An Improved Earnings Forecasting Model. Richard D. F. Harris Pengguo Wang 1

Transcription

1 An Improved Earnings Forecasing Model Richard D. F. Harris Pengguo Wang 1 p.wang@exeer.ac.uk Xfi Cenre for Finance and Invesmen Universiy of Exeer Business School Sreaham Cour Rennes Drive Exeer EX4 4ST, UK April The auhors very graeful for commens received from David Ashon, Kewei Hou and Sco Richardson.

2 An Improved Earnings Forecasing Model Absrac In his paper, we employ he earnings model developed in Ashon and Wang (2013) o forecas he one- o hree-year ahead earnings of individual companies. We find ha he model produces forecass of fuure earnings ha are less biased and more informaive han boh he consensus analyss earnings forecass repored by IBES and he recenly developed model-based forecass of Hou, van Dijk and Zhang (2012). Keywords: Earnings forecass; Cross-secional earnings model; Bias; Earnings response coefficiens. 2

3 1. Inroducion A long-held view abou he earnings forecass of sell-side analyss is ha hey are more accurae han forecass derived from ime-series models of earnings (Fried and Givoly, 1982; Brown e al, 1987; Wiedman, 1996; Walher, 1997). As a resul, analyss earnings forecass have become widely used in he invesmen communiy and are increasingly imporan in fundamenal equiy analysis. In paricular, analyss earnings forecass are used eiher o esimae he fair value of an individual sock given an assumpion abou he expeced equiy reurn (derived, for example, from an equilibrium model of expeced reurns such as he CAPM), or o ascerain he expeced equiy reurn ha is implied by he curren marke price of he sock, i.e. o esimae he implied cos of capial. 2 Alhough commonly used by boh academics and praciioners, here is exensive evidence ha analyss earnings forecass are sysemaically biased upwards (O Brien, 1988; Mendenhall, 1991; Brown, 1993; Das e al. 1998). 3 This over-opimism in analyss earnings forecass has poenially serious consequences for decision making: if analyss earnings forecass are overly opimisic, esimaes of he expeced reurn ha are based on analyss earnings forecass will be oo high relaive o he marke s expecaion of fuure reurns. If his oversaed expeced reurn is used as a discoun rae for he purpose of capial budgeing, some posiive ne presen value projecs will be erroneously rejeced, causing a reducion in shareholders value. Aenion has 2 Eason (2009) provides a summary of he recen lieraure on he use of analyss forecass in esimaing he implied cos of equiy capial. Richardson e al. (2010) provide a comprehensive review of he uses of analyss forecass in fundamenal analysis. 3 There are a number of suggesed reasons for he sysemaic over-opimism of analyss earnings forecass (see Beckers e al, 2004; Ramnah e al., 2008). 3

4 herefore urned o developing models of individual companies earnings ha are able o generae forecass of fuure earnings ha are boh accurae and unbiased. Richardson e al. (2010) develop a generalised framework for forecasing earnings. In his framework, expeced one-period ahead earnings are specified as a funcion of curren earnings, book value, changes in book value and a se of poenially useful non-accouning variables. The non-accouning informaion se may include variables such as he curren marke price of equiy and he change in he marke price (i.e. he reurn). This specificaion capures a number of esablished feaures ha have been repored in he lieraure. Firs, earnings are highly persisen (Fama and French, 2006; Hou and Robinson, 2006). Second, equiy prices and reurns are leading indicaors of fuure earnings (Weiss e al., 2008). Third, earnings are generaed from asses, so ha operaing accruals (which are changes in ne operaing asses) may have explanaory power for fuure earnings. Finally, changes in he book value of equiy may reflec accouning conservaism, and so lagged book value may play a role in predicing fuure earnings. Consisen wih his framework, Hou, van Dijk and Zhang (2012, HDZ) develop a cross-secional model of one-period ahead earnings, employing oal asses, dividend paymens, earnings and accruals as explanaory variables. They show ha he earnings forecass ha are generaed by his model exhibi much lower bias and higher earnings response coefficiens (ERC) han he consensus analyss earnings forecass repored by IBES. 4 However, HDZ use heir model o forecas oal earnings, and so heir forecass are no direcly comparable wih IBES consensus earnings forecass, which are for earnings per share, no oal earnings. 4 A number of recen sudies apply he Hou e al. (2012) model in he conex of asse pricing and examining marke efficiency (Lee, So and Wang, 2011; Rusicus, 2011). 4

5 Recenly, Ashon and Wang (2013, AW) have developed a model of earnings based on heoreical foundaions. The AW model relies on hree basic assumpions: (i) capial markes are free of arbirage opporuniies, (ii) he clean surplus accouning ideniy holds, and (iii) dividends fully displace curren prices. Using hese assumpions, AW show ha one-period-ahead earnings can be wrien as a funcion of five variables: curren earnings, curren and lagged book values of equiy, and curren and lagged marke prices of equiy. The primary focus of AW is o simulaneously esimae he implied cos of equiy capial and he long-run earnings growh rae, exploiing he link beween equiy valuaion and forecass of fundamenal accouning and non-accouning variables. They employ analyss earnings forecass as an inpu in heir esimaion, bu do no explore he characerisics of heir earnings forecasing model. Neverheless, he AW model is a formalisaion of he general earnings forecasing framework of Richardson e al. (2010) and is consisen wih he Fama and French (2006) model used for forecasing firm profiabiliy. In his paper, we implemen he AW earnings model o generae forecass of one o hree-year ahead earnings for individual U.S. firms. We compare he performance of he forecass from he AW model wih hose based on he HDZ earnings model and wih IBES consensus analyss earnings forecass. We show ha all hree forecass have similar accuracy, bu in conras wih IBES consensus forecass, which display very significan upward bias, he AW and HDZ models generae forecass of fuure earnings ha are unbiased. The AW and HDZ model-based forecass also conain significanly more informaion abou fuure earnings. Of he wo model-based forecass, he AW model displays he greaes accuracy, lowes bias, and highes informaional conen wih respec o fuure earnings. Encompassing ess of he hree forecas series reveal ha he opimal combinaion of forecass would give weighs o 5

