Accounting Anomalies, Risk and Return

Transcription

1 Accouning Anomalies, Risk and Reurn Sephen H. enman* Columbia Business School Julie Zhu Boson Universiy *Corresponding auhor. We hank Seve Monahan and Sco Richardson for helpful commens. Ocober 2011

2 Accouning Anomalies, Risk, and Reurn Absrac. This paper invesigaes he quesion of wheher so-called anomalous reurns prediced by accouning numbers are normal reurns for risk or abnormal reurns. I does so via a model ha shows how accouning numbers inform abou normal reurns if pricing were raional. The model equaes expeced reurns o expecaions of earnings and earnings growh, so ha any variable ha forecass earnings and earnings growh also forecass required reurns if he marke prices hose oucomes as risky. The empirical resuls indicae ha many accouning anomaly variables forecas forward earnings and growh, and in he same direcion in which hey forecas reurns. These variables include accruals, asse growh, profiabiliy, invesmen, ne share issuance, and exernal financing. In shor, he observed anomalous reurns associaed wih hese accouning numbers are consisen wih he raional pricing.

3 Accouning Anomalies, Risk, and Reurn Numerous sudies have documened predicable reurns associaed wih accouning numbers; earnings-o-price, book-o-price, accruals, sales growh, and asse growh, o name a few, predic sock reurns in he daa, and quie consisenly so. The predicable reurns have been designaed anomalies (presumably meaning we don undersand hem) or, more boldly, abnormal reurns due o marke mispricing. Invesors reporedly develop anomaly rading sraegies under he manra of accouning arbirage. Ohers have aemped o explain he reurns as normal reurns for risk borne (in Fama and French 1996, Zhang 2007, Khan 2008, Guo and Jiang 2010, and Wu, Zhang, and Zhang 2010, for example). A modifying view aribues he reurns o limis in he abiliy o arbirage (in Shleifer and Vishny 1997, Mashruwala, Rajgopal, and Shevlin 2006, and Li and Sullivan 2011). 1 As long recognized (in Fama 1970 and 1991 among ohers), he aribuion of abnormal reurns and he associaed inference of marke inefficiency can only be made wih a valid asse pricing model ha ses he benchmark for he normal reurn for risk borne. In his spiri, many of he predicable reurns have been compared o normal reurns supplied by asse pricing models such as he CAM and a variey of muli-facor models, mos commonly he Fama and French (1993) hree-facor model and i varians. Bu hese models fail o be validaed, so he documened reurns indeed remain anomalous. Even wihou a generally acceped asse pricing model, one would be assised in he aribuion ask wih a model ha supplies an undersanding of how accouning numbers inform abou expeced (normal) reurns if pricing were raional. Our paper supplies such a model. The model equaes expeced reurns o expecaions of earnings and earnings growh so ha any variable ha forecass earnings and earnings growh also forecass expeced reurns if he marke prices hose oucomes as risky. Couching reurns in erms of earnings oucomes is paricularly 1 Richardson, Tuna, and Wysocki (2010) review anomalies research and Dechow, Khimich and Sloan (2011) provide a recen commenary on he accrual anomaly ha promoes he marke inefficiency view. A recen book Zacks (2011), wih conribuions from a number of auhors, goes hrough he anomaly research in deail wih a focus on execuable rading sraegies. 1

4 perinen o an invesigaion of accouning anomalies, for hese involve accouning numbers ha presumably forecas earnings in he fuure. The model connecs so-called anomaly variables o raional forecasing and hus o raional expecaions ha are a he hear of raional pricing. The empirical resuls indicae ha he observed anomalous reurns associaed wih many accouning numbers are consisen wih he raional pricing of hose numbers. These include accruals, asse growh, profiabiliy, invesmen, ne share issuance, and exernal financing. Bu noe up fron ha our model is no a model of equilibrium expeced reurns for risk, so we canno be conclusive (and such a model is, of course, elusive). Our conclusion ha he reurns are consisen wih raional pricing is weak: Our analysis indicaes ha he reurns associaed wih accouning anomalies are hose you d expec o see if he marke were efficien in is pricing. Tha is, measures involving accouning numbers, like earnings-o-price, book-o-price, and accruals logically indicae normal raher han abnormal reurns. The analysis hus places a higher bar for he researcher or invesor o mainain oherwise; hose mainaining ha he marke is inefficien wih respec o he idenified accouning informaion would have o show ha he observed reurns, hough consisen wih a raional pricing, are oherwise. We are undecided on he issue ourselves, bu he analysis does revise our esimaes of he likelihood ha anomalous reurns are due o marke inefficiency (downwards) and we expec he probabiliies of he reader o be so affeced. To give a sense of our approach, consider he predicable reurns associaed wih earnings-o-price ha have been repored (by Basu 1977 and 1983 and many ohers) wih he aribuion of anomalous reurns. The predicable reurns are exploied in conrarian and value versus growh invesmen sraegies wih he presumpion ha hey are due o marke mispricing. However, 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. Tha conjecure would be more persuasive wih a formal model of how he earnings yield relaes o risk and reurn. For a bond, a model is available: a bond pricing model direcs he inernal-rae-of-reurn calculaion ha supplies he expeced yield. The yield is readily acceped as an indicaion of risk and he associaed required reurn (as a rough cu); i would be considered quie brazen o claim, as a generaliy, ha bond reurns prediced by credi spreads are anomalous, even hough he sandard 2

