a re-examination of financial analysts' differential earnings forecast accuracy
TRANSCRIPT
A Re-Examination of Financial Analysts'Differential Earnings Forecast Accuracy*
PRAVEEN SINHA, State University of New York at Buffalo
LAWRENCE D, BROWN, State University of New York at Buffalo
SOMNATH DAS, University of Illinois at Chicago
Abstract. This research re-examines whether there are differences in the forecast accu-racy of financial analysts through a comparison of their annual earnings per share fore-casts. The comparison of analyst forecast accuracy is made on both an ex post (withinsample) and an ex ante (out of sample) basis. Early examinations of this issue byRichards (1976), Brown and Rozeff (1980), O'Brien (1987), Coggin and Hunter (1989),O'Brien (1990), and Butler and Lang (1991) were ex post and suggest the absence ofanalysts who can provide relatively more accurate forecasts over multiple years.
Contrary to the results of prior research and consistent with the belief in the popu-lar press, we document that differences do exist in financial analysts' ex post forecastaccuracy. We show that the previous studies failed to find differences in forecast accu-racy due to inadequate (or no) control for differences in the recency of forecasts issuedby the analysts. It has been well documented in the literature that forecast recency ispositively related to forecast accuracy (Crichfield, Dyckman, and Lakonishok 1978;O'Brien 1988; Brown 1991), Thus, failure to control for forecast recency may reducethe power of tests, making it difficult to reject the null hypothesis of no differences inforecast accuracy even if they do exist.
In our analysis, we control for the differences in recency of analysts' forecastsusing two different approaches. First, we use an estimated generalized least squaresestimation procedure that captures the recency-induced effects in the residuals of themodel. Second, we use a matched-pair design whereby we measure the relative forecastaccuracy of an analyst by comparing his/her forecast error to the forecast error of anoth-er randomly selected analyst making forecasts for the same firm in the same year on oraround the same date. Using both approaches, we find that differential forecast accura-cy does exist amongst analysts, especially in samples with minimum forecast horizonsof five and 60 trading days. We show that these differences are not attributable to dif-ferences in the forecast issuance frequency of the financial analysts. In sum, after con-trolling for firm, year, forecast recency, and forecast issuance frequency of individualanalysts, the analyst effect persists.
To validate our findings, we examine whether the differences in the forecast accu-racy of financial analysts persist in holdout periods. Analysts were assigned a "superi-or" ("inferior") status for a firm-year in the estimation sample using percentile rankings
* Accepted by Lane Daley, The authors gratefully acknowledge the contribution of I/B/E/S/International Inc, for providing the earnings per share forecast data, available through theInstitutional Brokers Estimate System, This data has been provided as part of a broadacademic program to encourage earnings expectations research. Comments and suggestionsof seminar participants at the 1993 Annual International Symposium on Forecasting, the1993 joint national meeting of ORSA/TIMS, the 1994 Annual Meetings of the AmericanAccounting Association, University of Arizona, University of Cincinnati, RutgersUniversity, State University of New York at Buffalo, and University of Waterloo aregratefully acknowledged.
Contemporary Accounting Research Vol, 14 No, 1 (Spring 1997) pp, 1-42 ©CAAA
Contemporary Accounting Research
on the distribution of absolute forecast errors for that firm-year. We use estimation sam-ples of one- to four-year duration, and consider two different definitions of analyst fore-cast superiority. Analysts were classified as firm-specific "superior" if they maintaineda "superior" status in every year of the estimation sample. Furthermore, they were clas-sified as industry-specific "superior" if they were deemed firm-specific "superior" withrespect to at least two firms and firm-specific "inferior" with respect to no firm in thatindustry. Using either definition, we find that analysts classified as "superior" in esti-mation samples generally remain superior in holdout periods. In contrast, we find thatanalysts identified as "inferior" in estimation samples do not remain inferior in holdoutperiods.
Our results suggest that some analysts' earnings forecasts should be weighted high-er than others when formulating composite earnings expectations. This suggestion ispredicated on the assumption that capital markets distinguish between analysts who areex ante superior, and that they utilize this information when formulating stock prices.Our study provides an ex ante framework for identifying those analysts who appear tobe superior. When constructing weighted forecasts, a one-year estimation period shouldbe used because we obtain the strongest results of persistence in this case.
CondenseLes auteurs s'interrogent de nouveau sur l'existence de disparites dans l'exactitude desprovisions annuelles de ben6fice par action formulees par les analystes financiers.L'^tude la plus complete des disparit6s dans l'exactitude des provisions des analystesfinanciers est celle d'O'Brien (1990), qui consiste dans l'examen des provisions derOsultats formulOes par tous les analystes financiers de la base de donnees I/B/E/S, entre1975 et 1982, pour neuf secteurs d'activite. Contrairement a la notion vOhiculee par lapresse populaire selon laquelle il existe bel et bien des disparites dans l'exactitude desprovisions de rOsultats formulOes par les analystes financiers {Institutional Investor ;The Wall Street Journal), O'Brien (1990) conclut qu'il n'existe pas de disparitOs signi-ficatives dans la capacitO des analystes financiers a prOvoir les rOsultats annuels desentreprises pour plusieurs annOes, une fois controlOs les facteurs relatifs a I'entreprise eta l'annOe. D'autres chercheurs qui se sont penchOs sur cette question (Richards, 1976 ;Brown et Rozeff, 1980 ; O'Brien, 1987 ; Coggin et Hunter, 1989 ; Butler et Lang, 1991 ;Stickel, 1992) sont Ogalement d'avis qu'il n'y a pas d'analystes capables de formulerdes provisions pour plusieurs annOes dont l'exactitude relative serait plus grande.Or, les conclusions des auteurs rOfutent ici celles des chercheurs qui les ont prOcOdOs :conformOment a la notion vOhiculOe dans la presse populaire, il existe bel et bien, con-statent-ils, des disparitOs dans l'exactitude des provisions de rOsultats formulOes par lesanalystes financiers. Les auteurs Otablissent l'existence de disparitOs importantes dansl'exactitude des provisions des analystes financiers et dOmontrent que la faible puis-sance des tests utilisOs dans les travaux prOcOdents, basOs sur de vastes Ochantillons,explique pourquoi les chercheurs n'ont pas observO de diffOrences dans l'exactitude desprovisions des analystes financiers, vu I'impossibilitO pour eux de controler adOquate-ment le caractere rOcent des provisions.Les conclusions des auteurs se fondent sur une comparaison de l'exactitude des prOvi-sions des analystes, ex post (k l'intOrieur de l'Ochantillon) et ex ante (en dehors derOchantillon). Leurs rOsultats sont basOs sur les provisions des diffOrents analystes rela-tives aux rOsultats annuels des sociOtOs dont l'exercice se termine en dOcembre, pour lesexercices terminOs entre 1984 et 1990 (dans le cas de l'Ochantillon ex post) et entre 1984et 1993 (pour l'Ochantillon ex ante). Ces donnOes ont OtO communiquOes aux auteurs parI/B/E/S International Inc.La question des disparitOs dans l'exactitude des provisions de rOsultats formulOes par lesanalystes est importante pour la recherche comptable axOe sur le marchO, qui fait appel
A Re-Examination of Financial Analysts' Differential Earnings .
a des approximations afin de determiner les resultats esperes des marches financiers. Sil'exactitude des pr6visions de certains analystes est superieure a celle des pr6visions decertains autres et si le marche financier en est informe, un poids plus important seraattribue aux analystes dont les previsions sont reputees etre plus exactes dans le calculdes resultats esp6r6s du marche. En pareil cas, le recours a une moyenne simple del'ensemble des previsions dont le caractere rdcent est le meme risque de mener k desconclusions erronees en ce qui a trait aux resultats esperes du march6.L'existence d'une relation positive entre le caractere recent de la prevision et l'exacti-tude de la prevision est clairement demontree dans la documentation (Crichfield et al,1978 ; O'Brien, 1988 ; Brown, 1991). Par cons6quent, le fait de ne pas pouvoircontrolerle caractere recent de la prevision peut reduire la puissance des tests, ce qui rend diffi-cile le rejet de l'hypothese nulle selon laquelle il n'y aurait aucune disparity dans l'ex-actitude des previsions, meme si ces disparites existaient veritablement. Les auteursexpliquent que les chercheurs ne sont pas parvenus, dans leurs travaux jusqu'a main-tenant, a 6tablir l'existence de disparites dans l'exactitude des previsions en raison dufait que le controle du caractfere recent de ces previsions 6tait inadequat (ou inexistant)dans leur analyse. Pour valider leurs observations, ils v6rifient si les disparites dansl'exactitude des previsions des analystes financiers persistent dans les p6riodesdecal6es. Ils relevent certains elements qui confirment la persistance des aptitudesprevisionnelles des analystes dont la « superiorite » est reconnue, mais non de celles desanalystes dont r « inferiorite » est reconnue.
En utilisant la methodologie et le procede de selection d'echantillon appliqu6s parO'Brien, les auteurs concluent, comme elle, qu'il n'existe pas de disparit6s dans l'ex-actitude des prdvisions des analystes. Ils notent cependant que le facteur non control^du caractere recent des previsions a une incidence marquee dans 1'analyse realis6e parO'Brien. Ils controlent done le facteur du caractere recent des previsions grace a deuxmethodes. Ils utilisent, en premier lieu, la methode des moindres carres gen6ralis6sestim6s, en vertu de laquelle les previsions successives des analystes d'un secteur d'ac-tivit6 sont mod61isees comme etant en correlation s6riale chronologique avec decalageunitaire. Ils ont recours, en second lieu, a un plan d'appariement par paires en vertuduquel ils associent et comparent les erreurs previsionnelles des analystes qui formulenta la meme date ou a peu pres des previsions pour une meme societe et une meme ann6e.En appliquant ces deux methodes, les auteurs constatent qu'il existe bel et bien des dis-parites dans l'exactitude des previsions des analystes, en particulier dans les echantil-ions dont les horizons previsionnels vont de 5 a 60 jours de bourse. Les auteurs d6mon-trent que ces disparites ne sont pas attribuables a des differences dans la frequenced'emission des previsions des analystes financiers. En somme, une fois contr616es lesvariables relatives a l'entreprise, a l'annee, au caractere recent des previsions et a lafrequence d'emission des provisions des differents analystes, r « effet » de l'analystepersiste.
Les auteurs se demandent ensuite s'il existe des disparites dans les tests ex ante(decales). Ils d6finissent les analystes superieurs, inferieurs et moyens dans les echan-tillons d'estimation et comparent leur performance a celle des analystes moyens dans lesechantillons decales. La sup6riorite (1'inferiorite) des analystes est definie a l'aide declassements percentiles etablis a partir de la distribution des erreurs previsionnellesabsolues des analystes pour chaque soci6te-annee de l'echantillon d'estimation. La clas-sification des analystes dans la categorie superieure (inferieure) est fondee sur des peri-odes d'estimation dont la duree varie de un a quatre ans, leur performance 6tant evalu6eau cours de l'annee suivante. Ces classifications sont op6rees separement, a l'aide d'ob-servations au niveau de la societe aux fins du classement percentile. Pour classer un ana-lyste dans la cat6gorie superieure dans un secteur d'activite donne, les auteurs s'assurentque ses previsions ont ete jugees superieures a l'egard d'au moins deux societ6s appar-tenant au secteur et n'ont 6te jugOes inferieures a l'egard d'aucune autre soci6t6 de ce
Contemporary Accounting Research
secteur. Les analystes sont ainsi classOs comme Otant supOrieurs (infOrieurs) tant h l'O-gard des sociOtOs qu'^ I'Ogard des secteurs d'activitO. Les tests effectuOs se fondent surle pourcentage absolu d'erreur prOvisionnelle relatif des analystes supOrieurs etinfOrieurs, mesurO par rapport a ceux qui sont classOs comme Otant « moyens » pour lameme pOriode d'estimation et le meme horizon.Les auteurs concluent que les analystes classOs comme Otant supOrieurs dans les Ochan-tillons d'estimation demeurent gOnOralement supOrieurs dans les pOriodes dOcalOes. Usconstatent, au contraire, que les analystes classOs comme Otant infOrieurs dans les Ochan-tillons d'estimation ne le demeurent pas, en gOnOral, dans les pOriodes dOcalOes.Les rOsultats de cette analyse laissent supposer que les provisions de rOsultats de certainsanalystes devraient avoir plus de poids que celles de certains autres dans le calcul derOsultats espOrOs composites. Cette suggestion s'appuie sur l'hypoth^se selon laquelleles marchOs financiers reconnaissent les analystes qui sont supOrieurs ex ante et utilisentcette information lorsqu'ils dOterminent le cours des actions. L'Otude foumit un cadre derOfOrence ex ante permettant de repOrer les analystes qui semblent supOrieurs. DansrOtablissement de provisions pondOrOes, l'utilisation d'une pOriode d'estimation d'un anserait appropriOe, Otant donnO que les rOsultats relatifs k la persistance sont les plusprobants dans ce cas.
