Accounting Structure, Specification, and Inference in Empirical Accounting Research. Stephen Penman Columbia University.

Transcription

1 Accouning Srucure, Specificaion, and Inference in Empirical Accouning Research Sephen enman Columbia Universiy reliminary January, 2011

2 This paper shows how he srucural feaures of accouning can be employed in empirical research o provide insighs ino valuaion, forecasing, risk assessmen, and asse pricing. A framework ha connecs he accouning srucure o sock reurns provides an undersanding of he anomalous reurns associaed wih accouning numbers and holds promise of unifying asse pricing in finance and valuaion research in accouning around an accouning characerizaion of risk and reurn. Beginning wih he early work of Ball and Brown (1968) and Beaver (1968), empirical accouning research has aemped o draw inferences abou accouning via correlaions wih sock prices. The documened correlaions describe boh he conemporaneous associaion beween accouning numbers and sock prices (or reurns), as in he Ball and Brown paper, and predicive associaions (wih fuure prices or reurns). In he former case, he correlaions are purpored o indicae he informaion conen or value relevance of accouning. In he laer case, he abiliy of accouning numbers o predic sock reurns is ofen given he designaion anomaly, wih he claim ha he marke does no process accouning informaion appropriaely. Considerable descripive knowledge has been gahered over he years by observing such correlaions. However, correlaions alone canno provide much insigh; indeed, making aribuions from correlaions can be dangerous. Economericians insis ha he discovery process idenificaion should firs aend o specificaion (of regression equaions) so ha he inerpreaion of observed correlaions can be made wihin a (regression) framework ha incorporaes all known srucural relaionships. There has been lile aenion o specificaion in empirical accouning research; many sudies plug accouning numbers ino regressions and hen observe esimaed coefficiens wihou consideraion as o wha numbers should appear in 1

3 he regression and in wha form, le alone predicions as o he size of he coefficiens. This paper brings specificaion o he ask of inerpreing correlaions. The key idea is ha accouning numbers are generaed from an accouning sysem ha has a formal srucure, and ha srucure mus be considered in he design of empirical analysis; he informaion conen of accouning numbers canno be inferred wihou consideraion of he srucural sysem ha generaes hem. Tha srucure is in he form of fixed accouning relaions ha ie he numbers ogeher like he one ha says ha equiy equals asses minus liabiliies (always). Furher, he sysem ies o sock prices and reurns in a formal way and ha formal relaionship dicaes he form of regressions of sock reurns on accouning numbers. The paper shows ha he inferences ypically made in capial markes research are alered, or a leas severely challenged, when one incorporaes accouning srucure in empirical design. For example, empirical work ypically esimaes a posiive coefficien on cash flow in regressions of conemporaneous reurns on cash flows and earnings bu, by developing regression specificaions as dicaed by he accouning srucure, one observes ha cash flows are negaively associaed wih reurns. Wih respec o predicive reurn regressions, he aribuion of predicive reurns as an anomaly is far more doubful when one recognizes how accouning numbers should be relaed o fuure reurns under a srucural relaionship. There is lile fresh empirical work in he paper. The paper merely pulls ogeher pas and curren empirical research o make wha is hoped o be a mehodological conribuion. In doing so, i poins o direcions for fuure research. Secion 1 lays ou he formal srucure of accouning. Secion 2 connecs he srucure o sock reurns, develops he specificaion for coemporaneous reurn regressions, hen applies he specificaion o he quesion of he informaion conen of earnings versus cash flows. Secion 3 connecs accouning numbers o 2

4 fuure sock reurns and, wih he recogniion of how he accouning srucure handles risk, brings he framework o he issue of inerpreing predicive correlaions as anomalies or reurn for risk. Wih an idenificaion of how accouning indicaes expeced reurns, Secion 4 explores he implicaions for developing accouning-based asse pricing models and, in so doing, bridges empirical work on valuaion in accouning wih asse pricing in finance. In each secion, he paper oulines an agenda for furher capial markes research, financial saemen analysis research, earnings qualiy research, and indeed asse pricing research. A all poins he emphasis is on providing insighs ino building acual pracical producs: valuaion mehods, financial saemen analysis, earnings qualiy diagnosics, and asse pricing models, no o menion insighs ino he accouning produc iself. Sadly o say, unlike research in finance, very lile produc developmen has come ou of capial markes research of he las 50 years despie he myriad of correlaions ha have been documened. Aenion o specificaion may change ha. 1. The Accouning Srucure for Reporing o Shareholders Much of capial markes research involves correlaions wih common sock prices, hus linking accouning o he value of he shareholders equiy claim. In he words of accouning heory, his research akes a proprieorship perspecive, as does his paper. Correspondingly, wih produc developmen in mind, he paper sees (useful) accouning research as an endeavor ha enhances pracical valuaion and equiy analysis, and is o be so judged. This is no o imply exclusion of oher uses of accouning, hough noe ha he accouning sysem is one ha, nominally a leas, racks shareholders equiy: The final, closing enry in he accouning process is he enry ha updaes he book value of equiy (wih he earnings for he period). Accouning srucure consiss of a se of fixed accouning relaions ha govern how accouning numbers, individually and collecively, combine o updae shareholders (book) equiy. 3

5 Shareholders view firms as generaing dividends o provide for heir (fuure) consumpion. The cash conservaion equaion dicaes how he ne cash from he business, free cash flow (FCF), is divided beween shareholders and ohers: FCF = d + F (1) where d is ne dividend o shareholders (cash dividends plus sock repurchases less sock issues) and F is cash o oher han shareholders. This equaion is he necessary ideniy ha drives he bank reconciliaion. We will refer o he F cash flow as flows o he holders of he firm s ne deb bu wih he recogniion ha all non-equiy claims, including preferred shareholder claims, are deb claimans from he common shareholders perspecive. Ne deb refers o deb obligaions minus deb asses, so he F flow can involve saisfying own deb obligaions or buying issuers deb ( markeable securiies ). The accouning sysem is a sysem of balance shees and income saemens ha ariculae (such ha debis equal credis). The ariculaion is capured by a socks-and-flows accouning relaion under which successive socks (in he balance shee) are explained by flows in and ou of hose socks. Under cash accouning, he balance shee consiss (only) of ne deb (deb obligaions ne of deb asses held), equal o shareholder s equiy, and he socks-and-flows relaion is given by: Ne Deb = Ne Deb -1 FCF + d. (2) As Ne Deb equals he book value of common shareholders equiy (B) by he balance shee equaion, B = B -1 + FCF d. (3) 4

