An Accounting-Based Characteristic Model for Asset Pricing

Transcription

1 An Accouning-Based Characerisic Model for Asse ricing Sephen H. enman Columbia Business School Francesco Reggiani Bocconi Universiy Sco A. Richardson London Business School İrem Tuna London Business School November 9, 2015 We are graeful o seminar paricipans a Brisol Universiy, London Business School, Norges Bank Invesmen Managemen, Sockholm School of Economics, The Universiy of Chicago Booh School of Business, Universiy of Waerloo and o Andrew Ang, David Ashon, Ray Ball, Sephen Brown, Jason Chen, eer Chrisensen, Ken Daniel, Francisco Gomes, Ani Ilmanen, Ralph Koijen, aricia O Brien, Jim Ohlson, Tapio ekkala, Ruy Ribeiro, Tjomme Rusicus, Kari Sigurdsson, and Lu Zhang for helpful discussions and commens.

2 An Accouning-Based Characerisic Model for Asse ricing Absrac The paper presens an accouning framework for idenifying characerisics ha indicae expeced reurns. A model links expeced reurns o expeced earnings and earnings growh, so a characerisic indicaes expeced reurns if i indicaes expeced earnings and earnings growh ha he marke prices as being a risk. In applying he framework, he paper confirms book-oprice (B/) as a valid characerisic in asse pricing: B/ is associaed wih higher expeced earnings growh and also capures he risk of ha growh no being realized. However, he framework also poins o he forward earning-o-price (E/) as a risk characerisic. Indeed, E/, raher han B/, is he relevan characerisic when here is no expeced earnings growh, bu he weigh shifs o B/ wih growh. The framework also enables he separaion of he expeced reurn for operaing risk from ha due o financing risk. Wih his separaion, he paper revisis he puzzling negaive relaion ha has been observed beween leverage and realized reurns, a finding ha has been aribued o failure o conrol for operaing risk. We find a posiive relaion beween leverage and reurns when operaing risk characerisics idenified by our model are recognized.

3 An Accouning-Based Characerisic Model for Asse ricing 1. Inroducion A long sream of papers documens correlaions beween firm characerisics and fuure sock reurns. Empirical asse pricing research inerpres a number of hese observed correlaions as evidence of a risk-reurn relaionship and hus a basis for building asse pricing models. For he main par, characerisics have been idenified simply by observing wha predics reurns in he daa, a daa mining exercise ha has resuled in a proliferaion of characerisics. In a survey of published papers and working papers, Harvey, Liu, and Zhu (2013) find 186 predicors, a number hey say likely under-represens he oal. Green, Hand, and Zhang (2013 and 2014) find ha ha, of 333 characerisics ha have been repored as predicors of sock reurns, many predic reurns incremenally o each oher. A number of explanaions for he phenomena have been offered, alhough many of hese are jus conjecures. resumably o emphasize he severiy of he problem, Novy-Marx (2014) finds ha reurns prediced by many of he observed characerisics can be explained by sunspos, he conjuncion of he planes, he emperaure recorded a Cenral ark Weaher Saion in Manhaan, and oher seeming absurdiies. This paper presens a framework for idenifying valid characerisics. The framework develops from an expression ha connecs expeced reurns o expecaions of earnings and earnings growh under specified condiions on how earnings are accouned for. The key insigh is ha, if sock markes are efficien, prices are based on expeced forward earnings and subsequen earnings growh, discouned for he risk ha hose expecaions may no be achieved. Any characerisic ha indicaes ha risk will also indicae expeced reurns. We focus on one paricular characerisic ha appears prominenly in asse pricing models: book-o-price. This characerisic was idenified in a characerisic regression model, along wih he bea and size, by Fama and French (1992) (FF), who hen proceeded o consruc an asse pricing model in Fama and French (1993) wih common reurn facors consruced from he hree characerisics. Tha model sands as perhaps he premier empirical asse pricing model, hough subsequen research has expanded he se of characerisics o promoe addiional 1

4 common facors, resuling in a proliferaion of facors (as well as characerisics). 1 There is lile heory for why book-o-price migh indicae risk, hough conjecures abound. 2 Our framework provides an explanaion: under a specified accouning ha bears resemblance o GAA, B/ forecass expeced earnings growh ha he marke deems o be a risk. Our empirical analysis suppors he predicions from our framework. However, while he framework validaes B/ in he FF model, i also poins o earningso-price (E/) as a valid characerisic. Indeed, wih no expeced earnings growh, E/ alone predics he expeced reurn and B/ is irrelevan. Wih growh, he weigh shifs o B/. The paper also shows ha he relaive weighs are relaed o firm size, anoher FF facor: For smaller firms ha ypically have higher growh expecaions, B/ is imporan for forecasing reurns bu, for large firms wih lower growh expecaions, B/ is no imporan while E/ akes primacy. Furher, he paper shows how he relaive weighs on E/ and B/ depend on he accouning, wih he expeced reurn under fair value accouning (where B/ = 1) given by E/, bu wih he weigh shifing o B/ under hisorical cos accouning (where B/ is ypically differen from 1). FF facors are said o incorporae financing risk, bu here is no formal developmen o provide an explanaion. Our framework separaes accouning characerisics ha perain o operaing risk from hose ha perain o financing risk, wih he expeced reurns associaed wih each idenified and reconciled o he expeced equiy reurn in accordance wih he Modigliani and Miller (1958) leveraging equaion. This separaion enables us o revisi an issue long ousanding in empirical asse pricing: While a basic ene of modern finance, formalized in Modigliani and Miller (1958), saes ha, for a given level of operaing risk, expeced equiy reurns are increasing in financial leverage, research has had grea difficuly in documening a posiive relaionship beween leverage and average reurn. Indeed, papers largely repor negaive reurns o leverage, in Bhandari (1988), Johnson (2004), Nielson (2006), George and Hwang 1 Addiional facors include momenum (Jegadeesh and Timan, 1993), invesmen (Liu, Whied, and Zhang, 2009 and Chen, Novy-Marx, and Zhang, 2010), profiabiliy (Novy-Marx, 2012 and Fama and French, 2015), accruals qualiy (Francis, LeFond, Olsson, and Schipper, 2005), among ohers. 2 The conjecures abou book-o-price include: (i) disress risk (Fama and French, 1992), (ii) he risk of asses in place vs. risk of growh opions (Berk, Green, and Naik, 1999; Zhang, 2005), (iii) low profiabiliy (Fama and French, 1993), (iv) high profiabiliy (Novy-Marx, 2012), (v) invesmen (Chen, Novy-Marx, and Zhang, 2010; Gomes, Kogan, and Zhang, 2003; and Cooper, Gulen, and Schill, 2008) (vi) operaing leverage (Carlson, Fisher, and Giammarino, 2004), and (vii) q-heory (Cochrane, 1991 and 1996 and Lin and Zhang, 2013). 2

5 (2010), Ipplolio, Seri and Tebaldi (2011), and Caskey, Hughes and Liu (2012), for example. This is puzzling given how fundamenal is he idea ha leverage requires a reurn premium. enman, Richardson, and Tuna (2007) also documen a negaive relaion bu, in addiion, show ha he FF model, wih is B/ componen, does no adequaely price leverage risk. The failure of research o validae such a fundamenal enan of modern finance is presumably due o a failure o idenify and conrol for operaing risk. We are able o show ha, afer conrolling for operaing risk characerisics idenified by our framework, equiy reurns are increasing in leverage. As well as providing a commenary on FF, he framework in he paper inerpres he findings in enman and Reggani (2013) ha show ha he amoun of earnings expeced in he long erm versus he shor erm fuure is relaed o reurns. Our framework explains why expeced growh in long-erm earnings over he shor erm connecs o reurns and why E/ and B/ make he connecion, albei in varying degrees depending he accouning and how i is relaed o expeced growh. The paper furher unlevers hese pricing raios o accommodae leverage ha also bears on expeced earnings growh. The framework conrass wih ha in Lyle and Wang (2015) and Chaopadyhay, Lyle, and Wang (2015) ha employ he Vuolennaho (2002) auology o express reurns by a combinaion of book rae of reurn (ROE) and B/ raher han E/ and B/. Tha formulaion does no allow for expeced earnings growh, he feaure in our paper ha is conneced o expeced reurns and which provides an explanaion for he B/ effec in reurns. 2. Connecing E/ and B/ o Expeced Reurns We lay ou a framework ha connecs expeced reurns o forward earnings and subsequen expeced earnings growh. We hen esablish condiions under which (levered) E/ and B/ convey informaion abou expeced levered reurns and unlevered E/ and B/ convey informaion abou expeced unlevered reurns. Leverage hen explains he difference beween levered and unlevered expeced reurns implied by hese muliples. We employ he framework o criique he FF model and lay ou characerisic regression models ha conras wih heirs. 3

6 2.1 Expeced Levered Reurns We sar wih he clean surplus accouning relaion embedded in financial saemens. 3 This relaion saes ha he book value of common equiy, B, increases wih comprehensive income,, and decreases wih he disribuion of ne dividends o equiy holders, d: B +1 = B d +1. The equaion is ypically applied o subsiue earnings and book values for dividends in he numeraor of he so-called residual income model (see Ohlson 1995, for example). Bu ha research has nohing o say abou he denominaor of he valuaion model, he expeced reurn a which he numeraor is discouned he issue in his paper. Re-arranging he equaion, d +1 = +1 - (B +1 - B ) and subsiuing for ne dividends in he sock reurn (wih firm subscrips omied), he expeced dollar reurn is explained by expeced forward earnings and he expeced change in he premium of price over book value: E( +1 + d +1 - ) = E[ B +1 - ( - B )] (1) Dividing hrough by o yield he expeced one-year-ahead rae-of-reurn, 1 d 1 E( 1) ( 1 B 1) ( B ) E( ) E( R 1) E( ) (1a) The ideniy in equaion (1) has long been recognized for realized reurns, for example in Eason, Harris, and Ohlson (1992). We adap i here o apply o expeced reurns. 4 If here is no expeced change in he premium of price over book value, equaion (1a) shows ha he expeced rae-of-reurn is equal o he expeced (forward) earnings yield. However, given he earnings yield, a forecas of he expeced reurn is compleed wih a (pricedenominaed) forecas of he change in premium. 3 The formulaion requires ha clean-surplus accouning mus apply only in expecaion. Clean-surplus accouning may be violaed in accouning for earnings realizaions, bu expeced deviaions from clean-surplus mus be mean zero (as wih he unrealized gains and losses on markeable securiies ha are recorded in comprehensive income under GAA and IFRS accouning). 4 Our focus is on he one-year-ahead expeced reurn, he objec of mos of he research ha predics reurns, including our empirical work. However, a poins below, he expeced reurn is expressed as a consan over fuure periods for simpliciy, wih he undersanding ha muli-period expeced reurn is no necessarily he expeced reurn under an equilibrium asse pricing model (as ofen saed in inerpreing bond yields). Our ask is simply o idenify characerisics ha migh direc he consrucion of an asse pricing model, as in Fama and French. 4