This research re-examines whether there are differences in the forecast accura-cy of financial analysts through a comparison of their annual earnings per shareforecasts. The comparison of analyst forecast accuracy is made on both an expost (within sample) and an ex ante (out of sample) basis. Contrary to theresults of prior research and consistent with the belief in the popular press, wedocument that differences do exist in financial analysts' ex post forecast accu-racy. We show that the previous studies failed to find differences due to inade-quate (or no) control for forecast recency in their analysis. To validate furtherour findings, we examine whether the differences in the forecast accuracy offinancial analysts persist in holdout periods. We find evidence of persistence inforecasting ability for analysts identified as "superior," but not for those iden-tified as "inferior."
The issue of differential earnings forecasting accuracy amongst analysts isan important one for market-based accounting research that requires a proxyfor the market's earnings expectation. Consistent with the results in earlierstudies, showing that differential forecast accuracy amongst analysts is absent,most studies using analyst forecasts as proxies for the market's earnings expec-tation used averages of all available forecasts. If some analysts are more accu-rate than others and if the capital market is aware of this, the market's earningsexpectation should assign higher weights to forecasts of those analysts who aredeemed superior forecasters.
The rest of the paper is organized as follows. The next section presentsdetails of the ex post analysis, including data description and sample selection,literature review, replication of relevant research, discussion of the extant liter-ature's shortcomings, and results of our modified analyses. The following sec-tion provides details of the ex ante analysis, including the data, procedures foridentifying ex ante superior and inferior analysts, and test results. Conclusionsand directions for future research are presented in the last section.
A R e - E x a m i n a t i o n o f F i n a n c i a l A n a l y s t s ' D i f f e ren t i a l E a r n i n g s . . . . 5
Ex post analysisMotivationThe most comprehensive examination of ex post differential forecast accuracyof financial analysts is by O'Brien (1990), who examined earnings forecastsmade by all financial analysts in the Institutional Brokers Estimation System(I/B/E/S) database from 1975-82 for the nine largest industries. Contrary to thenotion in the popular press that differences in the earnings forecast accuracy offinancial analysts do exist (Institutional Investor, The Wall Street Journal),O'Brien concluded significant differences do not exist in the ability of finan-cial analysts to forecast firms' annual earnings numbers over multiple yearsafter controlling for firm and year effects, l Other examinations of this issue(Richards 1976; Brown and Rozeff 1980; O'Brien 1987; Coggin and Hunter1989; Butler and Lang 1991; Stickel 1992) also suggest the absence of analystswho can provide relatively more accurate forecasts over multiple years.2
It has been well documented in the literature that forecast recency is posi-tively related to forecast accuracy (Crichfield, Dyckman and Lakonishok 1978;O'Brien 1988; Brown 1991). Thus, failure to control for forecast recency mayreduce the power of tests, making it difficult to reject the null hypothesis of nodifferences in forecast accuracy even if they do exist. We show that, by not ade-quately controlling for forecast recency, prior research erroneously concludedthat differential earnings forecast accuracy amongst analysts was absent. 3
We re-examine the issue of differential forecast ability by defining an expost superior (inferior) analyst as one with smaller (larger) forecast error, con-ditional on the firm, year, and forecast recency. Using the entire sample of ana-lysts from the I/B/E/S detail database, we first replicate the analysis of O'Brien(1990). We find that significant differences do not exist in analyst forecastaccuracy and that forecast recency is significantly positively correlated withanalyst forecast accuracy purged of firm, year, and analyst effects. In our sub-sequent analysis, we control for forecast recency using two approaches: an esti-mated generalized least squares (EGLS) estimation procedure, and a matched-pair design. Our findings indicate that significant differences do exist in ana-lysts' ex post forecast accuracy once forecast recency is controlled for usingeither procedure.
Data and samplesFor the ex post analysis, we follow O'Brien's (1990) sample selection criterionto avoid "turning too many dials of the research machine at a time" (Beaver1989).4 O'Brien reported results on annual earnings forecasts made during thetime period, July 1975 to September 1982. These data are no longer available.I/B/E/S International Inc. provided us with individual analysts' annual earningsforecasts made between January 1984 and December 1990. Thus, O'Brien'ssample and ours are for two nonoverlapping, nearly consecutive, periods ofapproximately equal length.
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Each data point consists of an individual analyst's dated annual earningsper share (EPS) forecast for a given firm and year. We use the COMPUSTAT annu-al industrial file as our source of actual reported EPS (primary earnings pershare before extraordinary items; Data Item 58) and the COMPUSTAT quarterlyindustrial file as our source of annual earnings announcement dates. Forecastsof fully diluted EPS were converted to primary EPS using the ratio of primaryto fully diluted EPS (i.e.. Data Item 58 divided by Data Item 57) as reported inCOMPUSTAT. The share basis of individual analysts' earnings forecasts wasadjusted for size whenever stock splits or stock dividends were declared. Weuse the Center for Research in Security Prices (CRSP) monthly master file asour source of stock distribution announcement dates and the size of the distri-bution, and COMPUSTAT to identify each firm's industry affiliation using the firsttwo digits of the standard industry classification (SIC) code,5
The initial sample consists of all observations for which: (1) an analyst, anannual earnings forecast, and a forecast date are available from I/B/E/SInternational Inc.; (2) EPS data and the earnings announcement date are avail-able on COMPUSTAT; and (3) stock split and stock dividend information areavailable on CRSP, We report results for three samples with minimum forecasthorizons of five, 60, and 120 trading days.6 Consistent with O'Brien (1990), werestrict our analysis to firms with December fiscal year ends, and select onlyone forecast by an analyst for a firm in a year, conditional on the minimumforecast horizon in question. The selected forecast of an analyst in the sampleis the most recent one beyond the minimum forecast horizon. To ensure properestimation of model parameters, our sample, like O'Brien's, consists of the fol-lowing: (1) firms with one or more forecasts in each of the seven years,1984-90; and (2) analysts who have at least 10 forecasts in an industry in atleast three separate years.
The samples examined in this study pertain to the 14 largest industries (thenine with an asterisk were examined by O'Brien [1990]): SIC 20 (Food andKindred Products), SIC 26* (Paper and Allied Products), SIC 27 (Printing andPublishing), SIC 28* (Chemicals and Allied Products), SIC 29* (PetroleumRefining and Related Industries), SIC 33* (Primary Metal Industries), SIC 35*(Machinery, except Electrical), SIC 36* (Electrical and Electronic Machinery),SIC 37 (Transportation Equipment), SIC 38 (Measuring Equipment), SIC 48(Communications), SIC 49* (Electric, Gas, and Sanitary Services), SIC 60*(Banking), and SIC 63* (Insurance). This 14-industry subsample is henceforthreferred to as the final sample.
Table 1 (ALL) presents the total number of forecasts, analysts, firms, andindustries for the initial and final samples. The initial sample for the minimumforecast horizon of five trading days is 56,464 forecasts, representing 3,574analysts, 422 firms, and 46 industries. This forecast horizon's//naZ sample con-sists of 27,189 forecasts, representing 782 analysts, 297 firms, and 14 indus-tries. Consistent with the sample selection criteria, there are fewer forecasts,analysts, and firms with a minimum forecast horizon of 60 (120) trading daysthan there are with a minimum forecast horizon of five (60) trading days for
A Re-Examination of Financial Analysts' Differential Earnings . .
both the initial and final samples. The percentage reduction in the number ofanalysts is much more drastic than that in both the number of forecasts and thenumber of firms.
TABLE 1Effects of imposing data sufficiency requirements on the samples
sict
20
26*
27
28*
29*
33*
35*
36*
37
38
48
49*
60*
63*
ALL
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirms
ForecastsAnalystsFirmsIndustries
Sample minimum forecast horizon (in5
Number of forecasts.
Mlialisample
1375197
8
2211307
17
2286257
15
6149654
36
3717271
15
2231260
15
3215722
25
1989483
22
3489438
23
2583633
21
2769293
13
950153972
1288228
10
313119721
56464357442246
Finalssample
86545
8
13204415
15344915
403313836
26027415
14144914
11896523
7284315
21438822
9927018
17115413
605410772
6043510
20005221
27189782297
14
Percentage
oforiginalin final
62.922.8
100.0
59.714.388.2
67.119.1
100.0
65.621.1
100.0
70.027.3
100.0
63.418.893.3
37.09.0
92.0
36.68.9
68.2
61.420.196.7
38.411.185.7
61.818.4
100.0
63.719.9
100.0
46.9 •15.4
100.0
63.926.4
100.0
48.221.970.430.4
60Number of forecasts,Analysts and Firms
Initialsample
1229184
8
1857291
17
1982245
15
5286628
35
2877254
15
1726243
15
2637677
25
1682444
22
2922403
22
2234581
19
2398270
13
834551171
956207
10
290119321
48087343141446
Finalsample
73940
8
10553715
13114615
334312835
19436815
10224114
9045922
5583615
17117721
7575517
14715113
531810271
3852710
18635221
22380708292
14
trading days)
Percentage
oforiginalin final
60.120.7
100.0
56.812.788.2
66.118.8
100.0
63.220.4
100.0
67.526.8
100.0
59.216.993.3
34.38.7
88.0
33.28.1
68.2
58.619.195.5
33.99.5
89.5
61.318.9
100.0
63.720.0
100.0
40.313.0
100.0
64.226.9
100.0
46.520.670.530.4
120Number of forecasts.Analysts and Firms
IniiialSample
852157
7
943228
15
1194204
15
3211526
32
1441202
14
834183
14
1392500
20
835280
14
1691328
21
1390472
16
148018512
5832449
67
422143
7
174617319
284262936
35946
Finalsample
42828
7
4092213
6532915
16407731
8254214
4002314
1821419
1371013
ni4521
2461913
8924112
35778267
9377
9703719
11229431265
14
Percentageof
originalin final
50.217.8
100.0
'\2i.A9.6
86.7
54.714.2
100.0
51.114.696.9
57.320.8
100.0
48.012.6
100.0
13.12.8
95.0
16.43.6
92.9
45.913.7
100.0
17.74.0
81.3
60.322.2
100.0
61.318.3
100.0
22.04.9
100.0
55.621.4
100.0
39.514.773.830.4
Contemporary Accounting Research
Notes:t Industries are defined by the two digit standard industry classification (SIC) codes from the 1990
COMPUSTAT database. The nine industries marked with an asterisk (*) were examined by O'Brien(1990).
t The initial sample contains the most recent forecast from each analyst in the database made at leastX trading days prior to the announcement of annual earnings, for firms with fiscal year ending inDecember, with at least one forecast each of the seven years 1984-90, and with annual EPS avail-able on the COMPUSTAT. X refers to the minimum forecast horizon, and takes a value of five, 60, or120 trading days.
§ The final sample includes only those analysts with at least 10 forecasts in the industry, and withforecasts in at least three of the years 1984-90.
Table 1 also shows, by industry, information on the number of forecasts,analysts, and firms for each forecast horizon. For the minimum forecast hori-zon of five trading days, the number of forecasts used in the final sample rangesfrom a low of 604 (SIC 60) to a high of 6,054 (SIC 49), the number of analystsranges from a low of 35 (SIC 60) to a high of 138 (SIC 28), and the number offirms ranges from a low of eight (SIC 20) to a high of 72 (SIC 49). As expect-ed, the sample sizes drop as the minimum forecast horizon increases. For thefinal sample with minimum forecast horizon of 60 days, the smallest number offorecasts, analysts, and firms are 385 (SIC 60), 27 (SIC 60), and eight (SIC 20),respectively; the largest number of forecasts, analysts, and firms are 5,318 (SIC49), 128 (SIC 28), and 71 (SIC 49), respectively. For the final sample with min-imum forecast horizon of 120 days, the smallest number of forecasts, analysts,and firms are 93 (SIC 60), seven (SIC 60), and seven (SICs 20 and 60), respec-tively; the largest number of forecasts, analysts, and firms are 3,577, 82, and67, respectively, all for SIC 49.
