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Relative Accuracy of Judgmental and Extrapolative Methods in Forecasting Annual Earnings

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This paper identifies and analyses previously published studies on annual earnings forecasts. Comparisons of forecasts produced by management, analysts, and extrapolative techniques indicated that: (1) management forecasts were superior to professional analyst forecasts (the mean absolute percentage errors were 15.9 and 17.7, respectively, based on five studies using data from 1967–1974) and (2) judgemental forecasts (both management and analysts) were superior to extrapolation forecasts on 14 of 17 comparisons from 13 studies using data from 1964–1979 (the mean absolute percentage errors were 21.0 and 28.4 for judgement and extrapolation, respectively).These conclusions, based on recent research, differ from those reported in previous reviews, which commented on less than half of the studies identified here.
Electronic copy available at: http://ssrn.com/abstract=663665
1
Published in the Journal of Forecasting, Vol. 2, 437-447 (1983)
Relative Accuracy of Judgmental and Extrapolative Methods in Forecasting Annual Earnings
J. Scott Armstrong
University of Pennsylvania, Philadelphia, PA, U.S.A.
ABSTRACT
This paper identifies and analyses previously published studies on annual earnings forecasts.
Comparisons of forecasts produced by management, analysts, and extrapolative techniques
indicated that: (1) management forecasts were superior to professional analyst forecasts (the
mean absolute percentage errors were 15.9 and 17.7, respectively, based on five studies using
data from 1967-1974) and (2) judgmental forecasts (both management and analysts) were
superior to extrapolation forecasts on 14 of 17 comparisons from 13 studies using data from
1964-1979 (the mean absolute percentage errors were 21.0 and 28.4 for judgment and
extrapolation, respectively). These conclusions, based on recent research, differ from those
reported in previous reviews, which commented on less than half of the studies identified
here.
KEY WORDS: Annual, financial forecasts, Judgment vs. extrapolation, Management vs.
analyst Amalgamated forecasts
This paper examines the accuracy of those methods currently used in forecasting annual earnings
management judgment, outside analyst judgment, and extrapolations.
The first section draws upon research in finance and other fields to develop hypotheses concerning which
forecasting methods would be most accurate for annual earnings forecasts. Section 2 presents a quantitative analysis
of previously published studies, comparing management forecasts with analyst forecasts. In Section 3, a quantitative
analysis is made of the evidence on judgment and extrapolative forecasts. The final sections offer proposals for
further research and summarize the major conclusions.
1. Hypotheses on Methods and Accuracy
The literature on financial forecasting provides little indication of which forecasting methods should be
most accurate in a given situation. To obtain some initial hypotheses, evidence from the social sciences was
collected (Armstrong, 1978). This yielded the following conclusions for forecasting in situations involving large
changes:
(1) Causal methods provide more accurate forecasts than naive methods.
(2) Objective methods provide more, accurate forecasts than subjective methods.
(3) Independent (unbiased) experts are more accurate than those involved in the situation.
(4) Amalgamated forecasts are more accurate than the typical error for the components of the
amalgamated forecast.
Annual earnings forecasts qualify as a situation involving large changes. The average year-to-year change
in earnings (in absolute terms) is about 28 per cent: Carey (1978) reported 28 per cent, Collins (1976) reported 26
per cent, Copeland and Marioni (1972) reported 28 per cent, Green and Segall (1966) reported 30 per cent, Johnson
and Schmitt (1974) reported 29 per cent and Richards et al. (1977) reported 29 per cent.
Electronic copy available at: http://ssrn.com/abstract=663665
2
Unfortunately, the published research on annual earnings forecasts does not allow for direct testing of the
preceding four conclusions. The most popular methods used to forecast earnings, judging from the published
studies, are judgment (by either management or outside analyst) and extrapolation. Judgment involves causality (a
plus given the first conclusion) and subjectivity (a minus given the second conclusion). Extrapolation is objective (a
plus), but does not incorporate causality (a minus): The effects of these two key dimensions, causality and
objectivity, have been confounded in the research published to date.