7 Tha, of course, requires an explanaion of wha induces a change in premium. Firs noe ha payou does no affec premiums: dividends reduce book value, dollar-for-dollar, under he clean-surplus accouning operaion and also reduce price dollar-for-dollar under Miller and Modigliani (1961) (M&M) condiions. 5 Raher, an expeced change in premium is induced by expeced earnings growh, as shown in Shroff (1995). If dividends do no affec he premium, he expeced change in premium due o he change in book value comes from earnings, by he cleansurplus relaion: E( +1 B +1 ) ( B ) = E[(Δ +1 + d +1 (ΔB +1 + d +1 )] for all E(d +1 ) and, wih E(Δ +1 + d +1 ) se by a no-arbirage condiion given, he change in premium is deermined by E(ΔB +1 + d +1 ) = E( +1 ). Thus, for a given, lower expeced +1earnings implies an increase in he premium in +1. In oher words, is based on expeced life-long earnings a ime so ha, for a given price, he lower he earnings expeced for period +1, he higher are earnings expeced afer +1. Tha is expeced earnings growh. This simply reflecs he workings of accrual accouning: accrual accouning allocaes earnings o periods so, for oal lifelong earnings expeced in, lower +1 earnings means higher earnings in he fuure. The appendix demonsraes. However, while equaion (1a) supplies a calculaion for he expeced reurn, i holds for all accouning mehods for allocaing earnings o periods even accouning ha books earnings o periods randomly; equaion (1) is, afer all, a auology. The clean-surplus relaion is no sufficien; furher specificaion is necessary for he accouning allocaion o have implicaions for risk and he corresponding expeced reurn. Tha accouning mus convey informaion abou risk ha requires a discoun o he curren price,, he denominaor in equaion (1a), o yield an expeced reurn commensurae wih he risk. Tha is, he discoun (in price) of expeced life-long earnings is conveyed by he allocaion of hose earnings o periods. We consider four accouning cases. Wih a focus on B/, we evaluae how B/ indicaes he expeced reurn in each case, esablishing condiions under which B/ bears no relaion o he expeced reurn and condiions under which i does. The laer are he basis for our empirical ess: are he condiions saisfied in he daa? The four cases are demonsraed in he appendix. 5 Dividends increase financing leverage and hus he expeced reurn, bu ha is refleced in he E/ componen of he expeced reurn which is increasing in leverage (see laer). Some argue ha, because of ax effecs, price drops by less han a dollar per dollar of dividends. Accordingly, we conrol for he dividend yield in he empirical analysis. 5

8 A all poins, we assume ha he marke prices risk appropriaely (marke efficiency), as is sandard in asse pricing research Accouning where B/ has no Relaion o he Expeced Reurn Mark-o-marke accouning. Given E( +1 B +1 ) = B = 0 (and hus he expeced change in E ( 1) premium is zero), he expeced reurn equals he forward earnings yield,, by equaion (1a). The case is illusraed wih a mark-o-marke bond. The expeced one-period yield on a bond indicaes is expeced reurn and, under accrual accouning, he effecive ineres mehod equaes he expeced earnings yield o he bond yield. A bond canno have earnings growh beyond ha from a change in he effecive amoun borrowed, bu ha is deermined by he coupon rae, ha is, payou. Thus, here is no expeced change in premium. I follows ha he FF model does no apply o mark-o-marke bonds. Nor does i apply o equiies under mark-o-marke accouning: B/ = 1 irrespecive of he risk, so B/ canno indicae he expeced reurn. However, he expeced earnings yield indicaes he expeced reurn, ye he earnings yield does no appear in he FF model. Case I in he appendix demonsraes. ermanen income accouning (no growh). For socks, price usually differs from book value because of hisorical cos accouning, so one looks o feaures of hisorical cos accouning ha induce a premium and links B/ o expeced reurns. A benchmark case is ha of permanen income where earnings are recognized such ha expeced +1 is sufficien for all fuure earnings: wih full payou, E( +τ ) = E( +1 ) for all τ such ha here is no expeced earnings growh. Applying he clean-surplus relaion wih a consan expeced reurn, r, he expeced premium for all + τ is given by E( B ) s1 1 (1 r) s E( s r. B s1 ) s1 1 (1 r) s E( 1 r. B ). Thus expeced premiums are consan. Less han full payou resuls in earnings growh from reenion, bu ha does no affec premiums. Wih no expeced change in premium, E( R E( 1 1), by equaion (1a). ) 6

9 As hese conclusions hold for all B, i follows ha B/ does no indicae he expeced reurn in he no-growh case. Raher, he E/ raio conveys he expeced reurn, as in he case of mark-o-marke accouning. Case II in he appendix demonsraes. Accouning wih growh unrelaed o risk and reurn. Under mark-o-marke accouning and permanen income accouning, earnings), E( Earning ) 1. Adding growh (for posiive expeced r E ( ) 1 r g (1b) For a consan expeced reurn, r, his is a no-arbirage valuaion equivalen o he Gordon consan-growh dividend model wih full payou of earnings. ayou (reenion) oher han full payou adds o earnings growh, g, bu does no add value under M&M condiions nor does i affec he premium of price over book value (as shown above). The valuaion isolaes he growh ha poenially affecs price and he expeced reurn, r, and a he same ime is M&M consisen. Accouning can be applied o reduce +1 wih no implicaion for or r. Wih no such effec, he accouning mus increase g he accouning shifs earnings from +1 o subsequen periods, reducing he forward E/ raio and inducing earnings growh and an expeced change in he premium in equaion (1a). Bu here is no effec on price or curren book value; neiher expeced growh nor B/ indicaes he expeced reurn. Case III in he appendix demonsraes Accouning where B/ indicaes he Expeced Reurn From equaion (1b), E( 1 ) r g. (1c) For a given r, E/ is decreasing in expeced earnings growh a common view of he E/ raio. I is ofen saed ha B/ (or /B) forecass his growh; if so, B/ canno indicae he expeced reurn (as r is consan). However, r is also involved in he pricing, and r may be relaed o expeced earnings growh. E/ = r g, so if r increases wih g, price and he E/ raio are no 7

10 affeced; more growh jus means more risk wih no effec of he price. Furher informaion is necessary o disinguish wheher a given E/ is one wih high r and high g or low r and low g. The issue is wheher B/ conveys his informaion. To demonsrae analyically, we embrace he Ohlson-Juener (2005) valuaion model ha generalizes he Gordon model for all payous on an M&M consisen basis. Assume: A1. 1 g2 ( 1) r r ( 1) 1 2 rdividends 1 where g 2 1 > γ 1 is he growh rae in expeced earnings wo 1 years ahead (wih +1dividends reinvesed) and γ is (one plus) he growh rae in subsequen expeced abnormal earnings wih he propery ha 1 γ as τ ; ha is, γ is he very long-run growh rae in expeced earnings. (Here a subscrip greaer han indicaes an expeced value). The model suis our empirical endeavor, for i disinguishes growh in he shor erm, g 2, (for which one can observe realizaions) from long-erm growh ha is elusive empirically. Furher, γ is likely o be similar for all firms (in he long run), so g 2 and r are he inpus ha discriminae in he cross-secion. Thus our focus is on he connecion of B/ o g 2 and o r. Assume, A2. 2 rdividends 1 G. 1 B wih λ > 0. Thus, Seing γ = 1, B g2 G 1 1 B G 1 r r Therefore, 8

11 r 1 B ( G 1 1 ) ( G 1) 1 B (1d) Thus, r is increasing in B/ and he forward E/. The analysis can be generalized for γ > 1wih no effec on he direcional relaion beween B/ and r. And i can be generalized for B/ also forecasing γ. We sae wo proposiions which are he subjec of our empirical ess: in B/. 1. For a given 1, he wo-period-ahead earnings growh rae, g 2 is increasing 2. For a given 1, r is increasing in B/. roposiion 1 follows from assumpion A2 whereby g 2 is decreasing in 1 ROE and 1 B he relaion, B B follows from equaion (1d). While B/ forecass g for a given E/ under 1, B/ also indicaes r because r increases wih g 2 for a given. Case IV in he appendix demonsraes. Two special cases demonsrae when FF applies and when i does no. Special case A (Fama and French): Seing G = 1 in equaion (1d), r B 0 0 By seing G = 1, +2 + r.dividends +1 = +1 + λb 0, involving a naïve forecas from +1. B/ now explains r and E/ is no involved, as in Fama and French. Special case B (voided Fama and French): 9

12 Seing λ = 0, r ( G 1) 1 So, B/ is no involved. This is saisfied for G 1 = r and 1 r, he case for no expeced change in premium. These wo special cases are viewed as exremes. In general, he expeced reurn can be viewed as indicaed by boh E/ and B/ according o equaion (1d): B E ( R ) 1 1 w1 w2 (1e) wih he weigh, w, shifing o B/ when B/ adds o he forecas of growh given E/. The empirical analysis so indicaes. The analysis is somewha serile wihou an appreciaion of he accouning ha induces hese properies. Indeed, o predic a posiive associaion beween B/ and growh may come as quie a surprise, for i is commonly saed (wihou much documenaion) ha B/ is negaively associaed wih growh a high /B is a growh sock, no a high B/. Tha is he case if /B forecass growh ha adds o price bu no o he expeced reurn, bu hen B/ is no relaed o he expeced reurn. The crucial condiion in 1 is he negaive relaion beween ROE +1 and g 2 (due o assumed λ > 0). Two feaures of hisorical cos accouning under GAA sugges ha accouning induces his negaive correlaion, and hese feaures connec he accouning o risk. Firs, he realizaion principle ha governs he allocaion of earnings o periods saes: under uncerainy, earnings recogniion is deferred o he fuure unil he uncerainy has been resolved. Deferred earnings imply higher expeced earnings growh bu also lower curren earnings and ROE, ceeris paribus, and he applicaion of he principle under uncerainy ies he earnings deferral o risk. As an empirical maer, enman and Reggiani (2013) show ha he deferral of earnings recogniion is priced in he sock marke as if i indicaes risk. Second, conservaive accouning reduces ROE by rapid expensing of growing invesmen, and correspondingly induces earnings growh (Felham and Ohlson 1995; Zhang 2000). The rapid expensing is applied when he oucome of invesmens (in R&D and adverising, for example) are uncerain. Conservaive accouning also 10