6 Common equiy is updaed by free cash flow: Free cash flow is he flow measure of earnings under cash accouning (he cash flow saemen is effecively he income saemen), wih dividends paid ou of free cash flow. 1 Accrual accouning modifies cash accouning wih a specified srucure. Income from he business (operaing income, OI) replaces free cash flow as he flow from he business by he addiion of accruals: OI = FCF + Toal Accruals, (4) where oal accruals are also added o he balance shee as ne operaing asses (): Δ = Toal Accruals. (5) From equaions (4) and (5), he socks-and-flows equaion for he ne operaing asses is = -1 + OI FCF. (6) Accrual accouning furher disinguishes beween invesmens (I) cash ouflows (like hose for propery, plan and equipmen) ha are deemed no o perain o he curren period and so are capialized on he balance shee and oher operaing accruals (like receivables and payables) ha are also placed on he balance shee. Accordingly, Δ = I + Oher Operaing Accruals. (6a) I follows ha FCF = CFO I, as usually expressed, wih cash flow from operaions (CFO) simply he par of FCF no capialized o he balance shee. 2 1 One could imagine accouning where only cash is on he balance shee and here is no racking of he ne deb. This accouning reas borrowing as earnings (jus like poliicians hink of borrowing as revenue!): Equiy equals cash in his accouning so equiy is increased by borrowing. Wih an eye on he shareholder, he cash accouning in his paper discriminaes beween claims o cash flows from shareholders and ne deb holders. 5

7 Accrual accouning is also applied o rack he deb claim such ha an (accrual) ne financing expense (NFE) is added o he deb obligaion (wih he effecive ineres mehod, for example) as well as recognizing ha cash flows, ne of he dividend o he shareholders, reduce deb obligaions. Accordingly, he socks-and-flow eq. (2) is modified such ha Ne Deb = Ne Deb -1 + NFE - FCF + d. (7) Wih boh ne operaing asses and ne deb on he balance shee, he book value of common shareholders equiy, B = Ne Deb,. (8) and he updaing of shareholder s equiy is prescribed by ΔB = Δ ΔNe Deb. (9) Subsiuing equaions (6) and (7) for Δ ΔNe Deb., i follows ha ΔB = OI FCF NFE + FCF - d = Earnings - d (10) (where Earnings is operaing income from he business less ne financing expense). Eq. (10) saes he socks-and-flow equaion for (accrual) equiy, oherwise referred o as he cleansurplus equaion. The equaion summaries he final updaing of equiy: (comprehensive) earnings add o book value and dividends reduce book value. The preceding equaions lay ou he building blocks involved in he updaing: Eq. (6) and eq. (7) aggregae o eq. (10) bu is so doing, free 2 Free cash flow is someimes described as he ne of wo ypes of elemenal cash flows, cash flow from operaions minus cash invesmen. However, he division beween cash flow from operaions and cash invesmen is an accrual accouning noion: invesmens are cash flows ha he (accrual) accounan capializes o he balance shee. Reference solely o cash flows makes no such disincion. 6

8 drops ou of he calculaion of equiy. In shor, he saemen of shareholders equiy, he balance shee, he income saemen, and he cash flow saemen ariculae in a prescribe way o updae equiy. This srucure is quie familiar o he suden of basic accouning, hough presened in a lile differen form. U.S. GAA and IFRS follow his srucure, hough here is no always a clear disincion beween asses and liabiliies ha perain o he business () and hose ha perain o deb financing aciviies. Nor is here a clean disincion beween cash flows from he business (free cash flows) and he disposiion of hose cash flows o claimans. 3 (The proposed new financial saemen presenaion, wih is disincion beween operaing, financing and invesmen aciviies, improves his considerably). While he se of accouning equaions specifies he srucure of he accrual accouning sysem for updaing shareholders equiy, i does no specify he measuremen of he numbers ha go ino he sysem. Accouning measuremen will deermine he informaion conen of accouning numbers, bu I seek o show ha recogniion of he srucure is also imporan in making ha assessmen. 2. Conemporaneous Associaions Beween Accouning Numbers and Sock Reurns 4 A simple example illusraes he need o incorporae accouning srucure in evaluaing he informaion conen of accouning numbers via associaion ess wih sock reurns. Suppose one asks how he cos of goods sold (CGS) number on income saemens is priced in he marke. 3 For example, GAA includes ne ineres paymens as par of cash from operaions raher han disribuions o claimans from ha cash flow, and also reas invesmen in deb securiies as cash invesmens in he business raher han a disposiion of cash flow from he business. See Nurnberg (2006) for a comprehensive criique of he cash flow saemen. 4 Much of his secion is drawn from enman and Yehuda (2009). 7

9 To answer his quesion, one migh naively run he following cross-secional regression using a levels specificaion: i a bcgs e, i i where i is he marke value of he shares of firm i a dae. Or, using a changes specificaion wih sock reurns, R i as he regressand, R i CGS i 1 i. i (The issue of a levels versus changes specificaion is of course open.) Using daa from 1963 o 2001 for all NYSE and AMEX firms (as repored in enman and Yehuda 2009), he mean esimae of he coefficien, b, esimaed from annual cross-secional (Fama and Macbeh) regressions, is 1.12 (wih a -saisic of 13.52), and he esimae of is 0.23 (wih a -saisic of 8.62). As a maer of saisical correlaion, he esimaes are appropriae, bu hey do no inform. An accounan migh well objec: Cos of goods sold is an expense (a reducion in shareholder value), ye he esimaed slope coefficiens from hese equaions are posiive. The accounan s poin: Cos of goods sold is par of he calculaion of earnings; by accouning principle, i is involved wih he sales wih which i is mached o deermine gross margin, so cos of goods sold canno be considered wihou he maching sales. Specifying regressions under his dicae, i a b1 Salesi b2 CGS i e i R i Sales 1 CGS i i 2 i 1 i 1 i 8