For judgmental forecasts, the third conclusion suggests that outside analysts should generate more accurate
forecasts than management. However, in this situation management may have some control over earnings. This
control might lead one to prefer management over analysts. Thus, in Stewart”s (1973) survey, portfolio managers
expected management forecasts to be superior to analyst forecasts.
In view of an inadequate framework for enquiry, the assessment of methods for annual earnings forecasts
becomes primarily an empirical question. Which methods have proved most accurate?
Research on judgmental forecasts was reviewed by Richards and Fraser (1978), who concluded that there
were no differences in accuracy between analysts and managers.
Conclusions by researchers who have examined judgmental and extrapolative forecasts have been mixed.
Collins and Hopwood (1980) and Brandon and Jarrett (1977) concluded that judgment was superior; Gray (1974)
found judgment by analysts was better, but only in rapidly changing industries; Cragg and Malkiel (1968) concluded
that judgment performed “only a little better.” Others (Carey, 1978; Green and Segall, 1967; Richards and Fraser,
1978) have concluded that there were no differences. Lorek et al. (1976) concluded that extrapolation was superior.
An extensive review of the literature by Abdel-khalik and Thompson (1977-1978) concluded that judgment (by
analysts and by management) was about as accurate as extrapolations. They said: “Unfortunately, the evidence to
date is inconclusive” (p. 202).
Lorek et al. (1976) suggested amalgamated forecasts (conclusion four) as a logical area for research on
earnings forecasts. Prior research from other disciplines was clear-cut. Amalgamated forecasts were more accurate
than the average error for the components. All that is required is that there be some compensating errors; that is
cases where one method”s forecast is too low and another method”s forecast is too high. In earlier work (Armstrong,
1978, pp. 263-268), I reported that amalgamated forecasts were more accurate in 10 of 18 comparisons (the others
being ties). None of these studies, however, examined earnings forecasts.
This paper is an updated review of the empirical research on annual earnings forecasts. Much relevant
research has been published recently. For example, four of the five key studies on management versus analyst
forecasts were published after the Richards and Fraser (1978) review. Most of the 17 comparisons of judgment and
extrapolation were published after Abdel-khalik and Thompson (1977-1978). Unfortunately, no papers were found
that compared amalgamated earnings forecasts with those from judgmental and extrapolative methods.
The conclusions from this review differ substantially from those provided in the earlier reviews by
Richards and Fraser (1978) and by Abdel-khalik and Thompson (1977-1978).
2. Management vs. Analyst
The mean absolute percentage error (MAPE) was used to assess accuracy.
=
=
N
A
PA
MAPE
N
ii
ii
1
100
where
3
Aj is actual annual earnings for firm i,
Pi is forecasted annual earnings for firm i,
N is the total number of firms in the sample.
The MAPE has certain advantages: (1) it can be averaged across years as well as across firms; (2) it is easy to
interpret; and (3) it has been commonly used in previous research on earnings forecasts. Its major defect is that it is
not relevant for negative earnings or those near zero. Some studies discarded these observations, others used the
median rather than the mean, and some used a cutoff value for outliers (e.g. Brown and Niederhoffer, 1968).
Five studies allowed for direct comparisons of management and analyst forecasts of annual earnings per
share (EPS). The forecast horizon was less than one year and the final earnings report was available for the previous
year. Management was superior in all five studies, and the superiority of management forecasts was statistically
significant (p < 0.05) in three of them. With a null hypothesis that management and analysts are equal in accuracy,
the probability that management would be superior in all five studies is 0.03 (one-tailed binomial test assuming each
study to be independent and of equal validity). Over all five studies, management forecasts had a lower MAPE than
analyst forecasts (MAPEs of 15.9 vs. 17.7). A major shortcoming of these studies, however, is the limited time span
(1967-1974). Exhibit I summarizes the results.
Exhibit 1
Management vs. Analyst Forecast
MAPE*
Author (year)
Number
of
forecasts Years
(M)
Management
(A)
Analyst
Error ratio
(A/M)
Statistical
significance
Basi et al. (1976, p.