6 he AW forecass, HDZ forecass and IBES consensus forecass of abou 59.3%, 8.5% and 32.2%, respecively. The remainder of he paper is organized as follows. Secion 2 provides deails of he Ashon and Wang (2013) model. Secion 3 describes he daa ha is used in he analysis. Secion 4 evaluaes he relaive performance of he AW and HDZ modelbased earnings forecass and he IBES consensus earnings forecass. Secion 5 concludes. 2. The Ashon and Wang (2013) Model Ashon and Wang (2013, AW) develop a model relaing fuure earnings o a small number of observable accouning and non-accouning variables, wih he objecive of esimaing he implied cos of equiy capial. Consisen wih he Miller and Modigliani (1961) dividend irrelevance proposiion and he Ohlson (1995) model specificaion, AW firs assume ha cum-dividend equiy value can be wrien in erms of cum-dividend book value, earnings, and he ne presen value (NPV) of all fuure invesmen projecs: P + d = α 1 (b + d ) +α 2 e +ϑ, (1) where P is he equiy price a ime, b is he equiy book value a ime, d is ne dividend paymens a ime, e is earnings a ime and ϑ is he NPV of all fuure invesmens a ime, which capures he difference beween he equiy price and accouning fundamenal value. α1 and α2 are valuaion muliples. AW argue ha ϑ characerizes he firm s growh componen and also reflecs accouning conservaism, which is measured by he difference beween economic earnings and accouning 6

7 earnings, ( P + d P 1) e. This is because conservaive accouning may influence invesors beliefs abou expecaions of fuure growh. Specifically, AW assume ϑ = (1 + g) ϑ + α ( P + d P e ) + ε, (2) v, + 1 where g is he growh rae in he NPV of fuure invesmens, and ε v, + 1 is a mean zero error erm. Under he assumpion of no-arbirage opporuniies, we have E [P +1 + d +1 ] = RP, (3) where R = 1 plus cos of equiy capial. In addiion, he clean surplus accouning ideniy holds, i.e., b b 1 = e d. (4) AW hen show ha one period ahead expeced earnings can be wrien in erms of price, book value and earnings: R (1 + g) α (1 + g)( α + α 1) 1+ g α + α E [ e ] = P + e + b ( α1 + α2) ( α1 + α2) α1 + α2 (1 + g)( α 1) α α + b + P ( α α ) ( α α ) (5) This esablishes a heoreical link beween one period ahead forecass of earnings and five observable accouning and non-accouning variables. AW show his model is a formalizaion of he earnings forecasing framework of Richardson e al. (2010). I is also consisen wih he model of Fama and French (2006), in which a number of accouning raios including price-o-book, curren profiabiliy, dividend-o-book, accouning accruals and asse growh, are used o forecas fuure profiabiliy, or he forward earnings yield. Noe ha, via he clean surplus accouning ideniy, equaion (5) can be wrien as 7

8 E [ e ] α R (1 + g) α P (1 + g) α + α e = g + + b ( α + α ) ( α + α ) b ( α + α ) b (1 + g)( α 1) α d α P + + ( α + α ) b ( α + α ) b (6) Tha is, fuure profiabiliy can be wrien in erms of he growh of fuure invesmens, P e d,,, b b b P 1 P e d and and he produc erms g, g and g. Noe ha equaion (6) b b b b can also be wrien as: E [ e ] α R (1 + g) P (1 + g) α e = g + + b ( α + α ) ( α + α ) b ( α + α ) b (1 + g)( α 1) d α P b ( P b ) ( ). ( α + α ) b ( α + α ) b (7) The change in goodwill in he las erm may capure he propery of accouning accruals. While AW use analyss consensus earnings forecass as a proxy for he marke s expecaion of earnings in he heoreical model (5) o esimae he growh rae, g, and he implied cos of capial, R, we use he relaion (5) direcly o forecas one-period ahead earnings. For he purpose of presenaion, we rewrie he model as: E [e +1 ] = δ 1 P +δ 2 e +δ 3 b +δ 4 b 1 +δ 5 P 1. (8) We compare he earnings forecass of he AW model, given by equaion (8), wih hose generaed by he HDZ model, and wih IBES consensus analyss earnings forecass. 3. Sample Descripion Our sample consiss of prices and accouning daa in he inersecion of he Cener for Research in Securiy Prices (CRSP) monhly reurn file for he period July 1963 o June 2011 and he Compusa indusrial annual file for he period 1963 o

