University of Amsterdam, Amsterdam Business School
MSc Finance, Track Asset Management
Master Thesis
Title: Underreaction in Financial Analysts’ Earnings Forecast Revisions and Timeliness
Last name: Lu
First name: Xi
Student Number: 11375167
MSc FIN
July 2017
Supervisor: Florian Peters
Abstract
This thesis provides some evidence to support that financial analysts underreact when issuing forecast revisions, and timeliness is one of the important factors that strengthen underreaction. Based on the timeliness proxy and model from previous literature, the thesis reconstructs and adds some variables to further test quarterly effect. A new timeliness proxy, Percentage of Previous Forecasts, is proposed and proved to be valid. As both pursue and limit, timeliness triggers analysts’ underreaction, as well as earnings volatility and stakeholders’ loss aversion. A Logit Model for testing relevant factors of
underreaction is designed and provide contradictory evidence for timeliness factor. The thesis draws main supportive conclusions and a sub-doubt leading to mixed properties of underreaction, yet research
methods are practical to be an attempt for studying analysts’ behavior.
Statement of Originality
This document is written by Student [Xi Lu] who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Contents
1 Introduction ... 1
2 Literature Review ... 4
2.1 Timeliness and other determinants of analysts’ forecast properties ... 4
2.2 Forecast accuracy and information content of forecast errors and revisions ... 6
2.3 Analyst incentives, herding behavior and underreaction ... 6
2.4 Hypotheses ... 9
3 Methodology ... 10
3.1 Test procedures and models ... 10
3.1.1 Precondition Test ... 11
3.1.2 Factors that contribute to underreaction ... 13
3.2 Variable Construction ... 14
3.2.1 Cluster ... 14
3.2.2 %FORECAST and Percentage of previous forecasts ... 15
3.2.3 Other variables ... 16 3.3 Data ... 19 4 Empirical Results ... 20 4.1 Descriptive Statistics ... 20 4.2 Correlation ... 21 4.3 Association ... 23
4.3.1 Results of Mozes (2003)-based Model ... 23
4.3.2 Results of Logit Model ... 26
5 Robustness Test ... 28
6 Conclusion ... 30
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1
Introduction
Nowadays, stock prices react sensitively to surprises and disappointments resulting from the differences of actuals earnings from predictions. Analysts study individual firms, industry and
macroeconomy carefully, trying to exploit all possible information. Nevertheless, academic researchers have thoroughly discussed information environment of analyst reports, especially from the perspective of Efficient Market Hypothesis, and have documented inefficiency reflected by forecast error’s patterns including general optimism bias.
Analysts’ incentives include both external and internal factors. Reasoning are respectively plausible but generally mixed when contributing to mainstream explanation. Most discussed external factors are investment banking relationships and management communications. Intuitively leading to optimism, favorable predictions and recommendations are preferred, while negative predictions increase possibility of dropped coverage or underreaction. Internal factors work interactively and it seems impossible to separate intentional forecast error from unintentional inability. Analysts have limit expertise in addition to unideal time and information input, in addition to characteristics of decision processes resulting from behavioral and cognitive study.
Underreaction is an empirical finding that analysts respond partially to information content of various 0signals. Apparently, this is a kind of inefficiency resulting from the possibility that not all public information is incorporated to updated expectation of stock performance. To take a careful look at underreaction, researchers focus on forecast revisions, believing that analysts adjust forecasts when new information arrives. Assuming that the amount of information from initial forecast to actual
announcement is certain, and every new piece of information, revealed by specific events such as earnings and dividend announcements, conference calls, management forecasts, and interim accounting data, sales target, product and service updates, media coverage including client feedbacks, will trigger following analysts to issue new forecasts based on former estimates, thus generate revisions (Levine, 1998; Stickel, 1989).
With ideal rationale, a forecast can be regarded as a value of random variable with distribution around actual where deviations are forecast errors, to which extent the distribution of forecast error should be symmetric. However, previous studies have empirically documented that earnings information being underweighted (Mendenhall, 1991), and proposed plausible theories to explain. Forecast accuracy is an ex post concept measured by forecast error after corresponding actual value is announced, therefore any forecast prior to actual contains at least uncertainty throughout the time to announcement, i.e. forecast horizon, in the form of future information. Implied argument is that apart from this uncontrollable future
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uncertainty, analysts can still choose the level of information incorporated in updated forecasts, corresponding to different scale of forecast error. In other words, in spite of inseparable causes, this research assumes analysts’ discretion in additional forecast error by intentional underreaction. Systematic uncertainty attributed to forecast horizon and inaccuracy attributed to analyst-specific decision processes constitute total forecast error. Objective forecast difficulty and subjective underreaction appear on both components, yet underreaction can theoretically be zero.
