified firms according o he average of he daily observaions of he aribue over he pas T-monh period. To be included in he sample a sock will herefore require a complee hisory of daily observaions of he aribue for he pas T-monh period. These firms are hen divided ino M porfolios based on he breakpoins of he rank values of NYSE firms. The nex monh's value-weighed reurns of hese porfolios are hen calculaed. The absolue difference in reurns beween he firs and he las porfolios serves as a proxy for he risk premium relaed o he aribue. 2 This process is repeaed monhly for he sample period across various firm-relaed aribues. Afer he 2 Depending on he linear or nonlinear (e.g. FF (992) propose ha he relaion beween average reurn and earnings-o-price has a familiar U-shape) relaion beween he sock reurn and he firm relaed aribues he risk premium could be eiher equal o he reurn of he firs porfolio minus he reurn of he las porfolio (i is likely o be he oher way around) or he average of he boom and op porfolios minus he cenral porfolio (if U-shape). 8

9 repeiive process we form a ime series of monhly aribue-relaed risk premium for each aribue. Daily observaions of he accouning-relaed aribues such as book-o-marke earnings-o-price cash flow-o-price dividend yield and marke leverage are obained in he following manner. These aribues are firs measured a he fiscal yearend and all have he marke value of common equiy a ha paricular ime. Assuming ha he accouning elemens of hese aribues remain consan during he 7 monhs following he fiscal yearend hese aribues are recalculaed daily by updaing he marke value inpu for he 7 monhs following he fiscal yearend. 3 Furhermore we adjus he marke value of equiy so ha i can be immune from impacs of firm specified facors such as cash dividends and seasoned equiy offerings. Specifically we fix he number of shares ousanding a he fiscal yearend and adjus he sock price daily forward according o P P ) for he 7-monh period following he + = ( + + fiscal yearend. The nex sep is o esimae he sensiiviy of a firm's risk premium o he risk premium relaed o he h k aribue by running he following regression a he end of each monh: P = α + β P + e = 59 0 (7) i i A i A A i L k k k where P i is firm i' s risk premium for monh P is he risk premium relaed o he A k h k aribue represens he order of a monh relaive o he curren monh and k ranges from o 0. The 0 aribue-relaed risk premiums are marke leverage risk premium book-o-marke risk premium cash flow-o-marke risk premium dividends-o-marke risk 3 Since a he end of each of he firs five monhs following he yearend of fiscal year y he accouning measure of he fiscal year has no been publicly announced he mos recen accouning measure refers o ha of he fiscal year y. Therefore a period of 7 monhs raher han 2 monhs is relevan. 9

10 premium earnings-o-marke risk premium size risk premium rading volume risk premium momenum risk premium conrarian risk premium and marke risk premium. To be included in he risk-sensiiviy regression analysis a firm mus have a leas 36 consecuive monhly reurns back from he curren monh over he 5-year esimaion period prior o he curren monh. The regression is run across he 0 firm-relaed aribues so ha a he end of each monh firm i possesses a vecor of sensiiviy esimaes o he 0 firm-relaed aribues. This esimaion process is repeaed monhly for he sample period. To examine wheher hese aribue-relaed sensiiviies have predicive power over sock reurns we use he mehod of Fama and MacBeh (973) o run he following cross-secional regression a he end of each monh: K + = α A + + γ A + βi A + ei + i = N (8) i L k k k = k Under he null hypohesis es saisics for γ + can be obained as follows: A k A k γ 0 A k = (9) σ r A k where γ = T γ Ak Ak j T j= 3. Empirical esuls Table repors summary saisics for he quinile porfolios according o each of he firm-relaed aribues. Panel A and B of Table summarizes he case of -monh and 2-monh momenum sraegy. Consisen wih previous sudies we find ha he mean reurns of he quinile porfolios sored by asse-o-marke book-o-marke cash flow-o-marke and 0