13 reduces book value, he denominaor of ROE, bu ha serves o yield a higher ROE and lower growh expecaions when growh expecaions are realized and uncerainy is (successfully) resolved (and he forecas of g 2 is reduced under A2). Thus, he lower B/ associaed wih he high ROE indicaes a lower expeced reurn, in accordance wih equaion (1d). 6 This is only suggesive, of course, and here is no necessiy ha he realizaion principle and conservaive accouning for risky invesmens are relaed o priced risk. 7 Tha is he empirical quesion ha ess of 1 and 2 invesigae. While our focus is on B/ as an indicaor of risk and reurn, he framework is more general, capable of eneraining oher characerisics ha forecas risky earnings growh. For example, firm size is also involved in he FF model and one can readily conjecure ha small firms are hose wih risky expeced earnings growh, no ye recognized by accounans, ha requires a higher reurn. Indeed, our ess show ha, for small firms where here is ypically higher expeced earnings growh, B/ is a srong indicaor of he expeced reurn. In conras, for large firms wih lower expeced growh, E/ is more relevan. The framework here conrass wih ha in Lyle and Wang (2015) and Chaopadyhay, Lyle, and Wang (2015) ha also connecs accouning numbers o expeced reurns. Like equaion (1) hese papers sar from a auology (saed in Vuolennaho, 2002) ha expresses expeced reurns in erms of ROE and B/ raher han E/ and B/. In conras o our approach, hese papers add accouning srucure by assuming ha log ROE evolves according o an AR(1) process such ha ROE and he expeced reurn converge in he long run. For B/ < 1, an AR (1) process implies declining premiums (of price relaive o book value) and hus does no allow for expeced earnings growh (nor for a poenial increase in ROE under conservaive accouning), he feaure of our model which poenially explains expeced reurns and connecs E/ and B/ o hose reurns. 6 While he condiions for B/ o indicae he expeced reurn in equaion (1d) are developed for a posiive E/, GAA accouning can produce negaive E/ (and negaive ROE), along wih risky expeced earnings growh as wih negaive earnings and ROE due o he expensing of R&D for a sar-up firm where he gamble is on he R&D invesmen paying off. 7 Modeling how GAA accouning connecs o priced risk would appear o be a challenging ask. Ohlson (2008) lays ou a model where modified permanen income accouning produces earnings growh and he growh rae is se o equal he risk premium (and B is increasing in he growh rae). 11

14 The analysis in his secion is bes viewed as ha for a firm wih no financing leverage, for leverage changes he picure. 2.2 Expeced Unlevered Reurns A core ene of financial economics saes ha financial leverage adds o expeced reurns, ye empirical research has had difficuly documening a leverage risk premium in sock reurns. In his secion we show ha he accouning framework can be uilized o disinguish he expeced reurn due o operaing risk from ha due o financing. In conras o mos asse pricing models where he leverage componen is presumed o be subsumed by proposed facors (wihou much explanaion), he conribuion of leverage o he expeced reurn is explici. The separaion of operaing risk characerisics from leverage effecs modifies he analysis in secion 2.1. I also ses up he empirical work o show ha, in conras o previous research, leverage adds o average sock reurn. The analysis of unlevered reurns recass he balance shee and income saemen o idenify heir unlevered componens. In he balance shee, B = ND where (ne operaing asses) denoes he unlevered book value (also called enerprise book value) and ND is ne deb. The clean surplus relaion for he enerprise explains changes in raher han changes in B. The flows ha explain he change are no longer and Ne Dividends, bu raher Operaing Income from he enerprise, OI, and Ne Disribuions o all claimans (he sum of Ne Dividends, d, and Ne Disribuions o Deb Holders, F), ofen referred o as Free Cash Flow, FCF. increase wih operaing income and decrease wih ne disribuions o equiy and ne deb holders. Thus, he clean surplus relaion for he enerprise saes ha d +1 + F +1 = FCF +1 = OI +1 - ( +1 - ). Le 1 be he price of he firm (enerprise price) and ND 1 he price of he ne deb. As equiy price, ND 1 1 1, he dollar (levered) sock reurn can be expressed as: ND ND E( 1 d 1 ) E( 1 FCF 1 ) E( 1 F 1 ). (2) Tha is, he (levered) equiy reurn is he unlevered reurn afer deducing he reurn o he ne deb holders. The firs erm on he righ hand side is he expeced dollar (unlevered) reurn. 12

15 Subsiuing he clean surplus relaion for he unlevered firm and dividing hrough by he expeced unlevered (enerprise) rae of reurn, R 1 : yields E 1 FCF E( OI 1) E( 1 1) ( ( ) E( R 1 ) ) (2a) This is he unlevered version of equaion (1a); he expeced unlevered reurn is expressed in OI erms of he expeced enerprise forward earnings yield, 1 E( ), and expeced enerprise earnings growh ha produces an expeced change in he premium of enerprise price, I is clear ha he same analysis ha follows from equaion (1a) o relae levered E/ and B/ o expeced (levered) reurns also follows from equaion (2a) o connec unlevered (enerprise) E/ and B/ o unlevered reurns. Indeed, he demonsraions in cases I IV in he appendix are demonsraions of unlevered relaionships when here in zero financing leverage. Noe, in paricular, ha he condiions for B/ o indicae expeced levered reurns are also hose for he unlevered B/ o indicae expeced unlevered reurns. 2.3 Reconciling Levered and Unlevered Numbers In his secion we show ha, jus as levered and unlevered reurns reconcile hrough leverage, so do levered and unlevered E/ and B/ ha poenially explain hose reurns. From equaion (2), E E( FCF E( F ND ( R 1) ) ND ) ND E ( R 1 ) E( R 1 ) ND ND ND E( R 1 ) E( R 1 ) E( R 1 ), (3) 13

16 ND where E ) is he expeced unlevered reurn, E ) is he expeced reurn for ne deb, and ND ( R 1 ( R 1 is he amoun of leverage. This, of course, is he Modigliani and Miller (1958) leverage equaion underlying he sandard weighed average cos of capial calculaion. The same arihmeic reconciles he levered and unlevered earnings yields via financial leverage. Recognizing ha +1 = OI +1 Ne Ineres +1 (boh afer-ax) and making he sandard assumpion ha he book value of deb equals is marke value (ND = ), ND where ( OI 1 E ( 1 ) E( OI 1) ND E( OI 1) E( Ne Ineres 1) (4) ND E ) is he forward unlevered earnings yield and Ne Ineres 1 ND is he firm s borrowing rae as repored in he financial saemens. This expression is he accouning analog o he M&M expeced reurn equaion (3). Financial leverage increases he levered E/ over enerprise E/ provided ha he unlevered (enerprise) earnings yield is greaer han he borrowing rae. Leverage is risky and adds o he expeced reurn in equaion (3), bu leverage also adds o he expeced enerprise earnings yield in he same way, reinforcing he poin ha he expeced earnings yield is a basis for assessing risk and expeced reurn. Leverage does no affec ND premiums: 1 B ( 1 ND 1) 1 1 if ND = ND. Thus, he effec of leverage on he exceped levered reurn in equaion (1a) is via he expeced earnings yield. Accordingly, wihou E/ in he model, FF model relies on B/ (or firm size or bea on he marke facor) o pick up leverage. However, i is doubful ha B/ picks up leverage. Reconciling levered and unlevered B/, enman, Richardson, and Tuna (2007) show ha, if ND =, ND B ND 1. (5) Financial leverage, ND/, increases (levered) B/ for an enerprise book-o-price greaer han 1, bu reduces B/ for an enerprise book-o-price less han 1. Thus, if B/ indicaes risk, i is unlikely ha i reflecs boh operaing risk and leverage risk in a direcionally consisen way. 14

17 enman, Richardson, and Tuna (2007) indicae ha i does no: for a sample of over 120,000 US firm-years over he period, ha paper shows ha while unlevered book-o-price is robusly posiively associaed wih equiy reurns, financial leverage is robusly negaively associaed wih equiy reurns given he unlevered B/. The resuls are robus o violaions of he ND = ND assumpion. The negaive relaion beween leverage and reurns is sronges for he group of firms where < 1. This is abou 80 percen of firms and he firms where B/ is decreasing in leverage, so he posiive relaion beween B/ and reurns in FF is no capuring financial leverage. In shor, boh he B/ leveraging equaion (5) and relaed empirical findings indicae ha B/ canno handle differences in leverage risk in he cross-secion. Under Modigliani and Miller (1958) condiions, leverage does no affec price bu adds o he expeced reurn by he M&M equaion (3). By he same mah ha derives equaion (4), i is easy o show ha leverage also adds o expeced earnings growh: OI Ne Ineres Ne Ineres. (6) 1 1 OI OI Ne Ineres g 1 g 1 g 1 g 1 OI Ne Ineres Thus, he added expeced reurn from leverage ies o higher expeced earnings growh: while leverage increases expeced earnings growh in equaion (6), he expeced reurn also increases in equaion (3) o leave price unaffeced. The connecion of r o expeced earnings growh (wih price unaffeced) resonaes wih he proposiions in he las subsecion under which B/ is relaed o r and g 2. However, leverage reduces B/ in equaion (5), excep for he case where > 1, and is ypically less han 1. Thus, higher risk and growh associaed wih leverage ypically yields a lower, no higher, B/. This seeming conflic is explained by he modeling earlier. There, proposiion 1 links B/ o expeced earnings growh, g 2, via a negaive relaionship beween B/ and ROE +1 (for a B1 1 1 given E/):. However, wih he same mah ha derives equaion (4), ROE 1 15

18 1 OI 1 Ne Ineres 1 ND Ne Ineres 1 ROE R R (7) B ND B ND Thus, while leverage increases g 2, i also increases ROE +1, provided he unlevered book rae of OI 1 reurn, R 1, is greaer han he ne borrowing rae. Accordingly, while leverage increases r and g, i also increases ROE +1, and an increase in ROE +1 implies a lower B/ for a given E/. The leverage effec on ROE +1 implies higher g 2, hus he assumpion in A2 ha λ > 0 is violaed. Accordingly, in assessing he relaionship of B/ o expeced reurn, i is imporan o differeniae he unlevered B/ from he leverage effec on (levered) B/. This accords wih differen accouning for (unlevered) operaing aciviies versus ha for financing aciviies. Accouning ha induces a posiive relaionship beween B/ and r (by deferring earnings recogniion under uncerainy) is applied o operaing aciviies under GAA. However, deb is approximaely carried a marke value. Wih approximae mark-o-marke accouning, leverage has no effec on he equiy premium and he effec of leverage on he expeced equiy reurn is capured by he E/ raio. Case V in he appendix demonsraes. 2.4 Characerisic Regressions To idenify characerisics ha indicae expeced reurns, empirical finance runs cross-secional characerisic regression models of forward sock reurns on observed characerisics o discover wha characerisics predic sock reurns. The Fama and French (1992) regression model wih bea, book-o-price, and size is an example. The preceding analysis imposes some discipline on he specificaion of characerisic regressions, so his secion lays ou crosssecional regression models implied by ha analysis. The analysis poins o E/ as well as B/ as indicaors of he expeced reurn. However, he wo are relevan under differen accouning condiions, wih B/ given weigh only in he case of expeced earnings growh and where risk is relaed o ha growh. Thus, wih accouning differing in he cross-secion ha presumably conains some no-growh firms, esimaing a crosssecional model ha applies o all firms is a doubful exercise. However, we are ineresed in how a cross-secional model like ha of FF would be modified by our analysis and wha a ypical model would look like. Furher, he earnings deferral accouning ha jusifies he inclusion of 16