This is when the concept of timeliness be introduced. Ceteris paribus, analysts who publish timely forecasts will have less time to process certain information than the later, generating reasonable inaccuracy. It makes sense that analysts are aware of the inevitable forecast error. On the other hand, throughout whole forecast period, there are usually several times when new information about state of operation become available to analysts, scilicet, there is certainly some future indications about the tendency since last actual. Analysts translate the future knowledge into the need of adjusting room. Hence, an underreacting analyst will make a smaller revision against fully-responding.
An analyst’s tradeoff between timeliness and accuracy determines the time lag before new forecast release and forecast error. This is the rationale, also suggests considering forecast horizon as a control variable.
Further reasoning takes behavioral theory like loss aversion in to account. The Prospect Theory described by Kahneman and Tversky (1979) argues that people are more sensitive to losses than to gains of the same magnitude. In the specific case when investors examine forecasts and are aware of the bad signal by negative earnings forecasts, forecast revisions represent changes rather than absolute magnitude of forecast, which is consistent with the original design of Kahneman and Tversky (1979) value function. However, for discussing analysts’ inefficiency, this research focuses on the other implication. People who are consistent with their own beliefs are usually considered reliable, while people who often contradict themselves are incapable of providing good opinions. Similarly, when an analyst’s forecast contradicts his preceding estimate, investors and buy-side clients may consider him less excellent. Raedy et al. (2006) conclude it as asymmetric loss function about analysts’ reputation of expertise. Consequently, analysts tend to prefer same sign of forecast errors and revisions, namely revisions that lead newer forecast towards actual are preferred. This forms an important motivation of underreaction when issuing timely forecasts: analysts deliberately reflect only partial information leaving room for further adjustment.
In addition to the behavioral consideration, this thesis is designed to test quarterly revision. Analysts incentives vary with changes in circumstances, personal expectations, both of which is relevant with quarterly variability. Intuitively, economic entities propose plans and expectations at the beginning of
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fiscal year, modify them according to interim performance feedbacks and finally report whether targets are met or not at the end. Thus, interim announcements reflect partly the established fact and room for improvement remains, while final announcements are confirmed judgement about the firm’s operation, management and potential. Different properties are known to security market participants and
corresponding reactions are then predictable. When it comes to analyst forecast behavior, it is plausible to infer that information provided by announcements in different quarter will be processed differently, regardless of information content. Literature provides evidence that bad news tends to be delayed until last fiscal quarter. Considering that the majority of firms adopt a same fiscal year as calendar year, for simplicity, this research will separately observe forecast revisions issued in four calendar quarters.
The rationale of this thesis bases on theories and concepts from early primary literature, but
methodology bases firstly on Mozes (2003) to empirically test underreaction and the effect of timeliness. Basic rationale assumes basic relationship between forecast error and revisions, then observes adverse additional effect brought by factors that eliminates a part of the basic relationship. Measures of analyst inefficiency are constructed about forecast error, using cluster mean as consensus and absolute value to capture magnitude. Volatility of time-series earnings affect forecast difficulty when analysts using existent information to make forecasts. Higher volatility implies higher uncertainty. As for proxy of timeliness, the original paper creates the concept of forecast immediacy, indirectly using the percentage of analysts that have already followed the most recent information release and the absolute value to measure the magnitude of revision. Timelines-triggered under adjustment is supported by empirical results
conditional to the Forecast Immediacy measure and the model testing for basic as well as additional relationship between cluster consensus forecast error and forecast revision. In order to be evident with better robustness, alternative timeliness proxy and improved model are necessary.