11 earnings-o-marke bear a posiive relaion wih hese aribues. However average reurns according o dividends-o-marke and rading volume raios do no appear o have a consisen paern across he porfolios. As expeced size quiniles exhibi a negaive relaion wih average reurns in which smaller porfolios end o have larger reurns. The conrarian sraegy also appears o be effecive when using he pas 5-year reurns. Among he preliminary findings he mos surprising resul comes from he negaive relaion beween momenum porfolios and heir average reurns when using pas one-monh reurns. However he negaive relaion is reversed when he momenum sraegy is implemened using he pas 2-monh reurns. This finding highlighs he sensiiviy of he momenum sraegy o he pas informaion and explains why previous sudies on he momenum sraegy (e.g. FF (996)) usually exclude he firs monh reurn when he sraegy is implemened. Since AMEX/NASDAQ socks end o be relaively small Table also shows ha here are more socks in he low quinile porfolio especially hose formed by cash flow-o-marke dividends-o-marke earnings-o-marke and firm size. On he oher hand rading volume and shor-erm reurns of AMEX/NASDAQ socks are found o be concenraed a boh end of he specrum compared wih hose of NYSE socks. In conras long-erm reurns of AMEX/NASDAQ socks are usually higher han hose of NYSE socks and are found in he highes quinile porfolio. In addiion o he preliminary findings sored in quinile porfolios in Table we also conduc he same analysis by forming porfolios in deciles. Tables 2 shows ha he paerns on he average reurns across he porfolios in each aribue are consisen wih hose repored in Table. One apparen difference however is he difference in he magniude of he average reurns beween he lowes and he highes ranked porfolios. The differences in he average reurns are usually larger in deciles han in quiniles. This implies ha here could be differences

12 in he porfolio ranks and average reurns when he socks are divided ino differen numbers of porfolios. In our nex analysis we examine he average risk premiums of he 0 firm-relaed aribues. To measure he risk premiums we ake he difference in reurns beween he firs and he las porfolios relaed o he aribue. Depending on he relaion beween he sock reurn and he firm-relaed aribue he risk premium could be eiher equal o he reurn of he firs porfolio minus he reurn of he las porfolio or he oher way around. For asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke earnings-o-marke and rading volume he risk premium is defined as he excess reurn of he highes rank porfolio relaive o he lowes rank porfolio. On he oher hand size risk premium is he difference beween he reurn of he smalles-size porfolio and he reurn of he bigges-size porfolio. The momenum-relaed risk premium is defined as he reurn of he highes-reurn porfolio excess of he reurn of he lowes-reurn porfolio while he conrarian-relaed risk is defined in he opposie way. The marke risk premium is he marke reurn minus he risk free rae. Monhly marke reurns are value-weighed reurns of he qualified socks a he end of he monh. Average risk premiums of hese aribues are compued as he simple averages of monhly measures of hese aribues. As expeced and shown in Table 3 average risk premiums from he decile porfolios are usually greaer han hose from he quinile porfolios. I also confirms he linear relaionship beween reurns and hese aribues. Furhermore he size of he average risk premiums across he aribues varies subsanially. isk premiums relaed o book-o-marke size and momenum appear o be among he larges while hose relaed o rading volume dividends-o-marke and earnings-o marke are much less significan. These findings are also 2