19 B/ as a characerisic is pervasive across he cross-secion ha adheres o GAA. So we firs esimae a model ha includes boh E/ and B/ and hen invesigae condiions, implied by our framework, where he weigh shifs from B/ o E/. Under our analysis, E/ is idenified and B/ explains reurns for a given E/ under specified condiions. Thus, our saring poin is he following characerisic regression: E( ) B 1 R 1 a b1 b2 1. (8) A es for b 1 >0 is a es of he relevance of E/. (We also include size and bea, also FF characerisics, o ensure ha hey do no explain he omission of E/ in he FF model). The b 2 coefficien is prediced o be posiive if, given E/, B/ indicaes growh ha is priced as risky. Wih his saring poin, we hen invesigae wheher B/ is less imporan in explaining reurns (and E/ more imporan) in condiions where ex ane here is presumed o be less expeced earnings growh. A characerisic unlevered reurn regression is similarly specified based on Equaion (2a): R 1 E( OI ) 1 2, (9) 1 1 This is jus a subsiuion of unlevered variables for he corresponding levered variables in regression (8). Adding leverage o explain levered reurns, R 1 E( OI ) ND (10) 1 1 Our framework predics β 3 > 0 if financial leverage adds o expeced reurns and if he included operaing variables are sufficien o conrol for operaing risk. However, he E/ and B/ leveraging equaions (4) and (5) indicae ha here is a kink in he relaion beween leverage and reurns for given unlevered E/ and B/. For B/, he kink is a = 1. For E/, he kink is a E ) equal o he borrowing rae: when he unlevered ( OI 1 yield is less han he borrowing rae, E/ is decreasing in leverage. The Bank of America Merrill Lynch BBB corporae bond index repors ha he average effecive yield for BBB raed 17

20 corporae issuers over he 1996 o 2011 period is abou 6.5 percen. Thus, an afer-ax borrowing rae of abou 4 percen (a before-ax rae of 6.5 percen wih a 35 percen ax rae) implies ha he kink in equaion (4) is a an unlevered E/ of 4 percen (and an unlevered /E of 25). Accordingly, our esimaion of equaion (10) is carried ou for subsamples around hese kinks. Furher, he M&M equaion (3) indicaes an ineracion beween operaing risk and leverage, a poin sressed in Skogsvik, Skogsvik and Thorsell (2011) who noe he imporance of ineracion erms when assessing he relaion beween leverage and reurns. Our empirical ess accommodae his ineracion. The es for β 3 > 0 serves o validae our characerisic model. rior research has generally found a negaive relaion beween leverage and equiy reurns, even afer conrolling for conjecured operaing risk characerisics. 8 This negaive relaion can be explained by leverage being negaively correlaed wih omied operaing risk facors. This is no unreasonable if capial srucure decisions are endogenous wih respec o he perceived cos of defaul and he afer-ax benefis of deb financing. Indeed, heoreical models of capial srucure (Leland 1994) sugges ha firms wih higher levels of operaing risk will endogenously choose lower levels of leverage. Our characerisic model suggess ha operaing risk can be idenified hrough he expeced enerprise earnings yield and enerprise B/. If so, we will have conrolled for operaing risk, bu only if he idenified operaing variables are sufficien o idenify operaing risk. This qualificaion is imporan because addiional omied characerisics (wih which leverage is correlaed) migh indicae risky growh. We benchmark our regressions agains an unlevered version of he FF characerisic model: 8 Bhandari (1988) finds a posiive relaion beween monhly reurns and leverage in annual cross-secional regressions over he years bu no from , and finds ha mos of he leverage effec is concenraed in Januarys in years before Johnson (2004) finds a weak uncondiional posiive relaion beween leverage and fuure reurns bu, afer conrolling for underlying firm characerisics (for example, volailiy), he relaion beween leverage and fuure reurns becomes negaive. George and Hwang (2010) documen negaive reurns o leverage, which hey explain wih a model of marke fricions relaed o he coss of disress. Nielsen (2006) finds negaive reurns o leverage afer conrolling for he hree Fama and French facors and momenum, and aribues he negaive relaion o correlaed operaing characerisics. Oher aemps o idenify correlaed omied (operaing) characerisics include Gomes and Schmid (2010) and Obreja (2013). Ippolio, Seri, and Tebaldi (2011) and Caskey, Hughes, and Liu (2012) aribue he negaive reurns o deviaions from opimal capial srucure. 18

21 R ND (11) (wih an accommodaion for he kink in he B/ leveraging equaion (5)). This equaion unlevers he B/ and adds leverage. enman, Richardson, and Tuna (2007) repor a negaive coefficien on leverage from his regression (wih and wihou bea and size, he oher wo FF characerisics) and hus conclude ha he FF model does no price leverage appropriaely. Among heir conjecures is he conenion ha he model does no deal wih operaing risk appropriaely (wih which leverage may be negaively correlaed). Our characerisic model suggess ha he earnings yield is missing. Thus regression (11) serves as a benchmark o evaluae wheher he addiion of he unlevered earnings yield in regression (10) urns he observed negaive coefficien on leverage o posiive. 3. Daa and Summary Saisics Our analysis covers all U.S. lised firms on Compusa during he years ha also have prices and monhly sock reurns on CRS. We exclude financial firms (wih SIC codes ) because he separaion of operaing aciviies and financing aciviies is less clear for hese firms. We require he following daa iems o be available for a firm-year o be included in our analysis: book value of common equiy (Compusa iem CEQ), common shares ousanding (CSHO), earnings before exraordinary iems (IB), long-erm deb (DLTT), and sock price a he end of he fiscal year (RCC). Oher variables are se equal o zero if hey are missing, bu our resuls are no paricularly sensiive o his reamen. Firms wih negaive denominaors in raio calculaions (such as ) were deleed from he sample a any sage of he analysis ha required hese numbers, as were firms wih per-share prices less han 20 cens. Our resuls are similar if we insead use a cu-off of $1.00 per-share. A oal of 170,096 firm-year observaions are available for our analyses. For he regression analysis, we exclude firm-year observaions where any of he accouning raios are in he op or boom 2 percen of he disribuion for he relevan year. The number of firms available for he regression analysis each year ranges from 298 in 1962 o 5,287 in 1997, hough ha number varies depending on he regression specificaion. 19

22 Table 1 summarizes he disribuion of variables involved in he analysis. We repor perceniles for all of our primary variables based on he pooled se of daa. Inferences are similar when averaging perceniles from sors each year. The noes o he able describe how each variable was calculaed, bu a few addiional commens are warraned. The regression specificaions require forecass of forward earnings (for year +1). We esimae forward earnings o be he same as repored earnings for year before exraordinary and special iems. In suppor, he average Spearman rank correlaion beween realized +1 / and / is Using an esimae of forward earnings based on curren (recurring) earnings no only enhances he coverage o he full range of B/ raios and firms sizes bu also avoids (i) he problems of (behavioral) biases and noise in analyss forecass evidenced in Bradshaw, Richardson, and Sloan (2001), Hughes, Liu, and Su (2008), and Wahlen and Wieland (2011), and (ii) he challenge of unlevering earnings forecass in a consisen manner across boh analyss and firms. The (marke) leverage variable is calculaed wih he sandard assumpion ha he marke value of deb,, can be approximaed by he book value of ne deb, ND. enman, ND Richardson, and Tuna (2007) find ha esimaes of Fama and French unlevered regressions are robus wih his approximaion in he cases where here have been apparen changes in credi worhiness ha affec he marke value. Table 2 repors average earson and Spearman cross-secional correlaions beween he variables in able 1, wih bea and size added. In all cases, we calculae he pairwise correlaion each year and repor averages of correlaions across years. E/ and B/ are posiively correlaed wih boh levered and unlevered equiy reurns for he following year, consisen wih he predicions from equaion (1a). E/ and B/ are also correlaed wih each oher (Spearman correlaion of 0.292). E/ and he unlevered earnings yield, OI/, are highly correlaed (Spearman correlaion of 0.896), as are levered B/ and he unlevered B/,, (Spearman correlaion of 0.908). Financial leverage, ND/, has very lile uncondiional correlaion wih eiher levered or unlevered reurns, bu ND/ is posiively correlaed wih boh he levered and unlevered B/ raios. Leverage is negaively correlaed wih he unlevered earnings yield. So he failure of leverage o forecas reurns may be due o is correlaion wih he operaing earnings yield, omied in mos ess in he lieraure, bu appearing in regression equaion (8). 20

23 4. Book-o-price and Subsequen Growh We firs conduc ess of 1, a condiion ha is necessary for B/ o indicae expeced reurns in our framework: for a given E/, is B/ posiively relaed o subsequen earnings growh? Surprisingly, while i is ofen claimed ha B/ is negaively relaed o growh, here is lile documenaion of he relaion. 9 anel A of able 3 repors average realized earnings growh raes wo years ahead (+2) for en porfolios formed from ranking firms on levered B/ each year, and anel B repors average realized operaing income growh raes for en porfolios formed on enerprise (unlevered) book-o-price,, each year. The averages are he mean of median growh raes for porfolios each year. These growh raes are hose ha an invesor would have experienced in invesing in he respecive porfolios. 10 To accommodae firms wih negaive earnings and a small earnings base, we compue growh raes by deflaing earnings changes wih he absolue values of he level of earnings as described in he noes o able As growh in year +2 is affeced by invesmen in year +1, boh panels also repor growh raes in residual earnings o conrol for growh from added invesmen. In boh cases, residual earnings are calculaed wih a charge agains beginning book value using he risk-free rae for he relevan year. For boh levered and unlevered B/ raios, higher B/ is associaed wih higher growh. The correlaion beween B/ and subsequen earnings growh a he individual firm level is low: an 9 Chan, Karceski, and Lakonishok (2003) repor a weak posiive correlaion beween B/ and earnings growh when forming porfolios based on realized earnings growh over he nex five and en years. However, in heir regression analysis, hey repor no evidence of a relaion beween B/ and fuure earnings growh bu a srong negaive associaion beween B/ and fuure sales growh. Lakonishok, Shleifer, and Vishny (1994) repor a posiive associaion beween B/ and fuure earnings growh a leas when comparing differences in geomeric average growh raes across he op and boom decile of socks formed on he basis of B/. Finally, in a recen paper, Chen (2012) finds evidence of a posiive associaion beween earnings growh and B/. The mixed previous research on he uncondiional relaion beween B/ and fuure earnings growh is no surprising as enman (1996) demonsraes ha B/ can be associaed wih high growh, no growh, and negaive growh. Research has explored he relaion beween B/ and profiabiliy (reurn on equiy), for example in enman (1992) and Fama and French (1995) who documen a negaive correlaion beween he wo in he cross-secion. 10 The growh raes are no an esimae of expeced earnings growh raes because E(. Raher, hey are he average ex pos growh oucomes experienced by invesors. 2 1 E( ) E( 11 The resuls are robus o calculaions of earnings growh as oal porfolio earnings in +2 relaive o ha in +1 and are similar when we require base earnings o be posiive. 2 1 ) ) 21

