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FACULTY WORKING
PAPER NO. 1259
Evidence on Surrogates for Annual Earnings
Expectations Within a Capital Market Context
William S. Hopwood
James C. McKeown
College of Commerce and Business Administration
Bureau of Economic and Business Research
University of Illinois. Urbana-Champaign
^it:!,::
BEBR
FACULTY WORKING PAPER NO. 1259
College of Commerce and Business Administration
University of Illinois at Urbana-Champaign
June 1986
Evidence on Surrogates for Annual Earnings
Expectations Within a Capital Market Context
William S. Hopwood
The Florida State University
James C. McKeown, Professor
Department of Accountancy
EVIDENCE ON SURROGATES FOR A^MIAL EAPNINGS
EXPECTATIONS I-ttlHIN A CAPITAL llARKET CONIEXI
ABSTFACT
This study compared the abilities of statistical model forecasts
versus financial analyst forecasts to serve as surrogates for market
expectations of quarterly and annual earnings per share. We extended
previous research in terms of our sample, the statistical models
considered, by introduciing methodological refinements, and by controlling
for timing advantages favoring financial analysts.
The market association tests indicate that for annual earnings
expectations the financial analysts forecasts more closely surrogate
the capital markets' expectation than do the statistical models. On
the other hand, similar tests indicated that neither of these two
sources of forecasts is dominant with respect to interim earnings.
Additional tests were performed on the null hypothesis that the
financial analysts exploit all information used by the time-series
models. The data indicate rejection of this hypothesis for both annual
and interim forecasts. Finally, forecast error analysis supports
previous research in finding that analysts' forecasts are more accurate
than those of statistical models. However, this superiority disappears
after controlling for hypothesized timing advantages favoring the
analysts .
EVIDENCE ON SURROGATES FOR ANNUAL EARNINGS
EXPECTATIONS WITHIN A CAPITAL MARKET CONTEXT
A substantial body of accounting research has relied on expectations
or forecasts of earnings or earnings per share. This is expecially true in
the capital market/informational content area. Examples of such studies
are those of Ball and Brown [1968], Beaver [1968], Beaver and Dukes [1972],
Brown and Kennelly [1972], Joy et al . [1977] and Kiger [1972].
The importance of the choice of the forecast used in capital market
research designs has been widely recognized. For example, Foster [1977, p.
2] wrote "choice of an inappropriate [forecast] model (one inconsistent
with the time series) may lead to erroneous inferences about the
information content of accounting data." This fact has contributed to
motivating a large number of studies comparing accuracy of competing
sources of earnings forecasts. Some have focused on the relative forecast
accuracy of statistical models (e.g.. Brown and Rozeff [1979], Griffin
[1977], Lorek [1979] and Watts [1975]). Others have focused on forecast
accuracy of financial analysts versus statistical models (e.g.. Brown and
Rozeff [1978] and Collins and Hopwood [1980]). These and other studies
have provided evidence that the financial analysts provide expectations of
earnings which are substantially more accurate than those generated by the
statistical models examined thus far.
While information on forecast accuracy has, to a degree, served as a
measure of the usefulness of a given source of forecasts, a number of
researchers (e.g.. Brown and Kennelly [1972], Foster [1977], Watts [1978]
and Fried and Givoly [1982] have noted that a more direct approach to
evaluating a forecast source is to examine the association between its
forecast error and abnormal security returns. For example. Brown and
Kennelly [1972, p. 104] write:
This experimental design permits a direct comparison between
alternative forecasting rules . . . The . . . contention is
based on the hypothesis (and evidence) that the stock market
is "both efficient and unbiased in that, if information is
useful in forming capital asset prices, then the market will
adjust asset prices to the information quickly and without
leaving any opportunity for further abnormal gain" (Ball and
Brown [1968]. There is, then a presumption that the consensus
of the market reflects, at any point, an estimate of future
EPS which is the best possible from generally available data.
Since the abnormal rate of return measures the extent to which
the market has reacted to errors in its previous expectations,
the abnormal rate of return can be used to assess the
predictive accuracy of any device which attempts to forecast a
number that is relevant to investors. [Emphasis added]
Along these lines, Foster [1977] investigated several models for
quarterly earnings and found that a model with both seasonal and non-
seasonal components best represented the market expectation for
earnings, where the "best expectation" was measured in terms of
association between model error and risk adjusted returns. Using
similar methods. Brown and Kennelly [1972] found that certain quarterly
models generated better surrogates of capital market expectations than
those generated from annual models.
The purpose of the present study is therefore to further
investigate the issue of financial analysts versus statistical model
expectations within a capital market context. The most significant
aspect of our research is that is considers interim earnings on a
quarter-by-quarter basis using daily security returns. To our
knowledge, there has been little or no previous research comparing,
within a capital market context, single financial analyst forecasts to
those generated from statistical models within an interim context
However, there are a number of other major contributions involved in the
present study. In a general sense, relative to previous research, we
consider a broader set of (18) statistical models. We also provide
certain critical improvements in the areas of sampling restrictions and
design methodology. Finally, we investigate the possibility that at
least some of the previously reported advantage of Analysts' forecasts
over statistical models might be attributed to a timing advantage.
The remainder of this paper consists of five sections. The first
sets forth in detail the contribution of our study relative to previous
research. Section two summarizes the eighteen statistical expectation
models. Sections three and four give annual and quarterly forecast
results, respectively. The last section includes a summary and
conclusions.
THE CONTRIBUTION OF THE PRESENT STUDY RELATIVE TO
PREVIOUS RESEARCH
The present study improves on previous research by providing
contributions in four broad areas. These are: 1) Financial analyst
forecasts are incorporated into the design, and we present capital
market results for forecast comparisons between analyst and statistical
models for both interim and annual earnings forecasts, 2) A number of
specific methodological refinements (some of which we view as critical)
are made, 3) We considerably broaden the set of statistical models
used. Our broader set includes multivariate time-series models and
those that exploit interim data, and, 4) We extend previous research by
investigating the hypothesis that financial analyst forecast superiority
over statistical models can be accounted for by a timing advantage.
Each of these areas is discussed individually.
Financial Analysts Forecasts and Interim Earnings
Previous studies comparing various forecasts in a capital market
context have typically either: 1) not incorporated financial analyst
forecasts, or 2) not incorporated abnormal returns for interim
periods. The present study therefore incorporates a very broad set of
statistical model forecasts, financial analyst forecasts and capital
market results for interim earnings. As stated above this is a major
contribution of the present research. The present section reviews the
relevant aspects of several major publications in this area of research.
The studies of Bathke and Lorek [1984], Brown and Kennel ly [1972]
and Foster [1977] showed, among other things, that different expectation
models provide forecast errors with varying degrees of association with
risk adjusted returns. However, none of these studies included
forecasts of financial analysts which, as cited above, have been shown
to produce the most accurate forecasts. The present study includes this
source of forecasts.
Also of importance is the Fried and Givoly [1982] study which
compared association between abnormal returns and annual forecast errors
from both statistical models and financial analysts. Their study
included forecasts from Standard and Poor's Earnings Forecaster
(financial analysts) and two statistical models: a variation on the
Ball and Brown [1968] index model and a random walk model with drift.
Their overall results (p. 97) indicated a correlation between abnormal
returns and annual forecast errors to be .33 for the analysts and .27
for the two statistical models. The authors noted, however, that their
results have limited generality. First, they only considered firms for
which at least four contemporaneous forecasts were available in the
Earnings Forecaster. They noted that this led to exclusion of firms to
which relatively less attention was given by analysts. Second they
considered only two time series models, both of which do not exploit
interim earnings information, whereas the analysts are able to use this
information. This is important since Hopwood, McKeown and Newbold
[1982] found that the disaggregated interim earnings have more
information than the annual earnings alone.
An additional limitation of the Fried and Givoly [1982] study is
that it focused on annual as opposed to interim earnings. In the
previous paragraph it was indicated that the models used to predict
annual earnings did not use quarterly data for parameter estimation.
The point here is that object of prediction was annual as opposed to
interim earnings. Therefore, in this respect, the interim results in
this paper are an extension of Fried and Givoly [1982].
A final problem with the previous literature is that many studies
have not controlled for timing advantages pertinent to analyst
forecasts. In particular, analysts' forecasts are released throughout
the entire year and sometimes right before the earnings announcement.
It should be no surprise that forecasts released relatively close to the
announcement date an: more accurate than those generated by statistical
models that generate forecasts made from different base points in time.
Methodological Refinements
Our methodology parallels that of Fried and Givoly {[1982], hence-
forth FG) In comparing the abilities of statistical model forecasts
versus financial analyst forecasts to serve as surrogates for market
expectations of annual earnings per share. However, In addition to
addressing different research questions, we Included a larger number of
statistical models that are more representative of those contained in
the current accounting literature. We also Incorporated a number of
other methodological refinements. First, we utilized the actual
announcement dates of the firms' earnings in computing the abnormal
returns. FG used the more restrictive and potentially biasing
assumption that earnings for all firms were announced at the end of
February.
Second, we used Spearman correlations to avoid distriubtional
problems. FG cited the investigation of Beaver, Clark and Wright [1979]
as justification for using the correlation coefficient as a measure of
association between forecast error and abnormal return. However, they
used the Pearson correlation whereas Beaver, Clark and Wright
investigated only the use of the Spearman correlation. This difference
is Important because it is well known that forecast error distributions
based on percentage accuracy metrics are nonnormal and highly skewed.
Third, we avoid the use of the weighted API statistic which we show
(see Appendix A) is heavily Influenced by bias. The issue of bias is
Important because for the FG data, the analysts have an overall negative
bias (over-prediction) in excess of 5% whereas the two statistical
models have a substantially smaller bias, less than 1.5%. The negative
bias for the analysts forecasts combined with the overall negative CAR
for their data produces a situation where the numerator in the weighted
API, (equation 3, Appendix A) is likely to be biased upward by causing
an excessively high number of positive cross products in the numerator
as compared to what would be obtained from the numerator of (equation 4,
Appendix A) which adjusts for bias. Similarly the weighted API
statistics for their index model are likely to be understated because of
a positive bias. Of course, we would expect the biasing effect to be
larger for the analysts since the magnitude of the bias in their
forecast was larger.