13 consisen wih hose documened in Fama and French (992) where porfolios formed by size and book-o-marke raio appear o generae he wider spread of porfolio reurns. Table 4 repors pairwise correlaions of monhly risk premiums of he firm-relaed aribues. Correlaions shown in Panel A and B are based on he and 2-monh momenum sraegies for he quinile porfolios and hose in Panel C and D are from he same momenum sraegies for he decile porfolios respecively. No surprisingly all accouning-relaed risk premiums have high correlaions where he magniudes end o be well above 0.5. If he sock price acually reflecs he sae of he firm hen hese accouning aribues such as asse-o-marke (AT_ME) book-o-marke (BE_ME) cash flow-o-marke (CF_ME) dividends-o-marke (DV_ME) and earnings-o-marke (EA_ME) should behave in a similar way. Therefore he high-degree co-movemens among he risk premiums of hese accouning-relaed aribues provide evidence supporing he relaionship beween reurns and he accouning aribues. In conras pairwise correlaions among risk premiums of he marke-relaed aribues such as rading volume (TDV) he momenum sraegy (MOMT) he conrarian sraegy (CONT) and he marke (VP_ET) end o be well below 0.5 and are relaively small when compared o hose among he risk premiums of he accouning-relaed aribues. Correlaions beween risk premiums of he accouning-relaed and he marke-relaed aribues are also quie small suggesing ha each ype of aribues (accouning vs. marke) is capuring differen aspec of risk premiums. In paricular he size-relaed risk premium appears o bear lile co-variaion wih oher risk premiums. These resuls sugges ha if sock reurns are spanned by risk premiums of hese aribues hen he accouning-relaed aribues as a whole he size aribue and he individual marke-relaed aribues can co-vary wih fuure movemens in sock reurns. In our nex analysis we examine he ime series averages of monhly cross-secional 3

14 correlaions beween sensiiviies (i.e. beas or loadings) of a firm s reurns o he firm-relaed aribues. The cross-secional pairwise correlaions beween he sensiiviies of a firm's reurns o he risk premiums of he 0 firm-relaed aribues are calculaed a he end of each monh. The monhly measures of sensiiviies of each sample sock s reurns o hese risk premiums are esimaed by running a ime-series regression of he sock s reurns on a risk premium. The sock s reurn is regressed on he risk premium of a specific aribue one each ime across he 0 risk premiums such ha a he end of each monh firm i possesses a vecor of 0 sensiiviy esimaes. This esimaion process is repeaed monhly for he period from Sepember 972 o December Consisen wih he resuls of Table 4 Table 5 shows ha he sensiiviies of he accouning-relaed aribues are highly correlaed. On he conrary hose of he marke-relaed aribues seem o share lile correlaion wih each oher. Among hem size is again found o correlae wih oher 9 firm-relaed aribues he leas. The findings also seem o be robus irrespecive of how many porfolios and momenum sraegy are formed. According o he resuls repored in Tables 4 and 5 where loadings of accouning-relaed aribue risk premiums end o be highly correlaed we es how each of hese sensiiviies ineracs wih hose of marke-relaed aribues in predicing fuure reurns. Table 6 repors Fama-MacBeh regression resuls. The accouning-relaed loadings in general do no perform well in predicing fuure sock reurns. Even he well-documened book-o-marke effec is only significan bu wih he opposie sign in he decile porfolios. On he oher hand he marke-relaed beas end o capure more variaion in fuure reurns. In paricular size and liquidiy effecs end o be significan and robus o differen porfolio formaion and momenum sraegy. However similar o he book-o-marke bea he coefficien of he bea of rading volume does no have he anicipaed sign. Boh marke and momenum beas also show up 4

15 significan on fuure sock reurns in mos of our regression ess. Conrary o earlier empirical findings we find ha he bea of conrarian sraegy does no have predicive power on fuure sock reurns. 4. Conclusions The purpose of his sudy is o invesigae wheher he observed empirical regulariies of previous sudies are consisen wih he raional expecaion framework in which curren available informaion can help predic fuure sock reurns. We do no emphasize on finding he correc asse pricing model nor argue abou he relaion beween he common risk facor and he documened characerisic. Furhermore insead of adoping he way of soring socks by an aribue a a specific poin in ime we form he porfolios based on daily observaions of he aribues over a pas period o smooh ou he cyclical and seasonal effecs. The resuls indicae ha a he porfolio level here appears o be a linear relaionship beween he beas of he firm-relaed aribues and he nex period sock reurn. We also find ha all he accouning-relaed risk premiums are highly correlaed. If he sock price acually reflecs he sae of he firm hen hese accouning aribues such as asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke and earnings-o-marke should behave in a similar way. Therefore he high-degree co-movemens among risk premiums of hese accouning-relaed aribues provide evidence supporing he relaionship beween reurns and hese accouning aribues. The Fama-Macbeh cross-secional regression resuls however do no overall offer evidence supporing a significan linkage beween accouning-relaed aribues and fuure sock reurns. On he oher hand firm size appears o have significan predicive power on fuure sock reurns. In general marke-relaed aribues appear o have sronger predicive power on 5

