Can the earnings fixation hypothesis explain the accrual anomaly?

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1 Can he earnings fixaion hypohesis explain he accrual anomaly? Linna Shi and Huai Zhang* Absrac This paper provides empirical evidence on wheher he earnings fixaion hypohesis can explain he accrual anomaly originally documened in Sloan (996). Our analyical model yields he predicion ha if invesors fixae on repored earnings, he effeciveness of he accrual sraegy will increase in he responsiveness of he sock price o earnings and he differenial persisence of cash flows relaive o accruals. Our empirical evidence confirms our predicion and lends suppor o he earnings fixaion hypohesis. Keywords: Accrual anomaly; Earnings fixaion hypohesis; Responsiveness of sock price o earnings; Persisence of cash flows and accruals. JEL Classificaion: G2, M4. *Corresponding auhor. Tel: Mailing address: Nanyang Business School, Nanyang Avenue, Singapore Zhang is from Nanyang Technological Universiy and Shi is from Syracuse Universiy. We would like o acknowledge helpful commens from wo anonymous referees, Kinwai Lee, Richard Sloan (he edior), Jacob Thomas, Frank Zhang and seminar paricipans a Nanyang Technological Universiy and Singapore Managemen Universiy.

2 . Inroducion Using a sample of NYSE/AMEX firms, Sloan (996) documens ha accruals are negaively correlaed wih fuure size-adjused reurns. Labeled as he accrual anomaly, his finding is robus o differen counry seings (Pincus e al. 2007), he inclusion of Nasdaq firms (Lev and Nissim 2006; Mashruwala e al. 2006; Zhang 2007), alernaive definiions of accruals (Xie 200; Hribar and Collins 2002), and consideraions of addiional risk/mispricing facors (Collins and Hribar 2000; Mashruwala e al. 2006; Hirshleifer e al. 2006). Alhough exensive evidence exiss on he robusness of he finding, consensus has ye o be reached on wha causes he accrual anomaly. Four non-muually exclusive explanaions have been proposed. The firs explanaion, he earnings fixaion explanaion, is raised in Sloan (996). He hypohesizes ha he accrual anomaly is caused by invesors fixaion on repored earnings and heir failure o appreciae he lower persisence of accruals. Several papers provide evidence in suppor of he earnings fixaion explanaion. One implicaion of he explanaion is ha invesors expecaions of fuure earnings are biased upwards (downwards) for firms wih high (low) accruals. Consisen wih his implicaion, Sloan (996) finds ha sock reurns are reliably posiive (negaive) for firms wih low (high) accruals a subsequen earnings announcemens, while Bradshaw e al. (200) show ha financial analyss forecass are relaively opimisic (pessimisic) for firms wih high (low) accruals. Dechow and Dichev (2002) provide evidence ha firms wih low accrual qualiy have less persisen earnings. Richardson e al. (2005) argue ha he measuremen error in accruals gives rise o he difference in persisence beween accruals and cash flows. Consisen wih he earnings fixaion explanaion, hey There is conflicing evidence for each of he four explanaions; however, a comprehensive review is ouside he scope of his paper. Please refer o Richardson e al. (200) for a more complee review.

3 demonsrae ha he less reliable accruals, which have a relaively low persisence level, are mispriced o a greaer exen. Their finding is also consisen wih Xie (200), who documens ha he magniude of he accrual anomaly is greaer for discreionary accruals, a less reliable accrual componen. Richardson e al. (2006) provide evidence ha emporary accouning disorions conribue significanly o he lower persisence of accruals. Specifically, hey documen ha he lower persisence of accruals exends o he accruals componen ha is unrelaed o sales growh and ha exreme accruals are sysemaically associaed wih alleged cases of earnings manipulaions. Dechow e al. (2008) decompose he cash flows ino hree componens and find ha invesors misprice he change in he cash balance componen in a similar manner o accruals. Their resuls imply ha he accrual anomaly subsumes he exernal financing anomaly. The second explanaion, he growh explanaion, argues ha he accrual anomaly is simply a special case of he growh anomaly, i.e., ha firms wih high growh have lower reurns. A key undersanding is ha accruals, compued as changes in working capial accouns, can also be inerpreed as growh in curren ne operaing asses. Fairfield e al. (2003a) argue ha, if he accrual anomaly is driven by accruals represening growh, hen anoher growh measure, i.e., he growh in longerm ne operaing asses, should have he same predicive power for fuure reurns as accruals. Their empirical resuls suppor his predicion. While Fairfield e al. (2003a) are no inconsisen wih he earnings fixaion hypohesis, heir findings sugges ha he lower persisence of accruals may be due o diminishing reurns o growh raher han accrual esimaion errors. Evidence in suppor of his noion is provided in Fairfield e al. (2003b). They hypohesize and find ha accruals are more highly associaed han cash flows wih he growh in invesed capial, which is he 2

4 denominaor in he measure of fuure earnings. In addiion, hey show ha here is no difference in he persisence level beween accruals and cash flows once he denominaor effec is considered. Zhang (2007) posis ha, if he growh anomaly is he underlying reason for he accrual anomaly, hen he accrual anomaly should be sronger when accruals are more likely o measure growh. Specifically, Zhang (2007) uses COVAR, he slope coefficien from a regression of accruals on he growh in he number of employees, as an indicaor of he exen o which accruals represen growh and shows ha he accrual sraegy reurn increases in COVAR. His evidence hus suppors he noion ha he accrual anomaly is driven by he growh anomaly. The hird explanaion aribues he accrual anomaly o risk. Kahn (2008) measures risk using a four-facor model moivaed by he Ineremporal Capial Asse Pricing Model. He finds ha risk explains a considerable porion of he cross-secional variaion in average reurns o high and low accrual firms. Wu e al. (200) inerpre accruals as working capial invesmens and aribue he accrual anomaly o firms opimally adjusing invesmens in response o discoun rae changes, as prediced by he q-heory of invesmen. 2 The fourh explanaion links he accrual anomaly wih he limi of arbirage. Mashruwala e al. (2006) find ha he accrual anomaly is concenraed in firms wih high idiosyncraic volailiy and high ransacion coss. Their evidence is consisen wih he noion ha he accrual anomaly is due o idiosyncraic volailiy and ransacions coss consraining he abiliies of risk-averse arbirageurs. Similar evidence is found in Ali e al. (2008), Collins e al. (2003) and Lev and Nissim (2006). We noe ha he limi of arbirage explanaion is no muually exclusive of he earnings fixaion and he growh explanaions. To he exen ha marke inefficiencies 2 Green e al. (2009) provides evidence ha he effeciveness of he accrual sraegy is relaed o he capial invesed by hedge funds o exploi i. Their evidence is seemingly inconsisen wih he risk explanaion. 3