We note also the possible impact of bias on FG's frequency analysis
(p. 96) which measured (in a 2 x 2 table for each forecast method) cases
where the signs of the forecast errors were consistent with the signs of
cumulative abnormal returns. One explanation why the analysis did
better for their negative CAR cases was that they simply had far more
forecast errors less than zero (630 versus 483 and 444). We avoid all
of these problems by simply using the Spearman rank correlation
coefficient, as originally suggested by Beaver, Clark and Wright
[1979]. We do not use the other measures of association because of the
problems stated above.
Fourth, the present study uses a market based methodology to
directly assess the relative ability of different models to surrogate
the market expectation. FG did not directly address this question. (It
appears that they were primarily interested in addressing a different
question, as discussed below.) This contrasts to the FG study is that
they computed the following set of partial correlations:
(A) R{E, FAF I MSM)
(B) R(E, FAF I IM)
(C) R(E, FAF I MSM. IM)
(D) R(E, MSM I FAF)
(E) R(E, IM I FAF)
where E denotes the realized earnings, FAF, IM and MSM denote forecasted
earnaings for the financial analysts, index model and modified
submartingale models respectively. Their data indicated that (A), (B)
and (C) were all nonzero while (D) and (E) were typically not different
from zero. This led them to conclude (p. 100) that analysts use
autonomous information and also fully exploit the time-series and cross
sectional properties of the earnings series that are captured by the MSM
and IM.
We note that these partial correlation tests relate only indirectly
to the surrogation issue for market expectations, since risk adjusted
returns are not included. Furthermore, ranking models based on the
correlation between their forecasts and realized earnings can be
misleading if the forecasts are biased. An example of this problem can
be seen from the hypothetical situation where a forecast method results
in forecasts exactly double the realized earnings. If this occurs for
all firms in a given year, there will be a correlation of 1, but this
forecast method clearly would not be preferred to a method that had a
correlation of .9, but with no bias. Of course, if the bias of the
former method is stable over time, one could adjust the forecasts by
dividing by two. If this were possible, the former method would be
preferred. The problem is that FG made such adjustments (p. 92) without
any reduction in forecast error, thus indicating a lack of stability in
bias over time.
Timing Advantage
As previously discussed, financial analysts have a potential timing
advantage over statistical models (henceforth SM's). SM forecasts are
effectively made based on information up to and including the most
recent earnings announcement. For example, consider a forecast of the
third quarter's earnings made one quarter into the future. A model that
uses interim earnings will incorporate the second quarter's earnings.
Therefore, this forecast is effectively made at the time of the second
quarter's earnings announcement date.
In the present example, the analyst's timing advantage arises
because the analyst's forecast will typically be made after the second
quarter's announcement. In fact the analyst's forecast might even be
released within t±ie two weeks before the third quarter's earnings
release. The present study controls for this timing advantage by
explicitly considering (in terms of the present example) the number of
days of timing advantage.
Statistical Expectations Models
The present study uses a broad set of 18 statistical expectation
models (discussed in a separate section) that forecast both interim and
annual earnings. This broad set of models removes at least three
limitations found in previous literature. First, as discussed above,
models forecasting interim earnings serve as a basis for comparing
interim forecasts of financial analysts versus statistical models within
a capital market context. Second, the incorporation of interim earnings
into the model forecasting annual earnaings allows the statistical model
10
access to a broader information set than used by studies (e.g., FG)
incorporating only annual data. This is important because interim data
can improve forecast accuracy for annual earnings (Hopwood, McKeown and
Newbold [1982]). Third, we use multivariate time series models which
can incorporate market information and simultaneously exploit the time
series properties of the earnings series.
MODELS PREVIOUSLY USED IN THE LITERATURE
Earnings expectation models can be classified as univariate and
multivariate. We use the term multivariate to include models which
consider the structural relationship between two or more variables. In
addition these models can be further classified as to those based solely
on annual data versus those based on quarterly data; therefore,
producing four categories of models. Each of these categories is
discussed invididually.
Multivariate Models Using Annual Data
These include the model of Ball and Brown [1968] who regressed an
index of annual market earnings changes against the annual earnings
changes of individual firms. This model is of the form:
(1) (y^ "Vi^ = ^^^^h - Vi^ ^n
Where y^ represents the annual earnings of the firm, x^ represents a
market-wide earnings index, and t is a time subscript denoting a
particular year. Also, a and 6 are estimated using historical data.
Multivariate Models Using Quarterly Data
Similarly, Brown and Kennelly [1972] used the same model as Ball
and Brown but applied it to quarterly, instead of annual, data. Hence-
9
forth, these will be referred to as the BB and BK models.
11
A priori, both the BB and BK models have the advantage of defining
expected earnings relative to the market's earnings. This type of
expectation eliminates the effect of market fluctuations on the
individual firm expectations. As long as a firm maintains a constant
earnings relation to the market from period to period, unexpected
earnings will be zero.
On the other hand, neither of these models explicitly models
earnings performance of a firm relative to previous performance for the
same firm. In other words, the times-series properties of earnings Are
not explicitly modeled. The BK model also ignores the fact that firm
earnings are seasonally correlated and therefore is likely to have a
problem of seasonally auto-correlated residuals.
To address these and other problems Hopwood and McKeown [1981]
Introduced two single input transfer function-noise models (henceforth
HMl and HM2) which, within a bivariate time-series context, structurally
relate a market index of earnings to the individual firm's earnings.
The two models are of the form:
(1^ ^t - yt-4 = 'o " "o (^-^-4^ ' h\-l " ^4^-4 " \
^2) ^t - yt-4 = V\ ^\-'t-A^ ' \% ^(^-^-4^ ■ ^^-1-^-5^^
Where y.^ denotes quarterly adjusted earnings per share, x^ denotes an
index of market earnings, [9,- ,(^„,'l'i ] are model parameters, a,, is an
1 0 i. •*
uncorrelated residual series, and n is the noise series or the error
from the transfer function part of the model.
12
Actual versus Forecasted Index Models
Note that all of the bivariate models (i.e., HMl, HM2, BK and BB)
can be based on either a forecasted or actual index. We have therefore
added the HMIF, HM2F, BKF and BBF models which are based on a forecasted
index. Henceforth we shall refer to the latter type of models as FI
(Forecasted Index) models, and the HMl, HM2, BK and BB models as AI
(Actual Index) models.
The question arises as to whether the AI or FI models are the more
appropriate models for investigation. One might argue that AI model
forecasts aren't really forecasts at all since they rely on knowing an
index value that exists in the same period to which the forecast
relates. Nevertheless, this use of the term "forecast" is well
entrenched in the literature. Therefore, the present paper seeks to
differentiate between the objectives of the two kinds of forecasts
rather than debate nomenclature.
Univariate Models Using Quarterly Data
Unlike the bivariate regression models, univariate models ignore
the firm's relation to the market (or other indicators) but explicitly
model the time-series properties of the earnings number. Collins and
Hopwood [1980] studied the major univariate time-series models found in
recent literature. These include: (1) a consecutively and seasonally
differenced first order moving average and seasonal moving average model
(Griffin [1977] and Watts [1975]), (2) a seasonally differenced first
order auto-regressive model with a constant drift term (Foster [1977]),
and (3) a seasonally differenced first order auto-regressive and
seasonal moving average model (Brown and Rozeff [1978, 1979]). In the
13
Box and Jenkins terminology, these models are designated as (0,1,1) x
(0,1,1), (1,0,0) X (0,1,0) and (1,0,0) x (0,1,1) respectively. In this
study, they are referred to as the GW, F, and BR models. Collins and
Hopwood [1980] found that the BR and GW models produced annual forecasts
which were more accurate than the F model. In addition, they concluded
that they also did at least as well as the more costly individually
identified Box-Jenkins (BJ) models. Most important, they found the
analysts' forecasts significantly more accurate than all of the
univariate models examined.
Univariate Models Using Annual Data
The results of a large number of studies provide a substantial
amount of evidence that annual earnings follow a random walk (henceforth
RW) or a random walk with a drift. Support for this conclusion comes
from Ball and Watts [1972], Beaver [1970], Brealy [1969], Little and
Rayner [1965], Lookabill [1976] and Salamon and Smith [1977]. In
addition, Albrecht et al . [1977] and Watts and Leftwich [1977] found
that full Box-Jenkins analysis of individual series did not provide more
accurate forecasts than those of the random walk or random walk with
drift.
Synthesis
The above models are summarized in Figure 1.
14
Structure:
Figure 1
Univariate
Multivariate
Data Used for Estimation:
Annual Quarterly
BJ
BR
RW-Drift
GW
BJ
F
I
II
BB
HMl
HM2
BK
III
IV
Previous research has focused on comparing models within Category
II (e.g., Collins and Hopwood [1980] and Brown and Rozeff [1979]), with-
in Category I (e.g.. Watts and Leftwich [1977]), or between Categories
II and IV (Hopwood and McKeown [1981]). Relatively little attention has
been devoted to comparing models between (I, III) and (II, IV), in spite
of the fact that models in both of these sets have been used to forecast
the same objective, annual earnings. The present research investigates
all four categories (and in addition financial analysts forecasts),
thereby providing a unified framework for model evaluation.
ANNUAL FORECASTS
Sample
The sample in this study includes all firms which met the following
criteria:
15
1. Quarterly earnings available on Compustat for all quarters for
the period 1962-1978 with fiscal year ending in December for
each year in that period.
2. Value Line Investment Survey forecasts available from the
period 1974-1978.'^
3. Monthly market returns available on the CRSP tape from 1970
through 1978.
These restrictions resulted in a sample of 258 firms. ^
The first criterion assured that a sufficient number of
observations (17 years or 68 quarters) were available for time series
modeling. Based upon the Box-Jenkins [1970] rule of thumb requiring
approximately 50 observations, 20 time-series models were estimated for
each firm based on 48, 49, ..., 67 observations. In other words, the
first model estimation used data for the 48 quarters beginning at the
first quarter of 1962 and ending with the 4th quarter of 1973. The next
model incorporated data from the first quarter of 1962 through the first
quarter of 1974.