10 The esimae of b 2 is reliably negaive (-3.94 wih a -saisic of ), as is he esimae of 2 (-0.74 wih a -saisic of -9.48); he esimaes of b 1 and 1 are reliably posiive, a 3.66 and 0.82 respecively. The marke prices sales as an addiion o shareholder equiy and cos of goods sold as a reducion, according o he accouning. The correced specificaions follow he form of an accouning relaion: Revenues - Cos of goods sold = Gross margin. Lipe (1986) and Ohlson and enman (1992), among ohers, invoke income saemen relaions of his form o examine he pricing of income saemen componens. Early empirical work on sock opion expense showed ha he expense was posiively correlaed wih sock reurns, jus like cos of goods sold in he univariae regression above. Bu Aboody, Barh, and Kasznik (2004) found ha, when one embeds income saemen relaions in a regression model, he sock marke prices grans of employee sock opions negaively, as an expense and as a liabiliy. (The finding challenges GAA and IFRS ha rea he gran as an increase in equiy.) Landsman (1986) and Barh (1994), among ohers, employ accouning equaions in specifying regression equaions involving asses, liabiliies and componens of earnings. Barh, Beaver, Hand, and Landsman (1999) refer o accouning and valuaion relaions o develop regression equaions involving earnings and cash flows. The poin is clear: A regression specificaion involving accouning numbers should be deermined by he srucure ha delivers he numbers, for ha srucure prescribes how hey are o be inerpreed, no as isolaed bis of informaion bu indeed as accouning numbers. A furher issue arises in inerpreing esimaed coefficiens in regression equaions like hose above: coefficiens on included variables are affeced by correlaion wih omied informaion (in he regression disurbance). The regression specificaions developed below no only mirror accouning relaions bu also provide a characerizaion of omied informaion and 9

11 an undersanding of how included variables correlae wih he omied informaion. Tha undersanding provides an inerpreaion of coefficiens observed on included variables. 2.1 Regression Specificaion While accouning relaions define srucure, hey do no define conen: The numbers for earnings, book value (and sales and cos of goods sold) are a maer of accouning measuremen and ha measuremen will deermine he coefficiens ha express how he numbers relae o prices. As a saring poin, suppose ha accouning measuremen were such as o produce a book value number equal o marke value such ha = B and Δ = ΔB. As, by eq. (10), ΔB = Earnings d, he sock reurn for period (wih he dividend moved o he lef-hand side) is d Earnings 1 R, (11) 1 1 wih no error erm. (Firm subscrips are undersood.) Wih his (ideal) fair value accouning, he coefficien on earnings is 1.0 and no oher informaion adds o he explanaion of reurns. This propery is due o accouning measuremen bu noe also ha he derivaion recognizes a srucural relaion in accouning: ΔB = Earnings d. Boh srucure and measuremen combine o produce he reurns-earnings relaion. Under alernaive accouning measuremen, book value can differ from he (marke) value of equiy, hus admiing an informaional role for oher accouning and non-accouning numbers. Suppose ha book value measures price wih error (as is ypical) such ha and hus = B + ( B ), 10

12 -1 = B + ( B ) ( -1 B -1 ). Again inroducing he accouning equaion (10), -1 + d = Earnings + ( B ) ( -1 B -1 ). (12) Tha is, he (undeflaed) sock reurn is always equal o earnings, ne of dividends, plus he change in he marke price premium over book value, as recognized in Eason, Harris, and Ohlson (1992) and Shroff (1995), for example. The expression is a auology ha characerizes he informaion beyond earnings ha complees he explanaion of reurns: Given earnings, addiional informaion is ha which resuls in a change in premium. 5 Eq. (10) is again he saring poin for incorporaing he accouning, for i involves he final (closing) enry o updae he book value of equiy o which all oher accouning numbers in he sysem aggregae. Expression (12) poins o anoher measuremen scenario where earnings are sufficien o explain reurns, as in model (11): Earnings are sufficien no only for he case where = B (model 11), bu also for he case of no change in premiums. If here is no change in premium, he sock reurn equals earnings. Saed in erms of accouning measuremen, i is no necessary for he balance shee o measure value for he accouning o be sufficien o explain prices and reurns; error in he balance shee is oleraed up o a consan, for here is also an income saemen ha repors earnings ha correcs he error. 6 Furher, he expression provides he insigh ha i is earnings measuremen ha creaes oher informaion. As ΔB = Earnings d 5 The relevan informaion could be informaion abou fuure pay-offs ( cash-flow news ) or abou changes in he rae ha discouns fuure cash flows ( discoun-rae news ). 6 In less formal erms, i does no maer if asses are missing from he balance shee if earnings from hose asses are flowing hrough he income saemen. The poin couners hose who demand ha accounans provide an informaive balance shee wih fair value accouning or by he recogniion of inangible asses on he balance shee. See enman (2009). 11