9 Consensus forecass of earnings are from he Insiuional Brokers Esimae Sysem (IBES) for he period 1976 o The adjused numbers of shares ousanding, adjused dividends a he end of he fiscal year, and adjused prices of equiy 3-monhs afer he fiscal year end are colleced from CRSP. Relevan accouning daa are colleced from Compusa. Firms wih negaive book values are deleed. Earnings are measured as ne income before exraordinary iems. We use median consensus forecass of earnings per share a he firs monh afer he corresponding prior-year earnings announcemens repored by IBES. All accouning variables used in our esimaions are divided by he adjused number of shares in issue o reduce heeroscedasiciy and increase comparabiliy across ime. In consrucing he daa se, consisen wih earlier research, we omi firms in he exreme percenile of earnings, book values, prices, and one period ahead earnings forecass, o reduce he effecs of ouliers (Ball e al., 2000). Firms wih a price per share less han $1 are also deleed (Khan and Was, 2009). Annual sock reurns are calculaed from July of year o June of year +1. Summary saisics of he dependen and independen variables are repored in Table 1. < Inser Table 1 abou here> Panel A of Table 1 repors he mean, sandard deviaion, and he 1%, 25%, 50%, 75% and 99% quaniles of each series, for he period 1963 o For he IBES forecass, he sample is 1976 o We noe ha he sample sizes for IBES one- and wo-year ahead forecass are much smaller han for he oher variables. 5 This is parly because analyss end o cover relaively large, financially healh firms, and parly because of he relaively shor period of ime for which IBES forecass are available. In Panels A 5 IBES normally repors one- and wo-year ahead forecass of earnings plus forecass of long erm earnings growh. The number of observaions for hree-year ahead forecass is considerably smaller. 9

10 and B of Table 1, we repor summary saisics for boh he full sample, 1963 o 2011, and he common sample, 1976 o On average, he IBES earnings forecass are much higher han he realized earnings, reflecing he over-opimism of analyss forecass ha is well documened in he lieraure. Panel C repors he average annual cross-secional correlaion marix wih Pearson (Spearman) correlaions in he lower (upper) diagonals of he marix for he full sample. We noe ha he realizaions of fuure earnings have a slighly lower correlaion wih curren earnings han do he corresponding IBES earnings forecass for boh full and common samples. As expeced, curren earnings are highly posiively correlaed wih curren prices, book values and dividends. 4. Forecas Performance 4.1 AW Forecass and IBES Consensus Forecass Following he procedure described in Hou, van Dijk and Zhang (2012), we generae ou-of-sample forecass of earnings for each year from 1968 o 2011 using he following pooled cross-secional regression based on he AW model given by (8): 6 e j,+1 = δ 0 +δ 1 P j, +δ 2 e j, +δ 3 b j, +δ 4 b j, 1 +δ 5 P j, 1 +ε j,+1, (9) where e j, is he earnings per share of firm j in year, P j, is he equiy price and b j, is he book value of equiy. 7 The model is esimaed using an expanding window saring wih hree years 8 for he 1968 forecas year increasing o en years for he 6 Unlike Hou, van Dijk and Zhang (2012), we do no use negaive earnings and dividend dummies in our regressions. We find ha he inclusion of negaive earnings has a negligible impac on our resuls. 7 Using he clean surplus accouning ideniy, one can replace he lagged book value in (9) by dividends. This yields very similar resuls. 8 We use a leas five years of daa for one-year ahead forecass, a leas four years of daa for wo-year ahead forecass, and a leas hree years of daa for hree-year ahead forecass. 10

11 1973 forecas year, and hen a rolling window of en years unil he final forecas year of For each forecas year τ = 1968,,2011, he model is esimaed using only daa ha are available in year τ 1. The esimaed coefficiens from he pooled regression are hen muliplied by he independen variables as of year τ 1 o generae ou-of-sample one-year ahead forecass of earnings for year τ. Table 2 repors he annual esimaed coefficiens and -saisics from he pooled cross-secional regression (9) for each forecas year 1968 o I also repors he ime-series averages and Fama-MacBeh (1973) -saisics of he annual esimaed coefficiens. The esimaion resuls confirm ha earnings are highly persisen and ha prices lead earnings. Opening book value ( b 1 ) is significan in predicing fuure earnings, while curren book value ( b ) is no. The esimaed coefficien across all forecas years is negaive for he lagged price. All he Fama-MacBeh (1973) - saisics are significan excep for curren book value and he inercep. 9 The negaive coefficien on lagged price and he posiive coefficien of curren price wih similar magniude are a reflecion of he role of he equiy reurn in forecasing earnings. I shows ha a $1 change in prices will lead o a change in one-period ahead earnings of abou 4.2 cens, holding everyhing else consan. The significan coefficien on lagged book value may be associaed wih he accrual (or invesmen) anomaly as summarized in Richardson e al. (2010). The adjused R-squared of he regression varies from 33.5% o 62.5%, and reveals a decline in he explanaory power of he model from he lae 1980s o he beginning of 2000s. The model, on average, explains abou 47% of he variaion in one-year ahead earnings. 9 Noe ha he residuals of he cross-secional regression may be serially correlaed because forecased earnings may be serially correlaed over ime. However, he use of Newey-Wes sandard errors yields very similar resuls. 11