24 average Spearman correlaion of and an average earson correlaion of (The corresponding correlaions for he unlevered numbers are and ) Table 3 shows he correlaion is sronger a he porfolio level, wih high B/ paricularly associaed wih high growh. The same paern is seen in he residual earnings growh raes. Furher analysis (no repored) reveals ha he posiive relaion beween B/ and subsequen growh is primarily associaed wih mid-cap and small firms; for large firms (he op hird by marke capializaion), here is lile correlaion beween porfolio B/ and growh. Of course, growh wo years ahead is only one year of he subsequen earnings growh ha is relevan for he deerminaion of expeced reurns. However, survivorship issues overwhelm any aemp o measure realized growh oher han for he shor erm. 1 refers o he condiional correlaion of B/ wih growh (ha is, for a given E/), raher han he uncondiional correlaion. anel A of able 4 repors realized growh raes for 25 porfolios formed by ranking firms firs on enerprise earnings yield, OI/, and hen, wihin each OI/ porfolio, on heir enerprise book-o-price,. anel B repors residual enerprise earnings growh raes, wih a graphical depicion in Figure 1. These join porfolio sors are performed each year; he able repors mean of porfolio median growh raes across years. Enerprise earnings yield ranks growh negaively as expeced; /E raios indicae growh. Bu, for a given enerprise yield, higher is associaed wih higher subsequen growh on average. Condiionally, unlevered B/ is a srong indicaor of subsequen enerprise earnings growh. 1 is confirmed. Furher analysis (no repored) pariioned firms by marke capializaion and found ha, for large firms, porfolio OI/ and subsequen growh are posiively relaed, bu here is lile correlaion beween and growh wihin OI/ porfolios, expec in he lowes E/ porfolio; he condiional correlaion beween and subsequen growh is associaed primarily wih mid-cap and small firms. anels A and B show ha he relaionship beween enerprise B/ and earnings growh is paricularly srong in he lower enerprise E/ porfolios. The lowes E/ porfolios consis largely of loss firms where one migh expec earnings o be paricularly depressed, yielding 22

25 higher growh if firms recover, as he able indicaes hey do, on average. Neverheless, he differences across E/ porfolios poin o a non-lineariy ha we accommodae in our subsequen analysis. anels C and D repor ha earnings growh forecased by is risky. For a given enerprise E/, he sandard deviaion of subsequen enerprise earnings growh raes is increasing in enerprise B/ in panel C, as is he iner-decile range (he 90 h percenile minus he 10 h percenile of oucomes) in panel D. The iner-decile range is of paricular significance because i focuses on he exreme oucomes abou which invesors are presumably mos concerned. anel E repors beas (slope coefficiens) from ime-series regressions, for each porfolio, of wo year ahead earnings growh raes on he marke-wide earnings growh rae for he same year. These earnings growh beas are increasing in enerprise B/ for a given enerprise E/ porfolio. No only is he earnings growh of high B/ porfolios more volaile (anels C and D), hey are also more sensiive o sysemaic shocks o growh. The repored earnings growh beas in panel E are based on earnings growh raes for he median firm in each cell. In unrepored ess we have repeaed he esimaion of earnings growh beas using aggregae earnings growh across all firms in each cell. This approach will give considerably more weigh o larger firms who are less subjec o aggregae marke shocks. As expeced we see similar, albei reduced, differences in earnings growh beas across he 25 cells using his alernaive esimaion approach. anel F repors he fracion of firms ha ceased o exis in he second year ahead due o performance-relaed reasons, as indicaed by CRS delising codes. 12 The non-survivor raes are higher for he low E/ porfolio dominaed by loss firms, bu are also higher for he high B/ porfolios. Across all panels in he able we see ha high enerprise B/ firms are subjec o more exreme earnings growh oucomes as evidenced by (i) he dispersion in porfolio level measures of earnings growh, and (ii) he sensiiviy of growh o shocks o marke-wide earnings growh, 12 In unrepored ess, we have also examined he fracion of firms ha do no have he requisie daa o compue earnings growh in he subsequen year. The paern is very similar o ha repored in panel F. 23

26 and (iii) he higher percenage of non-survivors due o eiher low payoffs aribuable o firm failure and/or high payoffs due o firms being acquired by oher firms. In summary, given OI/, indicaes no only expeced earnings growh (panels A and B) bu also he risk surrounding he expeced growh (panels C - F). enman and Reggiani (2013) documen similar findings in a es of wheher he deferral of earnings recogniion under GAA is relaed o average sock reurns. In ha paper, porfolios were consruced o isolae he long-erm deferred earnings componen of expeced fuure earnings from he shor-erm componen, wih a furher demonsraion ha he porfolio consrucion ha resuled urned ou o be equivalen o a join sor on (levered) E/ and B/. Deferred earnings recogniion induces expeced earnings growh, so he associaion of deferred earnings wih average reurns in enman and Reggiani (2013) underscores our framework where he expeced reurns are increasing in expeced earnings growh if ha expecaion is a risk. anels C F here indicae ha is so. 5. Esimaing Characerisic Regressions 5.1 Regressions wih Levered Explanaory Variables The es of 1 in able 4 confirms he condiion in our framework for B/ o indicae expeced reurns. Wih his condiion saisfied, we now proceed o 2: for a given E/, is B/ correspondingly relaed o expeced reurns? While he variaion of earnings growh raes in able 4 indicaes ha B/ is associaed wih risky growh oucomes, he risk need no be priced risk. As is sandard in empirical asse pricing, we use average realized reurns o infer expeced reurns ha reflec priced risk. And, as is also sandard, he es of 2 is under he mainained assumpion of marke efficiency. Table 5 repors resuls from esimaing regression equaions (8) and varians. Crosssecional regressions are esimaed each year, and he repored coefficiens and R 2 are averages of esimaes across years, wih -saisics calculaed as he average coefficien esimae relaive o is sandard error esimaed from he ime-series of he coefficiens. In unrepored analysis we have esimaed all regression specificaions using monhly reurns raher han annual reurns, wih similar resuls. 24

27 Regression I shows ha B/ is significanly posiively associaed wih fuure reurns, as is well known. Regression II esimaes equaion (8): boh E/ and B/ joinly indicae fuure reurns, wih significanly posiive coefficiens on boh variables. The adjused R 2 is an improvemen over ha in Regression I wih B/ alone. Regression III adds he curren dividendo-price, D/. All else equal, dividends reduce fuure earnings, so he inclusion of D/ helps correc he forecas of forward earnings for he curren payou. Adding D/ also conrols for any ax effecs of dividends on reurns and he possibiliy ha D/ iself is an indicaor of expeced reurns via expeced dividend growh. The coefficien on D/ is negaive, consisen wih earnings displacemen, bu i is no significan, aking nohing away from E/ and B/ as expeced reurn characerisics. Regression IV adds bea and size, he oher FF characerisics, o Regression III. Size has a significan negaive coefficien, wih E/ and B/ reaining heir significance, while bea is insignifican. Noe also ha our measure of forward earnings is only an esimae, so any variable ha improves ha esimae has a role in he regression regardless of wheher i indicaes subsequen earnings growh. The resuls for hese regressions are consisen over sub-periods , , , and hough he weigh on E/ is higher in he earlier periods and he weigh on B/ higher in he laer periods. In summary, regression specificaions I o IV suppor B/ as a valid characerisic, as in he FF model, bu also indicaes ha E/ is missing from ha model Relaive imporance of E/ and B/ in explaining expeced reurns While hese regressions indicae ha boh E/ and B/ ypically predic reurns in he crosssecion, our framework demonsraes ha, in he case of no expeced earnings growh, only E/ is relevan. B/ akes on significance only wih expeced earnings growh, and only when ha growh is a risk of no meeing expecaions. Accordingly, we now pariion he cross-secion ino firms where a priori one expecs differen levels of expeced earnings growh. Our insrumen for expeced earnings growh is firm size. This is admiedly a crude proxy, based on he inuiion ha smaller firms are ypically hose wih higher growh (and riskier) prospecs while large firms are hose where growh expecaions have largely been 25

28 achieved. Bu here is anoher reason o pariion in size: he FF model includes size as a characerisic as well as B/ (and size loads negaive in Regression IV in able 5). However, raher han viewing size as anoher characerisic ha indicaes reurns incremenally o B/, we view size as a condiion under which he weigh on E/ in predicing reurns shifs o B/. We esimae weighs on E/ and B/ for size pariions using he Theil-Sen robus esimaor advocaed by Ohlson and Kim (2014). These weighs are he median values of w 1 and w 2 from fiing R 1 w1 E / w2 B/ for all possible combinaions of observaions. Table 6 repors he average weighs for en porfolios formed each year from a ranking on firm size. 13 The weigh on E/ increases wih firm size, and approaches o 1.0 for he larges porfolios, he weigh appropriae for no growh under our framework. Correspondingly, he weigh on B/ decreases wih firm size, effecively zero for he larger firms. For smaller firms (where higher growh is expeced), he weigh shifs from E/ o B/, again consisen wih our framework. The able also repors mean E/ and B/ for he porfolios, wih E/ increasing over porfolios and B/ decreasing. The fied reurns in he able are calculaed by applying he weighs o E/ and B/ for he porfolio (wih an inercep). These reurns are decreasing in firm size, consisen wih he sandard observaion ha average reurns are negaively relaed o size. 14 The las four rows of he able repor he same saisics for wo-year-ahead realized growh raes as in Table 4. I is clear ha he weigh in B/ and he associaed fied reurns are increasing in he porfolio mean growh raes, heir variaion around he mean, and heir sensiiviy o marke-wide shocks. The resuls here are consisen wih observaions (in Kohari, Shanken and Sloan, 1995 and Asness, Franzzini, Israel, and Moskowiz, 2014, for example) ha he B/ effec in sock reurns is considerably weaker for large firms. Bu now a raionale is supplied, one ha poins o E/ for hese firms raher han B/. Andrade and Chhaochharia (2014) observe ha E/ raher han B/ explains reurns for large firms; again, a raionale is supplied here. 13 In a comparison wih OLS coefficiens, here is considerably less variaion in he esimaes over years, aribued o exreme values having less influence. 14 These mean reurns should no be inerpreed as ex ane expeced reurns. Realized reurns over his sample period (o which he weighs were fied) were hose in an (on average) bull marke. Indeed, he fied reurns are (on average) higher han wha one ypically views as a reasonable required reurn. This is paricularly so for he small firms for, in his period, invesing in risky growh paid off. 26

29 I has been observed ha he FF porfolio sors on B/ also imbed a size sor ha obscures he weak B/ effec in large firms (in Lamber and Hübner, 2013 and Asness, Frazzini, Israel, and Moskowiz, 2014, for example). Consequenly, here appears o be a B/ effec in large firms in FF only because he sor on B/ is acually a sor on size. The analysis here goes furher, o quesion wheher size and B/ are wo separae characerisics. Size and B/ are clearly negaively correlaed over porfolios in able 6, and boh are associaed wih risky growh oucomes. Thus boh may be seen as a characerisic ha correlaes wih reurns. However, our framework and able 6 promoes only B/ as a characerisic, bu one ha receives a higher weigh wih smaller firms because smaller firms have higher, riskier growh expecaions. To be sure, firm size is bu one of many poenial characerisics ha could be used o idenify firms wih greaer expecaions of risky fuure earnings growh. One simple alernaive is o direcly measure invesmen aciviy ha is immediaely expensed, bu which produces expeced earnings growh from ha invesmen over he iniial reduced earnings. The wo mos common, and measurable, such invesmen aciviies are research and developmen (R&D) expendiures and adverising expendiures. In unrepored analysis, we have repeaed he analysis in able 6 bu insead sor firms on he basis of he inensiy of R&D and adverising expendiures. We assume a useful life of hree years for R&D and one year for adverising, and deflae his simple measure of inangible asses by eiher sales or ne operaing asses. The resuls are very similar o ha repored in able 6: for firms wih greaer inangible asse inensiy, B/ is more imporan in explaining expeced reurns. This is expeced in our framework as he conservaive naure of he accouning sysem defers he recogniion of earnings associaed wih his risky invesmen aciviy. In such siuaions, E/ is no longer a sufficien saisic for expeced reurns. Overall, he findings in able 6 confirm he insigh from our characerisic model ha boh E/ and B/ idenify expeced reurns. There is, however, an inconsisency wih he resuls in Fama and French (1992) who sugges ha E/ is no significan in monhly cross secional afer conrolling for size, bea, and B/. Our analysis here suggess an explanaion. As observed, he FF sors confound size and B/ such ha he reurn spread wihin large firms is aribued o B/ raher han size. While confirming he insignificance of B/ for large firms, able 6 also shows 27