5 exis, we expec hem o be more pronounced and enduring when arbirage risk is higher. We are ineresed in advancing our undersanding of wha explains he accrual anomaly. We hypohesize ha if invesors fixae on earnings, hen he effeciveness of he accrual sraegy will increase in (a) he sock price s responsiveness o curren earnings and (b) he differenial persisence of cash flows relaive o accruals. Our resuls are consisen wih he wo predicions and hus lend suppor o he earnings fixaion explanaion. We deem i a remoe possibiliy ha our resuls are consisen wih he risk explanaion because i is difficul o jusify our finding using risk. Concepually, he accrual anomaly can be explained by low accruals firms having high risk. I is, however, difficul o heorize ha he accrual risk premium depends on he differenial persisence of cash flows relaive o accruals or he sock price s responsiveness o curren earnings. Our resuls also canno be accouned for by he limi of arbirage explanaion because our inferences remain he same afer conrolling for idiosyncraic volailiy and ransacion coss. However, our resuls are poenially consisen wih he growh explanaion. The growh explanaion suggess ha he accrual anomaly is a special case of he more general growh anomaly. The growh anomaly is no well undersood, wih explanaions ranging from risk (Fama and French 992) o invesors naively exrapolaing pas growh (Dechow and Sloan 997). Concepually, i is possible ha he growh anomaly resuls from invesors fixaing on earnings and hus here is no inconsisency beween he growh explanaion and he earnings fixaion explanaion. 4

6 Noneheless, we conduc empirical analysis and find no evidence ha our resuls are enirely driven by he growh explanaion. Our paper conribues o he accouning lieraure in he following wo ways. Firs, since Sloan (996), much research has been done o invesigae why accruals are negaively correlaed wih fuure reurns, given he robusness of he accrual anomaly and he unique accouning naure of accruals. Four explanaions wih supporing evidence have been proposed, and no consensus has been reached afer more han a decade of research. Our paper advances our undersanding of he accrual anomaly by providing empirical evidence ha is consisen wih he earnings fixaion explanaion and is unlikely o be explained by he oher hree explanaions. Second, his paper shows ha he reurns o he accrual sraegy are posiively correlaed wih he sock price s responsiveness o repored earnings and he differenial persisence of cash flows relaive o accruals. This finding is ineresing from he perspecive of invesors who aemp o use he accrual anomaly o generae rading profis. For example, we find ha he accrual sraegy yields a high hedge reurn of 2 percen when applied o firms in he highes earnings response coefficien (ERC) quinile, while i yields a negaive reurn when applied o firms in he lowes ERC quinile. Consequenly, he accrual arbirageurs should aemp o apply he accrual sraegy o firms whose price is highly responsive o earnings and whose cash flows are much more persisen han accruals. Our finding is hus informaive o invesors ineresed in applying he accrual anomaly o sock rading. The res of he paper is organized as follows. Secion 2 develops predicions based on he earnings fixaion explanaion. Secion 3 discusses sample formaion and variable definiion. Secion 4 repors our main empirical resuls. Secion 5 discusses he growh explanaion. Secion 6 concludes. 5

7 2. Predicions 2.. A simple model We argue ha if invesors fixae on earnings, he associaion beween accruals and fuure reurns will be relaed o (a) he sock price s responsiveness o repored earnings and (b) he differenial persisence of cash flows relaive o accruals. To illusrae his poin, assume ha earnings (EARN ) consis of wo componens, cash flows (CF ) and accruals (ACCR ). We have EARN = CF + ACCR () Sloan (996) provides srong cross-secional empirical evidence ha accruals are less persisen han cash flows. Wihou loss of generaliy, we ake he persisence level of cash flows as and ha of accruals as Paccr. Given ha accruals are less persisen, Paccr is less han in general. If invesors are raional, he expeced earnings for year + can be described by he following equaion: E (EARN + )= EARN + = CF + Paccr*ACCR (2) where E (.) expecaion a ime. If invesors fixae on repored earnings and do no differeniae he differen persisence of accruals and cash flows, he expeced earnings for year + can be described by he following equaion: E (EARN + )= CF + ACCR (3) In his case, naïve invesors will be surprised a year + and abnormal reurns for earnings surprise a year + will be: ABNORMAL RETURN + = c* (EARN + - E (EARN + )) =c* (CF + Paccr*ACCR - CF - ACCR ) 6

8 = - c*(- Paccr)*ACCR (4) where c measures he responsiveness of he sock price o earnings componens. To he exen ha Paccr is less han and c is posiive, his analysis suggess ha fuure reurns will be negaively correlaed wih accruals, which is consisen wih he empirical finding in Sloan (996). Moreover, he associaion beween accruals and fuure reurns depends upon c, he measure of how responsive he sock price is o curren repored earnings, and ( - Paccr), he differenial persisence of cash flows relaive o accruals. The higher he c or ( - Paccr), he sronger he correlaion beween accruals and fuure reurns and he higher he arbirage reurns based on he accrual sraegy. This leads o hree esable empirical predicions: P. The accrual sraegy reurn is higher for firms wih high responsiveness of sock price o earnings; P2. The accrual sraegy reurn is higher for firms wih high persisence of cash flows relaive o accruals. P3. The combined effec of differenial persisence and he price s responsiveness o earnings on he accrual sraegy reurn is greaer han he effec of eiher of he wo alone. If empirical resuls confirm hese predicions, he evidence will be consisen wih he earnings fixaion hypohesis Model limiaions Like any model, he one described in Secion 2. makes many simplifying assumpions. The following discussion of he key simplifying assumpions is inended o help readers appreciae he caveas o consider in inerpreing our resuls; i also suggess guidelines for fuure exensions of our analysis. 7