TABLE 2Descriptive statistics by industry on analyst annual absolute forecast error for the threesamples with minimum forecast horizon of five, 60, and 120 trading days
IJt
SIC
20
26
= l^jt-
Year
8485868788899084858687888990
Min
0.00.00.00.00.00.00.00.00.00.00.00.00.00.0
Mai
1.80.50.90.62.12.81.03.11.82.21.92.11.51.8
Sample minimum forecast5
Mean
0.30.10.10.10.10.40.10.70.20.30.30.30.40.3
Median StdDev
0.10.00.10.00.10.00.00.30.1O.I0.20.10.20.1
0.50.10.20.10.20.80.31.00.20.30.30.40.40.5
Min
0.00.00.00.00.00.00.00.00.00.00.00.00.00.0
Mai
1.50.51.80.42.12.91.03.11.22.01.72.12.22.0
horizon60
Mean
0.30.10.20.10.10.40.20.90.20.30.40.40.40.4
(in trading
tledian StdDev
0.10.00.10.00.10.10.10.40.20.20.30.20.30.2
0.50.10.30.10.20.80.31.00.20.30.40.40.40.5
Min
0.00.00.00.00.00.00.00.00.00.00.00.00.00.0
days)
Mai
1.51.91.20.42.12.81.03.51.42.22.42.11.32.1
120Mean
0.40.20.30.10.10.30.30.90.40.50.50.50.50.6
(1)
Median StdDev
0.0.0.
0.0.0.0..0.0.:
0.60.40.4
) 0.10.20.50.4
) 1.0! 0.3i 0.4
0.4 0.40..! 0.50.4 0.40.:i 0.7
A Re-Examination of Financial Analysts' Differential E a r n i n g s . . . .
TABLE 2 (conf)
Sample minimum forecast horizon (in trading days)*
SIC
27
28
29
33
35
36
37
Year
84
8586
8788
89
9084
85
8687
88
8990
8485
8687
8889
9084
8586
87
88
89
9084
8586
8788
899084
8586
8788
89
9084
85
8687
88
8990
MiB
0.0
0.00.0
0.00.0
0.0
0.0
0.00.0
0.00.0
0.0
0.00.0
0.00.0
0.00.0
0.00.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.00.0
0.00.00.0
0.0
0.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.00.0
Max
2.4
1.34.0
4.58.4
3.24.4
1.715.4
10.4
11.3
6.0
5.92.9
5.06.0
8.321.6
9.2
5.2
4.513.1
17.1
21.2
4.97.4
9.4
7.3
6.5
13.712.5
5.812.8
16.2
10.01.2
4.05.1
1.84.6
1.31.2
7.8
3.3
12.5
9.38.5
7.222.1
5Mean
0.2
0.11.0
0.60.9
0.50.4
0.11.2
0.4
0.7
0.20.4
0.3
0.81.4
1.22.3
1.31.5
0.52.3
2.7
1.3
0.7
1.0
1.0
1.3
0.91.4
1.3
0.30.6
1.1I.O0.2
0.4
0.5
0.30.3
0.10.2
0.9
0.61.5
1.00.7
0.7
1.9
Median
0.1
0.10.4
0.1
0.1
0.1
0.1
0.10.1
0.1
0.1
0.1
0.10.1
0.30.5
0.50.2
0.51.2
0.31.1
1.2
0.5
0.20.4
0.4
0.6
0.3
0.10.4
0.10.2
0.1
0.30.1
0.10.1
0.10.1
0.0
0.1
0.3
0.3
0.3
0.3
0.30.20.3
StdDev
0.5
0.21.31.1
2.2
0.8
1.00.2
2.5
1.4
2.2
0.51.1
0.5
1.01.8
1.95.9
2.01.5
0.62.8
4.3
2.8
1.1
1.3
2.0
1.91.2
3.02.3
0.61.4
2.72.0
0.3
1.00.9
0.30.7
0.2
0.3
1.60.7
2.8
2.11.3
1.04.0
Min
0.0
0.00.00.0
0.0
0.0
0.0
0.00.0
0.0
0.0
0.0
0.00.0
0.00.0
0.00.0
0.00.0
0.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.00.0
0.00.0
0.0
0.00.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.0
0.0
Mai
2.21.4
4.04.88.4
3.3
4.0
2.516.4
10.0
11.35.7
6.2
2.9
5.07.3
9.32199.4
5.2
4.013.1
17.1
27.1
5.36.4
9.4
7.5
6.515.2
12.5
5.812.8
16.215.5
1.5
5.85.1
1.54.6
1.3
1.9
9.3
4.0
11.5
9.68.5
6.022.1
60Mean
0.20.21.1
0.6
0.8
0.60.4
0.2
1.1
0.4
0.7
0.3
0.50.3
0.91.41.4
2.5
1.61.7
0 6
2.62.8
1.1
0.8
1.1
1.2
1.31.2
1.91.4
0.50.81.4
1.00.3
0.70.7
0.30.4
0.2
0.3
1.1
0.7
1.7
1.10.7
1.02.1
Median Std Dev
0.
0.
0.4
0.30.4 1.2
0.
0.
0.2
2.1
0.2 0.90.
0.0.
0.
0.
0.
0.0.
0.9
0.32.6
1.3
1.9
0.5
1.20.4
0.5 1.10.6 1.7
0.6 2.00.4 6.1
0.8 2.11.4 1.4
0.3 0.81.
1.5 2.85 4.2
0.6 2.7
0.3 1.1
0.5 1.4
0.4 2.1
0.4 1.8
0.5 1.6
0.3 3.50.4 2.4
0.2 0.80.3 1.7
0.2 3.2
0.3 2.10.2 0.4
0.2 1.3
0.2 0.90.2 0.30.
0.
0.
1 0.8
1 0.3
1 0.5
0.3 1.6
0.5 0.70.5 2.8
0.3 2.2
0.3 1.3
0.5 1.30.3 4.4
Min
0.00.0
0.00.0
0.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.00.0
0.00.0
0.00.0
0.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00.0
0.00.0
0.00.0
0.00.0
0.00.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.00.0
Mai
1.91.3
4.04.88.4
3.4
4.1
2.57.4
10.9
10.7
5.76.2
2.8
4.57.3
8.321.99.2
5.3
4.013.6
19.127.1
5.66.4
8.7
8.2
6.8
15.213.2
3.5
12.816.6
5.71.2
12.95.71.1
2.5
1.5
1.3
9.3
4.3
12.0
9.1
8.5
10.021.8
120Mean
0.10.21.2
0.7
1.0
0.60.4
0.2
0.9
0.5
0.8
0.3
0.60.3
0.91.41.4
2.5
2.0
1.9
0.93.23.2
1.2
1.0
1.4
1.3
1.2
2.52.4
2.2
0.6
0.91.7
1.00.2
2.30.8
0.30.2
0.3
0.2
1.2
0.6
2.0
0.8
0.8
0.93.0
Median Std Dev
0.10.1
0.80.1
0.1
0.20.1
0.2
0.1
0.1
0.1
0.1
0.10.1
0.50.7
0.80.4
1.11,6
0.61.7
1.7
0.6
0.4
0.8
0.5
0.5
2.0
0.5
0.60.3
0.30.3
0.50.10.4
0.20.2
0.1
0.1
0.1
0.5
0.3
0.7
0.30.4
0.20.4
0.20.3
1.21.2
2.3
0.9
0.9
0.31.9
1.2
1.9
0.6
1.30.5
1.11.7
1.96.0
2.51.5
1.13.4
4.7
3.1
1.4
1.5
2.0
1.9
2.5
4.3
3.50.72.1
3.51.4
0.4
4.71.40.4
0.50.4
0.31.6
0.7
3.3
1.61.4
1.76.0
10 Contemporary Accounting Research
TABLE 2 (conf)
Sample minimum forecast horizon (in trading days)*~ 5 ~ 60 120
Min Mai Mean Median Sid Dev Min Max Mean Median StdDev
0.0 0.5 0.2 0.1 0.2 0.0 1.1 0.2 0.1 0.3
0.0 3.1 0.3 0.1 0.6 0.0 2.2 0.3 0.1 0.6
0.0 5.1 0.4 0.1 1.0 0.0 1.8 0.2 0.1 0.4
0.0 2.6 0.2 0.1 0.4 0.0 1.1 0.2 0.1 0.2
0.0 17.0 1.2 0.1 3.6 0.0 17.0 1.2 0.1 3.5
0.0 7.2 0.9 O.I 2.0 0.0 7.1 1.2 0.2 2.3
0.0 2.8 0.5 0.1 0.9 0.0 2.8 0.7 0.2 1.0
0.0 2.9 0.2 0.2 0.3 0.0 2.9 0.3 0.2 0.5
0.0 6.8 1.0 0.2 2.0 0.0 6.7 0.8 0.2 1.8
0.0 3.0 0.5 0.2 0.6 0.0 3.1 0.6 0.2 0.7
0.0 3.3 0.3 0.1 0.5 0.0 3.1 0.4 0.2 0.5
0.0 4.1 0.4 0.1 1.0 0.0 4.1 0.5 0.1 1.0
0.0 2.4 0.4 0.1 0.6 0.0 2.9 0.5 0.1 0.7
0.0 4.2 0.5 0.2 0.8 0.0 4.4 0.6 0.2 0.9
0.0 10.8 0.3 0.2 1.0 0.0 10.8 0.3 0.2 0.9
0.0 7.4 0.5 0.2 1.0 0.0 7.4 0.4 0.2 0.8
0.0 11.0 0.7 0.2 1.8 0.0 11.0 0.6 0.2 1.7
0.0 5.5 0.5 0.2 0.8 0.0 5.5 0.5 0.3 0.8
0.0 5.6 0.6 0.2 1.1 0.0 5.6 0.6 0.2 1.1
0.0 5.6 0.5 0.2 0.9 0.0 5.7 0.5 0.2 0.8
0.0 10.9 0.6 0.2 1.2 0.0 11.0 0.7 0.2 1.2
0.0 2.3 0.5 0.3 0.6 O.I 0.4 0.3 0.3 0.2
0.0 3.8 0.9 0.4 0.9 0.3 3.4 1.4 1.0 1.3
0.0 4.2 0.7 0.6 0.7 0.0 1.9 0.6 0.5 0.6
0.0 21.2 2.1 0.9 3.8 0.1 32.8 6.1 0.9 10.0
0.0 8.7 0.9 0.2 1.9 O.I 8.7 1.7 0.6 2.5
0.0 20.3 2.8 1.0 5.6 0.1 20.6 6.0 2.6 7.8
0.0 8.6 2.0 0.9 2.7 O.I 8.7 2.3 0.9 3.3
0.0 9.8 1.0 0.5 1.6 0.0 9.8 0.8 0.4 1.3
0.0 16.8 2.1 0.4 3.9 0.0 16.0 2.0 0.4 3.6
0.0 11.4 0.5 0.3 1.2 0.0 11.9 0.7 0.4 1.5
0.0 4.0 0.5 0.3 0.5 0.0 4.0 0.5 0.3 0.6
0.0 4.1 0.6 0.4 0.6 0.0 4.1 0.6 0.4 0.7
0.0 8.5 1.1 0.8 1.1 0.0 2.2 0.8 0.6 0.6
0.0 7.5 1.2 0.7 1.5 0.0 7.5 1.2 0.8 1.6
Note.s:* The columns Min and Mar provide the minimum and maximum values, and the column Std Dev provides the stan.
dard deviation of analyst absolute forecast error corresponding to the year and industry of the row. Industries aredefined by the two digit Standard Industry Classification (SIC) codes from the 1990 COMPUSTAT database.