249)
88 1970-1971 10.1 13.8 1.36 0.011
Imhoff (1978,
p.846)
95 1971-1974 16.1 16.7 1.04 n.s.
Jaggi (1978, p.28) 156 1971-1974 26.7 28.3 1.06 0.05
Ruland (1978) 65 1970-1973 14.72 16.03 1.09 0.01
Barefield et al.
(1979, p. 144)
134 (1967-1969)
(1972-1974)
11.7 13.8 1.18 0.06
Averages3 15.9 17.7 1.11
* MAPE is the Mean Absolute Percentage Error.
1 This significance level was reported in Basi et al (1977). A critique of Basi et al is provided by Albrecht et al.
(1977b)
2 These results were provided in a private communication from Ruland.
3 All studies were weighted equally. The average ratio was based on the averages from the management and analyst
columns. The geometric mean of the error ratios for each study was 1.14.
Why were the management forecasts superior? One possible explanation is because of “inside
information”; another is management”s control over performance; a third is that management may influence
reported earnings; finally, management may have more recent information than the analysts have.
Managers sometimes have inside information. Brooks (1969) describes one such case – Texas Gulf
Sulphur. Finnerty (1976) and Jaffe (1974) showed that insiders outperformed the market. Ruland (1978 79) showed
that management”s inside information was valuable in predicting changes in the price of the firm”s stock. Additional
support was provided by Nichols and Tsay (1979) who found that the announcement of long-term forecasts affected
the stock price. Given that management has inside information, their forecasts should be superior to analysts”
forecasts, all other things being equal.
4
The superiority of management forecasts over analyst forecasts might also be explained by management”s
impact on performance. Forecasts by management often become targets, with efforts then being made to reach them.
Reported earnings can be manipulated to bring them into line with management”s forecast. For example,
extraordinary items are often a significant component of earnings per share (Nichols, 1973) and are subject to
control by management. Since 1973, however, changes in generally accepted accounting procedures (GAAP) have
made it more difficult to manipulate earnings by arbitrarily classifying certain events as extraordinary. Nevertheless,
management still can smooth earnings. To avoid pressure from stockholders, management can decrease expenditures
to boost earnings in bad years. To avoid high expectations among stockholders (and in some cases to avoid
government regulation), management would increase spending to bring earnings down in good years. Kamin and
Ronen (1978) and Smith (1976) found evidence that firms engage in smoothing (more often in management-run
than in owner-run companies). Circumstantial evidence on smoothing was also provided by Niederhoffer and Regan
(1972) and by Kross (1981): firms with poor earnings reported earnings later, which could relate to attempts to
improve reported earnings.
Managers have more recent information than analysts. This is especially true just prior to the release of the
interim reports. If this more recent information on the current earnings were valuable, one would expect analysts to
improve relative to management after the publication of the interim reports. Jaggi (1978) found that management
forecasts were significantly better than analysts before, but not after, the release of interim reports (Jaggi (1980)
provided additional analyses of these data). Ruland (1978) also found that management”s superiority over analysts
decreased after the release of interim reports. Similarly, Crichfield et al. (1978) found that the later in the year that
analysts made forecasts, the better their forecasts.
3. Judgment vs. Extrapolation Forecasts
Below, forecasts from both management and analysts are grouped. The common assumption was made that
management and analysts depended primarily upon their judgment in producing the forecasts. Firth”s (1975)
description of how experts forecast earnings is consistent with this assumption. Of course, many of these analysts
would also have had access to quantitative forecasts as an input to their judgments.