9 The firs limiaion of our model is ha we assume ha cash flows are appropriaely priced. This assumpion is inconsisen wih he empirical finding in Dechow e al. (2008) ha invesors misprice he change in he cash balance componen of cash flows. We can poenially relax his assumpion and consider mispricing of cash flows. However, doing so akes our focus away from he accrual anomaly. In addiion, cash flows are negaively relaed o accruals (Sloan 996), and his correlaion is likely o inroduce a collineariy issue ino our empirical analysis. The second limiaion is ha we do no disinguish among accruals componens. Thomas and Zhang (2002) decompose oal accruals according o he working capial accoun and show ha differen accrual componens are mispriced o differen exens. Classifying accrual componens according o reliabiliy, Richardson e al. (2005) find ha differen accrual componens have differen levels of persisence. We do no make disincions among accruals componens because our prioriy is o explain he anomaly based on oal accruals. The hird limiaion is he implici assumpion ha he differenial persisence and he price s responsiveness o earnings are sable when we go from curren period o he nex period. To see his poin, suppose ha he sock price s responsiveness o earnings is high in he curren period and drops o zero in all fuure years. In his case, he mispricing will never be reversed, based on a sric inerpreaion of he fixaion hypohesis. The implici assumpion is however suppored by our unabulaed empirical resuls. 3 3 Specifically, we find ha he correlaion beween he measure esimaed using daa from year -8 hrough year and he measure esimaed using daa from year + hrough year +9 is posiive and significan a he 0.0 level, for boh he sock price s responsiveness o earnings (ERC) and he differenial persisence of cash flows relaive o accruals (PERDIF). In addiion, we find ha nex-year ERC (PERDIF) increases in curren ERC (PERDIF). Nex-year ERC (PERDIF) is 234 percen (99 percen) higher for firms in he op decile han for firms in he boom decile of curren ERC (PERDIF). 8

10 3. Sample formaion and variable measuremen 3.. Variable measuremen 3... Accruals This secion discusses sample formaion and variable measuremen. Following Hribar and Collins (2002), we define accruals as follows. ACCR = EARN CF (5) where ACCR is oal accruals in year, EARN is earnings in year, measured by Income Before Exraordinary Iems (Compusa Annual Iem #23), and CF is cash flows in year, measured by Cash Flows from Operaing Aciviies (Compusa Annual Iem #308) minus Exraordinary Iems & Disconinued Operaions (Compusa Annual Iem #24). All he variables are deflaed by average oal asses in year Fuure reurns Following Sloan (996), we use size-adjused reurns o measure fuure abnormal reurns. Size-adjused reurn (SAR +) represens he difference beween he firm s buy-and-hold reurn and he buy-and-hold reurn on a value weighed porfolio of firms in he same CRSP size deciles. Size deciles are deermined by he disribuion of marke values of all he NYSE/AMEX firms a he beginning of he calendar year. SAR + is compued over he 2-monh holding periods, beginning four monhs afer curren fiscal year end. Specifically, SAR + is compued using he equaion below. ( + ris ) ( + SAR + = rps ) (6) s s where r is and rps are reurns in monh s for firm i and size porfolio p, respecively. When a firm deliss, we use he delising reurn in he delising monh and assume a reurn equal o he firm s size-mached porfolio for he remainder of he 9

11 year. If a firm s delising is due o liquidaion or a forced delising and he delising reurn is missing, he delising reurn is se o -00 percen. This reamen is consisen wih Sloan (996) Measures of he price s responsiveness o earnings and differenial persisence We use he slope coefficien from he following ime-series regression o measure he price s responsiveness o earnings 4 : RET = η 0 + ηearnings + ε (7) where RET is cumulaive sock reurn in year, and EARNINGS is Dilued EPS Excluding Exraordinary Iems (Compusa Annual Iem #57) 5 in year divided by Closing Price in Fiscal Year End (Compusa Annual Iem #99). We use observaions from he curren year and prior eigh years o run his regression. For each regression, we require ha here be a leas four observaions wih no missing daa. The coefficien from he above regression ( η, which we refer o as ERC ) consiues our measure of he sock price s responsiveness o earnings. We measure he persisence of cash flows relaive o accruals hrough he following ime-series regression: EARN = β + β ACCR + β CF + ε (8) where EARN +, ACCR, and CF are defined as in Equaion (5). We use daa from he curren year and prior eigh years and require a leas four observaions wih no missing daa in his regression. The coefficiens β and β 2 represen he persisence of accruals and cash flow respecively, and β2 β measures he differenial persisence 4 We obain similar evidence when we measure he price s responsiveness o earnings by regressing reurns on changes in earnings. 5 Bens e al. (2003) sugges ha managers aemp o manipulae dilued EPS by share repurchases, which implies ha he marke pays aenion o he dilued EPS. In his spiri, we use dilued EPS o esimae sock price responsiveness o earnings. Unabulaed resuls show ha using Basic EPS insead of Dilued EPS o esimae ERC does no change our empirical resuls. 0

12 level of cash flows relaive o accruals and is referred o as PERDIF for he sake of convenience Sample Formaion Our sample exends from 988 o 2006, because prior o 988, he cash flow saemen daa iems needed for compuing accruals are unavailable. To mainain consisency wih Sloan (996), we include only NYSE and AMEX firms. We require accruals and nex year s size-adjused reurns o be non-missing for a firm-year observaion o be included in our sample. Following Guierrez and Kelly (2008), we require he sock price a he end of he fiscal year o be greaer han $5 per share, because he bid-ask bounce conaminaes low-price firms reurn informaion. Unlike Sloan (996), we do no require nex year s earnings o be non-missing in our sample o avoid he poenial foresigh bias documened in Kraf e al. (2006). 6 We also exclude all financial firms according o he SIC code. The final sample consiss of 27,373 observaions. 4. Empirical resuls from esing predicions 4. Replicaion of he accrual anomaly We firs replicae he accrual anomaly, using our sample. Specifically, we form en accrual deciles every year and examine he size-adjused reurns and oher firm characerisics for each decile. Our empirical resuls are repored in Table. For size-adjused reurns, we repor he mean value, which can be inerpreed as reurns o an equally weighed porfolio, and he associaed saisics. Consisen wih Sloan 6 Kraf e al. (2006) find ha his foresigh bias improves he performance of he accrual sraegy. Among firms wihou daa on nex year s earnings or accruals, he mean and median values of sizeadjused reurns are posiive (negaive) for hose classified as high (low) accruals firms.