12 <Inser Table 2 abou here> Similarly, a modified version of equaion (9) can be used o forecas wo-year and hree-year ahead earnings: e δ + δ P + δ e + δ b + δ b + δ P + ε, 2,3, (10) j, + k = 0 1 j, 2 j, 3 j, 4 j, 1 5 j, 1 j, + k k = where, for each forecas year τ = 1968,,2011, he model is esimaed using only daa ha are available in year τ-k, and used o generae ou-of-sample k-year ahead forecass of earnings for year τ. The resuls of he wo-year and hree-year ahead forecas regressions, no repored here, are similar o hose of he one-year ahead regression. However, as expeced, he adjused R-squared falls wih he forecas horizon, varying from 20.4% o 49.2% for he wo-year ahead forecass and from 14.6% o 49.0% for he hree-year ahead forecass. We now evaluae he earnings forecass from he AW model in erms of forecas bias, forecas accuracy and he earnings response coefficien. Following prior sudies, forecas bias is defined as he mean difference beween realized earnings and forecas earnings, scaled by price. Forecas accuracy is defined as he mean absolue value of he difference beween realized earnings and forecas earnings, scaled by price. The earnings response coefficien (ERC) is he slope in a regression of equiy reurns on earnings surprises, measured by he difference beween realized earnings and forecas earnings. The ERC measures he exen o which forecas earnings coincide wih he marke s expecaions of earnings. Table 3 repors he forecas bias and forecas accuracy measured across firms and over he sample period, and he ime series average of he cross-secional ERCs. Resuls are repored for full sample, i.e., he AW earnings forecass for he sample, and for IBES consensus forecass for he 12

13 sample in Panel A. To enable a comparison beween he wo ses of forecass, we also repor resuls for he common sample over in Panel B. 10 <Inser Table 3 abou here> Panel A of Table 3 repors he bias, accuracy and ERC of he AW forecass and he IBES consensus forecass for he full sample. For he AW forecass over he period, he bias of he one- and wo-year ahead forecass is similar (-0.004), while he accuracy of he one-year ahead forecass is slighly beer (0.071 vs ). For he IBES consensus forecass over he period, he one-year ahead forecass are boh less biased and more accurae han he wo-year ahead forecass ( vs for he bias and vs for he accuracy). Panel B repors he bias, accuracy and ERC of he AW forecass and he IBES consensus forecass for he common sample, Again he biases of he AW forecass are much smaller han hose for he IBES consensus forecass ( vs for one-year ahead forecass, vs for wo-year ahead forecass, and vs for hree-year ahead forecass). The negaive bias of he IBES consensus forecass reflecs he common finding ha analyss forecass are biased upwards (O Brien, 1988; Mendenhall, 1991; Das, Levine and Sivaramakrishnan, 1998). The AW forecass are slighly less accurae han he IBES consensus forecass a he one-year horizon (0.058 vs ) bu more accurae a he wo- and hree-year horizons (0.068 vs and vs , respecively). The pairwise -ess show ha he differences in boh bias and accuracy beween he AW forecass and he IBES consensus forecass are saisically significan. In he common sample, he ERCs for he IBES consensus forecass are smaller han for he AW forecass for he 10 As above, we use a leas five years daa for one-year ahead forecass. IBES forecass sar from

14 one-, wo- and hree-year ahead forecass (0.91 vs for he one-year ahead forecass, 0.65 vs for he wo-year ahead forecass, and 0.47 vs for he hree-year ahead forecass). This suggess ha he AW model based forecass provide a beer approximaion of he marke s expecaions of fuure earnings. This is consisen wih findings in Hou e al. (2012). The differences beween he average ERC are also significan for he one-, wo- and hree-year horizon. 4.2 AW Forecass, HDZ Forecass and IBES Consensus Forecass Hou, van Dijk and Zhang (2012, HDZ) inroduce a compelling forecasing model for earnings based on prior empirical findings. Specifically, hey express expeced oneperiod ahead oal earnings in erms of a small number of accouning variables as follows: E[ e + = α 0 + α1a + α2d + α3dd + α4e + α5nege + α6ac (11) 1] where e denoes he oal earnings of a firm a ime, oal common dividend paymen, A is oal asses, D is he AC is oal operaing accruals, which is equal o he change in non-cash curren asses less he change in curren liabiliies, excluding shor-erm deb and axes payable, minus depreciaion and amorizaion expense. DD is a dummy variable ha equals 0 for dividend payers a ime and 1 for non-payers, NegE is a dummy variable ha equals 1 for firms wih negaive earnings a ime and 0 oherwise. HDZ employ heir cross secional model o forecas he earnings of individual firms, and find ha heir model produces earnings forecass ha are comparable o IBES consensus forecass in erms of accuracy, bu exhibi lower levels of bias. In addiion, hey find ha he ERC associaed wih he model-based forecass are larger han he 14

15 ERC for IBES consensus forecass. However, hey forecas oal earnings raher han earnings per share, while IBES consensus forecass are for earnings per share. Their model-based forecass are herefore no direcly comparable wih IBES consensus forecass, since one would have o ake ino accoun changes in he number of shares ousanding. Here we implemen he HDZ model o forecas one-year ahead earnings per share, based on he following regression: e = + A + D + DD + e + NegE + AC + (12). j, + 1 γ j0 γ j1 j. γ j 2 j, γ j3 j, γ j4 j, γ j5 j, γ j6 j, ε j, + 1 The model is esimaed over he period 1968 o 2011 using he same procedure ha was used for he AW model-based forecass in he previous secion. We also reesimae he AW model using he same sample. 11 Descripive saisics for he coefficien esimaes in he HDZ and AW models using he common sample are repored in Panels A and B, respecively, of Table 4. The coefficiens on dividends ( γ 2 ) in he HDZ model, and on price ( δ 1 ) and lagged book value ( δ 4 ) in he AW model are significanly posiive in explaining one-year ahead earnings. This confirms ha curren prices lead earnings afer conrolling for oher accouning variables. The coefficiens on accruals ( γ 6 ) and dividend dummy ( γ 3 ) in he HDZ model, and on lagged price ( δ 5 ) in he AW model are significanly negaive. The coefficiens on asses ( γ 1 ) and he earnings dummy ( γ 5 ) in he HDZ model, and book value ( δ 3 ) in he AW model are no significanly differen from zero. We also noe ha curren earnings in boh models ( γ 4 and δ 2 ) is an imporan predicor of fuure earnings. The mean values of he coefficiens on asses, dividends, earnings and accruals in he HDZ 11 The sample used o esimae he HDZ model is smaller han ha used o esimae he AW model in Table 2 because of missing daa for he accouning iems ha are used o esimae accouning accruals in he HDZ model. 15