16 fuure sock reurns han accouning-relaed aribues. 6

17 eferences Banz olfn 98 The relaionship beween reurn and marke value of common socks. Journal of Financial Economics Black Fischer 972 Capial marke equilibrium wih resriced borrowing. Journal of Business Black F. M. Jensen and M. Scholes 972 The capial asse pricing model: Some empirical ess. Sudied in he Theory of Capial Marke Praeger Publishers New York. Blume Lawrence D. Easley and M. O Hara 994 Marke saisics and echnical analysis: The role of volume. Journal of Finance Bhandari Laxmi Chand 988 Deb/equiy raio and expeced common sock reurns: Empirical evidence. Journal of Finance Basu Sanjoy 983 The relaionship beween earnings yield marke value and reurn for NYSE common socks: Fuure evidence. Journal of Financial Economics Chan Louis K. Narasimhan Jegadeesh and Josef Lokonishok 996 Momenum sraegies. Journal of Finance Daar V. N. Naik and. adcliffe 998 Liquidiy and asses reurns: An alernaive es. Journal of Financial Markes DeBond Werner F. M. and ichard Thaler 985 Does he sock marke overreac? Journal of Finance Fama Eugene F. and J. D. MacBeh 973 isk reurn and equilibrium: Empirical es. Journal of Poliical Economy Fama Eugene F. and Kenneh. French 992 The cross-secion of expeced sock reurns. Journal of Finance Fama Eugene F. and Kenneh. French 993 Common risk facors in he reurns on socks and bonds. Journal of Financial Economics

18 Fama Eugene F. and Kenneh. French 995 Size and book-o-marke facors in earnings and reurns. Journal of Finance Fama Eugene F. and Kenneh. French 996 Mulifacor explanaions of asse pricing anomalies. Journal of Finance Fama Eugene F. and Kenneh. French 996 The CAPM is waned dead or alive. Journal of Finance Jegadeesh Narasimhan and Sheridan Timan 993 eurns o buying winners and selling losers: Implicaions for sock marke efficiency. Journal of Finance Lakonishok Josef Andrei Shleifer and ober W. Vishy 994 Conrarian invesmen explanaion and risk. Journal of Finance Linner John 965 The valuaion of risk asses and he selecion of risky invesmens in sock porfolio and capial budges. eview of Economics and Saisics Sharpe William F. 964 Capial Asse Prices: A heory of marke equilibrium under condiions of risk. Journal of Finance Gervais Simon on Kaniel and Dan H. Mingelgrin 998 The high volume reurn premium. Journal of Finance Timam K. and S. Daniel 997 Evidence on he characerisics of cross secional variaion in sock reurns. Journal of Finance Mar Timam K. and S. Daniel 998 Characerisics or covariances? Journal of Porfolio Managemen Summer