13 (and if dividends do no affec premiums), hen he change in premium, Δ = ΔB, is a propery of he measuremen of earnings. 7 The idenificaion of oher price-relevan informaion is sharpened by an undersanding of wha a change in premium amouns o. The inuiion is easy o grasp: if price increases more han book value, he marke is anicipaing higher earnings in he fuure han hose ha updae he book value currenly. Tha is, an increase in he premium is due o informaion ha forecass earnings growh. More sricly, he forecas mus be of residual earnings growh (or abnormal earnings growh), for only growh in excess of he required reurn adds o price. Formally, by subsiuing d = Earnings ΔB from eq. (10) for dividends in he dividend discoun model of he price, he premium a any poin, τ, is given by B E( Earnings 1 rb ) r g using a consan expeced growh rae, g, and a consan required reurn, r, for simpliciy. (This, of course, is he sandard residual earnings model.) Accordingly, eq. (12) can be expressed as 1 d Earnings E Earnings 1 rb ( Earnings rb ) 1 r g Earnings g ( Earnings rb ) 1 (13) r g Given Earnings and B -1, a well-specified regression adds oher informaion if ha informaion indicaes g. 8 Again earnings measuremen creaes he change in premium and he expeced 7 Dividends do no affec he difference beween price and book value if dividends displace price one-for-one (as under Miller and Modigliani 1961 condiions) because dividends also displace book value one-for-one by accouning principle (eq. 10). 12

14 growh implied: For a given price, lower curren earnings means higher earnings in he fuure by he propery ha accrual accouning allocaes oal (life-long) earnings o periods. Dividing eq. (12) hrough by equiy price a he beginning of he period, and leaving informaion abou growh unidenified in he regression disurbance, a reurn regression equaion is specified: 1 1 d R a b 1 Earnings 1 b 2 B 1 1. (14) The deflaion by price iniializes for informaion in price a he beginning of he period, so variables are relaive o expecaions a ha poin. The inercep and slope coefficiens are such ha he disurbance is mean zero. The regression coefficiens hus ake on values based on he correlaion of he included variables wih he disurbance, ha is, heir abiliy o explain changes B in premiums and hus growh. Beginning-of period book-o-price, 1 1, eners he regression as a maer of he mah, bu akes on a non-zero coefficien only if i forecass growh. As a benchmark, b 1 = 1, and b 2 = 0, bu only if earnings and book value (relaive o beginning-ofperiod price) are uncorrelaed wih growh. A b 1 > 1 implies an earnings muliplier, and ha muliplier means ha earnings relaive o beginning-of-period price indicaes growh (as an E/ raio or a /E raio indeed does). The specificaion recognizes earnings as he primary accouning variable ha explains price changes, for earnings updae equiy, by equaion (10). This poin has been emphasized in he discussion of levels versus changes specificaions, in Eason and Harris (1991) for example. 8 As Earnings +1 rb (Earnings rb -1 ) = Earnings +1 + rd (1+r)Earnings, one can refer o he growh as abnormal (cum-dividend) earnings growh ha explains he /E raio, as in Ohlson and Juener-Nauroh (2005). 13

15 Accordingly, he original Ball and Brown (1968) sudy, wih is earnings change variable did no quie have i righ, hough he paper cerainly sands as a correlaion exercise (and repors robus correlaions indeed). The formulaion here poins o he reason why changes in earnings migh ener he regression: Changes in earnings (growh in earnings) have an informaional role if hey forecas subsequen growh ha induces a change in premium. The specificaion also recognizes a role for book value (oher han for he case where = B ): Book-o-price loads wih a nonzero b 2 coefficien if i indicaes growh, a poin explored laer in he paper. The excepion is he case of no change in premium (no growh) where b 1 = 1, and b 2 = 0. 9 Since Ohlson (1995), researchers have added book value o reurns-earnings regressions, bu wihou recogniion of wha hey are capuring: growh. One final poin ha is relevan o maerial laer in his paper: Eq. (12) applies for boh efficien and inefficien marke prices; ha is, a change in premium may be due o informaion abou growh bu could also be due o he marke mispricing earnings and informaion abou growh. 2.2 An Illusraion: he ricing of Earnings and Cash Flows In conemporaneous reurn regressions, capial markes research ypically presumes ha marke is efficien in pricing informaion and hus inerpres he associaion of accouning numbers wih reurns as indicaive of heir informaion conen. Here we summarize he enman and Yehuda (2009) applicaion of he above framework o he issue of he pricing of earnings and cash flows. This is an imporan issue, for accouning is disinguished by is embrace of accrual accouning (in eq. 6, 7, and 10) as opposed o cash accouning in eq. (3). Numerous sudies have run 9 This resonaes wih he Ohlson (1995) and Felham and Ohlson (1995) valuaion models where price is expressed as a weighed average of earnings and book value bu wih he weighs shifing compleely o book value for = B and compleely o earnings for he case where earnings are sufficien. 14

16 regressions of reurns on earnings and cash flows (and various ransforms of hese measures) and have found ha boh are posiively relaed o reurns, on average, wih boh providing incremenal informaion conen over he oher (see, for example, Rayburn 1986; Wilson 1987; Dechow 1994; Bowen, Burgsahler and Daley 1987; Clubb 1995; Francis, Schipper and Vincen 2003). Bringing accouning srucure o he issue provides a predicion ha conflics wih hese findings: Free cash flow decreases ne operaing asses () in eq. (6) bu also decreases ne deb in eq. (7) so, as B = Ne Deb, shareholders equiy is unaffeced by free cash flow. Indeed, eq. (10) shows ha, in he updaing of book value, ΔB, earnings are imporan bu free cash flow drops ou in he calculaion; accrual accouning implicily embraces he ene of modern finance ha cash flows are irrelevan o shareholder value. In shor, he coefficien on cash flow should be zero. Does he marke price he accouning numbers as if earnings add o price bu cash flow does no? The following regression specificaion (wih annual reurns) conforms o eq. (14) bu adds free cash flow, 1 1 a b 1 Earnings 1 b 2 B 1 1 b 3 d 1 b 4 FCF 1 Coefficiens saisics Average R 2 = 0.14 eriod:

17 Dividends (he cash flow o shareholders) have been moved o he righ-hand side as a possible informaion variable (in accordance wih he lieraure ha sees a signaling role for dividends). The esimaes are from enman and Yehuda (2009) where regressions are run in cross-secion every year from on NYSE and AMEX firms. Mean coefficien esimaes are repored under he regression equaion, along wih -saisics esimaed from he ime series of regression coefficiens (in he mode of Fama and MacBeh). I is clear ha earnings are posiively relaed o price changes, bu he esimaed coefficien on free cash flow is no significanly differen from zero, in accordance wih he accouning: Given earnings, free cash flow is irrelevan o he updaing of he book value of equiy and, given earnings and book value, free cash flow is irrelevan o he updaing of price. Marke pricing affirms he accouning. This comes from aenion o specificaion, and noe ha he average R 2 of 14% is significanly higher han ha ypically observed in capial markes research. The coefficien on earnings is greaer han he benchmark of b 1 = 1.0, and he framework supplies he inerpreaion: Earnings (relaive o beginning-of-period price) is correlaed wih informaion abou growh and hus akes on a growh muliplier. Noe also ha b 2 is greaer han zero, indicaing ha book-o-price forecass growh, a poin we will have much o say abou laer. 10 The zero coefficien on cash flow also has a corresponding inerpreaion: Given earnings, book value, and dividends, free cash flow is no an indicaor of growh on average. These regression findings perain o he pricing of he equiy. Corresponding regressions can be developed for he operaions, ha is, for he pricing of he firm (he enerprise) raher han 10 The dividend variable akes a negaive coefficien, consisen wih he dividend displacemen propery of dividends reducing prices prices. The size of he coefficien less han he -1.0 prediced for dividend displacemen indicaes ha more dividends (relaive o price) indicae lower growh, given earnings and book values. (Dividend changes added o he regressions load wih a posiive coefficien, consisen wih he dividend signaling conjecure.) 16

18 he equiy. Assuming ha marke value of ne deb is equal o is book value, he price of he ne operaing asses (he price of he firm or enerprise price), same logic ha go o eq. (12), Ne Deb. Following he ( ) and ). ( Bu, = OI FCF, by he socks-and-flows equaion for operaing aciviies, eq. (6), so subsiuing for Δ and deflaing by he beginning-of-period marke value of he operaions, he unlevered version of regression eq. (14) is as below. The operaing income yield, OI 1 (he enerprise earnings yield) replaces he earnings yield, he enerprise book-o-price replaces equiy book-o-price, and he dividend from operaions o all claimans (free cash flow) replaces he dividend o shareholders OI FCF 3 1 (15) Coefficiens saisics Average R 2 = 0.22 eriod:

19 Operaing income loads wih a muliplier, 2.21, bu he coefficien on free cash flow is negaive: Given operaing income and book value, higher free cash flow means lower enerprise value. This accords wih he accouning, as saed in he socks-and-flows equaion for operaions: = OI FCF, ha is, operaing income adds o he book value for operaions bu free cash flow reduces book value, and he marke prices firms in he same way on average. Effecively, free cash flow is a payou from he firm (ha reduces is value), wih ha payou disribued o he shareholders and ne debholders, as in eq. (1). Noe ha he average R 2 of 22 percen is quie impressive for a reurns regression wih jus hree accouning variables. The earlier research ha documened posiive coefficiens on cash flows deal wih cash flow from operaions (CFO) raher han free cash flows. The following regression mainains his focus by dividing free cash flow ino cash flow from operaions and cash invesmen (I): FCF = CFO I,. The period covered is , wih 1987 marking he adven of he modern cash flow saemen in he U.S OI CFO 3 CFO 1 I 3 I 1 (15a) Coefficien saisic Average R 2 = 0.15 eriod:

20 The esimaed coefficien on Invesmen is 1.30, wih he marke saying ha a dollar of invesmen is worh $1.30 on average. Tha is wha one expecs wih posiive ne-presen-value (NV) invesing. Inerpreed wihin he regression framework, posiive-nv invesmen adds o earnings growh and ha is growh ha he marke prices as adding value. The coefficien on CFO is very close o -1.0: a dollar of cash from operaions reduces he price of he firm by a dollar, on average. This is very differen from prior research ha repors a posiive coefficien on cash flows, bu accords wih he accouning. Firs, cash flows from operaions perain o he firm, no he equiy. Second, in evaluaing CFO, one mus conrol for invesmen of cash back ino he firm. Jus like sales mus be recognized in evaluaing cos of goods sold according o an accouning relaion, so mus cash invesmen in evaluaing cash flow from operaions: FCF = CFO I,. The finding also accords wih he economics (ha he accouning recognizes): Residual cash (afer invesing in he business) is invesed deb asses, used o reduce deb obligaions, or pay dividends, and hese aciviies are broadly viewed in he heory of finance as zero-ne-presen-value aciviies. Accordingly, he cash flow is valued as reducing he value of he firm dollar-for dollar, unlike cash invesmen in he business ha adds value o he business and is valued on average a $1.30 per dollar. The accouning srucure capures his, and so does he marke. Bu noe ha he marke s pricing of he accouning is only idenified wih he appropriae specificaion. 2.3 Research Direcions These findings have immediae implicaions. They broadly affirm accrual accouning for financial reporing (and he dismissal of cash accouning). They repor he ypical muliplier on 19