16 model are similar o hose repored in Hou e al. (2012). The mean adjused R-squared coefficien is almos he same for he wo models. <Inser Table 4 abou here> We also implemen he HDZ model o forecas wo- and hree-year ahead earnings per share, based on he following regression: e j, + k = γ j0 + γ j1 Aj. + γ j2 Dj, + γ j3 DDj, + γ j4 e j, + γ j5 NegE j, + γ j6 AC j, + ε j, + k, k = 2,3. While he mean values of he coefficiens on he key variables are similar o hose repored in Hou e al. (2012), he adjused R-squared is much lower han hey repor. This is explained by he fac ha we are using he HDZ model o forecas earnings per share raher han oal earnings. 12 Table 5 compares he forecas bias, forecas accuracy and average ERC for he AW and HDZ model-based forecass and for he IBES consensus forecass. Panel A of Table 5 repors he forecas bias, forecas accuracy and average ERC over he sample for he AW and HDZ model-based forecass. For he one-year ahead forecass, he bias of he AW model is significanly lower han he bias of he HDZ forecass ( vs ). For he wo- and hree-year ahead forecass, he bias of he HDZ forecass is significanly lower han ha of he AW model ( vs for wo-year ahead forecass, vs for hree-year ahead forecass). However, he AW forecass are significanly more accurae han he HDZ forecass for all hree forecas horizons ( vs , vs , vs for one-, wo- and hree-year ahead forecass respecively). In addiion, he average ERC for he AW forecass is higher han ha of he HDZ forecass for all hree 12 We obain adjused R-squared saisics ha are similar o hose repored by Hou e al. (2012) when we use oal numbers raher han per share numbers in our regressions. 16

17 forecas horizons, bu he difference is significan only for he one-year ahead forecass (0.79 vs. 0.74). <Inser Table 5 abou here> Panel B of Table 5 repors he forecas bias, forecas accuracy and average ERC over he sample for he AW and HDZ model-based forecass, and for he IBES consensus forecass. For he one-year ahead forecass, he AW model has he lowes bias (-0.004), followed by he HDZ model (-0.009), hen he IBES consensus forecass (-0.034). The -ess confirm ha he IBES consensus forecass are very significanly biased upwards for all hree forecas horizons. Moreover, he bias of he AW forecass is significanly lower han ha of he HDZ forecass for he one- and hree-year ahead forecass bu no for he wo-year ahead forecass. Forecass based on he AW model are more accurae han hose based on he HDZ model ( vs. 0.06, vs , vs for he one-, wo- and hree-year ahead forecass respecively), bu slighly less accurae han he IBES consensus one-year ahead forecass (wih a mean absolue forecas error of ). The pairwise -ess show ha hese differences are saisically significan. For he one-year ahead forecass, he highes average ERC is for IBES consensus forecass (0.789), followed by he AW forecass (0.762) and he HDZ forecass (0.710). Pairwise -ess reveal ha he difference beween he average ERC for IBES forecass is no significanly differen from ha for he AW forecass, and he difference beween he average ERC for he AW forecass is significanly differen from ha for he HDZ forecass. For he wo- and hree-year ahead forecass, he average ERCs for boh he AW forecass and HDZ forecass are larger han ha for IBES consensus forecass. However, hey are no saisically significan excep for he hree-year ahead forecass. Our findings herefore sugges ha he AW model and 17

18 he HDZ model-based forecass of fuure earnings are significanly less biased han analyss forecass, bu he AW forecass and analyss forecass are more closely associaed wih he marke s expecaions of earnings han he HDZ model-based forecass a he one-year horizon. 4.3 Efficiency and Encompassing Tess In his secion, we evaluae he efficiency of he AW and HDZ model-based forecass and IBES consensus forecass, and compare he incremenal informaion ha hey conain abou realized earnings. An earnings forecas is efficien if i opimally reflecs currenly available informaion, and is herefore associaed wih a forecas error ha is unpredicable. In is weakes form, his requires ha he forecas error is uncorrelaed wih he earnings forecas iself. Weak efficiency is esed by esimaing he following Mincer-Zarnowiz regression: e j,+1 = α + βê j, + v j,+1 (13) where ê j, is he forecas made a ime of he earnings of firm j a ime +1. If he earnings forecass are weakly efficien, he slope coefficien, β, should be equal o one. If β is significanly differen from one hen condiioning on he forecas iself, he forecas error is predicable. The R-squared saisic from he Mincer-Zarnowiz regression measures he informaion conen of he forecass, irrespecive of heir bias and inefficiency. <Inser Table 6 abou here> Panel A of Table 6 repors he resuls of esimaing he Mincer-Zarnowiz regression for he AW and HDZ forecas series over he common sample. For boh he AW forecass and he HDZ forecass (Models 1 and 2), we can rejec he 18