Hence, this thesis proposes a second timeliness proxy, Percentage of Previous Forecasts. Intuitively, given certain information, more forecast revisions before a certain revision stand for lower timeliness because other analysts are acting more quickly. Moreover, the rationale for introducing a Logit Model in this research is to not only test the direction that various factors influence underreaction phenomenon, but also quantify the effect from the perspective of probability. Above all, analysts have incentives to choose to underreact so the estimate of probability can be helpful to describe analysts’ decision process.
The thesis’s first model’s results support the existence of underreaction and provide evidence for various factors that strengthen underreaction, among which the most detailed studied one is timeliness. The timeliness proxy proposed by this thesis is proved to be at least as good as Forecast Immediacy,
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while more flexibility is argued. Other factors like volatility and loss aversion also increase underreaction. Forecast revision performs quarterly variability, which can also be explained from the perspective of underreaction. However, the Logit Model with strong logic is proven to be empirically contradictory to the first model’s results about timeliness factor. Logit Model results do support that issuing unfavorable revision will strongly increase the probability of underreaction, which is consistent with behavioral incentives about loss aversion. Conclusion drawn from contradictory timeliness factor might result from divergence of model or the different nature captured by each model. Prudently, overreaction behavior might offset underreaction in some cases, especially when it comes to insignificant tendency by combing individual decision process. Thus, the main doubt is not the practicability of Logit Model itself, but the object to be studied. On the other hand, test results support that quarterly effect exists and analysts underreact more at the end of the year.
The remainder of the thesis proceeds as follows: Section 2 is literature review, briefly collating theoretical backgrounds about determinants of analysts’ forecast properties, forecast accuracy and information content, and finally analysts’ incentives including rationale of underreaction in forecast revisions. The Last part of Section 2 explains the main hypothesis and three specific sub-hypotheses to be tested by correlation and association methods. Section 3 first provides methodology by illustrating the rationale of underreaction in detail. Two main models are then presented with detailed explanation about variable construction. Section 4 provides empirical results starting from data source and description statistics to correlation test for underreaction, finally regressions results. Section 5 discusses robustness based on the concern of alternative timeliness proxy and model availability. Section 6 is conclusion and further discussions.
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Literature Review
2.1
Timeliness and other determinants of analysts’ forecast properties
Among abundant studies about financial analysts revealing the fact that forecasting requires
complicated analysis and decision process, analyst inefficiency is documented as inefficient information processing. According to Efficient Market Hypothesis (Eugene F. Fama, 1970), when empirical results provide evidence that forecast errors are predictable, inefficiency occurs and prove the inability of analysts to fully incorporate available information into updated forecasts. Relevant factors that affect analysts’ forecasts are studied thoroughly.
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Most discussed time factors are forecast timeliness and forecast horizon. Brown (1993a) reviews literature about the role of financial analysts and suggests that forecast timeliness is a crucial attribute for effective proxies of forecast accuracy. Cooper et al. (2001) takes one high-tech industry and one low-tech industry as example to study market response to forecast revisions and finds that timely revisions induce higher response, also suggesting that timeliness is valued more than ex post accuracy when forecasts as input of investment decisions. Mozes (2003) concludes that high forecast timeliness causes lower accuracy compared to later forecasts, but increases forecast usefulness to the extent that it does lead forecast to be closer to actual. Mozes (2003) then suggests that timeliness be regarded as investor usefulness requirement rather than only a reason of higher forecast error, therefore separate evaluation of analysts who tend to provide timely forecasts and analysts who tend to provide later but accurate might be appropriate because both properties are useful from investors’ standpoint. This is consistent with Trueman (1990)’s conclusion from theoretical model based on Bayes’ Theorem, that investors attach importance to timely forecasts because they believe earlier updating analysts have better ability to explore private information. Therefore, weak analysts have incentives to imitate this behavior, resulting in inevitable underreaction to protect themselves from own belief’s’ conflicts. Nevertheless, Hong et al. (2000b) finds that less experienced analysts have incentives to trade off both timeliness and accuracy to avoid deviating from the consensus forecasts. When it comes to forecast horizon, short-term conclusions are roughly consistent. Bandyopadhyay et al. (1995) shows that the importance of earnings forecasts as input of stock price prediction rises as forecast horizon increases. Clement and Tse (2003) finds that investors respond more strongly to high forecast horizon. Mozes (2003) indicates that forecasts with longer horizon are more useful to investors.