19 Table. Summary Saisics of Monhly eurns of Porfolios Formed in Quiniles (July 963 o December 2003) We form he porfolios based on daily observaions of he aribue over a pas period. To be included in he sample a sock mus have a complee hisory of daily observaions of all he aribues for he pas 2-monh period and furhermore complee daa of daily pas reurns for he pas 5-year period. We use a 5-year period o implemen he conrarian (i.e. CONT) sraegy while he momenum (MOMT) sraegy is esed using reurn daa of he pas -monh and 2-monh periods. A he end of each monh we rank firms wih complee daa respecively according o he average of he daily observaions of each of he aribues over he specified period. The qualified socks are hen divided ino quiniles based on he breakpoins of he rank values of NYSE firms. The nex monh's value-weighed reurns of hese porfolios are hen calculaed. Panel A : Aribue quinile for he -monh momenum sraegy Low High Asse-o-marke (AT_ME) Mean reurns ( % ) Number of socks Book-o-marke (BE_ME) Mean reurns ( % ) Number of socks Cash flow-o-marke (CF_ME) Mean reurns ( % ) Number of socks Dividends-o-marke (DV_ME) Mean reurns ( % ) Number of socks Earnings-o-marke (EA_ME) Mean reurns ( % ) Number of socks Size (CAPT) Mean reurns ( % ) Number of socks Trading volume (TDV) Mean reurns ( % ) Number of socks Conrarian (CONT) Mean reurns ( % ) Number of socks

20 Momenum (MOMT) Mean reurns ( % ) Number of socks Table - Coninued Panel B : Aribue quinile for he 2-monh momenum sraegy Low High Asse-o-marke (AT_ME) Mean reurns ( % ) Number of socks Book-o-marke (BE_ME) Mean reurns ( % ) Number of socks Cash flow-o-marke (CF_ME) Mean reurns ( % ) Number of socks Dividends-o-marke (DV_ME) Mean reurns ( % ) Number of socks Earnings-o-marke (EA_ME) Mean reurns ( % ) Number of socks Size (CAPT) Mean reurns ( % ) Number of socks Trading volume (TDV) Mean reurns ( % ) Number of socks Conrarian (CONT) Mean reurns ( % ) Number of socks Momenum (MOMT) Mean reurns ( % ) Number of socks

21 Table 2. Summary Saisics of Monhly eurns of Porfolios Formed in Deciles (July 963 o December 2003) We form he porfolios based on daily observaions of he aribue over a pas period. To be included in he sample a sock mus have a complee hisory of daily observaions of all he aribues for he pas 2-monh period and furhermore complee daa of daily pas reurns for he pas 5-year period. We use a 5-year period o implemen he conrarian (i.e. CONT) sraegy while he momenum (MOMT) sraegy is esed using reurn daa of he pas -monh and 2-monh periods. A he end of each monh we rank firms wih complee daa respecively according o he average of he daily observaions of each of he aribues over he specified period. The qualified socks are hen divided ino quiniles based on he breakpoins of he rank values of NYSE firms. The nex monh's value-weighed reurns of hese porfolios are hen calculaed. Panel A : Aribue decile for he -monh momenum sraegy Low High Asse-o-marke (AT_ME) Mean reurns ( % ) Number of socks Book-o-marke (BE_ME) Mean reurns ( % ) Number of socks Cash flow-o-marke (CF_ME) Mean reurns ( % ) Number of socks Dividends-o-marke (DV_ME) Mean reurns ( % ) Number of socks Earnings-o-marke (EA_ME) Mean reurns ( % ) Number of socks Size (CAPT) Mean reurns ( % ) Number of socks Trading volume (TDV) Mean reurns ( % ) Number of socks Conrarian (CONT) Mean reurns ( % ) Number of socks

22 Momenum (MOMT) Mean reurns ( % ) Number of socks Table 2- Coninued Panel B : Aribue decile for he 2-monh momenum sraegy Low High Asse-o-marke (AT_ME) Mean reurns ( % ) Number of socks Book-o-marke (BE_ME) Mean reurns ( % ) Number of socks Cash flow-o-marke (CF_ME) Mean reurns ( % ) Number of socks Dividends-o-marke (DV_ME) Mean reurns ( % ) Number of socks Earnings-o-marke (EA_ME) Mean reurns ( % ) Number of socks Size (CAPT) Mean reurns ( % ) Number of socks Trading volume (TDV) Mean reurns ( % ) Number of socks Conrarian (CONT) Mean reurns ( % ) Number of socks Momenum (MOMT) Mean reurns ( % ) Number of socks