Application of the Models to the Capital Market
The market model of the form:
(2) ELlnd . R.^ - R^^)] = a. . 3,ln(l . R^^ - R^^)
was estimated, where (2) is the log form of the Sharp-Lintner [Lintner,
1965] capital asset pricing model and R^-^ represents the return on
asset i in period t, R^.^ represents the return on a value-weighted
market index in period t and R^^ is the risk free (treasury bill) rate
of return in period t. The estimation of a. and 3- was done using
ordinary least squares regression for each year in the hold-out period.
The estimations were performed in each case by including monthly data
16
for the 5 years preceding the hold-out year. The sum of the residuals
(post-sample forecast errors) from these models when applied to the
hold-out years (the twelve months up to and including the annual earn-
ings announcement date) constitute risk-adjusted abnormal returns. The
market index used was the value-weighted market index containing
dividend and price returns as supplied on the CRSP tape.'
The next phase was to estimate the association between the
unexpected annual earnings from the earnings expectation models and the
annual cumulative abnormal returns (CAR's). (These were computed by
adding the monthly returns.) This approach was outlined by Foster
[1977, p. 13]:
This analysis examines whether there is an association between
unexpected earnings changes and relative risk adjusted security
returns. Given a maintained hypothesis of an efficient market,
the strength of the association is dependent on how accurately
each expectation model captures the market's expectation
Foster applied this approach assuming a long investment given that the
unexpected earnings was positive and a short investment given that it was
negative. He then proceeded to measure the abnormal returns for different
forecast methods given this investment strategy.
Subsequent to Foster's research, Beaver, Clarke and Wright [1979] showed
that the magnitude of the unexpected earnings is an important determinant of
the size of the associated abnormal return (also see Joy et al. [1977]).
Furthermore, these empirical results were supported by the analytical work of
Ohlson [1978]. We therefore measured association via Spearman's rank
correlation between the scaled ((Actual - Predicted)/ jPredicted| ) unexpected
17
earnings of the individual models and the residuals (annual CAR) and averaged
these results across 4 hold-out years.
ANNUAL FORECAST RESULTS
Forecast accuracy results were computed, based on mean absolute relative
errors for all of the models discussed in Section 1. For each quarterly model
the mean annual errors are given tor forecasts made 4, 3, 2 and 1 quarters
prior to year end. For 4 quarters prior to year end, the annual forecast is
the sum of the forecasts for each of the one through four quarters ahead. For
3 quarters prior to year end, the annual forecast is the actual first quarter
earnings plus forecasts of the second, third and fourth quarter's earnings.
Therefore, realizations were substituted for forecasts as the end of the year
approached. Also, all of the statistical forecast models were reestimated and
reidentified as new quarters of earnings became available.
Model Performance
Table 1 gives the forecast errors, based on the mean absolute relative
error, defined as the average of | (actual-predicted)/(actual ) | . Each column
represents errors for different quarters relative to year end. Note in column
1 (which represents four quarter ahead annual forecast errors) that the
financial analysts forecasts are most accurate. This superior forecast
accuracy is consistent with many other studies (e.g.. Brown and Rozeff [1978])
and is therefore no surprise. Therefore these data simply confirm that our
sample does not differ substantially in this respect from other studies. We
also note that among the time series models using quarterly data, the HMl
model has the lowest average error for four quarter ahead forecasts. However,
it is also important to note that the difference between the best and worst -
18
TABLE 1 ABOUT HERE
(other than BBF) of these models is fairly small. Also it appears (consistent
with Collins and Hopwood [1980]) that the differences between all forecast
methods tend to decrease as the year end approaches.
Capital Market Results
Tables 2 through 4 give the rank correlations (as defined above) between
forecast errors and abnormal returns. In each table, each forecast method is
associated with 2 lines of data. The first line gives the rank correlation
and the second line the associated t values for the null hypothesis of a zero
correlation. Note in Table 2 that the analysts have the highest association
in each of the test years. Also the right hand column of Table 2 indicates
that (for the ranks pooled across years) the analyst association is
substantially higher than that of all of the statistical models.
TABLES 2 THROUGH 4 ABOUT HERE
Table 3 gives the rank correlations between risk adjusted returns and
model errors with the analyst errors held constant. This shows that the model
forecast errors have no consistent pattern of association with abnormal return
beyond that which is explained by the analysts. On the other hand. Table 4
strongly indicates that the analyst errors have a significant association with
abnormal returns even when the model errors are partialled out (models are
partial led out one at a time).
19
Finally, note in Table 2 that the BBF and BKF models have substantially
lower rank correlations, thus indicating that the market does react at the
individual firm level to forecast errors for the index.
Rank Correlations Between Actual Earnings and Forecasts
Tables 5 through 7 present results comparable to those in Tables 2
through 4, but using actual earnings instead of abnormal returns, and
forecasted earnings instead of forecast errors. We present these numbers
TABLES 5 THROUGH 7 ABOUT HERE
for comparability to Fried and Givoly [1982], though, as discussed above,
there are limitations to their interpretation. The most significant aspect of
this analysis is Table 6 which indicates that virtually all of the models
appear to have significant explanatory power beyond that of the analysts.
Note, however, that these results do not carry over into a capital market
context (i.e., they are inconsistent with Table 3). There are at least two
possible explanations for this finding. The first is (as discussed in Section
1) that there are problems with the statistics. If this is the case, then our
data indicate that this correlation is not a good surrogate for the capital
market based statistic used in Tables 2 through 4. A second explanation is
that the analysts do not utilize all information available and exploited by
the statistical models.
If the latter is true, then an interesting hypothesis may also be true.
That is, the analyst forecasts are (at least for our sample years and models)
the best surrogate for the market expectation even though they are not
optimal. One possible explanation for this is that the analysts' expectations
20
strongly influence (or even completely determine) the market expectation, even
when not optimal .
QUARTERLY FORECAST RESULTS
Tables 8 through 14 are direct analogs of tables 1 through 7, but are
based on quarterly (as opposed to annual) forecasts. Table 8 gives forecast
errors for forecast horizons extending 1, 2, 3 and 4 quarters into the
future. Tables 9, 10 and 11 give correlations between forecast errors and
CAR. Finally, tables 12, 13 and 14 give correlations between forecasts and
reported earnings.
Overall, the quarterly forecast error results in Table 8 are similar
to t±ie annual resiilts reported in the previoijs section. The analysts
consistently produce the most accurate forecasts. For example, for one
quarter ahead forecasts the average analyst error is .2804 while the next best
average is .3450 for the HM2 model. In summary, these results are consistent
with previous literature supporting superiority of analysts forecasts.
Table 9 indicates a consistent pattern of significant association between
the forecasts of all forecast methods and CAR. These data are again
consistent with our annual forecast data. Table 10 reports the correlation
between the statistical model forecast error and CAR after controlling for the
financial analyst forecast error. These data indicate for the large part that
the statistical models do retain some marginal association with CAR, even
after controlling for the analyst forecast error. For example, the GW model
has significant (alpha=.05, one tailed) t-values in 14 out of the 20 quarters
(i.e.. quarters 1, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 17, 18, 20).
21
Table 11 presents the correlations between analyst forecast errors and
CAR with the model forecast errors partial led out. These data indicate an
overall pattern of significance, but there are many cases where the t-values
are small. For example, for the GW model the t-value is significant at
alpha=.05 in only 9 out of the 20 quarters. Therefore, taken together tables
10 and 11 are consistent with the hypothesis that the analyst forecasts do not
uniquely capture the markets' expectations for earnings. Furthermore, the
large number of significant correlations in table 10 are supportive of the
hypothesis that the statistical model forecasts have incremental explanatory
power relative to analyst forecasts in terms of explaining CAR.
Tables 12, 13 and 14 represent results similar to Tables 9, 10 and 11,
but forecasts are correlated with actual earnings. As expected. Table 12
shows that forecasts and earnings are highly correlated. However, note that
Table 13 contains a large number of significant correlations. For example the
t-values are significant (alpha=.05) for the GW model in 17 out of the 20
quarters. Therefore these data are consistent with the hypothesis that the
analysts' forecasts do not fully exploit the univariate time-series properties
of reported quarterly earnings. Similarly, the results of Table 14 support
the hypothesis that the time-series models do not fully exploit the
information available to the analysts.
TABLES 8 THROUGH 14 ABOUT HERE
Timing Advantage Hypothesis
The present section investigates the hypothesis that the advantage of
analysts over statistical models is due to a timing advantage. Such a
22
possibility arises because analysts typically make their forecasts closer to
the announcement date of the target earnings than do the statistical models.
Consider, for example, forecasts of the second quarter's earnings. The
statistical models rely on the first (and previous) quarter's earnings and are
therefore effectively made from the date that the first quarter's earnings are
announced (although using only information throijgh the end of the first qxxarter)
However, in this case the analysi; forecast will often be made weeks later.
Therefore, there exists the possibility that the findings of "superiority" in
favor of the analysts can be accounted for by this timing advantage (based on
the analysts' opportunity to observe economic events in the second quarter
before making the forecast).
To test for a timing advantage, we first investigate the correlation
between the difference = (BJ absolute relative forecast error - Analyst
absolute relative forecast error) and the number of days separating these two
Q
forecasts. If there is an analyst timing advantage then this correlation
should have a tendency to be positive in each of the 20 quarters of our data
sample. In other words, we would expect that a larger number of days
separating the analyst forecast from the model forecast would be associated
with a larger timing advantage. Table 15 presents this correlation statistic
for each of the 20 quarters over the sample period. Note that the
correlations are positive in all 20 quarters. Under the null hypothesis of no
timing advantage, a simple sign test rejects the null hypothesis at the .01
level. Furthermore, the individual correlations are significant at the .05
level in 12 cases. Overall, Table 15 is supportive of an analyst timing
advantage.