30 ha E/ and size are posiively correlaed over size porfolios. Thus, for large firms where E/ is paricularly imporan, size proxies for E/ Regressions wih Unlevered Explanaory Variables and Added Leverage In his secion we aemp o validae our characerisic model by revisiing he puzzling negaive relaion beween financial leverage and fuure equiy reurns observed in previous papers. The negaive relaion has been aribued o a failure o conrol for operaing risk characerisics appropriaely. So we es wheher a posiive relaion is now observed afer conrolling for he operaing risk characerisics idenified by our model. We sar by confirming ha he negaive relaion observed earlier holds for our sample. Regression I in able 7 repors he esimaes of benchmark FF regression (11). Consisen wih enman, Richardson, and Tuna (2007), here is a negaive relaion beween financial leverage and fuure reurns. In unrepored analysis, we spli each cross-secion based on wheher is greaer han or less han one, ha is, around he kink in equaion (5). As in enman, Richardson, and Tuna (2007), he negaive leverage relaion is sronges for less han one where he majoriy of firms lie and where leverage decreases B/; he average coefficien on leverage (no repored in he able) is wih an associaed es saisic of Adding bea and size o he regressions does no aler he picure, and hus he conclusion remains ha he FF model does no accommodae leverage risk. 15 Holding aside he model supporing our analysis, i is imporan o reconcile our empirical ess wih hose of Fama and French (1992). If we (i) resric our ime period o heir sample period, , (ii) compue E and B consisen wih Fama and French (1992), (iii) use he same lagging convenions (i.e., use financial saemen daa from he mos recen fiscal year-end no laer han December of year when looking a reurns ha sar in July of year +1), (iv) include an indicaor variable for negaive firms and only compue E/ for firms where E > 0, and (v) use monhly reurn inervals as opposed o he annual reurn inervals, we coninue o find ha boh B/ and E/ are associaed wih he cross secion of fuure sock reurns. I is only when we (i) require all componens of E and B as measured by Fama and French (1992) o be non-missing (i.e., non-missing income saemen deferred axes, preferred dividends, and balance shee deferred axes), and (ii) include all firms (i.e., do no remove securiies wih closing share price of less han $0.20) ha we can find a sub-sample where, empirically a leas, E/ is no significan in explaining fuure sock reurns. This is no surprising as he smalles firms are hose firms wih he larges expecaions for earnings growh, and one would expec B/ o be more imporan as i capures hose expecaions of subsequen earnings growh. 28

31 Regression II adds he enerprise earnings yield, he missing operaing characerisic idenified by our model, o he benchmark regression, as in equaion (10). The mean coefficien on leverage is close o zero. The addiion of unlevered size and bea in Regression III does no change his coefficien significanly. These findings are similar when excluding firms wih operaing losses and hose wih negaive ne deb (ha is, cash-rich firms). They also hold for various sub-periods from However, he analysis in secion 2.3 indicaes ha (i) he direcional effec of leverage on levered numbers differs around a kink and (ii) here is an ineracion effec beween leverage and operaing risk o be accommodaed. The remaining regressions in panel B of able 7 recognize hese poins. Regressions IV and V repea regression III for firms wih greaer (less) han 1. For > 1, where he B/ premium in reurns is paricularly srong and where leverage has a posiive effec on B/ in equaion (5), we see a posiive (bu no saisically significan) relaion beween leverage and reurns wih he addiion of he enerprise earnings yield o he FF variables. However, he mean coefficien on leverage for < 1 (where he majoriy of firms lie) is close o zero, indicaing no incremenal effec for leverage. The remaining regressions in he able exploi he E/ leveraging equaion (4). Regression VI esimaes regression equaion (10) bu wih he added ineracion beween he enerprise earnings yield prescribed by equaion (4). We exclude firm-year observaions where OI < 0 because he ineracion wih leverage will produce a negaive number, which is no readily inerpreable. The ineracion erm in regression VI is marginally significan. Regressions VII o IX inroduce he kink in equaion (4) around he enerprise earnings yield equal o he borrowing rae. (We use he 10-year U.S. Treasury rae, R f, as he hreshold given he scarciy of qualiy corporae borrowing cos daa back in ime.) For OI > R f in regression VII, he average coefficien on leverage is posiive. Furher, he average coefficien on he ineracion variable in Regression VIII is reliably posiive, while he average coefficien on he main effec of leverage is negaive. Applying he esimaed coefficiens o he average values of boh he leverage and 29

32 he ineracion variable in he cross-secion, we find ha he oal effec of leverage is posiive wih an associaed es saisic (no abulaed) of Finally, regression IX repors a posiive and marginally significan posiive average coefficien on he ineracion erm by iself. Overall, he analysis indicaes a posiive condiional relaion beween leverage and fuure equiy reurns, bu ha relaion is no srong. The coefficiens on he leverage variables in hese regressions could be aribuable o leverage being relaed o an omied aspec of operaing risk. Bu our daa sugges oherwise. Firs, here is a very low correlaion beween leverage and fuure unlevered reurns in able 2. Second, in unrepored ess we esimae regression II in able 7 using unlevered reurns as he dependen variable. We find a weak negaive relaion (es saisic of -1.34), suggesing (weakly) ha firms wih higher (lower) leverage have lower (higher) operaing risk. The weakness of he relaion and is negaive sign sugges ha he posiive condiional relaion ha we documen beween leverage and fuure levered reurns canno easily be explained by leverage capuring operaing risk. Neverheless, here is no guaranee ha we have conrolled for operaing risk saisfacorily. Alernaive explanaions for he weak relaion beween leverage and reurns include (i) a biased sample period and (ii) measuremen error. The firs explanaion is unlikely as he sample period enailed significan growh in he sock marke and corporae profis where leverage, a leas on average, would have been rewarded favorably ex pos. The second explanaion is possible as our measure of leverage has assumed ha he marke value of deb can be approximaed by is book value of deb. While he book value of deb is ypically close o is marke value, he wo can diverge due o changes in ineres raes and crediworhiness. However, as in enman, Richardson, and Tuna (2007), we find he resuls hold for he subsample of firms wih highly raed deb where his concern abou measuremen error should be miigaed. 6. orfolio Analysis The analysis in Table 4 indicaes a non-lineariy across E/ porfolios in he relaionship beween B/ and subsequen earnings growh. To assess he robusness of he resuls in Table 5 o he lineariy assumpion underlying he regression analysis, we documen he relaion across 30

33 porfolios formed from he join sor of unlevered E/ and B/. This porfolio analysis also checks on he influence of ouliers. In able 8, porfolios are formed each year by ranking firms firs on OI and hen, wihin each OI porfolio, on. This porfolio consrucion mirrors ha in able 4. anel A repors average reurns across he 25 joinly sored porfolios. Alhough he relaion is no monoonic, average reurns are increasing in OI as evidenced by he significan difference beween he high and low OI porfolios (es saisic of 3.07). Reurns are also increasing in for each of he OI porfolios. Significanly, he average reurns exhibi a paern over porfolios similar o he average earnings growh raes in panel A of able 4. Furher, jus as he correlaion beween and growh raes is observed primarily in mid-cap and small firms, furher analysis (no repored) shows ha he posiive correlaion beween porfolio and average reurns is primarily associaed wih mid-cap and small firms; for large firms, here is a posiive correlaion beween E/ and reurn, bu lile correlaion beween and reurn wihin OI porfolios, consisen wih he resuls in able 6. The reurns in able 8 also have he same paern over porfolios as he sandard deviaion and iner-decile range of earnings growh raes in panels C and D: for a given enerprise earnings yield, enerprise B/ indicaes risky growh, and ha is associaed wih higher reurns on average. Specifically, he average correlaion in earnings growh beas repored in panel E of able 4 and oal reurns repored in panel A of Table 8, down he columns, is

34 This is clear evidence of B/ capuring sysemaic exposure o risky subsequen earnings growh ha is priced. 16 In panel B of able 8, we repor alphas (esimaed inerceps) from esimaes of Fama and French ime-series facor regressions wih four facors (including momenum). The significan inerceps confirm ha he relaion beween B/ and E/ and fuure reurns canno be explained by he sandard se of facors. Resuls are similar wih he original FF hree facors, and wih a liquidiy facor added. This indicaes ha he join sor based on he characerisics idenified by our model exposes meaningful variaion in realized reurns ha canno be explained by exan facor models. To examine he effecs of leverage furher, we also considered porfolios using a hreeway sor. We firs sored on OI, hen sored on, and finally on leverage. To ensure ha enough firms populae each cell in every cross-secion, we consruc 64 (4x4x4) porfolios. Consisen wih he regression resuls in able 7, we found a posiive condiional relaion beween leverage and reurns for firms in he highes enerprise earnings yield porfolios. 7. Leverage in Ex os Reurn Regressions While supporing a posiive relaionship beween leverage and reurns, he resuls for leverage in able 7 are no srong. Regressions of his sor are no very powerful for idenifying differences in expeced reurns. Indeed, while he repored R 2 in able 7 are higher han ypically observed for reurn regressions, hey are sill quie low. As ofen observed, he reason is ha realized reurns are a poor meric o deec small differences in expeced reurns because he variaion in realized reurns due o he unexpeced reurn componen is far greaer han ha of he expeced reurn componen (see e.g., Elon, 1999). Furher, he relaive conribuion of leverage o he expeced reurn is ypically small. To increase he power of he ess, we repea he analysis, bu now wih a conrol for earnings news ha explains par of he unexpeced componen of realized reurns. 16 We find similar resuls when porfolio assignmens are based on levered E/ and B/. For a closer comparison o Fama and French (1992), who separaely rea firms wih negaive earnings, we have repeaed our analysis wih all negaive earnings firms in one porfolio and assigned he posiive E/ firms across four porfolios by rank. We find similar resuls. 32