5 bond pricing model is no a generally acceped equilibrium asse pricing model for he required reurn. 2 For he equiy earnings yield he issue is more difficul, for hree reasons. Firs, equiies do no involve fixed conracual paymens so reconciling expeced payoffs o price via an inernal rae-of-reurn calculaion in more problemaical. Second, unlike a bond yield, he earnings yield also reflecs anicipaed earnings growh, so an inernal rae-of-reurn calculaion mus involve a growh forecas. Bu forecass of (long-erm) growh are elusive. Indeed, growh may be relaed o risk. 3 Third, 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. The expeced earnings yield on a bond equals he expeced bond yield under he effecive ineres mehod, bu he accouning for equiy earnings in no way guaranees a correspondence. The model of expeced reurns in his paper accommodaes hese hree issues. Significanly, he model incorporaes he earnings yield bu also idenifies book-o-price as a par of he raional assessmen of normal reurns, a measure ha robusly predics reurns and one on which Fama and French have buil a pricing model. Furher, accouning feaures such as accruals, growh in asses, and reurn on asses (ha are said o yield anomalous reurns) are also idenified as indicaing he required reurn. These are he very variables which (in previous sudies) indicae addiional reurns over he benchmark Fama and French reurns. By using he Fama and French benchmark reurn o indicae anomalies, previous sudies have in effec documened he incompleeness of he Fama and French model in explaining how accouning numbers relae o expeced reurns. 1. The Model The model adaps he characerisic reurn model of enman, Reggiani, Richardson, and Tuna (2011) o idenify how accouning variables relae o expeced reurns. As indicaed, he model does no explain equilibrium expeced reurns in he cross-secion (like a formal pricing model 2 This is so, even hough he implied bond yield is a rough measure of risk premium: i ignores he erm srucure and he sochasic naure of he erm srucure. 3 Considerable research aemps o esimae he required reurn (or he implied cos of capial ) from esimaes of he forward earnings yield and assumpions abou growh, bu has had difficuly validaing he esimaes agains acual average realized reurns. For a review, see Eason (2007). 3

6 does). Wih some excepions (noably he Fama and French model wih is book-o-price facor), asse pricing models do no bring accouning aribues direcly o he modeling of expeced reurns, and i is his difficuly ha we aemp o handle. 1.1 A Model of Expeced Reurns Explained by he Adjused Forward Yield The model expresses expeced raes-of-reurn for period +1 in erms of forecass of he forward earnings yield, he curren (ime ) book-o-price raio, and addiional anomaly variables o be idenified by empirical analysis. By he clean-surplus accouning operaion for equiy, d +1 = +1 + B B +1 where d is he ne dividend o common equiy, are (comprehensive) earnings available o common, and B is he book value of common equiy. Subsiuing for dividends in he (undeflaed) sock reurn (wih firm subscrips omied), E( +1 + d +1 ) = E[ B +1 ( B )]. (1) Dividing hrough by o yield expeced rae-of-reurn, 1 d 1 E( 1) 1 B 1 ( B ) E( ) E( R 1) E( ) (1a) The ideniy in Eq.1 has long been recognized, for example in Eason, Harris, and Ohlson (1992) and Shroff (1995). If here is no expeced change in he premium over book value, Eq. 1a shows ha he expeced rae-of-reurn is equal o he expeced earnings yield, as Ball (1978) conjecured. This benchmark case is he case for a mark-o-marke bond (where he expeced change in premium, and indeed he premium, is zero). However, equiy earnings are deermined by accouning principles ha do no necessarily produce a consan premium, and only a paricular accouning measuremen permanen earnings saisfies he zero expeced change in premium condiion. 4 The ideniy insrucs ha any alernaive measuremen of earnings o his benchmark induces an expeced change in premium. If expeced earnings are depressed below ha which would indicae he expeced reurn (by accouning ha expenses R&D expendiures, for example), here mus be an expeced change in premium: book value increases wih he 4 I can be shown ha he consan premium case corresponds o earnings being sufficien o forecas fuure earnings (wih no oher informaion required) such ha +1 = (1+r) rd + ε +1, wih ε +1 mean zero (and so a all poins in ime). This measure of earnings is ofen designaed permanen earnings. 4

7 earnings bu prices are expeced o increase more han book value because low earnings are added o book value. Accordingly, he expeced change in premium mus be accommodaed in forecasing he expeced reurn, and any variable ha predics he change in premium will add o he explanaion of he expeced reurn. The model hus explains he expeced reurn by he forward earnings yield adjused for informaion ha forecass he change in premium. The deflaion by is no incidenal. Indeed i is imporan. The deflaion expresses he lef-hand side as an expeced rae-of-reurn, bu also discouns righ-hand side variables by he expecaion in price a and for he risk (and he price of risk) ha discoun expecaions. Thus forward earnings (for +1) are relaive o he expecaion of hose earnings a ime, discouned for he risk, rendering a risk-adjused yield. Any expeced change in premium is similarly discouned, so only a forecas of a change in premium over and above ha forecas in curren price adds o he expeced reurn, and ha forecas mus perain o a discoun for he risk in he growh expecaion ha is imbedded in he curren price. 5 Thus, o he exen ha prices appropriaely discoun for risk, he model incorporaes raional pricing; he model builds in raional pricing wihou he need o specify an asse pricing model. The picure is more concree wih an appreciaion of wha a change of premium means. The inuiion is easy o grasp. rice is he expecaion of fuure earnings and a change in price is a change in ha expecaion (for a consan discoun rae). The change is book value is deermined by earnings so, if price is expeced o increase more han earnings, he marke is anicipaing higher earnings in he fuure (afer year +1) han he +1 earnings ha updae book value. 6 Tha is, a change in premium is forecased by informaion ha forecass earnings growh subsequen o +1 earnings. 7 Again earnings measuremen creaes he change in premium and he 5 This is he poin in Berk (1995) ha any variable ha relaes o expeced payoffs is priced lower he more risky he expeced payoff. 6 Book value is also affeced by dividends. Dividends reduce he book value, one-o-one, by he clean surplus equaion. Bu, if dividends also reduce price one-o-one, dividends do no affec he difference beween price and book value or he change in ha difference. If dividends reduce price less han dollar-for-dollar because of ax effecs, premiums will expand. Resuls are no affeced wih a conrol for he dividend yield, however. See enman, Reggiani, Richardson, and Tuna (2011). 7 More formally, by subsiuing d +τ = +τ - ΔB +τ from he clean-surplus equaion ino he dividend discoun model of he price for all fuure periods, +τ, he expeced premium a any poin, +τ, is given by 5