21 earnings and inerpre ha muliplier as associaed wih growh. 11 They indicae ha cash flow does no forecas growh, on average, nor adds value; indeed, cash flow reduces he value of he firm, one-for-one, as in he accouning. 12 They documen ha he dividend displacemen propery of accouning (dividends reduce book value) is also eviden for prices. They affirm ha invesmen in he business is, on average, priced as adding value. They poin o accrual accouning valuaion mehods (raher han discouned cash flow mehods). They poin o separaing operaing aciviies from financing aciviies in financial saemen analysis. I is impressive how far one ges by aenion o specificaion. This being said, he specificaions o his poin are minimal, hey involve only he aggregaes of he accouning sysem, earnings and book values and heir unlevered equivalens. While one mus be impressed wih he R 2 repored wih jus a couple of bis of accouning informaion, decomposiion of hese boom-line measures of he income saemen and balance shee may well enhance he R 2 and hus enhance our undersanding of he informaiveness of accouning. Analysis of line iems is financial saemen analysis, so he framework poins o how financial saemen analysis works for valuaion: Line iems (and raios of line iems) add o he explanaions of price i hey inform abou growh, and adding seleced line iems o hese regressions will affirm he financial saemen analysis as such. A muliplier on a paricular line iem can be invesigaed, for example on a resrucuring charge ha reduces earnings dollar-for-dollar bu may add growh. An earnings qualiy diagnosic, proposed o idenify inflaed income, is validaed by inclusion is he regression because inflaed earnings 11 To calibrae, he coefficiens in he levered regression imply a railing /E of 16, close o he hisorical average, if he average sock reurn is 12 percen (which is he average hisorical sock reurn). 12 The resuls are on average for he cross-secion. This does no mean ha cash flow canno indicae growh in specific cases, for example, when accruals are high relaive o cash flows because of earnings managemen (hus indicaing lower earnings growh in he fuure). The nex secion indicaes ha his is indeed so. 20

22 means lower fuure earnings (growh) and he regression would so ideniy. In evaluaing hese quesions, here is considerably more srucure o he accouning sysem beyond he bare-bones srucure in Secion 1 ha migh be exploied. 3. redicive Associaions Beween Accouning Numbers and Sock Reurns Conemporaneous reurn regressions aemp o ascerain informaion conen wih he presumpion ha marke prices reflec all available informaion efficienly. Tha presumpion is called ino quesion by research ha documens ha accouning informaion predics fuure sock reurns. While i is acknowledged ha predicive correlaions migh jus exhibi reward for risk, here is a srong endency in he research o aribue he findings o marke mispricing, or a leas o ag i as an anomaly. Almos any accouning variable scaled by price predics sock reurns indeed, he inverse of price does so bu surely all he documened anomalies canno be addiive. 13 There is a need for a framework o provide cohesion and ha framework would serve us well if i also helped o idenify wheher he predicable reurns are abnormal reurns from mispricing or expeced reurns for risk borne. The aspiraion o sor ou mispricing from raional pricing is likely o be disappoined. I is well recognized (in Fama 1970 and 1991, for example) ha one can only idenify abnormal reurns agains an agreed-upon model of normal reurns for bearing risk. Despie 50 years of research, we do no have such an asse pricing model, validaed and acceped. However, I hope o show in his secion ha an undersanding of he srucure of how accouning numbers relae o fuure reurns can help in he inerpreaion of predicive correlaions and dampen enhusiasm for he marke inefficiency inerpreaion. Again, aenion o specificaion enhances idenificaion. 13 For a review of accouning anomalies, see Richardson, Tuna, and Wysocki (2010). 21

23 The relaionship beween accouning numbers and fuure reurns is idenified via he same srucure ha led o eq. (12) and (14) for conemporaneous reurns, bu now wih expeced +1 reurns idenified wih expecaions of +1 earnings and he expeced +1 change in premium. Rolling eq. (12) forward one period and deflaing by he curren price, E ( 1 d ) E( Earnings 1) E( 1 B 1) ( E( R 1) B ). (16) The deflaion by yields he expeced +1 rae-of-reurn on he lef hand side. I also deflaes he righ-hand side for he marke s expecaion, a ime, of forward (+1) earnings and he change in premium and for he risk surrounding hose expecaions (ha discouns he price). Moving o he resuling regression specificaion, as before, R a b E( Earnings ) b B. (17) Eq.(17) idenifies he expeced year-head reurn via he forward earnings yield and he curren book-o-price. If b 1 = 1.0 and b 2 = 0, he expeced +1 reurn is given by he forward earnings yield and he analysis in he las secion shows ha his is he case where price equals book value or where he is no expeced change in he premium, ha is, no expeced growh. Valuaion heory so affirms: he E/ raio equals he required reurn wih no growh. Bu here is a furher insigh: Any variable ha forecass a change in premium (discouned for he marke s risk-adjused expecaion a ime ) will also forecas expeced reurns. As explained in he las secion, ha is a forecas of growh, so any variable ha forecass growh ha is priced as risky will add o he explanaion of expeced reurns. 22

24 The idenificaion of book-o-price (B/) in eq. (17) ses off bells because he Fama and French asse pricing model idenifies book-o-price as indicaing firms sensiiviy o facors ha are priced as risky. The idenificaion of he expeced reurn via E/, B/, and growh is aken up in he nex secion. Here we apply he framework o he inerpreaion of predicive reurn correlaions in accouning research. In regression forma, ha research ypically has +1 reurns on he lef-hand side, as in eq. (17), and accouning variables like accruals and growh in ne operaing asses (Δ) on he righ-hand side. More ofen, ess compare fuure reurns on porfolios formed on he accouning variable, hus replicaing feasible rading sraegies (and avoiding he linear consrain of (linear) regressions). Conrols are inroduced for risk facors, wih he predicable reurn ha is lef unexplained by hese risk facors hen idenified as an anomaly or, more boldly, as abnormal reurns o mispricing. Bu here is he difficuly: We do no have an accepable asse pricing model o esablish normal reurns for risk. Indeed, adding variables like B/, size, and momenum as conrols for risk is mere conjecure, for hese variables have been included in nominaed asse pricing merely by observing correlaions daa dredging no from analyical developmen. In shor, here has been lile aenion o specificaion, neiher in anomaly research nor in he idenificaion of benchmarks agains which an anomaly is impued. This leaves an inerpreive mess; he aribuion o abnormal reurns is a sab in he dark. Eq. (16) and (17) help sor hings ou. Suppose one documens ha earnings-o-price predics reurns, as in Basu (1977) and (1983) and were emped o designae he correlaion as an anomaly (as in he Basu papers). Tha would be overreaching as an inference, for he srucure ha connecs accouning numbers o expeced reurns says ha (forward) earning-oprice should predic reurns under raional pricing: The earnings yield is an indicaion of risk and 23