23 Table 3. Average isk Premiums of he Firm-relaed Aribues for Quinile and Decile Porfolios This able documens average risk premiums of he aribues invesigaed in he sudy. The difference in reurns beween he firs and he las porfolios serves as a proxy for he risk premium relaed o he aribue. Depending on he relaion beween he sock reurn and he firm-relaed aribue he risk premium could be eiher equal o he reurn of he firs porfolio minus he reurn of he las porfolio or he oher way around. For asse-o-marke book-o-marke cash flow-o-marke dividends-o-marke earnings-o-marke and rading volume he risk premium is defined o be he excess reurn of he highes rank porfolio relaive o he lowes rank porfolio. Size risk premium is he difference beween he reurn of he smalles-size porfolio and he reurn of he bigges-size porfolio. The momenum-relaed risk premium is defined o be he reurn of he highes-reurn porfolio excess of he reurn of he lowes-reurn porfolio while he conrarian-relaed risk is defined he oher way around. The marke risk premium is he marke reurn minus he risk free rae. Monhly marke reurns are value-weighed reurns of he qualified socks a hen end of ha monh. Average risk premiums of hese aribues are he simple averages of monhly measures of hese aribues. Panel A : -monh momenum sraegy Panel B : 2-monh momenum sraegy Quiniles Deciles Quiniles Deciles AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ETf

24 Table 4. Correlaions beween isk Premiums of Firm-relaed Aribues for he Quinile and Decile porfolios Correlaions are calculaed from he ime series of monhly risk premiums of pairwise combinaions of he firm-relaed aribues hypohesized in his paper. AT_ME denoes he raio of book asses o marke equiy or he marke leverage. BE_ME represens he book-o-marke equiy (BE is he shareholder's equiy plus deferred axes of balance-shee preferred sock minus he book value of preferred sock). CAPT is he marke capializaion of firms (sock price imes number of shares ousanding). CF_ME is he cash flow-o-marke equiy (cash flow CF is earnings before exraordinary iems bu afer ineres depreciaion axes and preferred dividends plus depreciaion). CONT denoes he conrarian sraegy based on he pas 5-year reurn daa. DV_ME is he raio of dividends paid o he marke equiy. EA_ME represens he earnings-o-marke equiy (earnings is income before exraordinary iems plus income-saemen deferred axes minus preferred dividends). MOMT denoes he momenum sraegy based on eiher pas -monh or pas 2-monh reurn daa. TDV represens he urnover raio of he sock (he number of raded shares divided by he number of shares ousanding). Finally VP_ET denoes he marke risk premium which is he marke reurn minus he risk free rae. Monhly marke reurns are value-weighed reurns of he qualified socks a hen end of ha monh.. The sample period expands 436 monhs from Sepember 967 o December Panel A: The -monh momenum sraegy for he quinile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

25 Table 4- Coninued Panel B: The 2-monh momenum sraegy for he quinile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

26 Table 4- Coninued Panel C: The -monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

27 Table 4- Coninued Panel D: The 2-monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

28 Table 5. Time series averages of Correlaions of isk Sensiiviies of Firm-relaed Aribues for he Quinile and Decile Porfolios This able presens ime series averages of monhly cross-secional correlaions beween sensiiviies (i.e. beas or loadings) of a firm s reurns o he firm-relaed aribues hypohesized in his paper. The cross-secional pairwise correlaions beween he sensiiviies of a firm's reurns o he risk premiums of he 9 firm-relaed aribues and he marke are calculaed a he end of each monh. The monhly measures of sensiiviies of each sample sock s reurns o hese 0 aribue-relaed risk premiums are esimaed by running a ime-series regression of he sock s reurns on a risk premium each ime. To be included in he sample a firm mus have a leas 36 consecuive monhly reurns back from he curren monh over he 5-year esimaion period prior o he curren monh. The sock s reurn is regressed on he risk premium of a specific aribue one each ime across he 0 risk premiums so ha a he end of each monh firm i possesses a vecor of 0 sensiiviy esimaes. This esimaion process is repeaed monhly for he period from Sepember 972 o December Panel A: -monh momenum sraegy for he quinile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