8 expeced growh implied: rice anicipaes oal life-long earnings so, for a given price, lower forward earnings means higher earnings in he fuure by he propery of accrual accouning ha allocaes oal (life-long) earnings o periods. Wih he deflaion by curren price, only expeced growh ha is deemed risky will add o he required reurn. Growh ha represens predicable earnings no relaed o risk will be refleced in a higher and hus cancelled by he deflaor,. I is no difficul o undersand why growh migh be a risk. If forward earnings are a risk, as indicaed by he forward earnings yield, so mus subsequen expeced earnings ha yield he growh. Growh firms are shocked in recessions and correspondingly do well in good imes. Financing leverage adds expeced earnings growh bu also adds risk. 8 Operaing leverage (fixed coss o variable coss), ypically E( 1 rb ) E( B ) r g wih 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. 1a can be expressed as E E( ) E rb ( ( R 1) ( r g) rb ) E ( 1) ge( 1 rb ) ( r g) Sricly, he growh is residual earnings growh bu, for a given B, and r, an expeced change in he +1 premium resuls from expeced earnings growh over he forward year. Felham and Ohlson (1995) show ha residual earnings growh induces a change in premium. Wih E(R +1 ) equal o he required reurn, r, he required reurn appears on boh sides here (albei wih a denominaion by price ha discouns fro risk). The formulaion is merely o show ha expeced earnings growh induces a change in premium. As +1 rb ( rb -1 ) = +1 + rd (1+r), one can refer o he growh as abnormal (cum-dividend) earnings growh ha explains he /E raio, as in Ohlson and Juener-Nauroh (2005). Abnormal earnings growh is hus (cum-dividend) earnings forecased in excess of he permanen earnings predicion in he preceding foonoe (and ha forecas corresponds o he case of no expeced change in premiums). 8 E OI OI In I is always he case ha g g ELEV g g 1 where 6 g is he growh rae for (boom-line) earnings, OI In g is he growh rae in operaing income (income before ne ineres), g is he growh rae in ne ineres expense on deb and ELEV 1 Ne Ineres 1 / measures leverage in he income saemen. So, provided 1 OI In leverage is favorable such ha g g > 0, leverage levers up he growh in earnings. See enman (2011), Chaper 4. E

9 seen as risky, levers earnings growh wih good sales oucomes bu magnifies downside oucomes. Indeed, he basic economic principle of risk and reurn suggess ha growh is risky: one canno have more earnings wihou aking on more risk, on average. And accouning operaes o connec risk o growh: under uncerainy, accrual accouning defers earnings o he fuure and deferred earnings yields expeced earnings growh, as highlighed in enman and Reggiani (2010). Wheher he risk associaed wih earnings growh is priced risk is an open quesion, of course, bu ha is aken care of in he price deflaor. From Eq. 1a, E( 1) B 1 B 1 E ( R 1) E( ) 1 (1b) This expression idenifies he book-o-price raio, B/, as a conender for a variable ha predics a change in premium and hus poenially growh relaed o risk. Saing his equaion on an expos (realized reurn) basis and adding accouning variables as A j, j = 1, 2,, N ha furher predic growh, we specify a cross-secional regression equaion o ake o he daa ha is free o fi inercep and slope coefficiens such ha ε +1 is mean zero: E( ) B R (1c) N 1 1 a b1 b2 b2 j Aj 1 j 1 For he case of no expeced change in premium (no growh), b 1 = 1 and he oher b coefficiens are equal o zero. This is he case for a mark-o-marke (and a consan-rae) bond: he expeced earnings yield indicaes he expeced reurn. This benchmark suggess ha forward E/ is he primary variable for expeced reurns, wih B/ and oher variables adding o expeced reurns only if hey predic growh ha is associaed wih differenial risk in he cross-secion. Noe, however, ha in a cross-secional regression, forward E/ could be correlaed wih he growh and so i could be ha b Noe also ha here is no necessiy for a linear model, hough many reurn predicion papers run linear regressions. Nor is i necessary ha coefficiens on 9 Such would be he case under he permanen income growh model of Ohlson (2008) where all growh is priced as risky. (The permanen income model wih growh implies ha no informaion oher earnings, along wih a growh parameer, is relevan o valuaion). 7

10 variables be he same for all firms in he cross secion. These migh be issues for furher invesigaion. Here he issue is merely wheher he resuls from anomalies research can be explained by fiing a model of expeced reurns like Eq. 1c. Fama and French include a B/ facor in heir asse pricing model bu wih lile explanaion as o why B/ migh indicae risk and expeced reurn. 10 The model here provides an explanaion: B/ indicaes expeced reurn for risk if i forecass growh ha is priced as risky. enman and Reggiani (2010) elaboraes. Boh enman and Reggiani (2010) and enman, Reggiani, Richardson, and Tuna (2011) show ha B/ indeed predics earnings growh empirically. Furher, higher B/ is also associaed wih higher variaion in growh oucomes. The analysis shows ha he Fama and French model omis he earnings yield which is shown here o be primary. 11 So, clearly, if so-called anomaly variables such as accruals and growh in asses forecas he forward earnings yield in he cross-secion, hey may be proxying for an omied variable in he Fama and French model (and accordingly ha model would no be a saisfacory benchmark for assessing abnormal reurns). Tha observaion leads o he following. A Model of Expeced Reurns Explained by he Adjused Curren Yield The forward earnings yield is no observable, of course; he expecaion mus be developed from curren informaion. 12 A good saring poin for forecasing is curren earnings. Curren earnings are sufficien for forecasing in he benchmark case of no change in premiums, so one can sar wih curren earnings and ask wha informaion forecass ha forward earnings differ from curren earnings. Replacing forward earnings in Eq. 1c wih curren earnings, 10 Conjecures abou B/ and risk include disress risk, he risk of asses in place, and he risk of growh opions. 11 Fama and French (1992) claim ha book-o-price subsumes he earnings yield, bu his claim is doubful in ligh of he enman and Reggiani (2008) resuls. See also papers where profiabiliy (earnings relaive o book value) adds o reurns prediced by B/. 12 Sell-side analyss forecass of forward earnings are available, bu sudies have shown ha hey do no capure he financial saemen informaion compleely. See, for example, Bradshaw, Richardson, and Sloan (2006) and Wahlen and Wieland (2011). 8