13 (996), he mean value of size-adjused reurns o he lowes decile is significanly higher han ha o he highes decile. The hedge porfolio wih a long posiion in he lowes decile and a shor posiion in he highes decile yields an annual reurn of 5.93 percen. Given ha he deciles are formed on accruals, i is no surprising o see ha accruals go up from he lowes o he highes deciles. Consisen wih Sloan (996), CF is negaively correlaed wih accruals. The mean (median) value of CF is 0.54 (0.74) for he boom accrual decile and (-0.005) for he op accrual decile. We also examine he bea, he marke value and he book-o-marke raio, hree proxies for risks. Consisen wih Sloan (996), here is no obvious paern for hese hree proxies, which implies ha he hree risk proxies canno explain he accrual anomaly. [Inser Table here] 4.2 Porfolio analysis resuls We nex use porfolio analysis o es our empirical predicions. We require ha boh ERC and PERDIF o be non-missing, reducing he sample size o 2,63 firm-year observaions The sock price s responsiveness o earnings We firs provide resuls based on our measure of he sock price s responsiveness o earnings: ERC. Specifically, we form five quiniles based on ERC and en deciles based on accruals independenly each year. We invesigae wheher he reurns o he accrual sraegy are more pronounced for higher ERC quiniles. Panel A of Table 2 repors he empirical resuls based on ERC quiniles. The column hedge repors he hedge reurn o he porfolio wih a shor posiion in he 2

14 op accrual decile and a long posiion in he boom accrual decile. The hedge reurn goes up from -3.5 percen, no significan a he 0.0 level (p-value=0.335), for he lowes ERC quinile, o 2.26 percen, significan a he 0.0 level (p-value=0.00), for he highes ERC quinile. When we examine he reurn o he hedge porfolio each year, we find similar evidence. The mean value of he yearly hedge reurns goes up from percen for he lowes ERC quinile (p-value=0.566), o.33 percen for he highes ERC quinile (p-value=0.02). For each ERC quinile, we examine he mean and median values of differences in accruals beween he boom and op deciles and find no evidence suggesing ha our resuls can be aribued o wider disribuions of accruals in he op ERC quinile, as he disribuions are he wides for he middle raher han he highes quinile. [Inser Table 2 here] In sum, our resuls sugges ha he accrual sraegy generaes higher reurns for firms wih high price responsiveness o earnings, lending suppor o P The differenial persisence Nex, we provide resuls based on he differenial persisence of cash flows relaive o accruals. Specifically, we form five quiniles based on PERDIF 7 and en deciles based on oal accruals independenly each year. We invesigae wheher he reurns o he accrual sraegy are more pronounced for higher PERDIF quiniles. Panel B of Table 2 repors he empirical resuls. The hedge column repors he hedge reurn o he porfolio wih a shor posiion in he op accrual decile and a long posiion in he boom accrual decile. The hedge reurn goes up from percen, significan a he 0.05 level (p-value=0.0), for he lowes PERDIF quinile, 7 Secion 3..3 provides deails on how we compue PERDIF. 3

15 o 7.42 percen, significan a he 0.0 level (p-value=0.000), for he highes PERDIF quinile. We obain similar findings when we examine annual hedge reurns. The mean value of he annual hedge reurns goes up monoonically from percen for he lowes PERDIF quinile (p-value=0.026), o 7.83 percen for he highes PERDIF quinile (p-value=0.000). For each PERDIF quinile, we examine he mean and median values of differences in accruals beween he boom and op deciles, and we find no evidence suggesing ha our resuls can be aribued o differen disribuions of accruals in differen PERDIF quiniles. In sum, our evidence suggess ha he reurns o he accrual anomaly increase in he differenial persisence of cash flows relaive o accruals, lending suppor o P Boh he differenial persisence and he sock price s responsiveness Our hird predicion is ha he combined effec of he differenial persisence and he price s responsiveness o earnings on he accrual sraegy reurn is greaer han he effec of eiher of he wo alone. We provide relaed porfolio analysis resuls in his subsecion. We independenly sor firms ino five ERC quiniles, five PERDIF quiniles and en accrual deciles each year. Combining ERC quiniles and PERDIF quiniles yields a oal of 25 porfolios. For each of he 25 porfolios, we repor he accrual sraegy reurn, compued as he reurn o he hedge porfolio wih a shor posiion in he op and a long posiion in he boom accrual decile, in Panel C of Table 2. We find evidence ha soring on boh ERC and PERDIF yields sronger accrual sraegy reurns. Specifically, when ERC and PERDIF are boh in he lowes quinile, he accrual sraegy reurn is percen, he lowes among all 25 porfolios. When ERC and PERDIF are boh in he op quinile, he accrual sraegy 4

16 reurn is percen, he highes among all 25 porfolios. Our un-abulaed resuls indicae ha his finding is no due o uneven disribuion of observaions among he 25 porfolios. In sum, our evidence suggess ha combining boh ERC and PERDIF leads o greaer spread in he accrual sraegy reurn, lending suppor o P Mulivariae regressions Model specificaions We nex conduc mulivariae regressions o alleviae he following wo concerns. Firs, prior lieraure provides srong evidence ha he firm s marke value of equiy, CAPM bea, he book-o-marke raio, and he earnings-o-price raio predic fuure reurns (Lakonishok e al. 994; Fama and French 992, 995, 996). I is ineresing o invesigae wheher our resuls survive conrolling hose predicors of fuure reurns. Second, Mashruwala e al. (2006) find ha he accrual sraegy reurn increases in idiosyncraic volailiy and ransacion coss. Their evidence is consisen wih he noion ha he exisence of he accrual anomaly is due o he limis of arbirage. If he sock price s responsiveness o earnings and he differenial persisence of cash flows are relaed o ransacion coss and idiosyncraic volailiy, heir finding can poenially explain our resuls. We firs examine wheher our resuls survive conrolling known predicors of fuure reurns. Specifically, we regress nex year size-adjused reurns on he accrual decile rank, he decile rank of ERC/PERDIF, and heir ineracion afer conrolling for he decile rank of firms size, bea, book-o-marke raio and earnings-o-price raio. Our model is as follows: For ERC: 5