25 reurn. Suppose, furher, ha one documened ha oher accouning variables accruals or Δ, for example predic reurns and were emped o make he anomaly or abnormal reurn inerpreaion. Tha would be a lile hasy for we undersand from eq. (16) and he inerpreaion of a change in premium as expeced growh in eq. (13), ha any variable ha predics growh ha is priced as risky adds o he assessmen of he required reurn. Indeed, a variable ha predics forward earnings (and hus he forward earnings yield) should also predic he required reurn. Finally, eq. (17) informs ha if B/ forecass risky growh, i is legiimaely added o he regression, no jus on he basis of observed correlaions, bu because i is dicaed by he specificaion. As noed earlier, eq.12 (and also eq. 16) hold for boh efficien markes (ha raionally price o yield he required reurn as he expeced reurn) and inefficien markes (where he expeced reurn includes he reurn o mispricing). So he framework here seemingly does no sor hings ou. One canno escape he adage ha one mus have a valid asse pricing model o do so. However, a model ha predics ha E/, B/, and oher accouning variables are appropriae indicaors of normal reurns (if he marke is efficien) mus surely bear on he conversaion. Once again, srucure brings (some) idenificaion o correlaions: If he observed predicable reurns are wha we would expec if he marke were efficien, why would one leap o a conclusion ha he reurns indicae marke inefficiency? More so given he significan persuasion in economic heory for (approximae) efficien markes and no compeing persuasive heory for he alernaive. Tha is he scienific mehod. Conjecures abound and credible behavioral heories abou invesors over- and under-reacion o accouning informaion (in aggregae) may well emerge bu a he momen, he analysis here suggess here is no imperaive for a scienis 24

26 o ascribe reurns o accouning numbers as anomalies if hose numbers forecas forward earnings or growh. To appreciae he poin, consider he predicable reurns associaed wih E/ documened by Basu 1977 and 1983 and many ohers wih he aribuion of anomalous reurns. Ball (1978) made he sraigh-forward conjecure ha earnings-o-price is a yield (a reurn on price) which, like a bond yield, migh be relaed o risk. Bu ha conjecure becomes an imperaive only wih a formal model of how he earnings yield relaes o risk and reurn. A bond model supplies i: he expeced yield is idenified via an inernal rae-of-reurn calculaion. (Accouning-wise, he effecive ineres mehod calculaes he expeced earnings yield.) The yield on a bond is readily acceped as an indicaion of is risk and required reurn even hough we do no have a generally acceped equilibrium asse pricing model for a bond (or any asse). Accordingly, i would be considered quie brazen o claim ha predicable bond reurns from bond yields are anomalous. For he equiy earnings yield he issue is more difficul, for wo reasons. Firs, unlike a bond yield, he earnings yield also reflecs anicipaed earnings growh, so an inernal rae-ofreurn calculaion from an equiy valuaion model mus accommodae a growh forecas, bu forecass of (long-erm) growh are elusive. Indeed, growh may be relaed o risk. 14 Second, earnings is an accouning measure i depends of how he accouning is done and here is no guaranee ha he GAA earnings yield capures risk and reurn. Bu our framework accommodaes boh earnings measuremen and growh (hey are in fac complemens) and, wih he discoun for risk in in eq. (16), admis only hose variables ha predic risk-adjused growh. Indeed, he model for he expeced reurn here is a generalizaion of he bond reurn 14 apers ha have ried o esimae he implied cos of capial for equiy as an inernal raed of reurn from growh forecass have been remarkably unsuccessful in producing measures ha validae agains subsequen average reurns. See Eason (2009) for a review. 25

27 model where here is no growh (and no expeced change in premium) for equiies where here is likely o be growh. 15 The empirical quesion, hen, is wheher so-called anomaly variables predic reurns because hey predic he forward earnings yield and he change in premium (growh) in eq. (16). If so, hey would be par of a raional deerminaion of he required reurn for risk. A lieraure survey reveals ha prominen accouning anomalies are accruals (in Sloan 1996), growh in ne operaing asses, Δ (in Fairfield, Whisenan, and Yohn 2003), and reurn on asses (Chen, Novy-Marx, and Zhang 2010). These are primary candidaes for explaining expeced reurns in his framework for hey are likely o forecas forward earnings and possibly growh. 16 As Earnings = CFO + Accruals (in he way ha accruals are defined in accrual anomaly papers), specifying accruals effecively decomposes Earnings ino cash flow and accrual componens, and hese wo componens have differen implicaions for forecass of forward earnings in Sloan I is he marke s failure o recognize he difference in persisence of cash flows and accruals ha is said o be he reason for he accrual anomaly, bu a raional marke recognizes such a difference and he reversal propery of accruals in forecasing forward earnings and he expeced reurn in eq. (16). Wih respec o Δ, Earnings + Ne Ineres (afer-ax) = Operaing income (afer-ax) = Free cash flow Δ by he clean surplus equaion for operaing aciviies (6), so Δ also decomposes he operaing componen of earnings ino componens ha may have differen implicaions for forward earnings. The framework also 15 Model (11) is he reurn model for a bond. Wih mark-o-marke accouning, he premium is zero (and hus he change in premium is zero). 16 There are many repored accouning anomalies bu many are relaed o he hree here. The growh in oal asses anomaly is relaed o growh in ne operaing asses, as is growh in long-erm (in Fairfield, Whisenan, and Yohn 2003). Anomalous reurns are also associaed wih invesmen (in Chen, Novy-Marx, and Zhang 2010 ), bu invesmen is par of Δ = I + Oher Operaing Accruals (eq. (6a). 26