11 B R (1d) N NN 1 a b1 b2 b2 j Aj b2 j Aj e 1 j 1 j N 1 As in Eq. 1c, variables A j, j = 1, 2,, N ake on a non-zero coefficien if hey forecas risky growh bu now addiional variables, A j, j = N+1, N+2,, NN add o he forecas of reurns if hey forecas ha forward earnings will be differen ha indicaed by curren earnings (and B/). 13 Considerable research indicaes ha accouning numbers add o curren earnings in forecasing forecas forward earnings. Ou and enman (1989, 1991), he early papers on forecasing reurns from financial saemen informaion, were in fac explicily designed o predic reurns wih accouning numbers ha forecas ha forward earnings will be differen from curren earnings. I would appear ha he primary accouning variables in anomaly research, accruals (in Sloan 1996) and growh in ne operaing asses, ΔNOA (in Fairfield, Whisenan, and Yohn 2003), are candidaes for explaining expeced reurns in his framework. As = Cash from operaions + accruals (in he way ha accruals are defined in his line of work), specifying an A j as accruals effecively decomposes curren earnings in regression (1d),, ino cash flow and accrual componens, so enerains he idea ha curren cash flow and accruals have differen implicaions for forecass of forward earnings (and hus for expeced reurns). I is his difference in persisence of cash flows and accruals ha Sloan (1996) conjecures is he reason for he marke s misundersanding ha yields abnormal reurns, bu recogniion of such difference is par of a raional forecas of forward earnings and he expeced reurn. 14 Similarly (ignoring axes), Ne Ineres = Operaing income = Free cash flow - ΔNOA by he clean surplus equaion for operaing aciviies, so designaing ΔNOA as an A j variable also decomposes he operaing componen of earnings ino componens ha may have implicaions for forward earnings. Indeed enman and Zhang (2006) find ha ΔNOA is a primary earnings forecasing variable, jus as i is he primary reurn forecasing variable in 13 The earnings yield here is earnings divided by end-of-period price, he reciprocal of he curren (railing) /E, no he curren earnings yield on beginning-of-period price. 14 The heme of he marke failing o undersand earnings persisence is mainained in Xie (2001), Barh and Huon (2004), and Richardson, Sloan, Soliman, and Tuna (2005), among many papers. 9

12 Fairfield, Whisenan, and Yohn (2003). The predicion of growh is less clear, bu ΔNOA (of which accruals are a par) is iself a growh variable. 15 The Expeced Reurn and he Required Reurn The inference ha added variables explain required reurns for risk presumes ha he price deflaor in Eq. 1a represens raional expecaions and discoun for risk. Tha is, he marke price is efficien. However Eq. 1a and subsequen expressions also hold for inefficien prices. If so, he expeced reurn is simply ha from buying a he curren marke price raher han he required reurn for risk. Accordingly, esimaion of regression equaion (1d) could merely be documening marke inefficiency and he predicion of abnormal reurns raher han normal reurns. Thus i would appear ha he formulaion helps lile in he aribuion of accouning anomalies o raional or irraional pricing. 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: Given his model, observed predicable reurns are wha we would expec if he marke were efficien. So why would one leap o a conclusion ha he reurns are anomalies or indicae marke inefficiency? More so given he significan persuasion in economic heory for (approximae) efficien markes and no compeing compelling heory for he alernaive. Tha is he scienific mehod. As Richardson, Tuna, and Wysocki (2010) poin ou, anomaly research needs o offer a credible alernaive hypohesis. To invoke opper, science progresses wih falsificaion of hypoheses. Conjecures abound as o why he marke migh be inefficien 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 o ascribe reurns o accouning numbers in he se, A j, j = 1, 2,, NN, o irraional pricing. For example, he conjecure ha he accrual anomaly is because invesors fail o undersanding how accruals and cash flows have differen persisence for forecasing forward earnings is challenged by he model, for he model says ha an undersanding of how 15 The se-up here differs from he Mishkin model ha anomaly sudies apply o idenify mispricing. Tha model equaes forecasing parameers for forecasing forward earnings o hose for forecasing reurns. I is appropriae for a permanen earnings accouning where unexpeced reurns equals unexpeced earnings bu no for he case of earnings ha differ from reurns because of expeced growh. Tha is, i is appropriae for he case of no expeced change in premiums in Eq. 1a. Tha is he case for a bond, and he original Mishkin papers indeed applied he model o he bond marke where he (no-growh) condiions are saisfied. 10

13 accruals forecas forward earnings (and growh) differenly is par of a raional deerminaion of normal reurns, so accruals should predic reurns in an efficien marke. (And he conjecure is unsubsaniaed, remaining jus a conjecure). If, empirically, he so-called anomaly variables ha predic reurns also predic forward earnings and growh, a condiion for heir being idenified as risk variables would be saisfied. Necessiy is no o be implied, however, for he variables could be predicing earnings and growh ha are no anicipaed by (inefficien) prices. A demonsraion of significan reurns (afer ransacion coss and oher limis o arbirage) o a zero-invesmen, riskless hedge posiion from a sraegy based on a paricular accouning number would, of course, be definie. Bu (again) in absence of a valid pricing model, he deerminaion of riskless is elusive. Documenaion of hisorical reurns o such a rading sraegy, reporing no negaive reurns over ime, would be persuasive bu i would have o be a long period of ime where he risk of he sraegy aking a hi (such as in he recen financial crisis) could be observed. Anomaly sudies ypically documen average reurns in he order of 9-10 percen per year wih zero ne invesmen posiions, bu o aribue hese reurns o abnormal reurns seems a bi of a srech. Can so much money be lef on he able? The sample periods ypically cover he good years, pos-1960 and pre-2000, where he payoffs o risk were likely o be posiive. Indeed, his was a period where he gamble on growh paid of handsomely for U.S. socks. Fama and French (2008) documen ha mos anomalies are observed consisenly over various pariions of he daa, indicaing ha somehing sysemaic is in play. In summary, he model revises ones view of accouning anomalies bu i is no definiive. I leaves us in he same sae as acceping bond yields as indicaing risk. This we readily do, seeing he difference beween he yield on governmen and corporae bonds and beween invesmen versus speculaive grade bonds as appropriae risk spreads. We are no enirely sure, for validaion requires a valid asse pricing model, bu in absence of a valid pricing model we accep he yield as serving us well. 16 The model here is simply he yield adjused for expeced growh, as befis an equiy invesmen. Neverheless, here is room for bond arbirage (apparenly), hough ha seems like hard work, reporedly earning nickels and dimes. In he same way, here is presumably also room for equiy arbirage (and accouning arbirage) for 16 I is ofen poined ou ha he expeced yield on a bond is no necessarily he same as he required reurn implied by an asse pricing model. 11