17 SAR + = β + β * RACCR + ϕ * RACCR * RERC + β * RSIZE + β * RBETA + β * RBTOM β * RETOP 5 + ϕ * RERC ε (9) For PERDIF: SAR + = β + β * RACCR + ϕ * RACCR * RPERDIF + β * RSIZE + β * RBETA + β * RBTOM β * RETOP + ϕ * RPERDIF + ε (0) For he combined effec of ERC and PERDIF: SAR + = β + β * RACCR + ϕ * RACCR * RERC * RPERDIF + ϕ * RERC * RPERDIF + ε + β * RSIZE + β * RBETA + β * RBTOM + β * RETOP () where SAR + is he size-adjused reurn for he 2-monh reurn window saring four monhs afer he curren fiscal year end; RERC and RPERDIF are, respecively, he decile rank of ERC and PERDIF; RACCR is he accrual decile rank; RSIZE RBETA, RBTOM and RETOP are, respecively, he decile rank of he firm s marke value of equiy, CAPM bea, he book-o-marke raio and he earningso-price raio. All he deciles are formed annually. The decile ranks are all scaled beween 0 and so ha he lowes decile akes he value of 0 and he highes decile akes he value of. If he accrual sraegy is more effecive for firms wih high ERC/PERDIF, we expec he ineracion erm beween he accrual decile rank and he decile rank of ERC/PERDIF o be negaive and significan in Model (9) and Model (0). If combining ERC and PERDIF yields higher spreads in accrual sraegy reurns, we expec he coefficien on he ineracion erm, RACCR*RERC*RPERDIF, in Model 6

18 () o be negaive and of higher magniude han he coefficien on he ineracion erm in eiher Model (9) or Model (0). We addiionally examine wheher our resuls are explained by idiosyncraic volailiy and ransacion coss (Mashruwala e al. 2006). Our empirical models are specified as follows. For ERC: SAR + = β + β * RACCR + ϕ * RACCR * RERC + ϕ * RPRICE + ϕ * RVOLUME + ε + ϕ * RACCR * RARBRISK + ϕ * RACCR * RPRICE 2 + ϕ * RACCR * RVOLUME + β * RSIZE + β * RBETA 4 + β * RBTOM + β * RETOP + ϕ * RERC + ϕ * RARBRISK (2) For PERDIF: SAR + = β + β * RACCR + ϕ * RACCR * RPERDIF + β * RBTOM + β * RETOP + ϕ + ϕ * RACCR * RARBRISK + ϕ * RACCR * RPRICE 2 + ϕ * RACCR * RVOLUME + β * RSIZE + β * RBETA ϕ * RPRICE ϕ * RVOLUME * RPERDIF + ε 3 + ϕ * RARBRISK 02 (3) For he combined effec of ERC and PERDIF: SAR + = β + β * RACCR + ϕ * RACCR * RERC * RPERDIF + ϕ * RACCR * RARBRISK + ϕ * RACCR * RPRICE 2 + ϕ * RACCR * RVOLUME + β * RSIZE + β * RBETA 4 + β * RBTOM + β * RETOP + ϕ * RERC * RPERDIF 4 + ϕ * RARBRISK + ϕ * RPRICE + ϕ * RVOLUME + ε (4) where RARBRISK is he decile ranks of residual variance from a regression of firmspecific reurns on he reurns of he CRSP equal weighed marke index over he 2 monhs ending one monh before he accrual porfolio formaion dae 8 ; 8 Our resuls hold when we form quiniles insead of deciles. 7

19 RPRICE is he decile ranks of CRSP closing sock price one monh before he accrual porfolio formaion dae; RVOLUME is he decile ranks of CRSP rading volume one monh before he accrual porfolio formaion dae. We form all deciles annually, and he value of he decile ranks is scaled beween 0 and. The oher variables are defined above. If our findings are robus owards consideraions of ransacion coss and idiosyncraic volailiy, we expec he coefficien on he ineracion erm beween he accrual decile and he decile rank of ERC/PERDIF o be negaive and significan. If combining ERC and PERDIF yields higher spreads in accrual sraegy reurns, we expec he coefficien on he ineracion erm, RACCR*RERC*RPERDIF, in Model (4) o be negaive and of higher magniude han he coefficien on he ineracion erm, RACCR*RERC, in Model (2) or he coefficien on he ineracion erm, RACCR*RPERDIF, in Model (3) Regression resuls To conrol for he cross-secional correlaion in residuals, we use he Fama- MacBeh regression (Fama and MacBeh 973). Specifically, we run he regression annually and repor he mean value of he annual coefficien esimaes wih is p-value based upon he disribuion of annual coefficien esimaes. We addiionally require measures of risk facors, idiosyncraic volailiy and ransacion coss o be nonmissing, reducing our sample size o 20,845 firm-year observaions. Panel A of Table 3 repors he regression resuls based on ERC. Model shows ha he coefficien on RACCR is -0.02, no significan (p-value=0.392), while he coefficien on RACCR*RERC is -0.07, significan a he 0.0 level (p- 8

20 value=0.060). This resul suggess ha he reurn o he arbirage porfolio wih a long posiion in he boom accrual decile and a shor posiion in he op accrual decile generaes a posiive and insignifican reurn of 2 percen for firms in he lowes ERC decile, while i generaes a reurn of 9 percen for firms in he highes ERC decile, wih he reurn difference significan a he 0.0 level. Resuls from Model 2 sugges ha his finding is robus owards consideraion of ransacion coss and idiosyncraic volailiy, as he coefficien on RACCR*RERC remains negaive and significan afer we conrol for he sock price, rading volume and idiosyncraic risk. [Inser Table 3 here] Panel B of Table 3 repors he resuls based on PERDIF. The coefficien on RACCR is posiive in boh Model and Model 2. This suggess ha he accrual sraegy generaes negaive reurns when applied o firms in he lowes persisence difference decile. The coefficien on RACCR*RPERDIF is negaive and significan for boh Model and Model 2, suggesing ha he higher he persisence of cash flows relaive o accruals, he higher he accrual sraegy reurns; his inference is robus owards consideraions of ransacion coss and idiosyncraic volailiy. The magniude of he coefficien indicaes ha he difference in he accrual sraegy reurn is 23 percen beween he lowes and he highes persisence difference decile. This finding is economically significan. Panel C of Table 3 repors he resuls based on combining PERDIF and ERC. The coefficien on RACCR is insignifican in boh Model and Model 2. This suggess ha he accrual sraegy generaes no significan reurns when applied o firms in he lowes PERDIF and he lowes ERC decile. The coefficien on RACCR*RERC*RPERDIF is negaive and significan in boh Model and Model 2, suggesing ha he higher he value of RERC*RPERDIF, he higher he accrual 9