Besides timeliness, announcements in different fiscal quarters have been proven to induce different responses. Literature as early as Mendenhall and Nichols (1988) has studied whether market reaction to announcement of bad news earnings is dependent on the fiscal quarter of the announcement. Documented delay announcements of bad news imply the fact that management chooses to avoid larger per-unit effect brought by unfavorable news in early quarters.
Studies on time-series variability of earnings started from Albrecht, Lookabill, and McKeown (1977). They examine time-series properties of actual earnings are presented by providing autocorrelations and comparing forecasts from three different models. Furthermore, Bhushan (1989a), Brennan and Hughes (1991) both find that the number of analysts following a firm is positively related to the variability of returns, so this thesis’s model setting include both factors as control variables. Luttman and Silhan (1995) suggests that forecast accuracy is negatively related to time-series variability of earnings.
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2.2
Forecast accuracy and information content of forecast errors and revisions
In practice, accurate forecasts provide solid support for investment decisions. In theory, efficient markets are equipped with accurate expectation reflecting all available information. Both make forecast accuracy significant.
Stickel (1992) proves that analyst expertise can be judged from forecast accuracy. Mikhail et al. (1997) document that analysts’ firm-specific experience is negatively related to forecast errors. The relationship between forecast errors and market reaction around earnings announcements is more noteworthy for more experienced analysts. Clement (1999) finds that more experience is associated with higher forecast accuracy. Analysts’ degree of specialization is also related. Yet Jacob et al. (1999) argues that analyst-company alignments play a significant role and analysts’ aptitude rather that experience that explains forecast superiority which is the pursuit.
Some researchers pay attention to the degree that forecasts reflect market expectation and market reaction to forecast accuracy or dispersion. Specifically, the concept of earnings surprise, one kind of forecast errors that reflects unexpected earning, is introduced. Kormendi and Lipe (1987) discusses the persistence of earnings surprise, its nature and market response. Abarbanell and Lehavy (2003) examines reasons of contradictory views on forecast bias by statistically showing two asymmetries in the
distributions of analysts’ forecast errors, with comprehensive descriptive tables and graphs sorted by information in abnormal returns and forecast errors.
Provided that analysts’ forecasts as a representative proxy of market expectation, new information can be quantified as adjustment market expectation with forecast revision as usual proxy, which is the
difference of forecasts before and after news release. Measurement error occurs across studies when different forecast measures are used to delegate specific market expectation. For example, Clement and Tse (2003) use the most recent forecast while Mozes (2003) uses cluster consensus forecast. Park and Stice (2000) specify the measure of forecast usefulness and find positive correlation between past usefulness and market response to forecast revisions. Gleason and Lee (2003) find that the market does not identify forecast revisions that provide new information from those merely move previous forecast toward consensus. Moreover, price adjustment process is faster for analysts with good reputation and for firms followed by more analysts. They draw conclusions about forecast revisions as signals that hinder the efficacy of market price discovery.
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Forecasting behavior is influenced by various incentives, some of which make analysts issue accurate forecasts while some others motivate optimistic bias and underreaction. In a broad sense, analysts are willing to perform better, under different criteria, to achieve good reputation, reward and career.
Some results are mixed. For instance, Hong and Kubik (2003) points out that relatively accurate analysts are more likely to experience favorable career. They further control for accuracy and find that favorable job separation depends more on optimism than accuracy in brokerage houses.
Large literature provide evidence for strong incentive to be optimistic, but not all of them point to earnings forecasts. Lin and McNichols (1998) find that with underwriting relationship, analysts’ growth forecasts and recommendations are significantly more optimistic while earnings forecasts are not larger. Irvine (2004) finds that optimistic recommendations generates higher trading commissions. Empirical support for optimism on earnings forecast includes Dugar and Nathan (1995), who find that at the presence of investment banking relationship, earnings forecasts perform optimism, but no less accuracy. Das, Levine and Sivaramakrishnan (1998) prove that analysts issue more optimistic forecasts for low predictability firms than for high predictability firms.