Table 2 provides for each of the 14 selected industries descriptive statisticson absolute forecast errors for the three minimum forecast horizons for eachyear. There are a total of 98 (seven years and 14 industries) descriptive statis-tics for each minimum forecast horizon. Not surprisingly, in the vast majority
SIC38
48
49
60
63
Year84
85
86
87
88
W89
90
84
85
86
87
88
89
90
84
85
86
87
88
899084
85
86
87
88
89
90
84
85
86
87
88
89
90
Min0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
0.0
Max1.5
3.0
5.1
2.6
16.7
7.2
2.8
9.6
6.9
3.0
3.3
3.8
2.1
4.2
10.8
7.4
11.6
5.6
5.7
6.5
10.9
3.4
4.1
4.2
21.2
8.7
6.2
6.3
6.3
16.1
10.9
3.5
4.6
8.5
6.7
Mean0.20.30.4
0.2
0.7
0.8
0.5
0.2
1.0
0.4
0.2
0.5
0.3
0.4
0.3
0.4
0.7
0.4
0.6
0.5
0.6
0.4
0.5
0.6
1.3
0.7
0.6
1.1
0.7
2.3
0.4
0.5
0.5
1.1
1.1
MedianO.I
O.I
O.I
O.I
0.1
0.1
O.I
0.1
0.2
0.2
O.I
0.1
O.I
0.2
O.I
O.I
O.I
0.2
0.2
0.2
0.2
0.3
0.3
0.4
0.3
0.2
0.2
0.7
0.5
0.5
0.1
0.3
0.4
0.8
0.6
Sid Dev0.3
0.5
0.9
0.3
2.3
1.8
0.8
0.7
2.0
0.5
0.4
1.1
0.6
0.8
1.0
1.0
1.9
0.8
1.1
0.9
1.1
0.6
0.8
0.6
3.2
1.6
1.0
1.2
0.8
4.1
1.1
0.5
0.5
I.I
1.4
A Re-Examination of Financial Analysts' Differential Earnings , , , , 11
of cases, the average absolute forecast error for a sample with minimum fore-cast horizon of five trading days is less than or equal to the corresponding num-bers for the sample with a minimum forecast horizon of 120 trading days. Morespecifically, the mean (median) absolute forecast error for the shortest horizonis less than that of the longer forecast horizon 85 (95) of 98 times. This findingoccurs because the average forecast age increases as the minimum forecasthorizon for the sample lengthens, and thus, older forecasts, which generallyhave larger forecast errors, are included.
Methodology and findingsO'Brien's (1990) initial model examines differential forecast accuracy amongstfinancial analysts by treating analysts, firms, and years as fixed effects. Thedependent variable, the individual analyst's absolute annual earnings forecasterror, |ejjj|, is defined as the following:
where the subscripts i,j, and t denote analyst, firm, and year, respectively; R^^is the j firm's reported earnings per share in year f; and F^u is the forecast ofearnings per share by analyst i for firm j and year t. The exact model specifi-cation is as follows:
kijti = -i + 8j + 7t + THijt (2)
where |Xj, 8:, and 7j represent the analyst, firm, and year "fixed effects,"respectively, and TIJJ{ is the random-noise term, assumed to be independentacross all observations.?
Panels A to C of Table 3 present the results of estimating equation (2) forminimum forecast horizons of five, 60, and 120 trading days, respectively.Consistent with O'Brien (1990), we do not find ex post differential analystforecast ability for the vast majority of industries. More specifically, for thesample with the shortest (five-trading-day) minimum forecast horizon, F sta-tistics that test for analyst effect are significant only in two of the 14 industries(i.e., SIC 49 and SIC 60). For the sample with the 60-trading-day minimumforecast horizon, the analyst effect is significant for only one industry (SIC 49),Finally, for the sample with the 120-trading-day minimum forecast horizon, theanalyst effect is significant for two industries (SIC 38 and SIC 49). The F sta-tistics that test for firm and year effects are generally significant at conven-tional levels. More specifically, they are significant for all 42 (14 industriestimes three horizons) tests of firm effects, and for 41 of 42 tests of year effects(the exception is SIC 35 for the 120-trading day minimum forecast horizon). Insum, our findings are very similar to O'Brien's when we adopt her model to alater time period of analysts' forecasts (1984—90 versus O'Brien's 1975-82),Thus, O'Brien's results are not sample specific; they generalize to a later timeperiod.
12 Contemporary Accounting Research
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14 Contemporary Accounting Research
Notes:* The number of analysts, firms, years, and forecasts in each industry sample is denoted by «[, m, /i(,
and N, respectively. The numerator degrees of freedom for F statistics corresponding to analysts,firms, years, and model are (nj-l), (ij-l), ( i f l ) , and («; + nj + /ij - 3), respectively. The denomi-nator degrees of freedom equals {N - n•^-n:- n^ + 2).
t Sample size, unadjusted /?2, and the full model F statistic are reported.
Sample selection criterion based on controlling for minimum forecast hori-zon is important because researchers require a measure of earnings expecta-tions at a particular point in time, and only a certain set of forecast data areavailable at that time. However, controlling for minimum forecast horizonwithout simultaneously controlling for forecast recency is inadequate becauseolder forecasts are generally less accurate than more recent ones (Crichfield etal. 1978; Brown, Griffin, Hagerman, and Zmijewski 1987; O'Brien 1988;Brown 1991). Thus, unless all forecasts have the same degree of recency foreach firm and year, the recency effect could contaminate the analyst effect, lead-ing to a failure to reject the false null hypothesis that no analyst effect exists.
Similar to O'Brien's Table 3, our Table 4 reports descriptive statistics andselective percentiles on the distribution of forecast ages, by industry, for ourthree samples with minimum forecast horizons of five, 60, and 120 tradingdays.8 For the sample with a minimum forecast horizon of five trading days,the median forecast age ranges from a low of 45 (SICs 29 and 60) to a high of62 (SIC 20). The mean and median forecast ages increase as the minimum fore-cast horizon increases monotonically for each of the 14 industries. For exam-ple, the median forecast age for SIC 60 increases from 45 to 103 to 178 as theminimum forecast horizon increases from five to 60 to 120 trading days.
TABLE 4Distribution of forecast age for samples with minimum forecast horizon of five, 60, and 120trading days
Panel A:
SIC2026272829333536373848496063
Samples with
N865
1,3201,5344,0332,6021,4141,189
7282,143
9921,7116,054
6042,000
minimum
10221216151115141620191620
930
forecast
253825302924302931333633352142
horizon of fivePercentiles
506249555445495054535656594558
75105718289666970847896
1021166687
trading days
90168114148149120118121132133144159181131151
Mean82.155.768.169.456.257.861.767.165.473.874.284.158.575.7
Std Dev65.741.255.557.650.744.352.354.448.559.460.569.360.957.2
A Re-Examination of Financial Analysts ' Differential Eamings . . . . 15
Panel B : Samples with minimum forecast horizon of 60 trading daysPercentiles
SIC2026272829333536373848496063
Panel C:
SIC2026272829333536373848496063
N739
1,0551,3113,3431,9431,022904558
1,711757
1,4715,318385
1,863
Samples
N428409653
1,640825400182137777246892
3,57793970
106465646567646365646466696764
257471737579737274747677897373
with minimum forecast
10124124124125123123125124123125126128132124
25132132137138136132134132133134139144149135
5010592991061059710397102111115120103102
horizon
75155125146146134127135126134144161176148143
90205173202197189173205186184199213224205204
of 120 trading days
Percentiles
50165152169168164154175165160165174178178171
75204194207198203187209207194202212219238207
90247223243237240234241251234239240248312237
Mean123.7105.2117.6119.5117.0109.0116.8111.8113.0121.1127.6138.3121.7118.1
Mean
178.9165.8178.8176.2176.8166.8180.1180.4170.6177.2182.7188.4204.9178.2
Std Dev64.745.659.257.053.147.057.754.350.359.260.967.166.560.0
Std Dev60.242.852.750.553.345.154.862.247.158.557.158.478.653.7
O'Brien (1990) attempted to control for the recency effect by modifyingequation (2) to incorporate dummy variables for four "forecast age categories"and by showing that the results from estimating the modified equation provid-ed no evidence of differential forecast ability.9 We replicated the modifiedequation for all 14 industries and the three minimum forecast horizons.Consistent with O'Brien's finding, our estimation results, omitted for simplic-ity, are very similar to those from estimating equation (2) and suggest a lack ofdifferential forecasting ability. 10
A potential explanation for not observing any analyst effect using dummycategories to control for forecast recency is that this approach controls forrecency across firms and years, but not within firm-years. Because recency cor-rection requires separating forecasts of different ages within a firm-year, the
16 Contemporary Accounting Research
dummy variable approach may not provide the intended control in instanceswhere the forecasts (in a given firm-year) do not span all four dummy cate-gories, u Thus, if differential forecasting accuracy were actually present in thesample, the dummy variable approach may not detect it.
Recency effect and the implications of using ordinary least squaresAnalysts make their annual earnings forecasts on different calendar dates andupdate them when they receive additional information such as other analysts'forecasts (Stickel 1990), quarterly reports (Abdel-khalik and Espejo 1978),management forecasts (Jennings 1987), and stock price changes (Brown,Foster, and Noreen 1985). Thus, a more recent forecast (e.g., one issued in thefourth quarter) will be conditional on additional earnings-relevant informationand consequently more accurate than the one issued earlier (e.g., in the secondquarter). The richer information set associated with the more recent forecastsuggests that, ceteris paribus, forecasts made closer to the upcoming earningsannouncement dates (recent forecasts) will be more accurate than forecastsmade farther from the earnings announcement date. Failure to control forrecency leads to recency-induced dependency in the forecasts. 12
There is considerable evidence of recency-induced correlation in analystforecast errors. Lys and Sohn (1990), using the Zacks Investment Researchdatabase, document significant positive serial correlation in firms' earningsforecast errors and forecast revisions by individual analysts. Mendenhall(1991), using Value Line forecasts, finds that consecutive errors in analysts'earnings forecasts for a given firm are positively correlated. Ali, Klein, andRosenfeld (1992), using I/B/E/S data, show positive serial correlation in theforecast errors of analysts' consensus forecasts.
To the extent that earnings forecast accuracy is a function of forecastrecency, the residuals from estimating equation (2) partly consist of the unex-plained component of forecast errors due to forecast recency. Utilizing ordinaryleast squares to estimate the regression model (equation [2]) when serial corre-lation exists in the error terms, results in inconsistent, and possibly inefficient,coefficient estimates (Greene 1993, 360). 13 To examine the potential effect ofomitting forecast recency, we perform a regression of ordinary least squaresresiduals of equation (2) on their recently lagged values within a firm-year withdata pooled over all firm-years, as follows:
where the subscript r refers to forecast recency. Equation (3) relates the errorassociated with a forecast of recency, r, to the error associated with a forecastof recency, r-l, for the same firm-year. The larger the r, the more recent is theforecast.
Table 5 presents estimates of p for each of the three samples and the 14industries, with data pooled over all firm-years. Because the number of fore-casts was different for each firm-year, pooling across firm years enables esti-
A R e - E x a m i n a t i o n o f F i n a n c i a l A n a l y s t s ' D i f f e r e n t i a l E a m i n g s . . . . 17
mation (and subsequently a correction) for all firm-years. The estimated coef-ficient varies from a low of 0.29 (SIC 38) to a high of 0.98 (SIC 27) for thefive-trading-day minimum forecast horizon, from 0.72 (SIC 26) to 0.97 (SIC27) for the 60-trading-day minimum forecast horizon, and from 0.57 (SIC 36)to 0.97 (SIC 27) for the 120-trading-day minimum forecast horizon. 14 Thus, asignificant positive correlation exists in the residuals for all 42 tests (i.e., threehorizons times 14 industries).
TABLE 5Serial correlation coefficients estimated from the residuals of equation (2) by pooling dataover firm-years, for the samples with minimum forecast horizon of five, 60, and 120 trad-ing days, given by industry*
SIC
2026272829333536373848496063
Sample minimum
5
0.890.740.980.970.960.760.680.770.920.290.890.930.590.94
forecast horizon (in trading days)
60
0.870.720.970.960.960.750.760.860.890.890.930.930.810.93
120
0.760.610.970.920.930.590.620.570.890.800.880.920.840.91
Notes:* Industries are defined by the Standard Industry Classification (SIC) codes from the 1990
COMPUSTAT database.(All correlations are significant at 0.01 level of confidence or better)
Forecast recency controlA proper control for forecast recency needs to capture the dependency in eachfirm-year's errors of two consecutive forecasts. When controlling for forecastrecency, two characteristics of our data need to be considered: (1) the data areunbalanced, so that there are a different number of analysts and firms eachyear; and (2) the observations are unevenly spaced with respect to forecastrecency.