21 sraegy reurns, regardless wheher ransacion coss and idiosyncraic volailiy are considered in he analysis. The magniude of he coefficien is 27 percen, suggesing ha he combined effec of ERC and PERDIF on he accrual sraegy reurn is more pronounced han he effec of ERC (7 percen) or PERDIF (23 percen) alone. To summarize, our mulivariae regression resuls sugges ha our main finding i.e., ha he accrual sraegy reurn increases in he sock marke s responsiveness and he differenial persisence of cash flows relaive o accruals is robus owards conrolling for ransacion coss, idiosyncraic volailiy and more risk facors. 5. The growh explanaion As we discussed in he Inroducion, our findings are seemingly inconsisen wih he risk explanaion and canno be accouned for by he limis of arbirage explanaion. However, i is possible ha he growh explanaion yields he same predicions, raising he concern ha our resuls are driven by he growh explanaion. In his secion, we discuss papers in suppor of he growh explanaion and he resuls of he empirical es we conduc o alleviae his concern. There are mainly wo papers in suppor of he growh explanaion: Fairfield e al. (2003a) and Zhang (2007). Fairfield e al. (2003a) find ha anoher growh measure, he growh in long-erm ne operaing asses (GRLTNOA), predics fuure reurns in he same way as accruals. They argue ha heir evidence suppors he noion ha he accrual anomaly is a special case of he growh anomaly. However, he growh anomaly is no clearly undersood and earnings fixaion is a possible explanaion for i. Thus, Fairfield e al. (2003a) do no provide evidence agains he 20

22 earnings fixaion hypohesis. Raher, hey sugges ha he lower persisence of accruals is due o diminishing reurns o growh. Zhang (2007) posis ha if he growh anomaly is he underlying reason for he accrual anomaly, hen he accrual anomaly should be sronger when accruals are more likely o measure growh. Specifically, Zhang (2007) uses COVAR, he slope coefficien from a regression of accruals on he growh in he number of employees, as an indicaor of he exen o which accruals represen growh and shows ha he accrual sraegy reurn increases in COVAR. Zhang s evidence hus suppors he noion ha he accrual anomaly is driven by he growh anomaly. A firs, our resuls may appear o be consisen wih he growh explanaion because ERC is relaed o growh. We agree ha ERC is relaed o growh, bu we are no aware of any heoreical or empirical evidence suggesing ha higher ERC indicaes a higher likelihood ha accruals represen growh. To empirically es wheher ERC/PERDIF is relaed o growh, we obain COVAR by regressing oal accruals on he percenage change in he number of employees, similar o Zhang (2007). We find no saisically significan relaion beween ERC/PERDIF and COVAR. This finding is inconsisen wih he noion ha he growh explanaion drives our resuls. 6. Conclusions Sloan s (996) finding ha accruals are negaively correlaed wih fuure reurns remains an inriguing research issue. Alhough he robusness of he finding is corroboraed by many research papers, i is no clear wha causes he accrual anomaly. Four explanaions have been proposed: he earnings fixaion explanaion, he growh explanaion, he risk explanaion and he limis of arbirage explanaion. This paper 2

23 aemps o advance our undersanding of he accrual anomaly. Using a simple heoreical model, we predic ha if invesors fixae on earnings, he reurns o he accrual sraegy increase in he responsiveness of he sock price o earnings (ERC) and he differenial persisence level of cash flows relaive o accruals (PERDIF). We find srong supporing empirical evidence, lending suppor o he earnings fixaion hypohesis. Our resuls are seemingly inconsisen wih he risk explanaion and canno be accouned for by he limis of arbirage explanaion. Theoreically, i is possible ha he growh explanaion, advocaed by Fairfield e al. (2003a) and Zhang (2007), yields he same empirical predicions as he earnings fixaion explanaion. We noe ha Fairfield e al. (2003a) do no argue agains he earnings fixaion hypohesis. Raher hey sugges ha he lower persisence of accruals resuls from diminishing reurns o growh. Following Zhang (2007), we compue a measure of he exen o which accruals represen growh. We find no saisically significan correlaion beween his measure and ERC/PERDIF. Our finding suggess ha he growh explanaion does no drive our resuls. Our paper conribues o he accouning lieraure in ha our evidence helps o answer an imporan research quesion, wha causes he accrual anomaly. A he minimum, our findings are ineresing o invesors who apply he accrual sraegy in sock rading, as we documen ha he accrual sraegy is more effecive when applied o firms whose sock prices are more responsive o earnings and whose cash flows are much more persisen han accruals. 22

24 References Ali, A., X. Chen, T. Yao, and T. Yu (2008). Do muual funds profi from he accruals anomaly? Journal of Accouning Research, 46 (), -26. Bens, D. A., V. Nagar, D. J. Skinner, and M. H. F. Wong, Employee sock opions, EPS diluion, and sock repurchases. Journal of Accouning and Economics, 36 (), Bradshaw, M. T., S. A. Richardson, and R. G. Sloan, 200. Do analyss and audiors use informaion in accruals? Journal of Accouning Research, 39 (), Collins, D., G. Gong, and P. Hribar, Invesor sophisicaion and he mispricing of accruals. Review of Accouning Sudies, 8 (2-3), Collins, D. W., and P. Hribar, Earnings-based and accrual-based anomalies, one effec or wo? Journal of Accouning and Economics, 29 (), Dechow, P., and I. Dichev, The qualiy of accruals and earnings: The role of accrual esimaion errors. The Accouning Review, 77 (supplemen), Dechow, P., S. Richardson, and R. Sloan, The persisence and pricing of he cash componen of earnings. Journal of Accouning Research, 46 (3), Dechow, P. and R. Sloan, 997. Reurns o conrarian invesmen sraegies: Tess of naïve expecaions hypoheses, Journal of Financial Economics, 43 (), Fairfield, P. M., J. S. Whisenan, and T. L. Yohn, 2003a. Accrued earnings and growh: Implicaions for fuure profiabiliy and marke mispricing. The Accouning Review, 78 (), Fairfield, P. M, J. S. Whisenan and T. L. Yohn, 2003b. The differenial persisence of accruals and cash flows for fuure operaing income versus fuure profiabiliy. The Review of Accouning Sudies, 8 (2-3), Fama, E., and K. French, 992. The cross-secion of expeced sock reurns. Journal of Finance, 47 (2),