14 someone who has an alernaive (perhaps behavioral) model of how accouning numbers forecas abnormal reurns raher han normal reurns. 17 Bu ha arbirageur migh well enerain he noion ha, jus like a be on earnings yield involves risk, he or she could be aking on risk in exploiing accouning anomalies. One is hoping and praying. The model has he following implicaions: Firs, for any variable ha predics reurns bu also forward earnings and/or growh, he abnormal reurn or even anomalous designaion is doubful: he variable looks like i is relaed o required reurns. Second, if one could idenify a variable ha fails o forecas forward earnings and growh (given E/ and B/), ha variable should no predic reurns (in effec, one would have a placebo o adminiser). Third, if one found a variable ha forecass reurns bu no earnings and growh, he efficien marke hypohesis is challenged; following opper, one would have a basis for falsificaion. Our empirical work deals wih firs poin. Idenificaion of Added Accouning Variables Ou ess invesigae wheher he accouning numbers ha have been nominaed in he lieraure as predicing anomalous reurns fi ino he se A j, j = 1, 2,, NN in Eq. 1d. The modeling indicaes ha he variables can ener in wo ways. Firs, variables A j, j = 1, 2,, N ener because hey predic growh ha is priced as risky. Second, variables A j, j = N+1, N+2,, NN ener as a correcion o he forecas of forward earnings from curren earnings. (A given variable could forecas boh.) Growh Forecass The following model serves o idenify variables ha forecas growh afer he forward year. Wih any forecas beyond wo years ahead subjec o significan survivorship bias, we focus on forecass of earnings growh wo years ahead. Wih a saring poin of he curren E/ and B/, a 2 1 a N B Sales j Aj u 2 (2) Sales 1 j 1 17 One could argue ha he pricing of equiies is much more speculaive han bonds (where he conracual payoffs are clear), so more subjec o behavioral biases. As ofen poined ou, hose biases would have o operae a he aggregae level of invesors. 12

15 is earnings per share and a 2 = r d ) where d +1 is dividend 2 ( f 2 1 per share in +1 and r f +2 is he yield on he one-year T bill for year +2. So = a 2 a = r d ). The reinvesmen of 2 ( f dividends recognizes ha dividends reduce earnings growh (or, alernaively pu, dividends can be reinvesed o earn more earnings).to deal wih negaive denominaors and o suppress ouliers, he forecas variable is calculaed as a 2 a a which ranges from -2.0 o is similarly defined. The inclusion of he ime- earnings change and sales growh incorporaes he curren earnings growh and sales growh in he forecas. Forecass of Forward Yield The following model is applied o forecas he forward earnings yield: 1 B (3) N j Aj 2 j 1 The addiion of Δ adds a ime-series benchmark o he cross-secional one. Empirical Work Daa and Variables Our sample covers all U.S. firms wih common sock lisings on Compusa files for any of he years, , and which have sock price and reurns for he corresponding years on CRS files. Financial firms (in SIC codes ) and uiliy firms (in SIC codes ) are excluded, as is common in anomaly sudies. Firms were deleed for any year in which Compusa repors a missing number for book value of common equiy, income before exraordinary iems, common shares ousanding, or oal asses. Firms wih negaive book value for common equiy or a per-share value of less han 50 cens were also eliminaed. rices ( in he denominaor of 13

16 he regressions above) were observed on CRS four monhs afer each fiscal year, by which ime he annual accouning numbers (for fiscal year ) should have been repored. Reurns (R +1 ), also observed on CRS, are annual buy-and-hold annual reurns from his dae, calculaed as compounded monhly reurns. Resuls are similar wih he reurn period beginning hree monhs afer fiscal-year end. Table 1 repors seleced perceniles, calculaed from daa pooled over firms and years, for variables in he analysis. The noes o he able deail how hese variables were calculaed. The columns in he able group he arge variables in regression equaions (1d), (2), and (3), hen he basic forecas variables, followed by anomaly variables. Basic forecas variables are hose in he regression equaions before adding he anomaly variables, bu hey also involve he main summary numbers from he accouning sysem, earnings, book values, and sales. The anomaly variables seleced for invesigaion are hose ha feaure prominenly in he lieraure (he main papers are referenced in he noes o he able), and are calculaed as in he earlier papers. 18 The firs four anomaly variables accruals (ACCR), growh in ne operaing asses (ΔNOA), reurn on asses (ROA), and invesmen (INVEST) involve accouning numbers o do wih he business operaions. Ne share issuance (NSI) and exernal financing (EXTFIN) concern financing aciviies bu also involve ineracion wih capial markes and hus migh have an elemen of marke iming. The momenum variable (someime referred o as Winners vs. Losers) is a price variable. I is someimes aribued o marke over- or under-reacion o informaion, hough he accouning lieraure also inerpres i as informaion in price ha leads fuure earnings. I is measured here as he sock reurn over he 12 monhs prior o one monh prior o he reurn period. (The one monh lag deals leaves ou he shor-erm reversal phenomenon ha has been documened). Momenum sudies ofen use a six-monh period bu we wish o align he price change wih he period over which he accouning informaion (ha migh also forecas earnings, growh, and reurns) becomes available. Resuls are similar wih momenum measured over six monhs. Means and sandard deviaions are repored below he perceniles, wih he op and boom 1% of observaions each year eliminaed, excep for reurns. 18 The Chen, Novy-Marx, and Zhang (2010) ROA measure is no exacly he ROA measure of ex books because i does no add back ineres in earnings in he numeraor (and accordingly is no enirely unlevered measure of profiabiliy. We use he label anomaly (meaning he phenomenon is no enirely undersood) wih some hesiaion, for some papers (such as he Chen, Novy-Marx, and Zhang paper) do offer heories for he phenomenon. Oher anomaly variables were considered in he empirical analysis, mos jus a variaion in he calculaion of variables in Table 1. 14