We address this problem using two approaches. The first, estimated gener-alized least squares, models the nature of dependency in the residuals and uses
18 Contemporary Accounting Research
the entire sample of forecasts in the estimation. The second controls for fore-cast recency by constructing a forecast accuracy measure that is recency con-trolled. This control requires a recency match for each forecast in the sample,and so, reduces the sample size. Each approach is discussed in turn.
Incorporating recency using an estimated generalized least squares proce-dure. The use of the estimated generalized least squares procedure to controlfor forecast recency requires specifying a functional form for the model, whichcaptures dependency in the residuals within a firm-year. Our sample consists ofan uneven number of forecasts in a given firm-year, and this number rangesfrom a minimum of one to a maximum of 43 (41, 27) for a sample with a min-imum forecast horizon of five (60, 120) trading days. For instances with onlyone forecast in a firm-year, there is no recency-induced dependency. However,when the number of forecasts in a given firm-year exceeds one, dependencyexists in the data, and a recency (age) correction is needed. In the absence ofwell-defined relationships, such as seasonalities in quarterly data, traditionalapproaches to dealing with time-induced dependency involve attaining themaximum possible lag given the data constraints (Ryan 1995).
In our sample, the choice of lag determines the proportion of the firm-yearsfor which the recency correction will be applied. If we choose a lag-one depen-dency in the residuals, the correction will be applied to all firm-years withrecency-induced dependence (i.e., those with at least two forecasts in a firm-year). If we choose, for example, lag-five dependency in the residuals, the cor-rection will be applied to only those firm-years with six or more forecasts. Thislatter section will leave a sizeable proportion of the sample without a recencycorrection. Thus, to maximize the extent of recency correction, we choose lag-one dependency for the residuals and modify equation (2) as follows:
with
Characterizing the variance-covariance matrix in this fashion ensures captureof recency-induced dependency within firm-year residuals as given by equation(4b), and independence in the residuals for consecutive firms and adjacentyears. 15 With an unequal number of observations for each firm-year, poolingover firm-years allows correcting for the recency effect in every firm-yearwhen the sample size is too small to allow estimation for each firm-year.'6
Equations (4a) and (4b) were jointly estimated for the three forecast hori-zons and the 14 industries. The estimates of the parameters in the model andthe variance-covariance matrix were obtained by using the maximum likeli-hood estimation procedure. Panels A to C of Table 6 present F statistics for the
A Re-Examinat ion of Financial Analys ts ' Differential Earnings . . . . 19
test of analyst, firm, and year effects in the model with the re-estimated stan-dard errors for the samples with minimum forecast horizons of five, 60, and120 trading days, respectively. In the presence of a recency effect, differentialforecast ability amongst analysts is evident in approximately 86 percent (i.e.,36 of 42) of the cases at levels of significance of .10 or better. More specifi-cally, differential forecast ability is evident in 13 of 14 industries for the mini-mum forecast horizon of five trading days (the exception is SIC 38), in 12 of14 industries for the minimum forecast horizon of 60 trading days (the excep-tions are SICs 20 and 27), and 11 of 14 industries for the minimum forecasthorizon of 120 trading days (the exceptions are SICs 20, 27, and 35).Consistent with the results in Table 3, there is a significant firm effect in most(35 of 42) estimations, suggesting that forecast errors for certain firms are sig-nificantly different than those of others, after controlling for analyst and year.However, the results do not indicate a significant year effect in a majority of(34 of 42) estimations, indicating that there is not much variation in forecasterrors from year to year after controlling for analyst and firm. 17
TABLE 6Estimated F statistics in the absolute forecast error model with analyst, firm, and year
effects, and auto-correlated errors, given by industry
Panel A: Samples with mininium forecast horizon of five trading days
|eijJ = ,jLi + 8j + 7t + 'nijt ('* )
Tl ; t r = P Tl it r.l + e ; , , (4b)
SICcode
Analyst F i r m Year
Prob. Prob . Prob .
2026272829333536373848496063
1.651111.812.372.532.472.091.382.621.103.025.041.432.13
0.010.000.000.000.000.000.000.060.000.270.000.000.060.00
1.181.791.681.611.572.055.803.351.9013.271.971.972.442.13
0.310.040.050.010.080.010.000.000.010.000.020.000.010.00
0.814.510.902.480.681.301.461.811.113.660.970.610.521.35
0.570.000.500.020.670.260.190.100.360.000.440.720.800.23
20 Contemporary Accounting Research
Panel B: Samples with minimum forecast horizon of 60 trading days
c , ^ Analyst Firm Yearcode
2026272829333536373848496063
Panel C:
SICcode
2026272829333536373848496063
F
0.883,211,042,492,761.521.282,212,151,681,854,142,201,85
Samples with
Prob.
0,670,000,400,000,000,020.080.000,000,000,000,000.000,00
minimumAnalyst
F
0,731.681,172,211,721,781,442,071.362,681,782,563,241,48
Prob.
0,840,030,250,000,000,020,150,040,060.000.000,000,010,04
F
0,901,511.881,741,572,266,843.462.095.391,972,011,311,94
forecast horizon ofFirm
F
0,661.301,892,041,532,464,051,211.903,181,642,030.742,24
Prob.
0,500,100,020,010,080,010,000,000,000.000,020,000,230,01
F
0,863,370.812,650,711,461,281,071,171,411,200,651,431,16
120 trading days
Prob.
0,690,210,020.000,100,000,000,280.010,000,080,000,620,00
F
1,172,910,751,030.751,780,731,731,001.140,760.850.571,64
Prob.
0,520,000,560,010,640,190,260,380.320,210,300,690,200,33
Year
Prob,
0,320,010,610,410,610,100,630.120,420,340,600,530,750.13
To test the setisitivity of our results to very old forecasts, whose large fore-cast errors could conceivably "drive" the results, we re-estimated equations (3)and (4) after excluding forecasts made more than 240 trading days prior to theearnings announcement date. The results, omitted for simplicity, do not alterour conclusion that differential ex post forecast accuracy exists amongstanalysts.
Incorporating recency using a matched-pair design. To determine the robust-ness of our results to an alternative methodology, we examine the issue of dif-ferential forecast ability using a matched-pair procedure that compares the ana-
A R e - E x a m i n a t i o n o f F i n a n c i a l A n a l y s t s ' D i f f e r e n t i a l E a r n i n g s . . . . 21
lyst's absolute forecast error with that of the absolute forecast error of anotheranalyst making a forecast for the same firm year on or about the same day.
If N analysts make their forecasts on a given day, with recency level r, forfirm 7 in fiscal year t, the "relative" absolute forecast error of any analyst /, forthis firm year is as follows:
= l- it - ' mjtrl (5)
or
where ^mitr ^^'^ ^mitr ^^^' respectively, the forecast and forecast error of a ran-domly selected match for analyst i from the remaining N-1 analysts makingforecasts on that date. Thus, a randomly selected analyst with a recency matchacts as a benchmark against which the analyst is compared. If we impose thisrequirement in all instances, a large proportion of the observations with noexact date match will be lost. To ensure a sufficiently large sample size whenan exact date match is absent, we did the following: (1) the matched forecast(Fj jfj.) is constructed by identifying the closest date (with at least two fore-casts) immediately preceding or succeeding the forecast day under considera-tion within a ± 5-trading-day window; (2) when the closest preceding and suc-ceeding dates (with a forecast) are equidistant, one date is selected at randomas a match date;l8 (3) when only one match is available on a given date (i.e., ifonly two forecasts are made on that date), one forecast is selected at random toavoid inducing dependency in the data; and (4) when both the preceding andsucceeding forecasts are unavailable within the ± 5-trading-day window, theobservation is deleted. The sample selection criterion was applied to these datafor each industry for each forecast horizon. 19 The reduction in the number ofobservations for the sample with minimum forecast horizon of 120 trading dayswas substantial, so we only report results for samples with minimum forecasthorizons of five and 60 trading days.
The major advantage of a matched-pair approach, in lieu of EGLS, is that itis a simple way to control for forecast recency without making assumptionsabout the effect of recency on forecast accuracy. To ensure that the deviationsfrom the exact matching procedure do not contaminate the analyst effect in anysystematic manner, we separated forecasts with an exact match from (1) thosewith a recency advantage (match less recent than the forecast) and (2) those witha recency disadvantage (match more recent than the forecast), by creating anadditional effect. An F test of this effect will indicate if there are systematicimprovements (losses) in forecast accuracy due to a +l-to +5-trading-day recen-cy advantage (disadvantage). We modified equation (2) by adding a recency-advantage/disadvantage (hereafter recency A/D) effect, and replaced the depen-dent variable with the recency-adjusted accuracy measure, as follows:
'•"/'^ijtm = (J i + Sj + 'Vt + ^m + ^ijtm (^)
where X, , designates the recency A/D effect.
22 Contetnporary Accounting Research
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24 Contemporary Accounting Research
The results of estimating equation (6) are reported in Table 7. For the sam-ple with a minimum forecast horizon of five trading days (panel A), the find-ings indicate that in a vast majority of industries, there are no significant firm,year, or recency A/D effects. Specifically, there are no instances of a significantfirm effect, two instances of a significant year effect (SICs 20 and 27), and noinstances of a significant recency A/D effect. The firm, year, and recency A/Dresults suggest that our matching procedure is effective in controlling for firm,year, and recency, respectively. More importantly, there is a significant analysteffect in 10 of 14 industries at the 0.10 level of significance, or better. Similarresults are evident in panel B for the 60-trading-day horizon. There are twoinstances of a firm effect (SICs 35 and 60), one instance of a year effect (SIC38), one instance of a recency A/D effect (SIC 60), and seven instances of ananalyst effect. Our "matching procedure" results corroborate our findings usingthe EGLS approach that an analyst effect exists.
Forecast accuracy of frequent versus occasional forecastersOur sample selection criterion requires that an analyst be included only if thatanalyst makes at least 10 forecasts in the industry. This criterion ensures thatthe included analyst is not an infrequent forecaster. However, differences existin the extent to which analysts revise and issue forecasts. Because frequentforecasters may be more accurate forecasters, it is conceivable that ourobserved results may be driven by a "forecast frequency" effect. To examinethis issue, we count the number of forecasts issued by the analyst for a givenfirm, prior to his/her selected forecast, and classify the analyst as a frequent(occasional) forecaster if the analyst's count is above (below) the mean of thenumber of forecasts issued for that firm by all analysts in the sample.2O To testif the observed differences in forecast accuracy were driven by this dichotomyof forecast frequency, we provide a control for this effect on the right hand sideof equation (6), as follows:
'•^/'^ijtmf = H + ^j + 'i't + ^m + <t>f + ^ijtmf (^)
where <j)f is the effect generated by separating frequent forecasters from infre-quent forecasters.
The results for minimum forecast horizons of five and 60 trading days arepresented in panels A and B of Table 8, respectively. Similar to the earlier find-ings in Table 7, the analyst effect is significant (0.10 level or better) in 10 of 14industries for samples with a minimum forecast horizon of five trading days,and in seven of 14 industries for samples with a minimum forecast horizon of60 trading days. The forecasting frequency effect is never significant. Thus, theanalyst effect, observed in our earlier analysis, is not "driven" by the frequen-cy effect, and differences in forecast accuracy of analysts exist even after con-trolling for the frequency of their forecast issuance.
A R e - E x a m i n a t i o n o f F i n a n c i a l A n a l y s t s ' D i f f e r e n t i a l E a r n i n g s . . . . 25
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26 Contemporary Accounting Research
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A Re-Examination of Financial Analysts' Differential Earnings , , , , 27
Ex ante analysis
Overview of ex ante analysisWe have established that differences in forecast accuracy of financial analystsexist over extended periods. However, these differences were found in estima-tion samples and may not extend to holdout samples. This part of the paperexamines whether the differences in forecast accuracy persist beyond the esti-mation period in one-year ahead holdout samples. We test for the robustness ofpersistence findings to two different (firm- and industry-specific) definitions offorecasting ability. We do observe persistence for analysts defined as ex antesuperior, but we do not find persistence for analysts defined as ex ante inferior.