25 Fama, E., and K. French, 995. Size and book-o-marke facors in earnings and reurns. Journal of Finance, 50 (), Fama, E., and K. French, 996. Mulifacor explanaions of asse pricing anomalies. Journal of Finance, 5 (), Fama, E. F., and J. D. MacBeh, 973. Risk, reurn and equilibrium: Empirical ess. Journal of Poliical Economy, 8 (3), Greene, J., J. Hand, and M. Soliman, Going, going, gone? The demise of he accruals anomaly. working paper, Universiy of Norh Carolina and Universiy of Washingon. Guierrez, R. C., and E. Kelly, The long-lasing momenum in weekly reurns. Journal of Finance, 63, Hirshleifer, D. A., K. Hou, and S. H. Teoh, The accrual anomaly: Risk or mispricing? Working Paper, Universiy of California a Irvine and Ohio Sae Universiy. Hribar, P., and D. W. Collins, Errors in esimaing accruals: Implicaions for empirical research. Journal of Accouning Research, 40 (), Jones, J. J., 99. Earnings managemen during impor relief invesigaions. Journal of Accouning Research, 29 (2), Khan, M., Are accruals mispriced? Evidence from ess of an ineremporal capial asse pricing model. Journal of Accouning and Economics, 45 (), Kraf, A., A. J. Leone, and C. Wasley, An analysis of he heories and explanaions offered for mispricing of accruals and accrual componens. Journal of Accouning Research, 44 (2),

26 Lakonishok, J., A. Shleifer, and R. W. Vishny, 994. Conrarian invesmen, exrapolaion, and risk. The Journal of Finance, 49 (5), Lev, B., and D. Nissim, The persisence of he accruals anomaly. Conemporary Accouning Research, 23 (), Mashruwala, C. A., S. Rajgopal, and T. J. Shevlin, Why is he accrual anomaly no arbiraged away? The role of idiosyncraic risk and ransacion coss. Journal of Accouning and Economics, 42 (), Pincus, M., S. Rajgopal, and M. Venkaachalam, The accrual anomaly: Inernaional evidence. The Accouning Review 82 (), Richardson, S. A., R. G. Sloan, M. T. Soliman, and I. Tuna, Accrual reliabiliy, earnings persisence, and sock prices. Journal of Accouning and Economics, 39 (3), Richardson, S., R. Sloan, M. Soliman, and I. Tuna, The implicaions of firm growh and accouning disorions for accruals and profiabiliy. The Accouning Review, 8 (3), Richardson, S. A., I. Tuna, and P. Wysocki, 200. Accouning anomalies and fundamenal analysis: A review of recen research advances. Journal of Accouning and Economics, forhcoming. Sloan, R. G., 996. Does sock price fully reflec informaion in accruals and cash flows abou fuure earnings? The Accouning Review, 7 (3), Thomas, J. K., and H. Zhang, Invenory changes and fuure reurns. Review of Accouning Sudies, 7 (2-3), Wu, J., L. Zhang, and X. F. Zhang, 200. The q-heory approach o undersanding he accrual anomaly. Journal of Accouning Research, 48 (),

27 Xie, H., 200. Are discreionary accruals mispriced? A reexaminaion. The Accouning Review, 76 (3), Zhang, X. F., Accruals, invesmen, and he accrual anomaly. The Accouning Review, 82 (5),

28 Table : Descripive saisics. The sample consiss of 27,373 firm-year observaions from Ranking on oal accruals Lowes Highes SAR + Mean 2.99% 2.44%.94% 2.79%.37%.53% -0.37% -0.5% -.90% -2.94% -value ACCR Mean Median CF Mean Median MV Mean Median Book-o-marke Mean Median CAPM Bea Mean Median Noes: SAR + -Size-adjused reurn during he nex year:, where r is and r ps are reurns in monh s for firm i and size porfolio p. Size deciles are deermined by he disribuion of he marke values of all he NYSE/AMEX firms a he beginning of he calendar year. SAR is compued over he 2-monh holding periods, beginning four monhs afer he fiscal year end. When a firm deliss, we use he delising reurn in he delising monh and assume a reurn equal o he firm s size-mached porfolio for he remainder of he year. If a firm s delising is due o liquidaion or a forced delising and he delising reurn is missing, he delising reurn is se o -00%. CF is cash flows in year, which is calculaed by Cash Flows from Operaing Aciviies (Compusa Annual Iem #308) Exraordinary Iems & Disconinued Operaion (Annual Iem #24), deflaed by average oal asses. ACCR is oal accruals in year, calculaed as Income Before Exraordinary Iems (Compusa Annual Iem #23) deflaed by average oal asses, minus cash flows (CF). MV is he marke value of equiy, which is he value of Closing Price in Fiscal Year End (Compusa Iem #99) muliplied by Shares Ousanding (Compusa Annual Iem #25). Book-o-marke is he book value (Compusa Annual Iem #60) divided by he marke value (MV). CAPM Bea is compued from he regression of where R i is monhly reurn of securiy i, and R m is he equally weighed index in NYSE/AMEX, using prior 36 monhs daa.