29 Panel B: 2-monh momenum sraegy for he quinile porfolios Table 5- Coninued AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

30 Table 5- Coninued Panel C: -monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

31 Table 5- Coninued Panel D: 2-monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET AT_ME.00 BE_ME CF_ME DV_ME EA_ME CAPT TDV CONT MOMT VP_ET

32 Table 6. Fama-Macbeh egression Esimaes A he end of each monh he following cross-secional regression is run: K i + = α A + + γ A + β i A + ei + i = L N k k = The es saisic for γ + is obained as follows: A k k k r 0 T Ak A = where k A = k σ r T A k j= γ γ. Ak j Panel A : -monh momenum sraegy for he Quinile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV MOMT CONT VP_ET (-.60) (2.809)** (-3.246)** (3.33)** (-0.394) (2.55)** (-.574) (2.82)** (-3.270)** (3.38)** (-0.395) (2.72)** (-.407) (2.767)** (-3.346)** (3.368)** (-0.24) (2.35)* (.263) (2.64)* (-3.240)** (3.433)** (-0.376) (2.69)* (-.52) (2.423)* (-2.933)** (3.304)** (-0.90) (2.476)** (-0.099) (-0.238) (-.402) (-0.080) (.37) (2.64)* (-2.747)** (3.93)** (-0.276) (2.099)* 42

33 Table 6 - Coninued Panel B : 2-monh momenum sraegy for he quinile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV MOMT CONT VP_ET (-.405) (2.780)** (-3.067)** (0.908) (-0.292) (2.085)** (-.420) (2.78)** (-3.6)** (0.996) (-0.373) (2.308)* (-.62) (2.773)** (-3.58)** (0.882) (-0.4) (.707)* (.630) (2.255)* (-3.234)** (0.735) (-0.285) (.63) (-.64) (2.509)** (-2.83)** (0.668) (-0.65) (.93)* (-0.069) (-0.73) (-.58) (-0.273) (.3) (2.223)* (-2.797)** (0.987) (-0.046) (.804)* 43

34 Table 6 - Coninued Panel C : -monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV MOMT CONT VP_ET (-.45) (2.093)* (-3.02)** (3.322)** (-0.545) (2.924)** (-2.8)** (2.446)** (-3.0)** (3.872)** (0.236) (2.940)** (-0.848) (.769)* (-2.979)** (3.50)** (-0.866) (2.653)** (.55) (.750)* (-3.224)** (3.477)** (-0.884) (2.307)* (-.794)* (.832)* (-3.000)** (3.743)** (-0.506) (2.504)** (0.286) (-.863)* (.990)* (0.606) (-.77) (2.037)* (-2.5)** (3.52)** (0.588) (.322) 44

35 Table 6 - Coninued Panel D : 2-monh momenum sraegy for he decile porfolios AT_ME BE_ME CF_ME DV_ME EA_ME CAPT TDV MOMT CONT VP_ET (-.582) (2.22)* (-2.856)** (2.050)* (0.44) (2.840)** (-2.65)** (2.45)* (-2.863)** (2.446)** (.298) (2.825)** (-.68) (.804)* (-2.659)** (2.34)* (0.08) (2.483)** (.877)* (.558) (-3.32)** (2.74)* (0.324) (2.84)* (-.97)* (.909)* (-2.522)** (2.238)* (0.75) (2.84)* (-0.047) (-.466) (2.64)* (0.576) (-.383) (2.07)* (-2.628)** (2.03)* (.522) (.373) 45