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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
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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.
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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.
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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.
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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:
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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 -
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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).
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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
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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).
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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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HECKMAN
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