23
INSERT TABLE 15 ABOUT HERE
To further investigate the timing advantage hypothesis and to provide an
alternative statistical approach, we also partition the quarterly forecast
accuracy results based on the number of days of timing advantage. Tables 16
through 20 give these results for 5 separate equal sample size sub-partitions
(Appendix B gives specifics on the timing advantages associated with each sub-
partition.) Table 16, the first sub-partition, includes cases where the
analyst timing advantage is the least. Going from Table 16 to Table 20 the
timing advantage increases and is largest in Table 20. Table 16 reveals that,
in contrast to the sample as a whole, the analyst forecasts are no longer the
most accurate after controlling for the timing advantage,. Note that in the
one-quarter-ahead case the analyst forecasts are no more accurate than those
of the BR and four HM models. Furthermore, in the four quarter ahead case the
analyst forecasts are not more accurate than any of the model forecasts,
including those of the BK forecasts which are generally quite poor (e.g.,) in
the one-quarter-ahead case the BK forecast errors are almost twice as large as
the BR forecast errors). Note on the other hand in the partition where the
analyst timing advantage is at a maximum (Table 20) that the analyst forecast
errors are consistently smaller than those of all models. This is true for
all forecast horizons, ranging from one to four quarters into the future.
Summary and Conclusions
This study investigated the use of statistical model forecasts versus
financial analyst forecasts as surrogates of capital market expectations for
both interim and annual eamirigs per share. In addition, this study provides
24
extensions to previous research by: incorporating fairly broad sampling
constraints, including a very general set of statistical models, making
certain critical methodological refinements and controlling for financial
analysts' timing advantages.
The empirical results for annual earnings indicated that the financial
analysts' forecast errors were more highly associated with risk adjusted
security returns than the forecast errors of statistical models. In addition,
the partial correlations between analyst errors (controlling for the
statistical model forecast errors) and risk adjusted security returns were
generally non-zero. On the other hand, the partial correlations between the
statistical model forecast errors (controlling for the analyst forecast error)
and risk adjusted security returns were not statistically significantly
different from zero. These data are consistent with the hypothesis that, in a
capital market context, the analysts' forecasts more closely approximate the
markets' expectation for annual earnings.
Similar tests were conducted for interim earnings forecasts. Both sets
of partial correlations described in the previous paragraph were non-zero. Of
particular interest is that the data indicated that the partial correlations
between risk adjusted security returns and statistical model forecasts
(controlling for the analyst forecast error) were typically non-zero. These
data are consistent with the hypothesis that analyst forecasts do not uniquely
surrogate for the markets' expectation of interim earnings.
We also investigated the association between earnings and forecasts. In
both cases the partial correlations between statistical model forecasts and
reported earnings were usually non-zero. These data are consistent with the
25
hypothesis that the financial analysts do not fully exploit the information
contained in previously published time series data.
Finally, the empirical forecast accuracy results were consistent with
previous literature and overall the financial analysts produced the most
accurate forecasts. This was true for both interim and annual forecast
errors. However, detailed analysis of the interim forecasts indicated that
the advantage of the financial analysts were essentially due to a timing
advantage. After controlling for the timing advantage the analysts' forecasts
were no longer the most accurate forecasts.
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34
Table 9
Rank Correlation of Quarterly Forecast Error with CAR
Quarter
Model
I
2
3
4
5
6
7
8
9
10
Grifffn-Watts
.2365
.1558
.2175
.2920
.2569
.1959
.3968
.1565
.2348
.2370
3.8181
2.4745
3.4946
4.7789
4.1697
3.1330
6.7806
2.4859
3.7815
3.8256
Griffln-Hatts with Constant
.2235
.1778
.2870
.3166
.2554
.2028
.4343
.1624
.1867
.2412
3.5972
2.8340
4.6985
5.2251
4.1433
3.2489
7.5614
2.5810
2.9749
3.8986
Foster
.1504
.1528
.2440
.3159
.2368
.2100
.3607
.2316
.3375
.2671
2.3863
2.4251
3.9466
5.2115
3.8220
3.3697
6.0666
3.7341
5.6116
4.3467
Foster with Constant
.1548
.1719
.2492
.3204
.2415
.2172
.3685
.2414
.3400
.2739
2.4582
2.7376
4.0359
5.2948
3.9031
3.4900
6.2170
3.9016
5.6588
4.4670
Brown-Rozeff
.2213
.1602
.2094
.2407
.1945
.1184
.3844
.1595
.2219
.1614
3.5598
2.5450
3.3586
3.8809
3.1094
1.8709
6.5309
2.5346
3.5620
2.5658
Brown-Rozeff with Constant
.2512
.2207
.2397
.2264
.1834
.1300
.3824
.1301
.2247
.1522
4.0704
3.5494
3.8717
3.6386
2.9262
2.0561
6.4916
2.0574
3.6096
2.4157
Box-Jenkins
.2592
.2377
.2221
.2349
.2271
.1514
.3214
.0934
.1968
.1615
4.2085
3.8385
3.5722
3.7834
3.6581
2.4030
5.3236
1.4710
3.1420
2.5664
Brown-Kennel 1y (AI)
.0685
.2149
.2249
.0495
.0805
-.0733
.2577
.1218
-.1128
.1862
1.0772
3.4517
3.6194
.7753
1.2674
-1.1530
4.1826
1.9239
-1.7777
2.9721
Brown-Kennel ly (FI)
-.0045
.3138
.2073
.2161
.0839
-.0572
.2669
.1283
.2273
.1803
-.0700
5.1840
3.3228
3.4649
1.3204
-.8989
4.3435
2.0296
3.6531
2.8750
Kopwood-McKeown 1 (AI)
.2521
.1147
.2451
.0664
.1510
.0875
.3547
.1191
.0715
.1779
4.0867
1.8108
3.9647
1.0410
2.3961
1.3774
5.9501
1.8807
1.1217
2.8347
Hopwood-HcKeown 1 (FI)
.1192
.1632
.2468
.2538
.2162
.1254
.3677
.1429
.4103
.1743
1.8826
2.5947
3.9943
4.1078
3.4735
1.9832
6.2008
2.2646
7.0419
2.7761
Hopwood-HcKeown 2 (AI)
.3062
.1511
.2578
.1195
.1542
.0792
.3937
.1295
-.0592
.1687
5.0445
2.3979
4.1851
1.8840
2.4483
1.2464
6.7177
2.0478
-.9281
2.6845
Hopwood-McKeown 2 (FI)
.2103
.1900
.2456
.2091
.1617
.1009
.3981
.1761
.2568
.1704
3.3735
3.0346
3.9740
3.3463
2.5707
1.5912
6.8064
2.8063
4.1597
2.7116
Analyst
.1053
.2107
.2259
.1797
.1387
.0869
.3128
.1201
.2731
.2343
1.6605
3.3810
3.6364
2.8596
2.1967
1.3675
5.1647
1.8976
4.4431
3.7793
35
Table 9 Continued
Quarter
Model
11
12
13
14
15
16
17
18
19
20
Grif tin-Watts
.1829
.2315
.0983
-.2278
.2095
.1407
.1848
.2270
.0677
.1664
2.9184
3.7327
1.5500
-3.6700
3.3603
2.2287
2.9492
3.6556
1.0638
2.6469
Griffin-Watts with Constant
.1626
.1550
.0557
-.1828
.2109
.1354
.1561
.2077
.0973
.2426
2.5839
2.4601
.8749
-2.9157
3.3840
2.1440
2.4784
3.3294
1.5338
3.9222
Foster
.1757
.1653
.0425
-.0254
.2546
.2490
.1982
.1446
.2156
.2374
2.7995
2.6280
.6669
-.3987
4,1297
4.0322
3.1720
2.2926
3.4630
3.8330
Foster with Constant
.1741
.1669
.0390
-.0155
.2763
.2526
.2005
.1616
.2167