19 hypohesis ha β =1. The R-squared saisics reveal ha of he wo model-based forecass, he AW forecass are slighly more informaive han he HDZ forecass (wih R-squared coefficiens of 39.8% and 38.9%, respecively). The Mincer-Zarnowiz regression can also be used o measure he incremenal informaion conen of compeing forecass, and wheher one forecasing model is encompassed by anoher. In paricular, we can esimae he following regression of realized earnings on K compeing forecass ˆ : 1 K e j,,, eˆ j, e 1 K ˆ ˆ j, + 1 = + β1e j, + + βke j, + v j, + 1 α (14) If β k = 0 hen he forecass from model k do no conain any informaion abou realized earnings beyond ha conained in he oher models, and so he oher models encompass model k. More generally, he relaive magniude and saisical significance of he coefficiens β,, 1 β K measure he relaive informaion conen of he compeing forecas series. Panel A of Table 6 also repors he resuls of esimaing he encompassing regressions for AW forecass and HDZ forecass. While he AW forecass and HDZ forecass individually conain similar informaion abou one-year ahead earnings (Models 1 and 2), when combined (Model 3), boh remain significan, bu he AW forecass dominae he HDZ forecass in erms of boh magniude and saisical significance. Thus, while each series conains informaion relevan o fuure earnings ha is no conained in he oher series, he AW forecass are saisically more relevan. Panel B of Table 6 repors he resuls of esimaing he Mincer-Zarnowiz regression for he AW forecass, he HDZ forecass, and he IBES consensus forecass over he common sample. For all hree series, he slope coefficien is no significanly differen from one. The R-squared saisics reveal ha of he wo model- 19

20 based forecass, he AW forecass are more informaive han he HDZ forecass (wih R-squared coefficiens of 37.3% and 34.5%, respecively). Moreover, boh he AW and HDZ forecass are significanly more informaive han he IBES consensus forecass (wih an R-squared coefficien of 33.7% for Model 4). Thus, while he model-based forecass have similar efficiency compared o analyss forecass, hey neverheless conain more informaion abou fuure earnings. Panel B of Table 6 also repors he resuls of esimaing he encompassing regressions for (a) AW forecass and HDZ forecass, (b) AW forecass and IBES consensus forecass, (c) HDZ forecass and IBES consensus forecass, and (d) AW forecass, HDZ forecass and IBES consensus forecass. While he AW forecass and HDZ forecass individually conain similar informaion abou one-year ahead earnings (Models 1 and 2), when combined (Model 3), boh remain significan, bu he AW forecass dominae he HDZ forecass. Combining he IBES consensus forecass wih eiher he AW forecass or he HDZ forecass (Models 5 and 6) significanly reduces he imporance of he IBES consensus forecass, suggesing ha he model-based forecass conain much of he informaion ha is conained in analyss forecass. When all hree forecass are included (Model 7), he AW forecass dominae, followed by he IBES consensus forecass, followed by he HDZ forecass. Indeed, afer accouning for boh he AW forecass and he IBES consensus forecas, he role of he HDZ forecass is marginal. 5. Concluding Remarks Forecass of earnings per share are an imporan inpu o fundamenal equiy analysis. While analyss forecass of earnings are readily available, hey are well known o be sysemaically upwardly biased, which poenially leads o esimaes of he implied expeced reurn on equiy ha are oo high relaive o he marke s expecaion of 20

21 fuure equiy reurns. In urn, his will resul in he rejecion of posiive NPV projecs and a consequen reducion in shareholders value. Aenion has herefore recenly urned o developing models of individual companies earnings ha are poenially able o generae forecass of fuure earnings ha are boh accurae and unbiased. In his paper, we employ he recenly inroduced AW earnings model o forecas he earnings of individual firms. Our empirical analysis reveals ha he AW model generaes earnings forecass ha ouperform boh analyss consensus earnings forecass and he forecass generaed by he Hou e al. (2012) model, in erms of bias, accuracy, and informaional conen wih respec o fuure earnings. There are a number of ways in which he accuracy of he AW earnings forecass could be improved. For example, consisen wih common pracice, he cross-secional model could be implemened on an indusry basis o forecas earnings of firms in individual indusries. One could also apply he model in a ime-series seing using quarerly daa, o forecas earnings of individual firms. 21