17 Table 2 repors correlaions beween seleced variables, wih Spearman rank correlaions above he diagonal and earson correlaions below. The correlaion coefficiens are means over ime of esimaes from he cross-secion for each year. Some observaions are relevan o he ess ha follow. I is clear ha curren earnings-o-price, E/ =, is a srongly correlaed wih forward earnings-o-price, 1 ( he realized forward earnings yield), wih a Spearman correlaion of Book-o-price is also correlaed wih forward earnings-o-price (a Spearman correlaion if 0.155). Curren E/ is negaively correlaed wih wo-year-ahead earnings growh, a 2 1 (a Spearman correlaion of ), as expeced for he reciprocal of he /E raio which is ypically is seen as indicaing growh. Book-o-price has a small posiive correlaion wih wo-year-ahead earnings growh (0.072). The four anomaly variables in he able ha involve business operaions (ACCR, ΔNOA, ROA, and INVEST) are moderaely posiively correlaed wih E/ bu negaively wih B/. The correlaion of hese anomaly variables wih wo-year-ahead earnings growh is negaive, in he same direcion as he correlaion wih reurns, excep for ROA. These variables are posiively correlaed wih each oher, and all excep ROA wih exernal financing (EXTFIN and wih ne share issuance (NSI). Momenum (MOM) is posiively correlaed wih boh E/ and he conemporaneous change in earnings, indicaing ha some of he price change is associaed wih he earnings repored over he momenum period. Significanly, even hough momenum goes ino he denominaing price of he forward earnings yield, momenum is posiively correlaed wih he forward earnings yield (a Spearmen correlaion of 0.185), indicaing ha he momenum price change is also due, a leas in par, o informaion abou fuure earnings. This is consisen wih sudies ha show ha price leads earnings. The correlaion of momenum wih wo-yearahead earnings growh is negaive (hough small), however. The correlaion of all anomaly variables wih momenum is low (wih he excepion of ROA), bu i is posiive. 19 If invesors misprice accouning informaion he persisence of accruals, for example one would expec his o feed he conemporaneous momenum (ha is ofen characerized as over- or underreacion o informaion). 19 The mean Spearman correlaion beween momenum measured over six monhs and welve monhs is 0.667, and he mean earson correlaion is

18 The anomaly variables, oher han he financing variables, are posiively correlaed wih he (realized) forward earnings yield, bu of course hey are also posiively correlaed wih E/ ha forecass he forward earnings yield. All accouning anomaly variables are negaively relaed o wo-year-ahead earnings growh, in he same direcion as hey predic reurns, alhough he correlaions are quie low. Of course, he issue in our analysis is how hese anomaly variables predic forward earnings and growh condiional on E/ and B/. The wo financing variables, NSI and EXTFIN, are negaively correlaed wih boh he forward earnings yield and curren E/, consisen wih firms repurchasing more shares relaive o issues when earnings and expecaions of forward earnings are high relaive o he curren price. Uncondiional Correlaion wih Reurns The correlaion of he variables wih one-year-ahead reurns, summarized by correlaion coefficiens in Table 2, is elaboraed upon in Table 3. The able repors average reurns for en porfolios formed from ranking firms each year on he anomaly variables, and on E/ and B/. Unlike mos of he earlier anomaly sudies, he reurn period covers he recen financial crisis wih is downside reurn realizaions. E/ is posiively relaed o year-ahead sock reurns, monoonically excep for he lowes E/ porfolio (which conains loss firms). This is he Basu (1977 and 1983) finding, documened many imes since and apparenly employed in many conrarian rading sraegies. Our model suggess ha his finding could indicae added reurn for added risk. The reurns for B/, like hose documened in Fama and French (1992), are also fairly monoonic in he level of B/. The spread of reurns is he highes of any in he able, presumably he reason why reurns o book-oprice have been idenified as a leading anomaly. The reurns associaed wih he anomaly variables in Table 3 are similar o hose in he original papers, hough some do no appear o be as srong as previously repored (possibly due o he inclusion of he financial crisis years). Like hose papers, he reurn from going long on he high porfolio (10) wih a cancelling shor posiion in he low porfolio (1) each year is repored. (The cases wih negaive hedge reurns are hose where he direcion of he long and shor goes he oher way.) This so-called hedge reurn is ofen aribued o mispricing, paricularly when i survives agains reurn benchmarks from popular asse pricing models, 16