We proceed as follows. We first discuss our methodology and define ourfirm- and industry-specific approaches to identifying superior, inferior, andaverage analysts. We then present results based on three tests of persistence andfour durations of length of estimation sample. A summary and conclusion thenfollows.
Methodology
Sample selectionData on individual analysts' annual earnings per share (EPS) forecasts andreported earnings per share for 1984-93 were obtained from I/B/E/SInternational Inc. We use the COMPUSTAT quarterly industrial file as our sourceof annual earnings announcement dates to determine each forecast's recencyrelative to the annual earnings number being forecast.21 We identify superiorand inferior analysts in estimation samples of one-, two-, three-, and four-yeardurations, and evaluate their performance in one-year-ahead holdout samples.We construct nine one-year estimation samples (1984-92), with nine corre-sponding holdout samples (1985-93); eight two-year estimation samples(1984-85 to 1991-92) with eight corresponding holdout samples (1986-93);seven three-year estimation samples (1984-86 to 1990-92) with seven corre-sponding holdout samples (1987-93); and six four-year estimation samples(1984-87 to 1989-92) with six corresponding holdout samples (1988-93).
In each estimation sample, we control for forecast recency by includingonly those analysts who made forecasts between five and 180 calendar daysprior to annual earnings announcement.22 If an analyst made more than oneforecast for a given firm-year during this period, we selected his/her mostrecent forecast to ensure that we had only one forecast per analyst in each esti-mation firm-year. Additionally, we imposed a constraint of at least four uniqueanalyst forecasts to ensure proper interpolation of the percentiles used to clas-sify analyst into superior (inferior) categories. We analyzed each estimationand corresponding holdout sample using both a firm-specific and an industry-specific definition of forecasting ability.
28 Contemporary Accounting Research
Identification of superior and inferior analysts in estimation samplesWe needed to develop an approach to classify analysts as superior, inferior, oraverage in estimation samples. Previous studies, by not examining analysts inholdout periods, had no need to classify analysts into these categories. Theforecast accuracy metric used to determine the analyst type in each estimationperiod is the analyst's absolute annual earnings forecast error, as defined pre-viously in equation (1). To identify superior, inferior, and average analysts, weconstructed percentiles on the distribution of absolute forecast errors of ana-lysts for each firm-year in the estimation sample.
For estimation samples based on one (two, three, and four) year(s), an ana-lyst is designated superior for a given firm-year if his absolute forecast error isless than the 25th (33rd, 50th^ and 50th) percentile on the distribution ofabsolute forecast errors of that firm-year. Conversely, if the absolute forecasterror is larger than the 75th (66th, 50th^ and 50th) percentile on the distributionof absolute forecast errors of a firm-year, the analyst is designated as inferiorfor that firm-year. As all tests are conducted on holdout samples, our proceduredoes not possess a "look-ahead bias."
Firm-specific superior (inferior) analysts. An analyst is classified as superi-or (inferior) with respect to a firm if and only if he/she retains the superior(inferior) status for all years in the estimation sample. Thus, analysts are clas-sified as superior (inferior) for a firm, based on a one-year period in the esti-mation sample, if they have a forecast error of less (more) than the 25th (75th)percentile on the distribution of that firm's absolute forecast error in that esti-mation period. For estimation samples covering two years, analysts are classi-fied as superior (inferior) for a firm if their absolute forecast errors are less(more) than the 33rd (66th) percentile on that firm's yearly distribution ofabsolute forecast errors in both years of the estimation sample. Similarly, forestimation samples covering three- and four-year periods, analysts are classi-fied as superior (inferior) for a firm if their absolute forecast errors are less(more) than the median of that firm's yearly distribution of absolute forecasterrors in every year of the estimation sample.23 Analysts not identified as eithersuperior or inferior for a firm are designated as average.
Industry-specific superior analysts. The "Street" (e.g.. Institutional Investor,The Wall Street Journal) typically ranks analysts with respect to industry andacademic studies have performed industry-specific analyses (O'Brien 1990). Inthe firm-specific definition of forecast superiority, there is no assurance that asuperior analyst is superior with respect to more than one firm in an industry.Indeed, an analyst may be superior with respect to one firm in an industry butinferior with respect to other firms in the same industry.
To provide evidence consistent with the "Street" notion of superiority, wedefine analysts as superior with respect to an industry if they are superior withrespect to at least two firms in that industry and inferior with respect to none.
A Re-Examination of Financial Analysts' Differential Eamings . . . . 29
Similarly, we define analysts as inferior with respect to an industry if they areinferior with respect to at least two firms in that industry and superior withrespect to none.24 The four estimation samples (i.e., one to four years) used inthe firm-specific tests are also used in the industry-specific tests.
Performance of superior and inferior analysts in holdout periods
Test metricsThe forecast accuracy of test (superior and inferior) analysts is compared withthat of average analysts in holdout periods. Comparisons are made in holdoutperiods provided that (1) the test analyst made at least one forecast for the spe-cific firm/industry and (2) there exists an average analyst who can be matchedwith the test analyst with respect to firm, year, and recency of the forecast.25 Ininstances where an exact recency match cannot be found for the test analyst, wematched it with the closest forecast of an average analyst within the ±5 calen-dar days surrounding the forecast date. If no match could be found for this peri-od, the test analyst was dropped for that specific holdout year.
We define the analyst's absolute percentage forecast error, apfe, as follows:
(8)
Consistent with Foster (1977), apfe^^^ is not computed whenever R-^^ was zero,and is set to 100 whenever the computed value exceeded 100. We compute eachsuperior analyst's relative absolute percentage forecast error (rapfe) as theabsolute percentage forecast error of the matched average analyst minus that ofthe superior analyst:
(9)
where F^^i^ is the forecast of the matched average analyst for the firm in ques-tion. For inferior analysts, we reversed the order of the two terms on the righthand side of equation (9).
Tests of persistence. Tables 9 and 10 present the mean rapfe and its signifi-cance level, using a f-test, in each holdout year examined for superior and infe-rior analysts, respectively. The rows indicate the duration of the estimationsample, and the columns denote the performance in each holdout year. A posi-tive and significant mean rapfe suggests that superior analysts remain superiorin holdout periods. The results in panels A and B are based on firm- and indus-try-specific definitions of persistence, respectively.
We conducted three tests to estimate persistence for each duration of theestimation sample. First, we examined the proportion of holdout years withpositive mean rapfes. Assuming that positive and negative mean rapfes areequally likely, we computed the binomial probabilities associated with theobserved outcomes. Second, we examined how many of the positive meanswere significant at the chosen level of significance and computed the binomial
30 Contemporary Accounting Research
probabilities associated with the observed significant and positiveThird, we treated each mean rapfe as an independent observation, computed theoverall mean and standard deviation of the distribution, and performed a f-testto determine if the overall mean was positive and significant (Fama andMacBeth 1973; Bowen, Burgstahler, and Daley 1987).
Although these three tests are not independent, they need not provide iden-tical inferences. Thus, results robust to all three tests should be more indicativeof persistence than results holding for one or two tests. We collectively inter-pret the results of these three tests, for each analyst type, definition of analystsuperiority, and duration of the estimation sample, as providing "strong,""moderate," "weak," or "no" evidence of persistence depending upon whetherthree, two, one, or zero tests indicate persistence in holdout periods, respec-tively.
Superior analystsTable 9 presents the mean rapfe and its significance level, using a t-test, in eachholdout year examined for superior analysts. A positive and significant meanrapfe indicates that superior analysts remain superior in holdout periods. Theresults of tests on firm-specific and industry-specific definitions of superiorityare discussed next.
TABLE 9Mean relative absolute percentage forecast error (rapfe) of firm- and industry-specific supe-rior analysts (Number of firm analysts; analysts in parentheses)*
(9)
Overall Persistence
mean evidence
rapfe
Panel A: Firm-specific superior analysts
Holdout yearYears in
estimation
sample 1985 1986 1987 1988 1989 1990 1991 1992 1993
1 0.47 -0.79 1.05t 1.191 0.18 0.94t 1.23t 0.80§ 0.59 0.62$ Strong(902; (1,039; (1,102; (1,175; (1,063; (1,136; (1,206; (942; (910;520) 597) 600) 622) 592) 624) 656) 572) 557)
2 -1.83 2.22t 0.99 -1.06 1.29 2.92t 0.78 1.54§ 0.86§ Moder(184; (207; (227; (243; (233; (263; (235; (218; ate150) 167) 168) 179) 181) 210) 193) 179)
3 0.52 0.08 2.16t 0.38 1.34 -0.23 3.00* l.03t Strong(197; (204; (211; (245; (227; (228; (238;153) 152) 150) 179) 176) 179) 190)
-0.70 2.04t 0.09 2.56 -1.31 0.90
(64;54) (65;57) (57;52) (79;67) (68;60) (65;59)
0.60 None
A Re-Examinat ion of Financial Analys t s ' Differential Earnings . . . . 31
Panel B: Industry-specific superior analysts
Years in
estimationsample
1
2
3
4
1985
-0.39
(558;
883
1986
-1.81
(688;
96)
-2.25
(155;
11)
1987
1.29t(493;
74)
-1.20
(322;
17)
-0.17
(139;
17)
Holdout year
1988
1.85t(536;
81)
2.25t(269;
20)
0.48
(263;
16)
-0.10
(187;
7)
1989
0.34
(573;
81)
0.50
(267;
24)
1.97t(178;
14)
2.85§
(68;
3)
1990
0.55
(660;
93)
0.59
(255;
22)
1.82t(295;
25)
2.51
(45;
4)
1991
0.79
(719;
97)
1.23t(365;
27)
1.02t(412;
32)
0.24
(161;
9)
1992
0.53
(515;
89)
1.02
(200;
21)
1.95t(253;
26)
0.74
(64;
9)
1993
1.431:
(609;
79)
2.26t(269;
24)
1.04(266;
26)
2.03t(77;
5)
Overall Persistence
mean ••*''rapfe
0.51§
0.55
1.161:
1.38t
eviuence
Strong
Weak
Strong
Moderate
Notes:* Absolute percentage forecast error of the average analyst minus that of the superior analyst.
Superior analysts are determined in a one to four year estimation period. The estimation periodimmediately precedes the holdout year. For example, when the holdout year is 1991, the corre-sponding one, two, three, and four year estimation periods are 1990, 1989-90, 1988-90, and 1987-90, respectively. Superior and average analysts are recency matched in the holdout period.
t Significant at 0.01 level (one-tailed test).1: Significant at 0.05 level (one-tailed test).§ Significant at 0.10 level (one-tailed test).
Firm-specific analyses. The first row of Table 9, panel A, presents resultsbased on one year of data in the estimation sample to identify analyst type.Eight of the nine mean rapfes are positive, and five are statistically significantat the 0.10 level or less. The probability of obtaining eight or more positiverapfes, if positive and negative rapfes are equally likely, is 0.02. The probabil-ity of obtaining five or more positive and significant rapfes at the 0.10 level ofconfidence, if positive and negative outcomes are equally likely, is less than0.01. The overall mean rapfe, 0.62, is statistically significant at the 0.01 level.Collectively, this is strong evidence that superior analysts remain superiorwhen a firm- specific definition of superiority is considered and a one-yearperiod is used in the estimation sample to identify analyst type.
The second row of panel A presents results for samples using two years ofdata in the estimation sample to identify analyst type. Six of the eight meansare positive, and three are significant at the 0.10 level or less. The probabilityof obtaining six or more positive rapfes, if positive and negative rapfes areequally likely, is 0.14. The probability of obtaining three or more positive andsignificant rapfes at the 0.10 level of confidence, assuming that positive andnegative outcomes are equally likely, is less than 0.01. The overall mean rapfe,
32 Contemporary Accounting Research
0.86, is significant at the 0.10 level. This is moderate evidence that superioranalysts remain superior when the definition of superiority is firm specific anda two-year period is used in the estimation sample to identify analyst type.