.2451
2.7730
2.6555
.6115
-.2425
4.5089
4.0950
3.2095
2.5681
3.4813
3.9658
Brown-Rozeff
.1277
.1859
.0632
-.1916
.1639
.1362
.1674
.1494
.0064
.1337
2.0192
2.9681
.9925
-3.0621
2.6064
2.1563
2.6629
2.3704
.1010
2.1160
Brown-Rozeff with Constant
.1181
.2053
.0739
-.2174
.2172
.1232
.1580
.1969
-.0265
.1472
1.8659
3.2896
1.1629
-3.4936
3.4898
1.9465
2.5093
3.1491
-.4156
2.3338
Box-Jenkins
.2343
.1320
-.0019
-.1667
.2053
.1707
.1986
.2420
.0164
.1326
3.7795
2.0892
-.0291
-2.6514
3.2909
2.7167
3.1775
3.9111
.2569
2.0980
Brown-Kenelly (AI)
.2212
.1269
-.0279
-.1505
.2229
.0407
-.0666
.1328
-.0761
.1340
3.5577
2.0061
-.4371
-2.3880
3.5856
.6384
-1.0468
2.1023
-1.1976
2.1202
Brown-Kennel ly (FI)
.3092
.1285
-.0471
-.2141
.2166
.0483
-.0932
.1778
-.0191
.1037
5.0994
2.0322
-.7392
-3.4379
3.4805
.7577
-1.4689
2.8332
-.3000
1.6353
Hopwooa-McKeown 1 (AI)
.1495
.1742
.0442
-.1182
.2321
.1496
.2207
.1660
-.0122
.1857
2.3710
2.7741
.6938
-1.8665
3.7431
2.3726
3.5497
2.6410
-.1918
2.9636
Hopwood-McKeown 1 (FI)
.2505
.1788
.0352
-.1693
.2330
.1477
.2029
.1729
.0399
.1815
4.0589
2.8506
.5521
-2.6937
3.7582
2.3421
3.2499
2.7525
.6264
2.8950
Hopwood-HcKeown 2 (AI)
.0673
.1684
.0583
-.1680
.2128
.1675
.2028
.2010
-.0432
.1899
1.0576
2.6795
.9160
-2.6733
3.4167
2.6641
3.2477
3.2178
-.6783
3.0340
Hopwood-McKeown 2 (FI)
.1093
.1583
.0485
-.2034
.2070
.1626
.1918
.1932
-.0229
.1667
1.7240
2.5153
.7620
-3.2591
3.3178
2.5841
3.0649
3.0886
-.3592
2.6521
Analyst
.1399
.1391
.1154
.0804
.2482
.1129
.1165
.2361
.0614
.1747
2.2155
2.2037
1.8216
1.2654
4.0193
1.7819
1.8397
3.8103
.9656
2.7631
AI = multivariate model using actual index
FI = multivariate model using forecasted index
Note: Second row of each set is t-statistic testing correlation against a null hypotheses
of correlation equal to zero
36
Table 10
Partial Rank Correlation of Quarterly Model Forecast Error with CAR
(Analyst Forecast Error Held Constant)
Quarter
tedel
1
2
3
4
5
6
7
8
9
10
3r1f fin-Watts
.2130
.0192
.1157
.2345
.2214
.1802
.2784
.1059
.1124
.1455
3.4126
.3012
1.8228
3.7677
3.5534
2.8677
4.5377
1.6676
1.7674
2.3017
>1ff1n-Watts with Constant
.1983
.0582
.2044
.2650
.2190
.1871
.3285
.1145
.0362
.1508
3.1668
.9130
3.2683
4.2936
3.5139
2.9808
5.4435
1.8041
.5665
2.3872
-oster
.1142
.0081
.1402
.2644
.1976
.1948
.2361
.1995
.2463
.1811
1.7999
.1263
2.2172
4.2823
3.1546
3.1084
3.8027
3.1862
3.9705
2.8831
-oster with Constant
.1188
.0344
.1465
.2699
.2025
.2034
.2446
.2110
.2503
.1887
1.8725
.5385
2.3177
4.3789
3.2374
3.2517
3.9486
3.3787
4.0391
3.0081
3rown-Ro2eff
.1958
.0137
.1037
.1706
.1494
.0844
.2636
.1105
.0961
.0543
3.1249
.2137
1.6324
2.7047
2.3642
1.3251
4.2770
1.7407
1.5086
.8510
irown-Rozeff with Constant
.2311
.0978
.1353
.1525
.1349
.0985
.2525
.0712
.0872
.0345
3.7175
1.5388
2.1382
2.4104
2.1303
1.5488
4.0854
1.1166
1.3672
.5402
3ox-Jenlc1ns
.2388
.1338
.1159
.1667
.1861
.1247
.1735
.0290
.0424
.0500
3.8500
2.1130
1.8260
2.6412
2.9649
1.9666
2.7572
.4534
.6630
.7835
3rown-Kennel1y (AI)
.0406
.1545
.1709
-.0195
.0471
-.1162
.1662
.0662
-.1887
.0985
.6367
2.4473
2.7154
-.3051
.7381
-1.8311
2.6382
1.0390
-3.0019
1.5487
Brown-Kennel ly (FI)
-.0337
.2511
.1401
.1492
.0439
-.0936
.1727
.0738
.1533
.0902
-.5284
4.0610
2.2148
2.3570
.6875
-1.4720
2.7437
1.1584
2.4226
1.4172
lopwood-HcKeown 1 (AI)
.2319
-.0514
.1439
-.0329
.1111
.0458
.2069
.0557
-.0785
.0632
3.7312
-.8063
2.2763
-.5135
1.7496
.7182
3.3093
.8736
-1.2294
.9913
lopwood-HcKeown 1 (FI)
.0812
.0131
.1415
.1874
.1731
.0924
.2280
.0910
.3272
.0576
1.2754
.2048
2.2378
2.9800
2.7515
1.4518
3.6648
1.4310
5.4096
.9029
topwood-McKeown 2 (AI)
.2959
.0093
.1542
.0279
.1071
.0363
.2670
.0697
-.1909
.0752
4.8482
.1454
2.4433
.4355
1.6861
.5687
4.3367
1.0930
-3.0374
1.1803
lopwood-McKeown 2 (FI)
.1830
.0643
.1398
.1297
.1115
.0628
.2755
.1304
.1184
.0756
2.9143
1.0080
2.2102
2.0440
1.7565
.9849
4.4866
2.0586
1.8625
1.1872
37
Table 10 Continued
Quarter
iodel
Gri tf in-Watts
Gr1f fin-Watts with Constan
Foster
Foster with Constant
Brown-Rozef f
Brown-Rozeff with Constant
Box-Jenkins
Brown-Kennel ly (AI)
Brown-Kennel ly (FI)
Hopwood-McKeown 1 (AI)
Hopwood-HcKeown 1 (FI)
Hopwood-McKeown 2 (AI)
Hopwood-McKeown 2 (FI)
11
.1455
2.3017
.1179
1.8586
.1350
2.1329
.1323
2.0393
.0800
1.2560
.0656
1.0284
.1972
3.1482
.1951
3.1134
.2866
4.6829
.0957
1.5045
.2112
3.3816
.0064
.1002
.0566
.8871
12
.1874
2.9864
.0942
1.4817
.1140
1.7968
.1158
1.8242
.1319
2.0825
.1544
2.4465
.0652
1.0222
.0731
1.1481
.0775
1.2174
.1139
1.7939
.1222
1.9269
.1076
1.6948
.0953
1.4987
13
.0474
.7434
.0010
.0151
-.0156
-.2439
-.0209
-.3265
.0076
.1193
.0161
.2524
-.0531
-.8317
-.0707
-1.1092
-.0883
-1.3868
-.0195
-.3050
-.0305
-.4775
-.0014
-.0220
-.0137
-.2147
14
-.3021
-4.9608
-.2570
-4.1626
-.0917
-1.4417
-.0812
-1.2758
-.2680
-4.3547
-.2995
-4.9130
-.2191
-3.5142
-.2017
-3.2233
-.2770
-4.5131
-.1888
-3.0093
-.2515
-4.0666
-.2486
-4.0169
-.2840
-4.6360
15
.0943
1.4822
.0890
1.3991
.1440
2.2782
.1687
2.6785
.0356
.5575
.0932
1.4658
.0863
1.3554
.1271
2.0054
.1178
1.8575
.1094
1.7229
.1069
1.6828
.0938
1.4749
.0828
1.3003
16
.0906
1.4236
.0845
1.3276
.2239
3.5963
.2283
3.6700
.0865
1.3595
.0679
1.0654
.1310
2.0677
-.0071
-.1105
.0011
.0175
.1016
1.5979
.0990
1.5572
.1251
1.9737
.1187
1.8714
17
.1491
2.3594
.1145
1.8045
.1622
2.5731
.1649
2.6164
.1256
1.9821
.1141
1.7983
.1619
2.5686
-.1155
-1.8207
-.1446
-2.2877
.1889
3.0103
.1678
2.6649
.1671
2.6534
.1538
2.4371
18
.1369
2.1631
.1061
1.6703
.0521
.8163
.0694
1.0882
.0561
.8794
.1075
1.6920
.1662
2.6384
.0818
1.2844
.1147
1.8073
.0834
1.3106
.0797
1.2508
.1162
1.8317
.1028
1.6171
19
.0429
.6714
.0777
1.2195
.2092
3.3485
.2108
3.3752
-.0314
-.4911
-.0700
-1.0984
-.0177
-.2765
-.1127
-1.7761
-.0461
-.7228
-.0559
-.8763
.0081
.1264
-.0920
-1.4463
-.0681
-1.U678
20
.1063
1.6736
.1949
3.1105
.1817
2.8920
.1906
3.0386
.0724
1.1359
.0881
1.3851
.0797
1.2511
.1037
1.6322
.0588
.9225
.1336
2.1U96
.1267
1.9998
.1356
2.1422
.1078
1.6977
AI = multivariate model using actual index
I = mjltlvarlale model using forecasted index
Note: Second row of each set Is t-stat1st1c testing correlatl
of correlation equal to zero
on against a null hypotheses
38
Table 11
Partldl Rank Correlation of Quarterly Analyst Forecast Error with CAR
(Model Forecast Error Hela Constant)
Quarter
ode)
1
2
3
4
5
6
7
8
9
10
Griffin-Watts
-.0040
.1449
.1313
.0161
.0372
-.0382
.1106
.0318
.1815
.1409
-.0618
2.2915
2.0724
.2511
.5834
-.5988
1.7414
.4975
2.8827
2.2271
Griffin-Watts with Constant
.0005
.1287
.0952
.0038
.0337
-.0344
.0900
.0318
.2059
.1389
.0086
2.0306
1.4962
.0595
.5284
-.5392
1.4150
.4979
3.2869
2.1953
Foster
.0374
.1471
.1038
.0129
.0394
-.0336
.1437
.0004
.1378
.1252
.5859
2.3270
1.6335
.2017
.6172
-.5261
2.2730
.0063
2.1740
1.9756
Foster with Constant
.0330
.1283
.0994
.0118
.0350
-.0387
.1361
-.0058
.1385
.1209
.5166
2.0248
1.5639
.1838
.5488
-.6062
2.1509
-.0904
2.1850
1.9057
Brown-Rozeff
.0010
.1394
.1348
.0521
.0586
.0242
.1223