28 suggess i is no surprise ha reurn on asses predics reurns for is conains boh earnings and he book value ha are involved in he reurn on asses calculaion. Moreover, considerable empirical work indicaes ha reurn on asses is a robus predicor of fuure earnings. Indeed enman and Zhang (2006) find ha reurn on asses (or raher reurn on ne operaing asses) and Δ are he primary forecas variables and explain why his would be so as a maer of accouning srucure. As Δ = I + Oher Operaing Accruals (eq. 6a), accruals (and indeed invesmen in Chen, Novy-Marx, and Zhang 2010) adds o he forecas of forward earnings. The relaionship beween hese variables and fuure growh is less clear, bu Δ is a growh variable. enman and Zhu (2010, in progress) indicae ha accruals, Δ, and reurn on asses indeed forecas forward earnings and growh (among a number of oher anomaly variables hey look a). The panels below provide a summary. Again he regressions are run in he cross-secion in Fama and Macbeh syle over he period, 1962 o Regression (18) esimaes he associaion beween of forward earnings-o-price wih and a number of ime- variables. The saring poin is curren earnings-o-price, o which is added he B/ raio, as in he reurn model (17), curren changes in earnings (over price), and hen he anomaly variables, A, one a a ime The hree anomaly variables are measured as in he papers referenced above. is observed four monhs afer fiscal-year end (by which ime accouning daa for he prior fiscal year, daed, will have been repored). Earnings are before exraordinary and special iems, wih a ax allocaion o special iems. Resuls are similar when accruals and Δ are price deflaed. The op and boom 1% of each predicor variable is rejeced each year in esimaing he regressions. 27

29 Forecasing he Forward Earnings Yield Earnings 1 Earnings B Earnings A 1 (18) No anomaly variables Coefficien saisic Average R 2 = 0.29 A = Accruals/Average Asses Coefficien saisic Average R 2 = 0.30 A = Δ/Average Asses Coefficien saisics Average R 2 = 0.30 A = Reurn on Asses Coefficien saisic Average R 2 = 0.26 These resuls confirm ha railing E/ is posiively correlaed wih forward E/, so he findings of Basu (1977 and 1983) are idenified wih raional pricing. Given curren earnings-oprice, book-o-price appears o have lile role in forecasing he forward earnings yield, bu he anomaly variables do. Significanly, hey do so in he direcion in which hey forecas reurns: Higher accruals and Δ forecas lower forward earnings han curren earnings, jus as hey forecas lower reurns, and reurn of asses forecass higher forward earnings, as i does reurns. The coefficien on reurn on asses is no large, bu he regression already includes earnings and 28

30 book value which are he leveraged equivalens of he numeraor and denominaor of reurn on asses. Models for forecasing growh are in he nex panel. The forecas variable is he earnings growh rae wo years ahead, ha is, he growh afer year +1 ha is forecased in predicing he +1 change in premium in eq. (16) and hus he expeced reurn. Two-year-ahead growh is of course only a small par of long-erm growh so clearly his is a feeble aemp o develop a forecas (and he R 2 are also feeble). Again, he forecass reain E/ and B/, as in eq. (17). The curren change in earnings is added in he firs model, bu i is no significan so is dropped in he models ha add he anomaly variables The earnings change, boh in +2 and, are afer reinvesing dividends a he risk-free rae o adjus for he displacemen propery of dividends (and hus he noaion, Earnings a ). To handle negaive earnings, he +2 earnings growh rae is calculaed as a Earnings 2 2 which ranges from -2.0 o 2.0. Only firms ha survive wo years ahead are included in a Earnings Earnings 2 he esimaions. 1 29

31 Forecasing Earnings Growh Earnings Earnings a 2 1 Earnings 1 2 B Earnings 3 a A 4 u 2 (19) No anomaly variables Coefficien saisic Average R 2 = 0.02 A = Accruals/Average Asses Coefficien saisics Average R 2 = 0.02 A = Δ/Average Asses Coefficien saisic Average R 2 = 0.02 A = Reurn on Asses Coefficien saisic Average R 2 = 0.03 The curren E/ loads wih a srong negaive coefficien as expeced, for E/ (or raher /E) indicaes growh. The srong posiive coefficien on B/ is he focus of he nex secion of he paper, bu noe ha B/ forecass growh. The sign of he esimaed coefficiens on accruals and Δ imply lower expeced growh, and ha is consisen wih heir relaionship wih fuure reurns: If growh is priced as risky, higher accruals and Δ ha imply lower growh also imply lower expeced reurns ha reflec ha risk. 30

32 In conclusion, boh he forward earnings regressions and he growh regressions sugges ha he so-called anomalies are consisen wih he raional pricing of risk. An alernaive inerpreaion requires somehing else o be pu on he able. A behavioral heory, duly validaed, migh supply his (hough no a behavioral conjecure), bu ha would have o challenge he economic heory of raional pricing wih which he findings repored here, from enman and Zhu (2010, in progress), are consisen. Researchers claim ha he reurns o anomalies ha hey documen in many cases 10 percen or more per year on average are oo large o be explained as reurn for risk. Bu surely ha much money canno be lef on he able and so easily deeced ex ane (10 percen per year!)? There is anoher explanaion: Growh is risky and he las half of he wenieh cenury when hese reurns were observed were years when growh paid of handsomely, ex pos. In conras, posiions based on he anomalies apparenly performed badly in when growh expecaions ook a big shock. 3.3 Furher Research Forecasing and pricing go ogeher, for price is based on expeced fuure payoffs. The quesion hus arises as o how forecasing models are o be srucured. Models (18) and (19) presumably can be improved upon and, once again, accouning srucure implies a srucure for a forecasing model. Firs, eq. (10) says ha a forecas of earnings mus be consisen wih a forecas of change in equiy and dividends, and eq. (6) says ha forecass of operaing income mus reconcile o forecass of free cash flow and growh in ne operaing asses. A purely saisical approach can produce forecass ouside of hese bounds; he accouning srucure implies consrains on (he coefficiens of) forecasing models. Second, no only mus line iems (ha may appear in a forecasing model) ie o each oher in a srucured way according o accouning relaions, bu he iner-emporal properies of accouning should also be recognized in consraining he forecass; 31