22 References Ashon, D. and P. Wang Terminal Valuaion, Growh Raes and he Implied Cos of Capial. Review of Accouning Sudies 18 (1): Beckers, S., M., Seliarcs, and A., Thomson Bias in European Analyss' Earnings Forecass. Financial Analyss Journal 60 (2): Bradshaw, M., M. Drake, J. Myers and L. Myers A Re-examinaion of Analyss Superioriy over Time-Series Forecass of Annual Earnings. Review of Accouning Sudies 17: Brown, L Earnings forecasing research: I s implicaions for capial markes research. Inernaional Journal of Forecasing 9: Brown. L., B. Gay, and M. Turac Creaing a Smar Condiional Consensus Forecas. Financial Analyss Journal 64(6):74-86 Brown, L., G. Richardson and S. Schwager An informaion inerpreaion of financial analys superioriy in forecasing earnings. Journal of Accouning Research 25: Das, S., B. Levine, and K. Sivarmakrishnan Earnings Predicabiliy and Bias in Analyss Earnings Forecass. The Accouning Review 73: Eason, P.D PE Raios, PEG Raios, and Esimaing he Implied Expeced Rae of Reurn on Equiy Capial. The Accouning Review 79: Eason, P.D Esimaing he Cos of Capial Implied by Marke Price and Accouning Daa. Foundaions and Trends in Accouning 2: Eason, P.D., G. Taylor, P. Shroff, and T. Sougiannis Using Forecass of Earnings o Simulaneously Esimae Growh and he Rae of Reurn on Equiy Invesmen. Journal of Accouning Research 40: Fama, E.F., and K.R. French. 2006, Profiabiliy, Invesmen and Average Reurns. Journal of Financial Economics 82: Fama, E., and J. MacBeh Risk, Reurn and Equilibrium - Empirical Tess. The Journal of Poliical Economy 81:

23 Fried, D., and D. Givoly Financial Analyss Forecass of Earnings: a Beer Surrogae for Marke Expecaions. Journal of Accouning and Economics 4(2): Hou, K., and D. Robinson Indusry concenraion and average sock reurns. Journal of Finance 61: Hou, K., M. van Dijk, and Y. Zhang The Implied Cos of Capial: A New approach. Journal of Accouning & Economics 3(3): Kross, W., B. Ro and D. Schroeder Earnings Expecaions: he Analyss Informaion Advanage. The Accouning Review 65(2): Lee, C. M. C., E.C. So and C.Y. Wang Evaluaing Implied Cos of Capial Esimaes. Sanford Universiy working paper. Mendenhall, R Evidence on he Possible Underweighing of Earnings Informaion. Journal of Accouning Research 29: O Brien, P Analyss Forecass as Earnings Recommendaions. Journal of Accouning & Economics 10: Ramnah S., S., Rock and P. Shane The Financial Analys Forecasing Lieraure: A Taxonomy wih Suggesions for Furher Research. Inernaional Journal of Forecasing 24: Richardson, S., I. Tuna and P. Wysocki Accouning Anomalies and Fundamenal Analysis: A Review of Recen Research Advances. Journal of Accouning and Economics 50: Rusicus, T Marke inefficiency and implied cos of capial models. Norhwesern Universiy working paper. Walher, B Invesor Sophisicaion and Marke Earnings Expecaions. Journal of Accouning Research 35: Weiss, D., P.A. Naik and C.L. Tsai Exracing Forward-looking Informaion from Securiy Price: A New Approach. The Accouning Review 83: Wiedman, C The Relevance of Characerisics of he Informaion Environmen in he Selecion of a Proxy for he Marke's Expecaions for Earnings: 23

24 An Exension of Brown, Richardson, and Schwager [1987]. Journal of Accouning Research 34(2):

25 Table 1: Sample Descripive Saisics Panel A: Summary Saisics (full sample: ) eps reps1 reps2 afeps1 afeps2 p bps dps N mean sdev p p p p p Panel B: Correlaion Marix (full sample: ) eps reps1 reps2 afeps1 afeps2 p bps dps eps reps reps afeps afeps p bps dps

26 Panel C: Summary Saisics (common sample: ) eps reps1 reps2 afeps1 afeps2 p bps dps N mean sdev p p p p p Panel D: Correlaion Marix (common sample: ) eps reps1 reps2 afeps1 afeps2 p bps dps eps reps reps afeps afeps p bps dps Panels A and C of Table 1 repor descripive saisics for he period and respecively. eps is ne income before exraordinary iems divided by number of shares ousanding. reps1 and reps2 are he one- and wo-year ahead realizaions of earnings. afeps1 and afeps2 are he one-, wo-year ahead analys earnings forecass from 1976 o p is adjused price per share of equiy 3-monhs afer he fiscal year end. bps is book value of equiy per share. dps is common dividend per share. The number of observaions, mean, sandard deviaion (sdev), 1%, 25%, 50%, 75% and 99% quaniles are also repored. Firms in he exreme perceniles in earnings, book values, prices, afeps1 are deleed. Panels B and D repor he annual cross-secional correlaions, wih Pearson correlaions in he lower half and Spearman correlaions in he upper half. 26

27 Table 2: Coefficien Esimaes of he AW Model for One-Year Ahead Earnings Forecass year cons -sa P -sa e -sa b -sa b 1 -sa P 1 -sa Adj-R 2 N

28 mean FM -sa min median max Table 2 repors he coefficiens, -saisics, adjused R-squared coefficiens and number of observaions from he pooled cross-secional regressions esimaed each forecas year from 1968 o 2011 for one-year ahead earnings using he regression e j, + 1 = δ j1 Pj, + δ j 2 e j, + δ j3 bj, + δ j 4 bj, 1 + δ j5 Pj, 1 + ε j, + 1. P, b and e are price, book value and earnings a ime, respecively. The able also repors he mean, median, minimum and maximum value of each coefficien over he sample period, he Fama and MacBeh - saisic. 28