.0323
.1888
.1801
.0164
2.2033
2.1296
.8144
.9181
.3791
1.9283
.5061
3.0028
2.8662
Brown-Rozeff with Constant
-.0290
.0713
.1078
.0611
.0597
.0156
.1033
.0504
.1810
.1833
-.4534
1.1187
1.6977
.9557
.9354
.2602
1.6257
.7905
2.8750
2.9189
Box-Jenkins
-.0190
.0728
.1232
.0650
.0413
.0058
.1555
.0812
.1975
.1789
-.2981
1.1423
1.9437
1.0180
.6471
.0903
2.4633
1.2750
3.1472
2.8457
Brown-Kennelly (AI)
.0898
.1484
.1723
.1741
.1226
.1251
.2457
.0631
.3099
.1744
1.4111
2.3494
2.7374
2.7610
1.9331
1.9738
3.9672
.9902
5.0909
2.7729
Brown-Kennel 1y (FI)
.1104
.0829
.1670
.0865
.1191
.1141
.2400
.0582
.2170
.1762
1.7388
1.3015
2.6508
1.3558
1.8778
1.7973
3.8694
.9118
3.4721
2.8025
Hopwood-McKeown 1 (AI)
-.0270
.1850
.1062
.1705
.0934
.0446
.1102
.0580
.2749
.1670
-.4224
2.9468
1.6720
2.7028
1.4691
.6993
1.7353
.9089
4.4653
2.6518
Hopwood-McKeown 1 (FI)
.0588
.1357
.0985
.0444
.0444
.0167
.1050
.0471
.0802
.1688
.9215
2.1443
1.5494
.6944
.6963
.2607
1.6529
.7386
1.2562
2.6808
Hopwood-McKeown 2 (AI)
-.0657
.1488
.0873
.1380
.0829
.0509
.0919
.0499
.3243
.1808
-1.0302
2.3560
1.3718
2.1763
1.3013
.7982
1.4441
.7822
5.3546
2.8774
Hopwood-McKeown 2 (FI)
-.0015
.1128
.0992
.0715
.0736
.0358
.0965
.0130
.1520
.1794
-.0236
1.7772
1.5596
1.1191
1.1551
.5611
1.5182
.2037
2.4020
2.8547
39
Table 11 Continued
Quarter
;>de1
11
12
13
14
15
16
17
18
19
20
irif tin-Watts
.0842
.0145
.0769
.2184
.1651
.0327
.0372
.1520
.0321
.1191
1.3226
.2277
1.2074
3.5039
2.6209
.5125
.5829
2.4065
.5029
1.8776
3r1f fin-Watts with Constant
.0834
.0645
.1012
.2001
.1604
.0385
.0469
.1559
.0178
.0950
1.3100
1.0112
1.5921
3.1961
2.5435
.6024
.7354
2.4696
.2790
1.4944
Foster
.0823
.0703
.1085
.1191
.1319
-.0164
.0156
.1954
-.0305
.0809
1.2924
1.1029
1.7079
1.8778
2.0820
-.2565
.2447
3.1181
-.4782
1.2697
Foster with Constant
.0813
.0690
.1106
.1131
.1139
-.0200
.0142
.1873
-.0338
.0775
1.2775
1.0832
1.7424
1.7815
1.7947
-.3125
.2228
2.9844
-.5289
1.2162
Brown-Rozeff
.0984
.0437
.0970
.2066
.1922
.0402
.0340
.1929
.0687
.1344
1.5484
.6846
1.5261
3.3055
3.0652
.6294
.5321
3.0768
1.0772
2.1222
Jrown-Rozeff with Constant
.0998
.0252
.0902
.2252
.1540
.0465
.0388
.1703
.0892
.1295
1.5700
.3944
1.4183
3.6172
2.4402
.7282
.6071
2.7054
1.4022
2.0436
iox-Jenklns
.0545
.0787
.1268
.1647
.1661
.0237
.0039
.1572
.0618
.1394
.8538
1.2360
2.0013
2.6130
2.6372
.3715
.0611
2.4922
.9692
2.2041
Irown-Kennelly (AI)
.0914
.0930
.1322
.1574
.1689
.1056
.1497
.2126
.1035
.1531
1.4364
1.4621
2.0876
2.4955
2.6822
1.6625
2.3696
3.4054
1.6282
2.4244
irown-Kennelly (FI)
.0706
.0943
.1372
.1966
.1706
.1022
.1604
.1943
.0744
.1529
1.1080
1.4826
2.1678
3.1306
2.7093
1.6077
2.5437
3.1001
1.1674
2.4217
lopwood-McKeown 1 (AI)
.0796
.0423
.1084
.1683
.1416
.0238
.0056
.1890
.0821
.1176
1.2502
.6635
1.7070
2.6719
2.2391
.3730
.0875
3.0124
1.2894
1.8533
(opwood-McKeown 1 (FI)
.0235
.0457
.1140
.2045
.1381
.0249
.0141
.1812
.0475
.1166
.3680
.7161
1.7967
3.2707
2.1832
.3900
.2209
2.8836
.7436
1.8377
iopwood-McKeown 2 (AI)
.1231
.0493
.0997
.2019
.1605
.0125
.0037
.1711
.1018
.1129
1.9411
.7731
1.5688
3.2273
2.5444
.1954
.0576
2.7184
1.6017
1.7780
lopwood-HcKeown 2 (FI)
.1044
.0572
.1057
.2171
.1623
.0153
.0120
.1717
.0887
.1200
1.6428
.8974
1.6633
3.4820
2.5752
.2398
.1878
2.7276
1.3941
1.8921
\l - multivariate model using actual Index
"I " multivariate model using forecasted Index
<ote:
Second row of each set Is t-statlstic testing correlation against a null hypotheses
of correlation equal to zero
40
Table 12
Rank
Correlatl
on on Quarterly Basis
;~Actual
vs Forecast
Quarter
Model
1
2
3
4
5
6
7
8
9
10
Grif fin-Watts
.7858
.8917
.8794
.7527
.7241
.7297
.6996
.7107
.7753
.8013
18.8878
31.3952
29.3761
17.8951
15.7501
17.0751
15.6332
16.0674
19.4073
21.2589
Griffin-Watts with Constant
.7974
.8981
.8806
.7480
.7127
.7236
.6914
.6922
.7694
.7891
19.6436
32.5488
29.5582
17.6418
15.2407
16.7752
15.2815
15.2539
19.0466
20.3951
Foster
.7830
.8861
.8755
.7460
.7340
.7263
.7145
.6431
.6869
.7487
18.7141
30.4678
28.8127
17.5331
16.2115
16.9064
16.3060
13.3568
14.9456
17.9270
Foster wttn Constant
.7760
.8805
.8738
.7486
.7306
.7244
.7152
.6445
.6851
.7436
18.2894
29.6090
28.5873
17.6711
16.0519
16.8134
16.3396
13.4080
14.8699
17.6569
Brown-Rozeff
.7935
.9001
.8838
.7324
.7525
.7537
.7565
.7157
.7705
.8378
19.3810
32.9179
30.0423
16.8388
17.1371
18.3487
18.4714
16.2977
19.1109
24.3589
Brown-Rozeff with Constant
.7917
.8779
.8742
.7281
.7378
.7284
.7289
.7224
.7624
.8187
19.2653
29.2255
28.6349
16.6262
16.3948
17.0105
17.0039
16.6172
18.6272
22.6321
Box-Jenkins
.7680
.8370
.8336
.7359
.7072
.7337
.6399
.7216
.7460
.7429
17.8242
24.3772
24.0073
17.0110
15.0023
17.2748
13.2989
16.5784
17.7110
17.6189
Brown-Kennel ly (AI)
.5623
.7595
.7864
.5499
.7066
.7229
.5245
.6029
.6189
.7433
10.1092
18.6069
20.2475
10.3050
14.9793
16.7412
9.8375
12.0186
12.4599
17.6400
Brown-Kennel ly (FI)
.6433
.7673
.8216
.5910
.7022
.7220
.5553
.5067
.6093
.7343
12.4927
19.0679
22.9225
14.9623
14.7927
16.6968
10.6622
9.3496
12.1481
17.1721
Hopwood-McKeown 1 (AI)
.7375
.8663
.8636
.6905
.7247
.7318
.7033
.7252
.7703
.8422
16.2344
27.6418
27.2484
14.9419
15.7756
17.1812
15.7975
16.7531
19.1004
24.7921
Hopwood-McKeown 1 (FI)
.7580
.8725
.8738
.7346
.7522
.7309
.6946
.6973
.7266
.8421
17.2749
28.4628
28.5778
16.9486
17.1212
17.1368
15.4197
15.4747
16.7209
24.7824
Hopwood-McKeown 2 (AI)
.7496
.8721
.8561
.7003
.7799
.7364
.7207
.7010
.7273
.8448
16.8359
28.4052
26.3459
15.3542
18.6892
17.4178
16.6001
15.6346
16.7554
25.0608
Hopwood-McKeown 2 (FI)
.7512
.8675
.8636
.7284
.7553
.7457
.7170
.7130
.7808
.8443
16.9177
27.7884
27.2474
16.6387
17.2856
17.9046
16.4268
16.1724
19.7621
25.0063
Analyst
.8462
.8592
.8466
.8477
.8659
.8125
.8072
.7885
.8582
.8883
23.6071
26.7621
25.3054
25.0103
25.9643
22.3036
21.8337
20.3930
26.4379
30.7114
41
Table 12 continued
Quarter
•todel
11
12
13
14
15
16
17
18
19
20
GW
.8431
.7575
.7625
.7811
.8515
.8114
.8226
.7973
.7925
.7941
24.7429
18.2333
18.2594
19.8166
25.9264
22.1711
22.7325
20.9287
20.5899
20.37U3
Griffin-Watts with Constant
.8246
.7429
.7369
.8138
.8215
.8068
.8125
.7796
.7887
.7837
23.0034
17.4439
16.8864
22.1856
23.0068
21.8099
21.9024
19.7201
20.3257
19.6667
Foster
.7923
.6872
.7654
.8446
.8188
.7905
.8227
.8477
.7893
.8190
20.4922
14.8657
18.4234
24.9888
22.7775
20.6114
22.7467
25.3223
20.3681
22.2520
Foster with Constant
.7953
.6897
.7662
.8457
.8203
.7919
.8273
.8467
.7913
.8193
20.7007
14.9701
18.4736
25.1095
22.9069
20.7110
23.1463
25.2153
20.5021
22.2776
Brown-Rozeff
.8516
.7544
.7685
.8067
.8233
.8021
.8267
.8052
.7973
.8284
25.6340
18.0633
18.6091
21.6294
23.1597
21.4503
23.0952
21.5084
20.9282
23.0574
Brown-Rozeff with Constant
.8357
.7472
.7759
.8065
.8064
.8100
.8405
.8142
.8048
.8257
24.0080
17.6721
19.0509
21.6098
21.7730
22.0565
24.3781
22.2175
21.4806
22.8194
Box-Jenkins
.7844
.7170
.7822
.7627
.7788
.7750
.8047
.8015
.7420
.8263
19.9545
16.1637
19.4496
18.6823
19.8291
19.5801
21.3003
21.2343