Numerous extrapolation techniques have been used for earnings forecasts, ranging from the no change
(martingale) model to Box-Jenkins modeling (Mabert and Radcliffe (1974) describe the use of the Box-Jenkins
procedure in financial problems). Some studies found that errors were not sensitive to the choice of an extrapolative
technique. Among these were comparisons for seven extrapolative techniques by Brandon and Jarrett (1977), ten by
Johnson and Schmitt (1974), three by Hagerman and Ruland (1979), and twenty-one by Carey (1978). Other studies
have found differences. Frank (1969) found increased accuracy by weighting the most recent data more heavily
(exponential smoothing was more accurate than moving averages) as did Elton and Gruber (1972). Brandon and
Jarrett (1979) found that mechanical revisions improved extrapolation forecasts. In an analysis of over 4000
forecasts for the years 1973-1977, Ruland (1980) compared 8 extrapolative models. His major conclusion was that
the simple martingale model was superior to the models that incorporated information about trends. Albrecht et al.
(1977a) found the martingale model to be equal in accuracy to firm-specific Box-Jenkins models.
In general, then, it was difficult to generalize about the best way to extrapolate earnings. As a result, the
comparisons of judgment and extrapolation included all studies. That is, no studies were discarded because of poor
techniques. Furthermore, if a study used more than one extrapolative technique, the average error was calculated
across methods, with each component weighted equally.
Results
All studies that I found that compared judgment and extrapolation of annual earnings were included. All
forecasts were made with horizons of less than one year and were conditioned upon knowledge of earnings for the
previous year.
5
The MAPE was used as the measure of accuracy. MAPEs were given in most of the published studies. For
Ruland (1978), the MAPE was provided by personal correspondence. I calculated the extrapolation MAPE for
Barefield and Comiskey”s paper (1975) using data provided by Comiskey. Elton and Gruber (1972) provided data
on squared errors in their paper, which was converted to an estimate of MAPE. (I used the formula presented by
Brown (1963, p.283.) In making these calculations7 it was not possible to obtain an extrapolation forecast for 1967.)
The median absolute percentage error was used for Brown and Rozeff”s (1978) data because it was not possible to
estimate the mean. Drafts of my paper were sent to authors of each study included in Exhibit 2, so that they could
check my interpretation of their study.
Exhibit 2 [next page] summarizes the results. Judgment was more accurate than extrapolation for 14 of the
17 comparisons (significant at p < 0.05 by the two-tailed binomial test, assuming that these were independent
observations and using the null hypothesis that the methods do not differ in accuracy). For eight of the comparisons,
the superiority of judgment was significant at p < 0.05. For the 16 comparisons that allowed an estimate, the average
MAPE for judgment was 21.0, whereas for extrapolation it was 28.4.
Each of the three comparisons that showed extrapolation to be superior was suspect. In the work of
Hagerman and Ruland (1979), the high MAPEs were due to one outlier which was 4400 percent; judgment was
found to be superior using the median absolute percentage error. Lorek (personal communication) reported that he
was unable to replicate his findings on the superiority of extrapolation when using a new sample. Finally, Elton and
Gruber selected the best of nine extrapolative methods for comparison against the analyst forecasts; but even here
extrapolation had an insignificant advantage.
Sophisticated extrapolation methods were used in six of the comparisons (Lorek et al., Elton and Gruber
(3), Collins and Hopwood and Brown and Rozeff). Judgment was superior in four of these six comparisons. But the
two cases showing extrapolation to be superior (Lorek et al. and Elton and Gruber) were suspect, as noted in the
preceding paragraph.
Five studies (Hagerman and Ruland, Crichfield et al., Collins and Hopwood, Brandon and Jarrett and
Brown and Rozeff) used a criterion that compensated for the effect of outliers. Judgment was superior in each of
these comparisons.
Possible explanations for superiority of judgment
One possibility is that the samples were not typical of the total population. In the work of McDonald
(1973), managers expecting bad years were found to be less likely to make forecasts of their firm”s earnings. The
results from studies of management forecasts (such as the present study) are only applicable to situations where
managers publish their forecasts.
Part of the superiority of the judgment methods may be due to the advantages of management forecasts; that
is, inside information and the control over earnings by management. However, the analysts were also superior to
extrapolation: for the 12 studies allowing a comparison, the MA PE for the analysts” error was 17.7 compared with
27.4 for the extrapolations.
Experts possess information about a variety of factors that cause changes in earnings, such as recent tax
changes, new competitive developments, new products or new laws. It is possible that this additional information
allows them to forecast changes in annual earnings more accurately than can be done by naive extrapolations of
historical data.