29 Table 3. Bias, Accuracy and Earnings Response Coefficiens for AW forecass and IBES Consensus Forecass Bias Accuracy N ERC N Panel A: Full sample AW forecass, eps eps eps AW forecass, eps eps eps Panel B: Common sample AW forecass, eps eps eps IBES forecass, eps eps eps saisic -saisic -saisic H 0 : IBES consensus forecass = AW forecass, 1-year ahead H 0 : IBES consensus forecass = AW forecass, 2-year ahead H 0 : IBES consensus forecass = AW forecass, 3-year ahead Table 3 repors he forecas bias and forecas accuracy and he ime series averages of he value-weighed cross-secional earnings response coefficien for earnings forecass based on he regression e j, + 1 = δ j1 Pj, + δ j 2 e j, + δ j3 bj, + δ j 4 bj, 1 + δ j5 Pj, 1 + ε j, + 1 on a per share basis, and for IBES consensus forecass. Panel A and Panel B repor resuls for he full sample and common sample respecively. Forecas bias is he average difference beween realized earnings and forecas earnings, while forecas accuracy is defined as he average absolue value of he difference beween realized earnings and forecas earnings. The able repors he -saisics o es he null hypoheses ha he bias, accuracy and average ERC are equal for he AW forecass and he IBES consensus forecass over he period. 29

30 Table 4: Summary Saisics for Coefficien Esimaes of he HDZ Model and AW Model for One-Year Ahead Earnings Forecass Panel A: HDZ model consan -sa A -sa D -sa e -sa DD -sa NegE -sa Mean Sdev p p p p p AC -sa Adj-R 2 N Mean Sdev p p p p p

31 Panel B: AW model cons -sa P -sa e -sa b -sa b -1 -sa P -1 -sa Adj-R 2 N mean sdev p p p p p Table 4 repors he descripive saisics of he esimaed coefficiens of he HDZ Model (Panel A) and AW Model (Panel B) over common sample. The HDZ model is given by e = γ + γ A + γ D + γ DD + γ e + γ NegE + γ AC + ε, j, + 1 j0 j1 j. j 2 j, j3 j, j 4 j, j5 j, j6 j, j, + 1 where e is earnings a ime ; A is asses a ime ; D is common dividend paymen a ime ; AC is he oal operaing accruals. All variables are measured on per share basis. DD is a dummy variable ha equals 0 for dividend payers and 1 for non-payers a ime ; NegE is a dummy variable ha equals 1 for firms wih negaive earnings, 0 oherwise a ime. The AW model is given by e = δ + δ P + δ e + δ b + δ b + δ P + ε, j, + 1 j0 j1 j, j2 j, j3 j, j 4 j, 1 j5 j, 1 j, + 1 where P, b, and e are price, book value and earnings a ime respecively. The able repors he mean, sandard deviaion (sdev), 1%, 25%, 50%, 75% and 99% quaniles, adjused R 2 and number of observaions. 31

32 Table 5. Forecas Bias, Accuracy and Average Earnings Response Coefficien for AW Forecass, HDZ Forecass and IBES Consensus Forecass Bias Accuracy N ERC N Panel A: Common sample for AW and HDZ forecass, AW Forecass eps eps eps HDZ Forecass eps eps eps value -value -value H 0 : HDZ forecass = AW forecass, 1-year ahead H 0 : HDZ forecass = AW forecass, 2-year ahead H 0 : HDZ forecass = AW forecass, 3-year ahead Panel B: Common sample for AW, HDZ and IBES forecass, AW Forecass eps eps eps HDZ Forecass eps eps eps IBES Consensus Forecass, eps eps eps value -value -value 32

33 H 0 : HDZ forecass = AW forecass, 1-year ahead H 0 : IBES consensus forecass = AW forecass, 1-year ahead H 0 : IBES consensus forecass = HDZ forecass, 1-year ahead H 0 : HDZ forecass = AW forecass, 2-year ahead H 0 : IBES consensus forecass = AW forecass, 2-year ahead H 0 : IBES consensus forecass = HDZ forecass, 2-year ahead H 0 : HDZ forecass = AW forecass, 3-year ahead H 0 : IBES consensus forecass = AW forecass, 3-year ahead H 0 : IBES consensus forecass = HDZ forecass, 3-year ahead Table 5 repors he bias, accuracy and number of firm-year observaions and he average earnings response coefficien and number of annual observaions for he AW forecass, HDZ forecass and IBES consensus forecass. Panel A repors he resuls for he AW forecass and he HDZ forecass over common sample. Panel B repors he resuls for he AW forecass, he HDZ forecass and IBES consensus forecass over common sample. The HDZ model is given by e = γ + γ A + γ D + γ DD + γ e + γ NegE + γ AC + ε, j, + 1 j0 j1 j. j 2 j, j3 j, j 4 j, j5 j, j6 j, j, + 1 where e is earnings a ime ; V is he marke value of he firm; A is asses a ime ; D is common dividend paymen a ime ; AC is he oal operaing accruals. All are on per share basis. DD is a dummy variable ha equals 0 for dividend payers and 1 for non-payers a ime ; NegE is a dummy variable ha equals 1 for firms wih negaive earnings, 0 oherwise a ime. The AW model is given by e = δ + δ P + δ e + δ b + δ b + δ P + ε, j, + 1 j0 j1 j, j2 j, j3 j, j 4 j, 1 j5 j, 1 j, + 1 where P, b, and e are price, book value and earnings a ime respecively. Forecas bias is he average difference beween realized earnings and forecas earnings, while forecas accuracy is defined as he average absolue value of he difference beween realized earnings and forecas earnings. The able repors he -saisics o es he null hypoheses ha he bias, accuracy and average ERC are equal for each pair of forecass. 33