17.5360
22.8714
Brown-Kennel ly (AI)
.7214
.5935
.6157
.6373
.7534
.6668
.6826
.6707
.7072
.7525
16.4392
11.5902
12.1036
13.1013
18.2962
14.2881
14.6801
14.3276
15.8468
17.8111
Brown-Kennel ly (FI)
.6724
.5425
.5971
.5899
.7221
.6630
.6696
.6215
.7314
.6544
14.3342
10.1492
11.5303
11.5731
16.6707
14.1425
14.1706
12.5691
16.99U
13.4907
Hopwood-McKeown 1 (AI)
.8408
.7509
.7709
.8381
.8291
.8007
.8392
.8387
.7846
.8352
24.5065
17.8694
18.7473
24.3434
23.6839
21.3411
24.2477
24.3974
20.0490
23.6784
Hopwood-McKeown 1 (FI)
.8427
.7519
.7551
.8378
.8326
.8029
.8371
.8365
.7906
.8523
24.6991
17.9247
17.8429
24.3122
24.0016
21.5109
24.0497
24.1820
20.4550
25.3976
Hopwood-McKeown 2 (AI)
.8138
.7316
.7813
.8134
.8118
.8125
.8480
.8210
.7970
.8539
22.1005
16.8674
19.3921
22.1544
22.2036
22.2577
25.1497
22.7807
20.9071
25.5752
Hopwood-McKeown 2 (FI)
.8285
.7411
.7824
.8082
.8217
.8126
.8478
.8007
.8037
.8568
23.3498
17.3456
19.4623
21.7399
23.0216
22.2668
25.1206
21.1780
21.4014
25.9061
Analyst
.8474
.8659
.8767
.8988
.8904
.9051
.8968
.9124
.8697
.9147
25.1887
27.2095
28.2394
32.4755
31.2384
33.9909
31.8518
35.3237
27.9216
35.2893
42
Table 13
Rank Correlation on Quarterly Basis — Actual vs Forecast
Correlations Between Model Forecast and Actual-- Analyst Held Constant
Quarter
Model
GH
Griffin-Watts with Constant
Foster
Foster with Constant
Brown-Rozeff
Brown-Rozeff with Constant
Box- Jenkins
Brown-Kennel ly (AI)
Brown-Kennel ly (FI)
Hopwood-McKeown 1 (AI)
Hopwood-HcKeown 1 (FI)
Hopwood-McKeown 2 (AI)
Hopwood-HcKeown 2 (FI)
1
2
3
4
5
6
7
8
9
10
.2121
.5167
.5094
.1420
.1065
.1930
.1819
.2881
.2244
.3585
3.2194
9.5981
9.3966
2.2410
1.6028
3.1406
2.9476
4.7751
3.6344
6.0849
.2447
.5485
.5196
.1473
.0675
.1802
.1700
.2692
.2012
.3333
3.7434
10.4344
9.6531
2.3270
1.0127
2.9261
2.7497
4.4370
3.2418
5.6010
.2219
.4663
.4790
.1395
.0928
.2367
.1812
.1666
.1661
.2843
3.3759
8.3840
8.6624
2.2003
1.3951
3.8898
2.9368
2.6825
2.6581
4.6978
.1894
.4417
.4689
.1494
.0762
.2371
.1827
.1686
.1644
.2733
2.8603
7.8306
8.4264
2.3599
1.1435
3.8971
2.9621
2.7147
2.6306
4.5020
.2436
.5416
.5225
.1122
.1283
.2504
.2927
.2919
.1737
.3900
3.7260
10.2478
9.7283
1.7642
1.9367
4.1303
4.8794
4.8444
2.7831
6.7096
.1648
.4121
.4798
.0999
.1140
.2010
.2534
.2928
.1636
.3525
2.4777
7.1940
8.6803
1.5683
1.7179
3.2761
4.1743
4.8603
2.6167
5.9675
.1235
.3382
.3497
.1073
.0935
.2011
.1071
.3036
.1561
.2042
1.8456
5.7162
5.9258
1.6859
1.4060
3.2790
1.7173
5.0588
2.4944
3.3047
.1176
.3246
.4479
.0979
.3707
.2528
.1720
.1880
.2468
.2580
1.7564
5.4582
7.9524
1.5365
5.9732
4.1732
2.7820
3.0389
4.0189
4.2315
.2502
.3063
.4786
.0928
.2660
.2594
.1837
.1182
.1607
.2420
3.8323
5.1175
8.6520
1.4557
4.1304
4.2888
2.9779
1.8898
2.5687
3.9518
.0677
.4505
.4892
.1159
.2662
.2270
.1429
.3111
.2139
.3915
1.0064
8.0266
8.9037
1.8224
4.1327
3.7226
2.3013
5.1959
3.4545
6.7397
.2034
.4276
.5072
.1118
.1682
.2350
.1520
.2987
.2025
.3871
3.0814
7.5234
9.3414
1.7570
2.5531
3.8609
2.4512
4.9692
3.2633
6.6504
.0675
.4547
.4395
.1197
.1941
.2482
.1834
.2624
.2197
.4163
1.0032
8.1198
7.7681
1.8831
2.9608
4.0917
2.9741
4.3175
3.5536
7.2537
.1286
.3999
.4483
.0704
.0997
.2587
.1808
.2871
.1867
.4175
1.9235
6.9391
7.9606
1.1024
1.4990
4.2769
2.9299
4.7585
2.9995
7.2791
43
Model
11
12
13
Table 13 Continued
Quarter
14
15
16
17
18
19
20
GW
.5375
.2282
.1513
.2464
.3368
.2167
.2092
.0884
.1213
.1912
0.0389
3.6765
2.3660
4.0196
5.7016
3.5375
3.3550
1.4027
1.9325
3.0311
Gr1ff1n-Watts with Consunt
.4924
.2131
.0995
.2588
.2224
.2302
.1110
-.0189
.1313
.1971
8.9089
3.4217
1.5454
4.2370
3.6351
3.7697
1.7524
-.2995
2.0936
3.1231
Foster
.4581
.1814
.0740
.2195
.2141
.1657
.1670
.1568
.1316
.2355
8.1157
2.8924
1.1467
3.5569
3.4940
2.6775
2.6563
2.5105
2.0994
3.7692
Foster with Constant
.4670
.1824
.0649
.2206
.2081
.1650
.1635
.1421
.1288
.2323
8.3180
2.9103
1.0050
3.5765
3.3913
2.6670
2.5998
2.2702
2.0535
3.7152
Brown-Rozeff
.5469
.2155
.1185
.2516
.2075
.1786
.2083
.1511
.1298
.2519
0.2866
3.4607
1.8454
4.1110
3.3798
2.8933
3.3408
2.4168
2.0696
4.0490
Brown-Rozeff with Constant
.5106
.1636
.1096
.2795
.1566
.1810
.2153
.1104
.1724
.2078
9.3531
2.6002
1.7053
4.6025
2.5272
2.9338
3.4576
1.7570
2.7678
3.3041
Box-Jenkins
.3884
.1332
.1829
.2509
.1296
.1730
.1298
.1281
.0372
.2851
6.6369
2.1073
2.8764
4.0984
2.0837
2.7999
2.0537
2.0418
.5879
4.6275
Brown-Kennelly (AI)
.3581
.0385
.1201
.1457
.2156
.2114
.0773
.0415
.0938
.2801
6.0406
.6041
1.8695
2.3281
3.5191
3.4464
1.2157
.6569
1.4894
4.5388
Brown-Kennelly (FI)
.2840
.0213
.0977
.1120
.1360
.2160
.0660
-.0121
.1595
.1624
4.6641
.3346
1.5172
1.7818
2.1872
3.5255
1.0378
-.1912
2.5538
2.5606
Hopwood-McKeown 1 (A I)
.5078
.1614
.1094
.2385
.2253
.1295
.1958
.2004
.0308
.3721
9.2828
2.5648
1.7023
3.8825
3.6855
2.0806
3.1317
3.2342
.4878
6.2370
Hopwood-HcKeown 1 (FI)
.4937
.1832
.0847
.2633
.1991
.1358
.1830
.1795
.0763
.3353
8.9399
2.9235
1.3147
4.3153
3.2382
2.1849
2.9192
2.8843
1.2103
5.5373
Hopwood-McKeown 2 (AI)
.4556
.1370
.1275
.2408
.2221
.1805
.2137
.1315
.0653
.3955
8.0598
2.1692
1.9874
3.9231
3.6310
2.9243
3.4314
2.0975
1.0354
6.6979
Hopwood-McKeown 2 (FI)
.4827
.1486
.1253
.2564
.2386
.1794
.2130
.0629
.1125
.3368
8.6807
2.3573
1.9525
4.1947
3.9160
2.9065
3.4192
.9958
1.7905
5.5648
44
Table 14
Rdnk Correlation on Quarterly Basis — Actual vs Forecast
Correlations Between Analyst and Actual--Model Held Constant
Quarter
. Hodel
GH
Grlffin-Watts with Constant
Foster
Foster with Constant
Brown-Rozeff
Brown-Rozeff with Constant
Box-Jenkins
Brown-Kennel ly (AI)
Brown-Kennel ly (FI)
Hopwood-HcKeown 1 (AI)
Hopwood-HcKeown 1 (FI)
Hopwood-McKeown 2 (AI)
Hopwood-McKeown 2 (FI)
1
2
3
4
5
6
7
8
9
10
.5395
.2517
.2738
.6031
.6927
.5480
.5832
.5470
.6107
.6977
9.5041
4.1362
4.5189
11.8118
14.3748
10.4621
11.4407
10.3725
12.1688
15.4281
.5167
.2314
.2816
.6123
.7027
.5567
.5930
.5714
.6168
.7094
8.9507
3.7834
4.6583
12.0971
14.7806
10.7012
11.7374
11.0528
12.3647
15.9452
.5497
.2153
.2564
.6146
.6798
.5667
.5581
.6107
.7176
.7477
9.7612
3.5072
4.2106
12.1712
13.8733
10.9834
10.7201
12.2423
16.2583
17.8383
.5584
.2489
.2557
.6117
.6829
.5703
.5572
.6094
.7190
.7507
9.9849
4.0873
4.1981
12.0771
13.9901
11.0862
10.6937
12.2012
16.3248
18.0025
.5281
.1604
.2443
.6328
.6578
.5126
.5050
.5392
.6093
.6327
9.2250
2.5856
3.9991
12.7670
13.0694
9.5321
9.3250
10.1627
12.1252
12.9429
.5097
.2276
.2746
.6380
.6767
.5526
.5515
.5260
.6227
.6634
8.7878
3.7178
4.5333
12.9406
13.7571
10.5891
10.5353
9.8191
12.5580
14.0444
.5643
.4751
.4303
.6271
.7098
.5422
.6454
.5325
.6485
.7410
0.1375
8.5877
7.5682
12.5745
15.0816
10.3031
13.4668
9.9879
13.4414
17.4814
.7684
.6682
.6378
.7749
.7542
.5777
.7304
.6533
.7739
.7485
7.8106
14.2868
13.1453
19.1485
17.1925
11.3022
17.0421
13.6981
19.2848
17.8797
.7388
.6505
.5729
.6827
.7357
.5814
.7163
.7058
.7693
.7545
6.2607
13.6234
11.0956
14.5928
16.2593
11.4097
16.3617
15.8167
19.0021
18.2121
.6167
.4045
.3903
.6851
.7144
.5533
.5697
.5285
.6179.