35 The analysis also permis a sharper definiion of favorable and unfavorable leverage where he direcional effec of leverage on reurns differs. We esimae he following regression equaion: R OI OI ND (12) OI The inclusion of realized enerprise earnings, 1, conrols for unexpeced reurns due o he conemporaneous realizaion of earnings news. We also include lagged enerprise earnings, OI, because exensive prior research shows ha boh earnings levels and changes explain realized sock reurns (in Eason and Harris 1991, for example). Table 9 repors he resuls. Regression I repors he resuls from esimaing equaion (12). There is a posiive coefficien on he realized earnings yield and a significan increase in average R 2 over he regressions repored in able 7. This reinforces he poin ha expeced earnings are a risk so ha heir realizaions deermine realized reurns. The average coefficien on lagged earnings is negaive, indicaing ha lower prior earnings for a given earnings realizaion realized earnings growh is associaed wih higher reurns. This is implied by our characerisic model where expeced earnings growh is a risk, so realizaions of growh move reurns. Afer conrolling for earnings realizaions, we find a posiive bu sill insignifican associaion beween leverage and fuure reurns. However, he effec of leverage on reurns depends on wheher leverage is favorable; leverage levers up realized reurns if oucomes are favorable, bu reduces reurns if no. So, he remaining regressions in able 9 use sub-samples condiional on he earnings realizaion. Regression II confines he sample o posiive earnings realizaions and he remaining regressions examine cases wih earnings realizaions greaer han and less han he borrowing rae (proxied by he 10-year Treasury rae), he inflecion poin for favorable and unfavorable leverage in equaion (4). Regressions are run wih and wihou leverage ineracion erms. For regressions III V ha we idenify wih favorable leverage, he coefficien on leverage is srongly posiive and he overall effec of he leverage erm and he ineracion erm is posiive. In unrepored analysis, 33

36 we esimae regression II excluding he main effec for leverage and find he coefficien on he ineracion variable is wih a es saisic of In regression VI wih unfavorable leverage, an ineracion erm canno be calculaed when operaing income is negaive, bu we include a loss dummy variable. The average coefficien on leverage is negaive bu no saisically differen from zero, so we don observe a negaive leverage effec direcly. Bu he coefficien is considerably less han ha for regression III covering favorable earnings oucomes. In unrepored analysis, we also esimaed he regressions by defining favorable oucomes as OI +1 > OI and unfavorable ones as OI +1 < OI. For regression I for favorable news, he coefficien on leverage was wih a -saisic of 2.72, while ha for unfavorable news was wih a -saisic of The ineracion coefficien in regression II for favorable news was ( = 3.16) and ha for unfavorable news was ( = -0.02). In regression V excluding he leverage main effec erm, he coefficien on he ineracion erm was 0.77 ( = 4.16) for favorable news and ( = -0.15) for unfavorable news. In summary, afer conrolling for operaing risk characerisics and he conemporaneous earnings news, we can idenify a robus posiive relaion beween leverage and fuure reurns, albei asymmeric, wih he relaion sronger in he cases we have idenified leverage as favorable. These regressions emphasize he ex pos naure of leverage. In able 7 where he leverage resul was no srong, reurns include boh posiive and negaive leverage effecs. The analysis here is able o separae condiions where he leverage effec should be favorable, and in hose condiions leverage is srongly posiively relaed o reurns. Given he negaive relaion ypically observed in prior research, his resul in iself is imporan. Bu i also shows ha our framework idenifies a characerisic regression model where leverage is priced posiively. 8. Conclusion This paper develops a framework for idenifying characerisics ha indicae expeced reurns. Expeced reurns can be described in erms of expeced forward earnings and subsequen earnings growh under condiions prescribed by accouning principles. Characerisics ha indicae expeced earnings and subsequen earnings growh ha are a risk also indicae he expeced reurn for bearing ha risk, assuming he marke prices risk efficienly. 34

37 Research has searched for explanaions of why B/ forecass reurns. We esablish condiions under which B/ indicaes expeced reurns and hose where i does no. The condiions under which B/ is a valid risk characerisic involve a paricular form of accouning ha resembles GAA. We es empirically wheher hese condiions are saisfied. Our framework and he accompanying empirical ess show ha B/ indicaes expeced reurn because i forecass expeced earnings growh and he risk ha he expecaion may no be me. In one sense, he paper jusifies B/ in he Fama and French asse pricing model. However, i also idenifies E/ as missing from he Fama and French model. Indeed, when here is no expeced earnings growh, i is E/ ha indicaes expeced reurns and B/ is irrelevan. Wih expeced earnings growh, he weigh shifs o B/. The framework idenifies characerisics ha indicae he expeced reurn due o operaing risk versus hose ha indicae he financing risk premium in expeced reurns. The paper shows ha operaing and financing risk characerisics combine o explain he (levered) equiy reurn in he same way ha unlevered sock reurns and leverage combine o yield he levered equiy reurn under Modigliani and Miller (1958). Wih he separaion of operaing and financing risk, we documen a posiive relaion beween reurns and leverage. This conrass wih prior research ha has consisenly found a negaive relaion beween leverage and equiy reurns, a finding inconsisen wih basic principles of finance. We aribue he earlier negaive relaion as a failure o idenify operaing risk characerisics appropriaely. Our finding of a posiive relaion furher validaes our framework. Our paper is wrien under he assumpion ha markes raionally price risk, as is sandard in asse pricing in making inferences abou risk and reurn. However, our model indicaes expeced reurns for risk only under his assumpion. We have been careful o use he words, expeced reurn raher han required reurn. As always in empirical asse pricing, our empirical findings could be aribued o inefficien pricing if he characerisics predic reurns because he marke fails o incorporae informaion abou fuure earnings and subsequen earnings growh. So our paper does no resolve he long-sanding debae abou marke efficiency or he quesion of wheher reurns prediced by he idenified characerisics are due o he characerisics indicaing sensiiviy o common facors. Tha, of course, requires a valid facor model, bu he paper holds ou he prospec of developing such a model, one ha comes from an accouning-based framework. 35

38 Appendix: The expeced reurn under alernaive accouning Secion 2.1 inroduced equaion (1a): E E( E( B ( R 1) ) ) ( B ) This appendix demonsraes ha he second componen capures expeced earnings growh subsequen o period +1. I also demonsraes he calculaion of he expeced reurn in he four accouning cases in secion 2.1: case I wih marke-o-marke accouning; case II wih permanen income accouning and no expeced earnings growh; case III wih expeced earnings growh wih no relaion o risk; and case IV where expeced growh is priced as risky. These four cases assume no leverage. Case V hen adds leverage o sress he separaion of (unlevered) accouning numbers from he effecs of leverage. In each case he role of B/ in indicaing he expeced reurn is highlighed. We consider a single firm assumed o be a going-concern. We rack accouning numbers (book value of equiy, B, and earnings) for hree periods, +1, +2, and +3 afer he presen ime,, bu he example generalizes o many fuure periods. Successive book values are a he end of each period and earnings are a flow variable over periods, observed a he end of each period. Book value and earnings ariculae across ime periods via he clean surplus relaion. In he firs hree cases, we use a pre-specified required rae of reurn of 10 percen. In he fourh case, he accouning conveys risk and hence relaes o he required rae of reurn. In all cases, prices obey he iner-emporal no-arbirage condiion. Dividends make no difference o he premium, B, as dividends reduce book value and price dollar-for-dollar under Miller & Modigliani (M&M) assumpions (as will be demonsraed). Dividends do affec earnings growh via reenion, bu ha reenion does no add o value under M&M. Accordingly, he examples are wih full payou all earnings are disribued so earnings growh inroduced ino he examples is idenified as poenially value-adding growh. I is easy o show ha he demonsraions go hrough under any payou policy. In each case, he reader can confirm ha he valuaions agree wih hose from he residual income model and he Ohlson-Jeuner model. 36

39 I. = B (mark-o-marke accouning). Expeced reurn = 10%, no financing leverage This base case ses = B : mark-o-marke accouning which is applied in all subsequen periods. By no-arbirage residual income valuaion, book reurn on equiy (ROE) equals he required reurn of 10%, yielding +1 of 10 on book value of 100 a. Successive book values saisfy he clean-surplus relaion. rices a all poins saisfy he no-arbirage condiion: E( +1 + Dividends ) = 1.10, and so for subsequen periods. As price equals book value a all poins, he expeced change in premium is zero. The expeced reurn is equal o he forward earnings yield, as in equaion (1a). B/ = 1 for any required reurn, so B/ does no relae o he required reurn.. Time Dividends Book value (B) growh rae 1 0% 0% rice () remium ( B) Δremium yield 10% 10% 10% Δremium/rice -1 0% 0% 0% Expeced reurn 10% 10% 10% ROE 10% 10% 10% B/ Wih zero payou (reenion), +2 = 11and he earnings growh rae = 10%. Bu his comes only from reenion, wih no effec on. As B +1 = +1 = 110 and yield +1 = 10%, here is no effec on he expeced premium for +1 or he inferred expeced reurn. 37

40 II. B and permanen income accouning: no expeced earnings growh and consequenly no expeced change in premium. Expeced reurn = 10%, no financing leverage This case inroduces a premium over book value wih = 100 and B = 80. There is no expeced earnings growh in period +2 and beyond. Wih book values generaed according o he clean surplus relaion and prices generaed under he no-arbirage condiion, here are expeced premiums over book value in fuure periods bu no expeced change in he premium. Accordingly, he expeced reurn is equal he forward earnings yield, as in equaion (1a). B/ declines from case I, bu he expeced reurn does no.. Time Dividends Book value growh rae 0% 0% rice remium Δremium yield 10% 10% 10% Δremium/rice -1 0% 0% 0% Expeced reurn 10% 10% 10% ROE 12.5% 12.5% 12.5% B/

41 III. The case of B wih expeced earnings growh and consequenly an expeced change in premium bu no effec on he expeced reurn. Expeced reurn = 10%, no financing leverage. Wih Case II as a saring poin, earnings of 10 in +1 are now reduced by a 0.25 shif from +1 o +2, yielding expeced earnings growh for +2 of 5.38%. This is a pure one-period accouning shif unrelaed o value, wih earnings revering o 10 in +3 wih a growh rae of -2.68%. The earnings growh induces a change in premium: wih prices se by he no-arbirage condiion (and mainaining he same payou as in Case II), he premium of price over book value increases in period +1 (wih posiive earnings growh) and decreases in +2 (wih negaive growh). As in equaion (1a), he expeced equiy reurn of 10% is equal o he forward earnings yield plus he expeced change in he premium relaive o beginning-of-period price. However, while equaion (1a) yields a calculaion of he expeced reurn, here is no connecion beween he accouning (and he growh i generaes) and he required reurn. There is no effec on B/.. Time Dividends Book value growh rae 5.385% % rice remium Δremium yield 9.75% 10.25% 10.0%* Δremium/rice % -0.25% 0.00%* Expeced reurn 10.0% 10.0% 10.0% ROE 12.19% 12.85% 12.5% B/ in +2 = Case II + shif from +1 o +2 + from lower dividends (higher reenion) in +1 = ( ) = *Rounded 39