Typically, published accounting data lags behind actual events. Quarterly earnings are published about a
month after the end of a reporting period and annual earnings are published about two months after the end of the
year. Managers and analysts usually have more recent information than is published in these reports. In other words,
they have a better knowledge of current earnings. Previously (Armstrong, 1978, pp.84 89) I concluded that the
relative advantage of experts is in assessing how things are now, rather than how they will change in the future. If
current earnings estimates are unreliable, one might expect expert information to yield more accurate estimates of
the current rate of earnings.
Exhibit 2. Accuracy of Judgmental and Extrapolation Earnings Forecasts
MAPE2
Study Source1 Time span
# of
firms Judgment Extrapolation
Error ratio
(exploration/
judgment)
Statistical
significance Comments
Hagerman & Ruland (1979, p.
174, 175)
W.S.J. 1969-1973 98 (M) 76.4 65.3 0.85 0.05 Median percentage errors were
7.4 for judgment vs. 13.6 for
extrapolation.
Crichfield et al. (1978) S & P 1967-1976 46 (M) 1.0 n.t. Researchers unable to provide
MAPEs
Copeland & Marioni (1972, p.
505)
W.S.J. 1968 49 (M) 20.1 33.8 (2) 1.68 0.05
Lorek et al (1976, pp. 324,
325)
W.S.J. 1966-1970 37 (M) 13.0 5.6 0.43 0.01 Loreck was unable to replicate.
(Personal communication. See
also Lorek, 1979)
Ruland (1978) W.S.J. 1970-1973 65 (M) 14.7 21.5 1.46 0.01 MAPEs from personal
communication from Ruland
Ruland (1978) S & P. 1970-1973 65 (M) 16.0 21.5 1.34 0.05
Elton & Gruber (1972, p. B-
419)
S & P 1964-1966 213
177
84
(A) 12.2
(A) 14.8
(A) 14.1
11.9
15.0
16.8
0.98
1.01
1.19
n.s.
n.s.
n.s.
MAPE estimated from data of
E&G Table 3, where the best of
nine extrapolation models was
used
Klepczynksi, in Basi et al.
(1976, p. 245)
S & P 1966-1968 47 (A) 7.3 (2) 13.3 1.82 n.t.
Barfield & Comiskey (1975) S & P 1968-1972 100 (A) 16.5 27.9 1.69 0.01 Calculated extrapolation error
with data from Comiskey
Collins & Hopwood (1980,
p.398)
Value
Line
1970-1974 50 (A) 34.1 59.6 (4) 1.74 0.05 Judgment also superior when
MAPE was adjusted for
outliners.
Brandon & Jarrett (1977, p.
44)
S & P 1970-1974 27 (A) 20.3 60.9 (7) 3.00 n.s. Judgment was significantly
more accurate by the sing test.
Brown & Jarrett (1977, p. 44) Moody”
s
1972-1975 50 (A) 18.6 23.5(3) 1.26 0.05 Median error from B & R Table
2
Richards et al, (1977, p. 82) S & P 1969-1972 50 (A)) 18.1 24.2(3) 1.34 n.t.
Richards et al, (1977, p. 82) S & P 1972-1976 92 (A) 24.1 34.3 1.42 0.05
Fried & Givoly (1982, p. 91) S & P 1969-1979 424 (A) 16.4 19.8(2) 1.21 0.01
Averages (each comparison weighted equally)
21.0
28.4
1.35
1 W.S.J. = Wall Street Journal; S. & P. = Standard and Poor”s.
2 Where alternative forecasts were provided, an average error was calculated. The number of forecasts in the average is indicated by the number in
parentheses. All errors based on MAPE except as indicated under notes column. The (M) designates a management forecast and the (A) designates
an analyst forecas
6
It seems obvious that better information on the current situation should improve the annual earnings
estimate. Surprisingly, this argument was challenged by Green and Segall (1966, 1967), who concluded that interim
reports did not improve annual earnings forecasts. Numerous researchers contested this (e.g. Coates, 1972). Brown
and Rozeff(1979) reanalyzed data used by Green and Segall and found that interim reports had, in fact, led to
improvements in accuracy.