19 rendering he inference ha i is a riskless zero-ne-invesmen reurn (and hus pure arbirage). Noe ha, for many of he anomaly variables, he reurn differences are in he exremes, wih no much variaion over porfolios 3 o 7 or even porfolios 2 o 9 in some cases. The hedge reurn o ROA is no large, and he findings on profiabiliy variables in Fama and French (2006 and 2008) are indeed mixed. In Chen, Novy-Marx, and Zhang (2010), ROA is correlaed wih reurns in conjuncion wih invesmen, and we consider hem ogeher in our analysis. 20 The hedge reurn o momenum (based on welve monhs of reurns) is somewha lower ha ypically repored. 21 Esimaion of Models for Growh and he Forward Yield Our firs empirical ask is o documen how anomaly variables predic forward earnings and subsequen growh. Tables 4 and 5 repor he resuls from esimaing he forward earnings yield regression (3) and he earnings growh regression (2). Coefficiens and adjused R-sq are means from esimaes of annual OLS cross-secional regressions (Fama and MacBeh syle), wih he rejecion of he op and boom perceniles of explanaory variables each year. 22 The -saisics on coefficien esimaes are he mean coefficiens relaive o heir esimaed sandard errors, as described in he noes o he Table 4. Models are esimaed firs wih jus he basic forecas variables, hen adding anomaly variables one a a ime, and finally all ogeher. Our purpose here is no o build he bes forecasing model, nor do we mainain ha he linear form is appropriae. We merely endeavor o invesigae wheher hose variables ha are correlaed wih forward reurns in he exising research also predic he forward earnings yield and subsequen growh, and hus can be viewed wihin our framework as indicaing he required reurn for risk. Mos of he forecasing resuls in Tables 4 and 5 will come as lile surprise o 20 Oher profiabiliy variables relaed o ROA have been invesigaed in he lieraure. Novy-Marx (2010) documens ha gross profis-o-asses is posiively correlaed wih subsequen reurns. Ineresingly, he gross profis measure is advocaed as a beer forecas of fuure earnings han boom-line earnings, consisen wih he perspecive in his paper. 21 Taking 2002 and 2008 ou of he analysis, he hedge reurn is For he period covered by he Jegadeesh and Timan (1993) paper, he reurn was compared o heir (size-adjused) reurn of When momenum is measured over six monhs, he hedge reurn is Resuls were similar afer rejecing he op and boom wo percen and five percen of observaions each year and when running regressions adding 1.0 o each variable and aking logs. 17

20 hose familiar wih he ypical dynamics of accouning numbers: persisence is eviden bu wih some mean reversion. The forecas variable in he growh regressions in Table 5 is he realized 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. 1a and hus he expeced sock reurn. Two-year-ahead growh is of course only a small par of long-erm growh and, being realized growh, is likely o be affeced by ransiory earnings in eiher +1 or +2. So clearly his is a feeble aemp o develop a forecas, and he R 2 in Table 5 are indeed low. 23 In conras, he forward earnings regressions in Table 4 repor R 2 in he range of 35% o 38%. We firs consider he forecas models wih E/ and B/ alone, before adding he anomaly variables. I is clear in Table 4 ha he curren E/ is a srong indicaor of he forward earnings yield, which of course should come as no surprise: curren earnings forecass fuure earnings. Our model informs ha his feaure is o be expeced of a variable ha indicaes he required reurn, so he findings suppor he Ball (1978) conjecure ha he earnings yield indicaes risk and reurn; he findings of Basu (1977 and 1983) and ohers ha E/ predics reurns can be aribued o raional pricing of risk wih some jusificaion. Given E/, B/ adds o he forecas of he forward earnings yield in Table 4. The coefficien on E/ is less han 1.0, indicaing he mean reversion ha is ypical of earnings. The negaive coefficien on B/ furher indicaes he persisence of earnings: low (high) book value for given earnings (and price) indicaes higher (lower) subsequen earnings. This accords wih he sandard finding (in Freeman Ohlson, and enman 1982 and Fama and French 2000, for example) ha he book rae-of-reurn is persisen. 24 In he earnings growh model in Table 5, E/ forecass growh negaively, again no surprise given he undersanding ha a /E raio forecass earnings growh. B/, he 23 Survivorship bias would presumably be overwhelming in any consideraion of long-run growh. We repeaed he analysis in Table 5 wih earnings growh measured over wo years, +2 and +3. Resuls were similar o hose in Table 5, wih slighly higher R-square values, ranging from 3 percen o 4 percen. The mean Spearman correlaion beween he one-year forward growh measure and he wo-year growh measure is (earson 0.575). 24 u anoher way, price aggregaes more informaion han book value bu forecass long-run earnings. Thus he coefficien on E/ forecass mean reversion in he long run, bu B/ differeniaes susained earnings in he near erm. The change in earnings from o +1 will depend on he dividend in (ha displaces subsequen earnings because of payou). Tha dividend reduces price and book value (affecing boh E/ and B/). We ran Table 4 models adding Dividend /, wih lile difference in resuls. 18

21 characerisic so prominen in asse pricing models, is srongly posiively correlaed wih growh: given E/, B/ forecass growh bu in a direcion ha is opposie o he common dicum. enman and Reggiani (2010) elaborae on how E/ and B/ work ogeher o indicae growh and provide furher documenaion ha he growh forecased by he wo is indeed risky: higher expeced growh indicaed by E/ and B/ has higher variaion around i and is subjec o more exreme shocks. enman, Reggiani, Richardson, and Tuna (2011) furher invesigae boh he uncondiional and condiional (upon E/) relaionship beween B/ and subsequen growh. The curren change in earnings in Table 4 has a negaive sign indicaing he welldocumened ransiory naure of earnings changes. The earnings change and sales growh add lile o forecasing growh in Table 5 so we drop hem for he reporing here; resuls for he anomaly variables were lile differen wih hem included. 25 E/ and B/ are dicaed by our framework as he saring poin for forecasing earnings, growh, and reurns. Adding he anomaly variables asks wheher forecass are improved over hose involving hese boom-line accouning numbers. Tables 4 and 5 indicae he answer is in he affirmaive. Thus, if hese anomaly variables predic forward reurns because hey forecas forward earnings and growh, i is no because hey are jus capuring he forecas supplied joinly by E/ and B/. In he case of he four anomaly variables ha deal wih business operaions, ACCR, ΔNOA, ROA, and INVEST, he sign of he coefficiens make sense giving our undersanding of how accouning numbers evolve, and are consisen wih previous research. For example, accruals measured as he accrual componen of earnings relaive o oal asses capure componens of earnings and book value already in he forecas. Bu he accrual componens ends o reverse (over more han one period), so higher (lower) accruals predic lower (higher) forward earnings and growh relaive o curren earnings and book values. The same paern is eviden for ΔNOA and invesmen (INVEST) ha previous sudies have shown are negaively correlaed wih fuure earnings changes. 26 ROA akes on a posiive coefficien in 25 While no he subjec of he invesigaion here, he coefficien on he sales growh variable may be of ineres o hose (like Lakonishok, Shleifer, and Vishny 1994) who have observed ha sales growh is negaively correlaed wih fuure reurns. Sales growh is negaively correlaed wih fuure growh, indicaing a lower expeced reurn. Sales growh is a realizaion of earlier expeced growh and ha resoluion of uncerainy reduces risk and he required reurn. 26 See Fairfield, Whisenan, and Yohn (2003) and enman and Zhang (2006) who add explanaions for he phenomena. ΔNOA increases curren earnings (as expenses ha would oherwise be charged o earnings are added 19