42 IV. B wih expeced earnings growh and consequenly an expeced change in premium, bu now wih an effec on he required reurn. No financing leverage. The final case connecs earnings growh o risk and demonsraes he 1 and 2 properies in secion under which B/ indicaes risk and he required reurn. Case II again serves as he base case. In case IV, here is again a reducion of earnings in +1 o 9.75 (as in Case III), bu he forward E/ is mainained a he 10% in case II. Assuming A2 in secion and seing G = 1 and λ = 0.02, he forecas of cum-dividend earnings growh in +2 B is given by g2 = 16.41%. However, he growh adds o risk: Seing γ = 1 for 1 simpliciy (ha is, no abnormal growh afer +2 and hus no earnings growh wih full payou, as in he example), he required reurn increases from 10% in case II o 12.81% wih he mainained E/ raio of 10%: By equaion (1d) wih G = 1, r B 0 = = 12.81% (he Fama and French special case).wih his required reurn, he forecas of ex-dividend earnings in +2 is 10.10, in +3, and so for subsequen earnings by seing γ = 1.The A1 valuaion is saisfied. B/ increases from 0.80 in cases II and III o For he same E/ as in Case II, a higher B/ indicaes higher earnings growh, as in 1. Furher, 2 is demonsraed: For a given E/, a higher B/ indicaes a higher required reurn. The reader can coninue he comparaive saics, allowing G, λ, and γ o change.. Time Dividends Book value Cum-div growh rae 16.41% 16.29% growh rae 3.6% 3.47% Expeced reurn 12.81% 12.81% 12.81% rice

43 remium Δremium yield 10.00% % % Δremium/rice % 2.733% 2.660% Expeced reurn 12.81% 12.81% 12.81% ROE 12.19% 12.63% 13.07% B/ r 1 g2 ( 1) = r ( 1) = As γ = 0 (abnormal earnings growh afer +2 is zero, his is equivalen o , where in abnormal earing growh in coninuing wih no change. 41

44 V. B wih expeced earnings growh in operaions wih an effec on he required reurn. Now wih added financing leverage. This case adds leverage o case IV in he form of a deb o equiy swap a marke value ha leaves unlevered operaing aciviies unchanged: book value for operaions is now financed by 40 in equiy and 40 in ne deb. Wih no effec operaions, he numbers for operaing aciviies remain he same as in case III bu, wih a borrowing rae of 5%, earnings equal operaing income reduced by ne ineres on he deb. A full payou policy is mainained such ha free cash flow (which is he same as in case IV) is spli beween his dividend and deb service. The example shows ha leverage increases he earnings growh rae in +2 over he operaing income growh rae in accordance wih equaion (6) and also increases ROE +1 in accordance wih equaion (7). Leverage increases he expeced reurn in accordance wih equaion (3), bu price is unaffeced. Leverage does no affec he equiy premium bu affecs he forward E/ raio in accordance wih equaion (4) such ha he higher expeced reurn is indicaed by he increased (levered) E/ raher han B/. While he unlevered B/ remains he same as in case IV, he levered B/ decreases in accordance wih equaion (5).. Time Operaing income (OI) Ne ineres expense (a 5%) Dividends (d) aymen on ne deb (F) Free cash flow (FCF) Ne operaing asses () Ne deb (ND) Book value of Equiy (B) OI growh rae 3.6% 3.47% growh rae 4.529% 4.33% Expeced unlevered reurn 12.81% 12.81% 12.81% 42

45 Expeced equiy reurn % % % Unlevered price ( ) Ne deb ( ND = ND) Equiy price () Equiy premium Δremium yield % % % Δremium/rice % 4.547% 4.350% Expeced reurn % % % Financing leverage R 12.18% 12.63% 13.07% ROE 19.38% 20.25% 21.13% Unlevered B/ Levered B/ From equaion (3), he expeced equiy reurn for +2 = % (12.81% 5%) = %, and so for 57.5 subsequen years. This expeced reurn declines over ime because of a decline in leverage. 43

46 References Andrade, S., and V. Chhaochharia Is here a value premium among large socks? Unpublished paper, Universiy of Miami. Asness, C., A. Frazzini, R. Israel, and T. Moskowiz Fac, ficion, and momenum invesing. Journal of orfolio Managemen Berk, J., R. Green, and V. Naik Opimal invesmen, growh opions, and securiy reurns. Journal of Finance 54, Bhandari, L Deb/equiy raio and expeced common sock reurns: Empirical evidence. Journal of Finance 43, Bradshaw, M., S. Richardson, and R. Sloan Do analyss and audiors use informaion in accruals? Journal of Accouning Research 39, Carlson, M., A. Fisher, and R. Giammarino Corporae invesmen and asse pricing dynamics: Implicaions for he cross-secion of reurns. Journal of Finance 56, Caskey, J., J. Hughes, and J. Liu Leverage, excess leverage, and fuure reurns. Review of Accouning Sudies 17, Chan, L., J. Karceski, and J. Lakonishok The Level and ersisence of Growh Raes. The Journal of Finance 58, Chaopadyhay, A., M. Lyle, and C. Wang Accouning Daa, Marke Values, and he Cross Secion of Expeced Reurns Worldwide. Unpublished paper, Harvard Universiy and Norhwesern Universiy. Chen, H The Growh remium. Working paper, Universiy of Briish Columbia. Chen, L., R. Novy-Marx, and L. Zhang An alernaive hree-facor model. Unpublished paper, Washingon Universiy in S. Louis, Universiy of Chicago, and Universiy of Michigan. Cochrane, J roducion-based asse pricing and he link beween sock reurns and economic flucuaions. Journal of Finance 46, Cochrane, J A cross-secional es of an invesmen-based asse pricing model. Journal of oliical Economy 104, Cooper, M., H. Gulen, and M. Schill Asse growh and he cross-secion of sock reurns. The Journal of Finance 63, Eason,., and T. Harris as an Explanaory Variable for Reurns. Journal of Accouning Research 29,

47 Eason,., T. Harris, and J. Ohlson Aggregae accouning earnings can explain mos of securiy reurns: The case of long even windows. Journal of Accouning and Economics 15 (June-Sepember), Elon, E Expeced reurn, realized reurn, and asse pricing ess. Journal of Finance 54, Fama, E., and K. French The cross-secion of expeced sock reurns. Journal of Finance 47, Fama, E., and K. French Common risk facors in he reurns of socks and bonds. Journal of Financial Economics 33, Fama, E., and K. French Size and book-o-marke facors in earnings and reurns. Journal of Finance 50, Fama, E., and K. French A Five-Facor Asse ricing Model. Journal of Financial Economics 116, Francis, J., R. LaFond,. Olsson, and K. Schipper The marke pricing of accruals qualiy. Journal of Accouning and Economics 39, George, T., and C. Hwang A resoluion of he disress and leverage puzzles in he cross secion of sock reurns. Journal of Financial Economics 96, Gomes, J., L. Kogan, and L. Zhang Equilibrium cross-secion of reurns. Journal of oliical Economy 111, Gomes, J., and L. Schmid Levered reurns. Journal of Finance 65, Green, J., J. Hand, and F. Zhang The Supraview of Reurn redicive Signals. Review of Accouning Sudies 18, Green, J., J. Hand, and F. Zhang The remarkable mulidimensionaliy in he cross-secion of expeced U.S. sock reurns. Unpublished paper, Universiy of Norh Carolina a Chapel Hill. Harvey, C., Y. Liu, and H. Zhu and he cross-secion of expeced reurns. Unpublished paper, Duke Universiy. Hughes, J., J. Liu, and W. Su On he relaion beween predicable marke reurns and predicable analyss forecas errors. Review of Accouning Sudies 13, Ippolio, F., R. Seri, and C. Tebaldi The relaive leverage premium. Working paper, Bocconi Universiy, a hp://ssrn.com/absrac= Jegadeesh, N., and S. Timan Reurns o Buying Winners and Selling Losers: Implicaions for Sock Marke Efficiency. The Journal of Finance 48,

48 Johnson, T Forecas dispersion and he cross secion of expeced sock reurns. Journal of Finance 59, Lakonishok, J., A. Shleifer, and R. Vishny Conrarian invesmen, exrapolaion, and risk. The Journal of Finance 49, Lamber, M., and G. Hübner Comomen risk and sock reurns. Journal of Empirical Finance and Sock Reurns 23, Leland, H Corporae deb value, bond covenans, and opimal capial srucure. The Journal of Finance 49, Lin, X., and L. Zhang The invesmen manifeso. Journal of Moneary Economics 60, Liu, L., T. Whied, and L. Zhang Invesmen-based expeced sock reurns. Journal of oliical Economy 117, Lyle, M. and C. Wang The Cross Secion of Expeced Holding eriod Reurns and heir Dynamics: A resen Value Approach. Journal of Financial Economics 116, Miller, M., and F. Modigilani Dividend policy, growh and he valuaion of shares. Journal of Business, 34 (Ocober), Modigliani F., and M. Miller The cos of capial, corporaion finance and he heory of invesmen. American Economic Review 48, Nielsen, A Corporae governance, capial srucure choice and equiy prices. Working paper, rinceon Universiy, a hp://ssrn.com/absrac= Novy-Marx, R The oher side of value: The gross profiabiliy premium. Journal of Financial Economics 108, Novy-Marx, R rediciing anomaly performance wih poliics, he weaher, global warming, sunspos, and he sars. Journal of Financial Economics 112, Obreja, I Book-o-marke equiy, financial leverage and he cross-secion of sock reurns. Review of Financial Sudies 26, Ohlson, J , book values, and dividends in equiy valuaion. Conemporary Accouning Research 12, Ohlson, J Risk, growh, and permanen earnings. Unpublished paper, New York Universiy Sern School of Business. Ohlson, J., and B. Juener-Nauroh Expeced ES and ES growh as deerminans of value. Review of Accouning Sudies 10, Ohlson, J., and S. Kim Linear valuaion wihou OLS: he Theil-Sen esimaion approach. Review of Accouning Sudies, forhcoming. ublished online a Springer Link, June

49 enman, S An evaluaion of accouning rae-of-reurn. Journal of Accouning, Audiing, and Finance 6, , enman, S The ariculaion of price-earnings raios and marke-o-book raios and he evaluaion of growh. Journal of Accouning Research 34, enman, S., and F. Reggiani Reurns o buying earnings and book value: Accouning for growh and risk. Review of Accouning Sudies 18, enman, S., S. Richardson, and İ. Tuna The book-o-price effec in sock reurns: Accouning for leverage. Journal of Accouning Research 45 (May), Shroff, Deerminans of he reurns-earnings correlaion. Conemporary Accouning Research 12 (Fall), Shumway, T., The Delising Bias in CRS Daa. The Journal of Finance, 52, Skogsvik, K., S. Skogsvik, and H. Thorsell Disenangling he enerprise book-o-price and leverage effecs in sock reurns. Unpublished paper, Sockholm School of Economics. Vuoleenaho, T Wha Drives Firm Level Sock Reurns? Journal of Finance 57, Wahlen, J., and M. Wieland Can financial saemen analysis bea analyss recommendaions? Review of Accouning Sudies 16, Zhang, L The value premium. Journal of Finance 60,

50 Figure 1. Average residual enerprise earnings growh raes wo years ahead (+2) for porfolios formed from join sors of he enerprise earnings yield (OI/ ) and enerprise book-o-price (/ ) a ime. See noes o Tables 1 and 4 for he calculaion of variables. 48