29 Table 2: Porfolio analysis resuls. The sample consiss of 2,63 firm-year observaions from Panel A: Size-adjused reurns in accrual deciles across ERC quiniles Ranking on ACCR Pooled Year-by-year Range of accruals ERC Lowes Highes hedge p a mean p b dmean dmedian -.35% 0.2%.42% 3.76% 0.83% 4.42%.35% -0.96%.64% 2.6% -3.5% % % 3.62%.53% 2.24%.06% 0.93% 0.73% 0.97% 0.44% 3.03% -2.27% % % 6.67% 2.44% 2.05%.53% 2.06% -0.99%.27% -3.62% -2.69% 9.28% % % 3.36% -0.28% 5.5% -0.3% 0.58% -0.62% -.00% -0.02% -2.64% 4.76% % % 0.64% 2.2%.55% -0.66% 0.24% -.2% -.08%.40% -4.9% 2.26% % Panel B: Size-adjused reurns in accrual deciles across PERDIF quiniles Ranking on ACCR Pooled Year-by-year Range of accruals PER DIF Lowes Highes hedge p a mean p b dmean dmedian -4.3% 0.89% -0.87% -.79% -.72% 3.78% 0.70% -0.58%.43% 6.3% -0.44% % % -0.7% 2.% -0.4% 0.39% -0.27% -0.28% 2.5% 0.57% 3.94% -0.29% % % 2.53%.82% 2.23% -0.77% 2.50% 0.79% -.83% 0.85% -2.27% 5.32% % % 5.82% 2.92% 7.49% 0.69% -0.36% -0.89% -0.70% 0.8% -6.45%.43% % % 5.46%.44% 6.8% 4.0% 2.37% -.43% 0.25% -3.03% -8.83% 7.42% %

30 Panel C: The accruals sraegy reurn in ERC and PERDIF quinile combinaions PERDIF Lowes Highes Lowes % -.75% -0.82% 9.77% 6.24% %.75% 4.78% 2.52% 3.88% ERC % 6.6% 3.62% 9.53% 3.04% % -5.82% 6.4% 5.07% 3.28% Highes 8.92% -5.44% 9.4% 2.47% 44.60% Noes: ERC is he coefficien on EARNINGS ( η ) from he following regression: RET = η + η EARNINGS + ε where 0 RET is reurn in year, and EARNINGS is Dilued EPS Excluding Exraordinary Iems (Compusa Annual Iem #57) in year divided by Closing Price in Fiscal Year End (Compusa Iem #99) in fiscal year -. We require a leas four observaions from he curren year and previous eigh years for his regression. PERDIF is he persisence difference beween cash flows and accruals (β 2 -β ) from he following regression: EARN + = β 0 + βaccr + β2cf + ε where ACCR and CF are oal accruals and cash flows, respecively, in year and EARN + is earnings in year +. For more deailed definiion of ACCR, CF and EARN, please refer o Table. We require a leas four observaions from he curren year and previous eigh years for his regression. Decile ranks are based on oal accruals each year. hedge: he reurn o he hedge porfolio wih a long posiion in he boom accrual decile and a shor posiion in he op accrual decile. pa : he p-value associaed wih hedge, using a wo-ailed es. mean: he mean value of annual hedge porfolio reurns. pb : he p-value associaed wih mean, using a wo-ailed es. dmean: he mean value of differences in accruals beween he lowes and highes accrual deciles. dmedian: he median value of differences in accruals beween he lowes and highes accrual deciles. 29

31 Table 3: Fama-MacBeh regression resuls. The dependen variable is size-adjused reurns in year + (SAR + ). The sample consiss of 20,845 firm-year observaions from Panel A: The effec of ERC Model Model 2 Coeff. p-value Coeff. p-value Inercep RACCR RACCR*RERC RACCR*RARBRISK RACCR*RPRICE RACCR*RVOLUME RSIZE RBTOM RETOP RBETA RERC RARBRISK RPRICE RVOLUME Adjused R Panel B: The effec of PERDIF Model Model 2 Coeff. p-value Coeff. p-value Inercep RACCR RACCR*RPERDIF RACCR*RARBRISK RACCR*RPRICE RACCR*RVOLUME RSIZE RBTOM RETOP RBETA RPERDIF RARBRISK RPRICE RVOLUME Adjused R

32 Panel C: The effec of combining ERC and PERDIF Model Model 2 Coeff. p-value Coeff. p-value Inercep RACCR RACCR*RERC*RPERDIF RACCR*RARBRISK RACCR*RPRICE RACCR*RVOLUME RSIZE RBTOM RETOP RBETA RERC*RPERDIF RARBRISK RPRICE RVOLUME Adjused R Noes: SAR + : Size-adjused reurn for firm in year +. Please refer o Table for deailed definiion. RACCR: Decile ranks of ACCR for each year, scaled beween 0 and. Please refer o Table for he definiion of ACCR. RERC: Decile ranks of ERC in year, scaled beween 0 and. Please refer o Table 2 for he definiion of ERC. RPERDIF: Decile ranks of PERDIF (persisence difference beween cash flows and accruals) in year, scaled beween 0 and. Please refer o Table 2 for he definiion of PERDIF. RARBRISK: Decile ranks of ARBRISK, scaled beween 0 and. ARBRISK is he residual variance from a regression of firm-specific reurns on he reurns of he CRSP equally weighed marke index over he 2 monh ending one monh before he accrual porfolio formaion dae. RPRICE: Decile ranks of PRICE, scaled beween 0 and. PRICE is he CRSP closing sock price one monh before he accrual porfolio formaion dae. RVOLUME: Decile ranks of VOLUME, scaled beween 0 and. VOLUME is he CRSP rading annual volume one monh before he accrual porfolio formaion dae. RSIZE: Decile ranks of MV by he end of fiscal year, scaled beween 0 and. Please refer o Table for definiion of MV. RBTOM: Decile ranks of Book-o-marke raio by he end of fiscal year, scaled beween 0 and. Please refer o Table for definiion of Book-o-marke. RETOP: Decile ranks of Earnings-o-price raio by he end of fiscal year, scaled beween 0 and. Earnings-o-price = Dilued EPS Excluding Exraordinary Iems (Compusa Annual Iem #57) divided by Fiscal Year End Price (Compusa Annual Iem #99) by he end of each fiscal year. RBETA: Decile ranks of CAPM Bea in year, scaled beween 0 and. Please refer o Table for definiion of CAPM Bea. 3

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