The third row of panel A presents results for samples using three years ofdata in the estimation sample to identify analyst type. Six of the seven meansare positive, and two are significant at the 0.01 level or less. The probability ofobtaining six of seven positive rapfes, if positive and negative rapfes are equal-ly likely, is 0.06. The probability of obtaining two or more positive and signif-icant rapfes at the 0.01 level at significance, assuming that positive and nega-tive outcomes are equally likely, is less than 0.01. The overall mean rapfe, 1.03,is significant at the 0.01 level. Similar to the results for the one-year estimationsamples, the results provide strong evidence that superior analysts remain supe-rior when a firm-specific definition of superiority is considered and a three-year period is used in the estimation sample to identify analyst type.
The fourth row of panel A presents results for estimation samples usingfour years of data to identify analyst type. Four of the six means are positive,and one is significant at the 0.10 level. The probability of obtaining four ormore positive rapfes, if positive and negative rapfes are equally likely, is 0.34.The probability of obtaining one or more positive and significant rapfes at the0.10 level of significance, assuming that positive and negative outcomes areequally likely, is 0.26. The overall mean rapfe, 0.60, is not significant.Collectively, the results provide no evidence that superior analysts remainsuperior when a firm-specific definition of superiority is considered and a four-year period is used in the estimation sample to identify analyst type.
Industry-specific analyses. Panel B of Table 9 presents holdout-period resultsfor analysts deemed to be superior with respect to an industry. The holdoutperiod comparisons, once an analyst is classified as superior with respect to anindustry, include all firms in that industry for which the analyst made a fore-cast and for which there exists an appropriate recency match.27
Seven of the nine rapfes in the first row of panel B are positive, and threeare significant at the 0.05 level or less. The probability of obtaining seven ormore positive rapfes, if positive and negative outcomes are equally likely, is0.09, The probability of obtaining three or more positive and significant rapfesat the 0.05 level of confidence, if positive and negative outcomes are equallylikely, is less than 0.01. The overall mean rapfe, 0.51, is significant at the 0.10level. The three tests provide strong evidence that superior analysts remainsuperior in holdout periods when an industry- specific definition of forecastsuperiority is considered and a one-year period is used in the estimation sam-ple to identify analyst type.
Six of the eight rapfes in the second row of panel B are positive, and threeare significant at the 0.05 level or better. The probability of obtaining six ormore positive rapfes, if positive and negative rapfes are equally likely, is 0.14.The probability of obtaining three or more positive and significant rapfes at the
A Re-Examination of Financial Analysts' Differential Earnings . . . . 33
0.05 level or better is less than 0.01. The overall mean rapfe, 0.55, is signifi-cant at the 0.18 level. Collectively, this is weak evidence that superior analystsremain superior in holdout periods when an industry-specific definition of fore-cast superiority is employed and a two-year period is used in the estimationsample to identify analyst type.
Six of the seven mean rapfe% in row 3 of panel B are positive, and four aresignificant at the 0.10 level or better. The probability of obtaining six or morepositive rapfes, if positive and negative rapfes are equally likely, is 0.06. Theprobability of obtaining three or more positive and significant rapfes at the 0.10level or better is less than 0.01. Consistent with the results of these two tests,the overall mean rapfe, 1.16, is significant at the 0.01 level. Collectively, thisis strong evidence that superior analysts remain superior when a three-yearperiod is used in the estimation sample to identify analyst type and an industry-specific definition of superiority is employed.
Five of the six mean rapfes in row 4 of panel B are positive, and two aresignificant at the 0.10 level. The probability of obtaining five or more positiverapfes, if positive and negative rapfe are equally likely, is 0.11. The probabili-ty of obtaining two or more positive and significant rapfes at the 0.10 level ofconfidence, if positive and negative outcomes are equally likely, is less than0.05. The overall mean rapfe, 1.38, is significant at the 0.05 level. Overall, thisis moderate evidence that superior analysts remain superior when an industry-specific definition of forecast superiority is considered and a four-year periodis used in the estimation sample to identify analyst type.
Summary and discussion: Superior analysts. The evidence of forecast accu-racy persistence of superior analysts is strong when a one- or three-year esti-mation period is used to identify analyst type, regardless of whether forecastsuperiority is defined as firm- or industry-specific. When a two (four) year esti-mation period is used to identify analyst type, there is moderate {no) and weak{moderate) evidence of persistence for firm- and industry-specific definitionsof forecast superiority, respectively.
Using the industry-specific definition of forecast superiority, persistenceexists for a period of up to five years (four estimation years and one holdoutyear). Using the firm-specific definition of forecast superiority, persistenceexists for a period of up to four years (three estimation and one holdout year).28
For the firm and industry definitions combined, the evidence of persistenceis strong in four cases, moderate in two, weak in one, and absent in one. Out of24 separate, albeit not independent, tests of significance, 17 indicated persis-tence.29 Analysts identified as superior in estimation samples appear to remainso in holdout samples.
Inferior analystsTable 10 presents results for inferior analysts in a format identical to that ofTable 9 for superior analysts. The results in panels A and B are based on firm-
34 Contemporary Accounting Research
and industry-specific definitions of inferiority respectively. The first (second,
third, and fourth) row of each panel presents results based on one (two, three,
and four) year(s) of data in the estimation sample to identify analyst type
TABLE 10
Mean relative absolute percentage forecast error {rapfe) of firm- and industry-specific infe-rior analysts (Number of firm analysts; analysts in parentheses).*
- |(Rjt - Fn,jt)/Rjt|*IOO
Overall Persistence
Panel A: Firm-specific inferior analysts
Years in Holdout year
estimationsample
1
2
3
4
Panel B:
Years inestimationsample
1
2
3
4
1985
1.33*(971;551)
1986III0.20
(129;108)
1987
0.46(1,178;
611)
-0.53(270;196)
0.28(181;141)
1988
0.78t(1,244;
617)
I.21t(265;191)
1.07(200;151)
-1.87
(54;48)
1989
0.65§(1,169;
618)
1.05§(279;201)
0.77(178;144)
3.64§(47;44)
Industry-specific inferior analysts
1985
-0.14(637;
95)
1986
0.52(515;
89)
3.5 I t(273;
21)
1987
-1.00(547;
92)
-0.79(373;
33)
-0.14(217;
18)
1990
0.761(1,215;
604)
0.21(242;179)
-1.28(184;144)
-4.73(51;47)
Holdout year
1988
0.43
(563;
91)
-1.29(354;
25)
-1.72(163;
14)
0.49
1989
-0.67(724;
99)
0.97§(336;
36)
1.02(155;
16)
-0.76
1990
0.33(625;105)
-0.06(473;
31)
0.65(212;
14)
2.19
1991
0.03(1,256;
631)
1.50t(316;225)
0.48(173;122)
-3.02(47;42)
1991
-0.32(663;110)
0.47(328;
32)
-0.03(264;
24)
-0.78(27;3)
1992
-0.33(1,053;
579)
0.10(261;182)
-1.44(205;153)
-1.62(48;44)
1992
0.10(762;114)
1.03§(378;
31)
-0.20(237;
23)
8.17
(9;1)
1993
0.43(1,027;
542)
-0.52(270;192)
-0.07207;153)
0.74
(56;45)
1993
0.11(635;
94)
0.31(425;
38)
0.24
(321;
26)
0.99
meanrapfe
0.67t
0.46§
-0.03
-1.14
evidence
Strong
Moderate
None
None
Overall Persistencemean evidencerapfe
-0.07
0.52
-0.03
1.72
None
Weak
None
None
Notes:Absolute percentage forecast error of the inferior analyst minus that of the average analyst.Inferior analysts are determined in a one to four year estimation period. The estimation period
A R e - E x a m i n a t i o n o f F i n a n c i a l A n a l y s t s ' D i f f e r e n t i a l E a r n i n g s . . . . 3 5
immediately precedes the holdout year. For example, when the holdout year is 1991, thecorresponding one, two, three, and four year estimation periods are 1990, 1989-90, 1988-90, and1987-90, respectively. Inferior and average analysts are recency matched in the holdout period.
t Significant at 0.01 level (one-tailed test).t Significant at 0.05 level (one-tailed test).§ Significant at 0.10 level (one-tailed test).
Firm-speciflc analyses. Eight of the nine mean rapfes in row 1 of panel A arepositive, and five are significant at the 0.10 level or less. The probability ofobtaining eight or more positive rapfes, if positive and negative rapfes areequally likely, is 0.02. The probability of obtaining five or more positive andsignificant rapfes at the 0.10 level of confidence, if positive and negative out-comes are equally likely, is less than 0.01. The overall mean, 0.67, is signifi-cant at the 0.01 level. This is strong evidence that inferior analysts remain infe-rior when a firm-specific definition of inferiority is considered and a one-yearperiod is used in the estimation sample to identify analyst type.
Six of the eight rapfes in row 2 of panel A are positive, and three are sig-nificant at the 0.10 level or less. The probability of obtaining six or more pos-itive rapfes, if positive and negative outcomes are equally likely, is 0.14. Theprobability of obtaining three or more positive and significant rapfes, if posi-tive and negative outcomes are equally likely, is less than 0.01. The overallmean, 0.46, is significant at the 0.10 level of confidence. Two of three tests sug-gest persistence of inferior analysts in holdout periods, providing moderate evi-dence consistent with the phenomenon.
Only four of the seven rapfes in row 3 of panel A are positive, none are sta-tistically significant. Neither result is significant at conventional levels.Moreover, the overall mean rapfe, -0.03, has the "wrong" sign. These tests pro-vide no evidence that inferior analysts remain inferior when a firm-specific def-inition of forecast inferiority is considered and a three-year period is used in theestimation sample to identify analyst type.
Only two of the six rapfes in row 4 of panel A are positive, and only oneis significant at the 0.10 level. Also, the. overall mean rapfe, -1.14, has the"wrong" sign. Tests utilizing a four-year period in the estimation sample todefine analyst type and a firm-specific definition of forecast inferiority offer noevidence that inferior analysts remain inferior in holdout periods.
Industry-specific analyses. Using a one-year period in the estimation sampleto define analyst type, row 1 of panel B shows that five of the nine means arepositive, an insignificant result. None of the means are significant, and theoverall mean rapfe, -0.07, has the "wrong" sign. Collectively, these three testsprovide no evidence that inferior analysts remain inferior when an industry-based definition of inferiority is considered and a one-year period is used in theestimation sample to identify analyst type.
Using a two-year period in the estimation sample to define analyst type(row 2, panel B), five of the eight means are positive, and three are significant
36 Contemporary Accounting Research
at the 0.10 level or better. The probability of obtaitiing five or more positiverapfes, if positive atid negative rapfes are equally likely, is 0.36. The probabil-ity of obtaining three or more positive and significant rapfes, if positive andnegative outcomes are equally likely, is less than 0.01. The overall mean rapfe,0.52, is insignificant. Collectively, these tests provide weak evidence that infe-rior analysts remain inferior when an industry-specific definition of inferiorityis considered and a two-year period is used in the estimation sample to identi-fy analyst type.
Three of the seven means in row 3 of panel B are positive, and none aresignificant. The probability of obtaining three or more positive rapfes, if posi-tive and negative rapfes are equally likely, is 0.77. The probability of obtainingzero or more positive and significant rapfes, assuming that positive and nega-tive outcomes are equally likely, is 1.00. The overall mean rapfe, -0.03, is ofthe "wrong" sign. Collectively, the results provide no evidence that inferioranalysts remain inferior when an industry-specific definition of forecast inferi-ority is considered and a three-year period is used in the estimation sample todefine analyst type.
Four of the six means in row 4 of panel B are positive, and none are sig-nificant. Neither result is significant at conventional levels. Moreover, theoverall mean rapfe, 1.72, is not statistically significant. These tests provide noevidence that inferior analysts remain inferior when an industry-specific defin-ition of forecast inferiority is considered and a four-year period is used in theestimation sample to define analyst type.
Summary and discussion: Inferior analysts. When a one- (two-) year periodis used in the estimation sample to identify analyst type, there is strong (mod-erate) and no (weak) evidence of inferiority persistence for firm- and industry-specific definitions of forecast inferiority, respectively. When a three- or a four-year period is used in the estimation sample to identify analyst type, there is noevidence of persistence, using either definition of inferior analysts.