22 he predicion of forward earnings. The measure (earnings before exraordinary iems over lagged asses) is simply a refinemen of he earnings and book values already in he regression ha unlevers book values (in is denominaor); he resul indicaes ha his parial unlevering (and he consequen focus on operaions) adds o he explanaion of forward earnings. The coefficien on ROA in he growh regression is negaive, again consisen wih he noion ha a high book value (now unlevered) relaive o earnings forecass growh. 27 The financing variables, ne share issuance (NSI) and exernal financing (EXTFIN), also carry negaive coefficiens in boh Tables 4 and 5: added financing implies lower fuure earnings and growh. Boh variables are posiively correlaed wih accruals, ΔNOA, and invesmen (Table 2) so ha correlaion could explain he resul; financing variables are relaed o hese measures by he debis and credis of accouning. On he face of i, he negaive coefficiens (ha are condiional upon E/ and B/) indicae ha less ne financing is associaed wih increasing earnings and growh. One can conjecure raional scenarios for such a correlaion: increasing earnings generae more cash flow, hus less need for financing and more share repurchases and deb redempions; lower ne share issues (or higher ne repurchases) signal higher earnings and growh (which of course is he sandard signaling sory). Albei, hese are jus conjecures. Finally, momenum, he pure price variable, is inroduced. Momenum is ofen seen as a mispricing variable he marke becomes oo enhusiasic or oo depressed abou fuure prospecs hough Liu and Zhang (2011), among ohers, aribue i o raional pricing. Momenum carries a posiive coefficien in he forward earnings yield regression, consisen wih he marke raionally forecasing an earnings increase wih informaion beyond curren earnings and book value. The negaive coefficien in he growh regressions is more difficul o inerpre and may well indicae overpricing of growh prospecs. Bu higher anicipaed forward (+1) earnings imply lower subsequen (+2) earnings ceeris paribus: wih some growh expeced o o he balance shee) bu decreases fuure earnings (when hose expenses are charged o he income saemen). Marginal invesmen adds o earnings a a declining marginal rae and conservaive accouning adds o expensing in he near erm. See Harris and Nissim (2006) and Balachandran and Mohanram (2011). 27 The observaion ha, given E/, B/ forecass growh is equivalen o saying ha, for a given price, a higher book value relaive o earnings forecass growh. The relaionship beween ROA and growh reflecs an accouning propery: increasing invesmen wih conservaive accouning reduces curren ROA bu adds o fuure earnings growh. Growing R&D expendiure is an example: expensing R&D under conservaive accouning reduces curren earnings and ROA bu adds o expeced fuure earnings (growh). 20

23 be realized in he forward year, subsequen growh is lower. And, if growh is priced as risky, resoluion of uncerainy abou growh (because of earnings realizaions) implies a lower required reurn and hus a higher price; ha is, he price change aribued o momenum in fac reflecs posiive discoun rae news. 28 Table 2 indicaes ha a number of he anomaly variables are correlaed so he coefficien on a given variable migh jus be due o is correlaion wih ohers. The second las column in Tables 4 and 5 repors esimaes wih all he accouning anomaly variables relaed o business operaions, and he las column includes all variables. For he forward earnings yield regressions, all coefficiens remain saisically significan wih he excepion of invesmen. In he growh regressions, he average R-sq increases bu accruals and ΔNOA add lile o he forecas of growh given he oher variables Esimaion of Models for he Forward Reurn We now ie hose same variables ha forecas forward earnings and growh o forward sock reurns. Table 6 is laid ou in he same way as Tables 4 and 5, wih he same anomaly variables bu now for regressions wih he forward sock reurn on he lef-hand side. E/ and B/ ogeher forecas he forward earnings yield and growh so, wihin our framework, should forecas reurns. Similarly, anomaly variables add o forecass of reurns if hey incremenally forecas he forward earnings yield and growh. As in Tables 4 and 5, coefficiens in Table 6 are means from annual cross-secional regressions. 28 Resuls are similar when he momenum variable is measured over six monhs raher han 12 monhs. Resuls were also similar in he wo subperiods, and Resuls were similar for large-cap, medium-cap, and small-cap firms, excep ha he growh forecas resuls were weaker for he small-caps where financing variables played no role. Small firms may be hose where growh expecaions ake longer o realize. Large-cap firms are he highes 50 percen by marke capializaion of all CRS firms each year, and small-caps are hose wih he lowes 20 percen. A similar comparison is made across size groups when he same cuoffs are deermined from NYSE size deciles, as in Fama and French (2008). 29 Resuls for he growh regression were similar when he curren sales growh variable, Sales, was added back Sales 1 ino he regression and also wih a dummy variable for negaive curren earnings. Resuls for he forward earnings yield regression were also similar wih a dummy variable for negaive curren earnings. (In boh cases, he coefficien of he dummy variable was highly significan.) 30 The forecass referred o in Tables 4 and 5 are in-sample, as are mos of he anomaly sudies. Our purpose is o documen correlaions, no develop forecasing models, bu he ou-of-sample Spearman correlaion beween acual and fied values from mulivariae models was 0.54 for he forward earnings yield and 0.07 for growh forecass. 21