In summary, the evidence suggests that experts, including management and analysts, have valuable
information on a firm”s current status. This information apparently helps them make better forecasts than those
obtained from extrapolations.
4. Proposals for Further Research
The research to date has been useful for assessing differences in accuracy among the various forecasting
methods. But more could be done to explain the conditions under which one method would be better than another.
For example, under what circumstances is the accuracy of management forecasts likely to be superior to that of
analysts? To assess this question, detailed data would be required on the situation faced by each firm in the sample.
The possibility also exists that econometric models would yield superior forecasts, but little research was
found on this topic. Hagerman and Ruland (1979), Chant (1980) and Hopwood (1980) used crude econometric
models, but the accuracy of those models did not differ substantially from the accuracy of naive extrapolations. A
more relevant test would be to incorporate firm-specific causal information. Collins (1976) took a step in this
direction and found that a segmentation method with firm-specific data was more accurate than six extrapolative
methods. The use of econometric methods for each firm offers a promising area for further research.
Research using econometric methods would help to identify the importance of the two key dimensions
objectivity and causality—upon the accuracy of forecasts. A comparison of econometric and judgmental methods,
each of which examines causality, would allow for an examination of the importance of using causality in a more
objective manner.
Amalgamated forecasts also offer some promise. In view of the lack of research to date, efforts in this area
would be useful. Granger and Newbold (1977, pp.268-278) discuss procedures for combining forecasts.
5. Conclusions
The accuracy of management and analyst forecasts was compared by reanalysing data from previously
published studies. In each of the five studies allowing a comparison, management forecasts were superior. Across all
studies, the MAPEs for management and analysts were 15.9 and 17.7, respectively. Unfortunately, these results were
drawn from a limited time period, 1967 to 1974. Four possible explanations were proposed for management”s
superiority: (1) Managers sometimes have inside information; (2) managers exert control over performance; (3)
managers can influence the reported earnings; and (4) managers have more recent information. Additional research
is needed to assess the validity of each of these various explanations.
Judgmental forecasts (both management and analysts) and extrapolative forecasts were compared using
evidence from 13 studies. In 14 of the 17 comparisons, judgmental forecasts were found to be superior. Further
research is needed to determine whether the superiority of judgment is due to information on causality or to better
information about current earnings.
Research was suggested in additional areas. First, a more complete description is required of each firm”s
situation. Secondly, econometric models for each firm might be superior to either judgment or extrapolation.
Thirdly, amalgamated forecasts should be evaluated.
The implications for those who use annual earnings forecasts for financial planning within the firm, for
investment purposes by outsiders, or for research are:
7
1. Use earnings forecasts as published by top management if they are available. This conclusion
contrasts with the use of extrapolative forecasts in studies on market expectations (e.g. Beaver et
al., 1979).
2. Use published forecasts by outside analysts if published forecasts from top management are not
available.
3. Use extrapolations if judgmental forecasts are not available.
4.
When forecasts are available from more than one of the above sources, a weighted average might be considered,
perhaps with more weight on the forecasts by management than on extrapolative forecasts.
Acknowledgements
Robert Magee, Timothy R. Crichfield, Robert L. Hagerman and others commented on drafts of this paper. Eugene E.
Comiskey, Kenneth S. Lorek and William Ruland provided additional data. Much of the work on this paper was
done while the author was a Visiting Professor at IMEDE, Lausanne, Switzerland.
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... Men ging onder meer na of ondernemingen optimistisch dan wel pessimistisch waren bij het voorspellen en of de voorspelfouten samenhingen met de bedrijfstakindeling, met de conjunctuur, met het verloop van de historische winstreeks, etc. Voor een overzicht van de onderzoekresultaten kan worden verwezen naar bijv. Schreuder en Klaassen (1982), Armstrong (1983) en Brown e.a. (1984). ...
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