.6213
1.6186
7.0359
6.7303
14.6895
15.2786
10.6072
11.0467
9.8835
12.3993
12.5616
.6002
.3220
.3326
.6295
.6634
.5575
.5849
.5740
.6818
.6196
1.1298
5.4107
5.5980
12.6537
13.2676
10.7224
11.4930
11.1269
14.7059
12.5049
.5957
.3642
.3803
.6750
.6208
.5507
.5471
.5545
.6839
.6255
0.9992
6.2194
6.5285
14.2913
11.8506
10.5366
10.4161
10.5788
14.7915
12.7020
.5992
.3338
.3311
.6352
.6506
.5348
.5533
.5424
.5904
.6276
1.1022
5.6321
5.5711
12.8473
12.8210
10.1058
10.5871
10.2478
11.5423
12.7721
45
Table 14 Continued
Quarter
Model
11
12
13
14
15
16
17
18
19
20
GM
.5540
.6661
.6782
.7327
.5764
.7039
.6489
.7375
.5956
.7577
0.4783
14.0072
14.2671
17.0254
11.2402
15.7954
13.3760
17.2653
11.7236
13.0612
, Griffln-Watts with Constant
.5768
.6834
.7063
.6843
.6279
.7137
.6565
.7571
.6056
.7703
1.1208
14.6818
15.4232
14.8574
12.3586
16.2393
13.6518
18.3241
12.0315
13.7892
Foster
.6338
.7359
.6668
.6015
.6326
.7288
.6411
.6476
.6042
.7291
2.9046
17.0483
13.8307
11.9049
13.0166
16.9654
13.1006
13.4366
11.9906
16.5707
Foster with Constant
.6328
.7340
.6649
.5981
.6277
.7268
.6294
.6483
.5995
.7281
2.8689
16.9507
13.7613
11.8003
12.8494
16.3655
12.7029
13.4620
11.3435
16.5221
Brown-Rozeff
.5302
.6681
.6654
.6959
.6203
.7135
.6389
.7313
.5354
.7159
9.8477
14.0322
13.7819
15.3223
12.6023
16.2315
13.0274
16.9508
11.4179
15.9517
Brown-Rozeff with Constant
.5562
.6698
.6526
.7022
.6498
.7011
.6033
.7136
.5738
.7134
0.5399
14.1495
13.3134
15.5932
13.6234
15.6635
11.3663
16.1063
11.0791
15.8393
Box-Jenkins
.6148
.7031
.6511
.7546
.6944
.7489
.6737
.7344
.6774
.7260
2.2750
15.5083
13.2633
18.1810
15.3805
18.0135
14.2999
17.1093
14.5589
16.4239
Brown-Kennel ly (AI)
.6983
.7838
.7955
.8265
.7370
.8301
.7972
.8343
.7191
.8032
5.3636
19.7963
20.2958
23.2177
17.3768
23.7214
20.7128
23.9292
16.3611
21.3456
Brown-Kennel ly (FI)
.7260
.3035
.3025
.8419
.7583
.8321
.3041
.8527
.6997
.8497
6.6250
21.1725
20.7906
24.6726
13.5391
23.9133
21.2144
25.3125
15.4374
25.0637
Hopwood-McKeown 1 (AI)
.5351
.6644
.6609
.6250
.6089
.7104
.6029
.6768
.6058
.7313
9.9753
13.9415
13.6126
12.6594
12.2332
16.0885
11.8533
14.5362
12.0403
16.6796
Hopwood-McKeown 1 (FI)
.5144
.6661
.6324
.6323
.5929
.7075
.6063
.6785
.5952
.6859
9.4470
14.0089
14.4319
12.9035
11.7349
15.9535
11.9589
14.6026
11.7113
14.6620
Hopwood-McKeown 2 (AI)
.5819
.6369
.6449
.6818
.6498
.6966
.5785
.7037
.5790
.7011
1.2666
14.3230
13.0437
14.7346
13.6254
15.4746
11.1240
15.6588
11.2270
15.2945
Hopwood-McKeown 2 (FI)
.5572
.6763
.6426
.6944
.5313
.6963
.5793
.7315
.5664
.6749
0.5685
14.3997
12.9555
15.2589
12.9733
15.4597
11.1463
16.9633
10.3653
14.2278
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52
Appendix A
The Impact of Bias on the Weighted API Statistic
FG report a weighted API statistic computed as (without scaling)
n
(1) Z |FE. |.API
1=1 '
where the first term in the product is the absolute value of the forecast
error for firm i and API is the abnormal performance index for firm i.
Note that since API = Sign (FE.) CAR., which is the sign of the
forecast error times the cumulative abnormal return, then (1) becomes
n
I If^E-l • Sign (FE.) • CAR. which is of course
1=1 1 1 ^
n
(2) Z FE. • CAR
i=l ^
The above analysis is unsealed, whereas FG scaled by dividing by
n
I |FE. |. Therefore their weighted API on a scaled basis is
1=1
n FE. • CAR.
(3) Z - ^ ^
i=l '
Note the similarity between (3) and that of the sample Pearson
correlation coefficient for FE and CAR.,-, namely
53
n (FE. - FE) (CAR. - CAR)
(4) ^ —^ — r-T—^
FE CAR
In particular note that (3) reduces to (4) in the numerator when the mean
forecast error equals zero (i.e., unbiased forecasts) and the mean CAR equals
zero. Their denominator represents a different choice of a scale factor.
n
(This term assures that the investment sums to 1.) The term I \^^i\ m (3)
i=l ^
is a measure of dispersion similar to <5 in (4), but measures mean 'absolute
deviation for forecasts presumed to be unbiased (as opposed to mean squared
deviation for possibly biased forecasts). Therefore their scale factor is
also affected by bias.
Quarter
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
54
Appendix B
Maximum number of days of Analyst Timing
Advantage in Each Partition
9.00
18.00
25.00
57.00
92.00
14.00
22.00
38.00
72.00
94.00
11.00
18.00
37.00
65.00
98.00
18.00
36.00
64.00
91.00
134.00
9.00
15.00
25.00
51.00
92.00
15.00
21.00
36.00
70.00
95.00
14.00
18.00
37.00
67.00
94.00
11.00
18.00
35.00
65.00
92.00
4.00
14.00
28.00
65.00
88.00
11.00
22.00
46.00
74.00
95.00
9.00
17.00
43.00
74.00
99.00
11.00
25.00
59.00
80.00
130.00
8.00
22.00
52.00
71.00
87.00
9.00
30.00
56.00
74.00
95.00
11.00
32.00
60.00
74.00
95.00
11.00
36.00
60.00
74.00
105.00
3.00
21.00
56.00
71.00
120.00
14.00
32.00
60.00
77.00
94.00
11.00
35.00
64.00
77.00
163.00
16.00
36.00
60.00
78.00
106.00
55
NOTES
•'•Brown et a1 . [1985, 1986] provide some evidence in support of a timing
advantage. Our analysis is not so much concerned with whether such an
advantage exists, but rather whether the analysts outperform statistical
models given control for timing. Our analysis differs in other important
ways, including the set of statistical models considered and our incorporation
of earnings release dates for purposes of measuring timing advantage.
p
We use these and other abbreviations for convenience and do not wish
to imply that the authors necessarily advocated the general use of these
models.
■^We do not include the category I BJ model, since Box and Jenkins [1970]
suggest that a minimum of 50 observations be used in the modeling process. We
were unable to obtain annual series that met all of our sampling constraints
and approached this recommended minimum number of observations. Even if the
data were available, models incorporating a half of a century's data would be
problematic due to structural changes in the economy.
We did not delete firms with some missing Value Line data since there
were a considerable number of firms where only one number was unavailable.
However, this had virtually no effect on our overall sample size since the
percentage of missing data was less than 2%.
^These sample constraints apply to our annual analysis. The sampling
procedures and capital market analysis was slightly different for the
quarterly analysis. Specifically, the quarterly analysis required returns on
the daily CRSP tape to compute weekly returns (Tuesday to Tuesday) for the
period from the fourth quarter of 1972 through the fourth quarter of 1978.
The resulting sample contained 9 fewer firms (249 in total) than for the
annual analysis.
The logarithmic form of the market model is used so the variable being
analyzed equals the continuously compounded return. This also allows some
appeal to a central limit theorem argument (Fama [1976, p. 20]; Alexander and
Francis [1986, p. 145]) concerning normality of the variable.
The procedure to compute quarterly abnormal returns was analogous to
that used to compute annual abnormal returns. This log form of the market
model (risk free rates of return were generally not available for periods less
than one month) with a value weighted index was used. Regression estimations
were done for each holdout quarter (between 1974 and 1978) using OLS
regression and in each case including weekly data for the 65 weeks preceding
the week containing the first market day of the quarter. The residuals (post
sample forecast errors) from these models when applied to the holding periods
(the inclusive interval from the week containing the first market day of the
quarter to the week containing the announcement date) constitute risk adjusted
returns. The abnormal returns were then individually summed across each
holding period to give the firms' cumulative abnormal returns.
56
°This required the additional sampling constraint of requiring
availability of Value Line forecast publication dates. Due to resource
constraints we collected dates for a subsample of 182 firms. To insure that
this procedure had no biasing effect, we ran the forecast error analysis for
the subsample and sample as a whole and obtained virtually identical results.
Q
The statistical test in the various sub-partitions are based on the
distribution-free multiple comparison test (using Friedman Rank Sums) for
multiple treatment versus a control (Hollander and Wolfe [1973, p. 155].
57
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