Considering the four estimation periods as a group, there is virtually noevidence that forecast inferiority persists when the industry-specific definitionof forecast inferiority is used.3O in general, analysts who are inferior withrespect to an industry in a given estimation year(s) have forecast errors that areno different than those of average analysts in the subsequent holdout year.Using the firm-specific definition of forecast inferiority, there is evidence thatforecast inferiority persists for up to a three-year (two estimation and one hold-out year) period, but there is no evidence of persistence beyond the three-yearperiod. Moreover, in the one instance where the evidence is strongest using thefirm-specific definition of forecast inferiority (one-year estimation period),there is no evidence using the industry-specific definition of inferiority.
In sum, for the firm and industry definitions combined, the evidence ofpersistence is strong in one case, moderate in one other, weak in another, andabsent in five cases. Out of 24 separate tests of significance, only six indicate
A Re-Examination of Financial Analysts' Differential Earnings , , . , 37
persistence.31 Analysts identified as inferior in estimation periods do notappear to remain so in holdout periods.
Summary and conclusionsRichards (1976), Brown and Rozeff (1980), O'Brien (1987; 1990), Coggin andHunter (1989), and Butler and Lang (1991) conclude that differential earningsforecast accuracy amongst analysts is absent. This finding is contrary to thebelief in the popular press that differences in the forecasting ability of financialanalysts exist. In this study, we provide an explanation for this anomaly. Wedocument the presence of significant differences (both ex post and ex ante)amongst financial analysts and show that the prior research, using large sam-ples, did not observe any differences in forecast accuracy of financial analystsdue to a low power test resulting from a lack of adequate control for forecastrecency.
Using O'Brien's methodology, without controlling for recency, we con-clude, as she does, that differential forecast accuracy amongst analysts isabsent. We do, however, find a strong uncontrolled recency effect in O'Brien'sanalysis. Controlling for the recency effect via either an estimated generalizedleast squares estimation procedure or a matched-pair design, we find that dif-ferential forecast accuracy does exist amongst analysts, especially in sampleswith forecast horizons of five and 60 trading days. We show that these differ-ences are not attributable to differences in the forecast issuance frequency ofthe financial analysts. After controlling for firm, year, recency, and forecastissuance frequency, an analyst effect is still evident.
The study extends the results of ex post differences in forecast accuracyamongst analysts into an ex ante validation exercise. Because the "Street"believes that differences amongst analysts in earnings forecast accuracy persist,we defined superior, inferior, and average analysts in estimation samples, andcompared their performance relative to average analysts in holdout samples.We considered both firm- and industry-specific definitions of forecast superi-ority, and we used estimation samples of one to four years' duration to identi-fy analyst type.
We find that analysts identified as superior in estimation samples general-ly remain superior in holdout periods. In contrast, we find that analysts identi-fied as inferior in estimation samples generally do not remain inferior in hold-out periods. Additional research is necessary to determine whether our findingspertain to other data sets, time periods, and methods of defining analyst type.
Our results imply that some analysts' earnings forecasts should be weight-ed higher than others when formulating composite earnings expectations. Thissuggestion is predicated on the assumption that capital markets distinguishbetween analysts who are ex ante superior and that capital markets utilize thisinformation when formulating stock prices. Our study provides an ex anteframework for identifying those analysts who appear to be superior. When con-
38 Contemporary Accounting Research
structing weighted forecasts, a one-year estimation period should be usedbecause we obtain the strongest results of persistence in this case.
Endnotes1 Every October, Institutional Investor identifies members of its All American
Research Team. Team members are chosen partly on the basis of their earningsforecast ability. Team membership is valuable in that it often commands highersalaries, sometimes as much as hundreds of thousands of dollars higher (The WallStreet Journal, February 11, 1996, Cl l ) . Superior earnings forecasters werepresented by The Wall Street Journal on June 29, 1994, Rl 1, in the "All-StarAnalysts 1994 Survey." According to that article,"The All-Star Analysts Surveyalso throws a bit of cold water on the pure-luck theory. The fact that more than100 All-Stars are back from last year's roster is highly suggestive that trackrecords matter."
2 Stickel (1992) shows that a small subset of analysts, identified as members of theInstitutional Investor All American Research Team, have lower annual earningsforecast errors than do nonteam members. However, prior to becoming teammembers, these analysts' forecast errors are not significantly different from thoseof other analysts, and their forecast accuracy decreases prior to leaving the team.As our examination of the 1985-1990 October issues of Institutional Investorrevealed that the average length of stay on the team is less than two years,Stickel's findings are consistent with the contention that period-to-perioddifferences in analyst forecast accuracy disappear over time.
3 In her original model, O'Brien (1990) does not control for forecast recency. Hersubsequent analysis partially controls for recency by including four "agecategories." Richards (1976), Brown and Rozeff (1980), Coggin and Hunter(1989), and Butler and Lang (1991) made no controls for recency whatsoever.
4 Our ex ante analysis relaxes these sample selection constraints.5 The adjustment for size distribution was made only if the forecast date preceded
the stock distribution announcement date and the ex-date is before the fiscal yearend. If the ex-date is after the fiscal year end, the reported EPS is at the presplitlevel, so no adjustment is needed.
6 Samples with minimum forecast horizons of five (60,120) trading days includeonly those forecasts made at least five (60,120) trading days prior to the earningsannouncement. O'Brien (1990) reports results for a minimum forecast horizon of120 trading days only. She states that her results are invariant to the other fourminimum forecast horizons (5, 60, 180, and 240 trading days) she considers (p.289, footnote 4).
7 Equation (2) can be expressed in conventional regression form as:
where a is the intercept term common to all analysts, firms and years; Aj, F;, andY{ represent dummy variables corresponding to analysts, firms, and years; (xj, 8:,and y^ are the corresponding model parameters; /, J, and T are the number ofanalysts, firms, and years, respectively, and r\^:^ is the white noise-term. Thedesign matrix is composed of zeros and ones, corresponding to dummy variablesfor analysts, firms, and years. In this specification, the presence of a significantanalyst (firm, year) effect is evidenced by rejection of the null hypothesis ofequality of all ixjs (8jS, y^s).
A Re-Examination of Financial Analysts' Differential Earnings . . . . 39
8 O'Brien (1990) reports forecasts with a recency range of more than 211 tradingdays before the minimum forecast horizon of 120 trading days (see O'Brien'sTable 3 for SIC 49). This suggests that forecasts made more than one year priorto the earnings announcement may have been included in the sample. Therecency gap between current and old forecasts is even larger for samples withsmaller minimum forecast horizons because, in addition to the older forecasts,more timely forecasts are included. We present raw forecast ages in contrast toO'Brien, who presents forecast ages relative to the minimum forecast horizon.
9 Dummy categories were defined as (1) less than 22, (2) 23 to 44, (3) 45 to 66,and (4) more than 66 trading days from the minimum forecast horizon. (SeeO'Brien's Table 8.)
10 Estimation results using O'Brien's procedure to control for recency are availableupon request.
11 An examination of our data suggested that the use of four dummy categories didnot adequately control for forecast recency. We defined an adequate control forrecency as one in which, for a given firm year, there is at least one forecast ineach age category. We found the control based on age categories was adequateonly in 58 percent (48 percent, 25 percent) of the firm years for samples withminimum forecast horizons of five (60,120) trading days. This left a majority ofthe sample uncorrected for recency effects.
12 Dependency in the forecasts can be induced due to common shock in earnings,unanticipated by all analysts. This will result in all forecasts being correlated withthe shock (and each other), regardless of the recency order. However, it is therecency-induced dependency that we are trying to capture.
13 The direction of bias in test statistics involving hypotheses on the relativemagnitudes of the parameters in the model cannot be determined easily (Judge,Griffiths, Hill, Lutkepohl, and Lee 1985, 278-82), but the inefficiency could leadto higher standard errors of the coefficient estimates, making it harder to rejectthe null hypothesis of no firm, year, or analyst effect.
14 The correlation coefficients decrease monotonically as the minimum forecasthorizon increases for nine of the 14 industries. The monotonic decrease isexpected because the recency effect increases as the minimum forecast horizonshortens.
15 For this estimation, let T: denote the number of years of data for firm 7, J the total
number of firms, K= 2TJ the total number of firm-years, and n^ the number of
forecasts, arranged by descending order of forecast age, within a firm-year k .K
Thus, the total number of observations in the sample is N = Snj^.k=l
In conventional matrix notation, let ti denote the Nxl vector of error terms inequation (2), and ^ = E('riifi ) denote the NxN variance-covariance matrix. In theabsence of dependency in the residuals, as in OLS, <t>=o' I. where I is a NxNidentity matrix. In our model, equation (4), dependency in the data results in(t)=(T^2, where 2 is a block diagonal instead of an identity. Each block diagonalelement of S, 2k, corresponds to a separate firm-year k. There are a total of Ksuch blocks, and for any firm year k, the dimensions of the corresponding blockdiagonal matrix, 2k are nkxnk. All 2k are generated by the same AR(1) process,with the I'th row andy'h column element is determined as follows:
1 ifi=j2k (i,j) = Pl"J
pj-i
40 Contemporary Accounting Research
16 The efficient estimation of the variance-covariance matrix, typically used inaccounting, is in the context of equally spaced time-series observations. However,this is not a necessary condition for applying the technique. The only assumptionneeded for using this procedure is that the unexplained component of thedependent variable (in this case, forecast error) varies linearly with eachsuccessively ordered observation. In the context of forecast accuracy,improvements take place primarily as a result of information arrival. Becauseinformation does not arrive linearly in calendar time, it is appropriate to equallyspace the successive analyst forecasts.
17 The year effect, which is evident in Table 3, is not evident in Tahle 6. Thiscurious result is due to the fact that there exist significant differences in recencyacross years. We confirmed the existence of this effect by regressing forecastrecency on dummy variables for analyst, firm, and year, and by finding asignificant year effect in 40 of 42 regressions.
18 If more than one forecast is made on this match date, the matched forecast israndomly selected from the set of available forecasts.
19 The sample selection criterion includes firms with at least one forecast in each ofthe seven years and analysts with at least 10 forecasts in the industry in three ofthe years.
20 The analyst's forecast included in the sample depends upon the minimum forecasthorizon. Thus, the number of forecasts by an analyst varies for each forecasthorizon.
21 This sample was much larger than the sample used in the ex post analysis becauseno initial constraints were applied on analysts and firms.
22 Our control for recency is crude. To the extent that recency will be an issue inidentifying superior analysts, it will bias against finding any significantdifferences in the holdout periods.
23 For ease of exposition, we henceforth utilize the term superior in lieu of the morecorrect terminology, superior (inferior).
24 The "two-zero" rule was selected based on our intuition and desire to maintainadequate sample sizes.
25 If multiple forecasts of an analyst met the two conditions, we selected the oneclosest to the annual earnings announcement date.
26 To understand this test, consider an urn with 40 balls, 20 black and 20 white, todenote positive and negative differences. If the significance level is 0.05 (two-tailed test), we mark one of the 20 black halls and one of the 20 white balls asred. Now consider the probability of drawing a white ball, marked red, more thanthe observed number of times out of a stated number of total draws (withreplacement) from this urn.
27 As it is not required that the analyst previously made a forecast for all firms inthe industry, the number of observations in the holdout samples in panel B mayexceed those in panel A.
28 This apparent sensitivity of results to length of estimation period may be due tothe way we identified superior analysts for estimation samples covering the fouryear period. The use of the 50th percentile in this estimation sample may result ininclusion of analysts who are not all that superior. There is some evidenceconsistent with this view in the corresponding results using the industry-specificdefinition of forecast superiority. Since the industry-specific definition requiresthe "two-zero" rule with respect to identifying an analyst as superior, some of the'not all that superior analysts' are potentially eliminated, and we do findpersistence for the four-year estimation period using this definition.
A Re-Examination of Financial Analysts' Differential Eamings . . . . 41
29 24 = 4 estimation periods (1 to 4 years) x 2 definitions of persistence (firm- andindustry-specific) x 3 tests (proportion with positive mean rapfes, number ofpositive and significant mean rapfes, and mean of distribution of rapfes). 17 = 4strong (each with weight 3) + 2 moderate (each with weight 2) -i- 1 weak (withweight 1).
30 In 11 of 12 tests (four estimation periods x three tests per estimation period), wedid not obtain a significant result. The exception arises when a two-yearestimation period is used to define analyst type.
31 6=1 strong (with weight 3) + 1 moderate (with weight 2) + 1 weak(with weight 1).
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