Herding is subjected to information uncertainty and analyst ability. Trueman (1994) suggests that analysts’ lower self-confidence is related to herding behavior. Hong et al. (2000a) suggests that analysts’ career concerns like less experience is related to herding behavior. Graham (1999) develops a model implying that herding behavior more likely happens on analysts with high reputation or low ability, or with private information that is apparently inconsistent with public information. Clement and Tse (2005) study the factors that increase the likelihood of analysts issuing bold forecasts, and find that bold forecast revisions are more accurate than herding ones because they improve the previous forecast more, which is consistent with the idea that non-herding forecasts contain more private information. They also find that the correlation between herding forecast revisions and forecast errors is higher, indicating that herding forecast revisions reflect less information.
Herding behavior suggests possible underreaction. Given same amount of new information, analysts with herding behavior tend to underreact by incorporating less in their revisions than more independent analysts who make bold adjustments. Prior literatures empirically document underreaction through persistent forecast errors, and discuss implied reasons and incentives.
Mendenhall (1991) tests the persistence of earnings forecast error. From the underreaction-perspective of post-earnings-announcement drift, the systematic relationship between consecutive forecast errors can be intuitively translated into information possibly remains out of stock prices. The paper proposes that market participants use forecast revisions to reassess forecast error and there is a positive relationship
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between forecast revision and abnormal return. A dummy variable is created to indicate the pair signs of forecast error and revision. Besides, Abarbanell and Bernard (1992) find proof that analysts underreact to recent earnings, which yet only accounts for a part of the source of post-earnings-announcement-drift, underlying the consistency of analyst’s inefficiency with market prices. They base their study on empirical results of stock prices underreacting and overreacting to earnings announcements, and test autocorrelation in forecast errors. They test the relative underreaction of stock prices and analysts’ forecasts. To test analysts’ underreactions, they regress forecast errors on new information denoted by difference of actual earnings. Amir and Ganzach (1998) examines a tendency towards overreaction in forecast changes and underreaction in forecast revisions. Using nonparametric portfolio analysis, the paper presents relationship of positive or negative forecast errors and revisions. Then regression analysis considers both magnitude and direction of forecast error.
Raedy et al. (2006) suggest that analysts’ earnings forecasts underreact to both earnings-surprise and other earnings-related information. Analysts face an asymmetric loss function, which incur greater (less) reputation cost of forecast error when subsequent information causes a revision regarding investor expectations with opposite (same) sign as analyst’s prior revision. Therefore, analysts would prefer same sign of forecast error and prior revision, and rationally underreact to information about future earnings, where underreaction increases with the risk of subsequent disconfirming information i.e. uncertainty of the earnings distribution and the asymmetric cost associated with revision reversal. Specifically, the paper regresses forecast error separately on two kinds of information and study horizon-dependent effect by observing differences of coefficients from different forecast ages. In the following tests, this “sign” will be denoted by a dummy variable UNDERREACTION.
An important literature of this research is Mozes (2003), both as theoretical support as mentioned above and as methodology enlightenment. The paper mentions the idea that under adjustment behavior is a response to uncertainty brought by new information. Based on Mozes and Williams (1999), Mozes (2003) uses percentage of updated forecasts and absolute value of revision as proxies of forecast immediacy to test four hypotheses about analyst accuracy, forecast dispersion responding to the same information, under adjustment, and usefulness of revisions. In regressions, interacted terms in regression are designed to measure additional effects. Control variables includes number of analysts following the firm, forecast horizon, a dummy variable indicating negative revisions and time-series variability of earnings. To control the information set, Mozes (2003) constructs cluster as the time period when intensive forecast revisions are published.
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Above all, literature on financial analysts’ behavior, incentives and characteristics of forecasts perform mixed results, partly due to specific test period, different dataset and rationale behind hypotheses. After all, intuition and conclusions about behavior depend a lot on subjective inference.
2.4
Hypotheses
Previous studies have some support for timeliness-driven underreaction, yet the evidence is not sufficient to the extent that literature is not abundant. So, the main hypothesis of this research is: Analysts’ underreactions increase with timeliness of forecast revision. Underreaction is tested in two ways: firstly, with correlation between cluster revision and cluster forecast error, secondly with regressions.
Precondition Hypothesis: Analysts’ underreactions increasing with timeliness can be observed with I/B/E/S 1990-1994 data as well as 2006-2010 and 2011-2015. Hypothesis 1 is for precondition purpose due to different data source, using Mozes (2003) Model 3. Correlation test is adopted on the 2011-2015 sample period in this thesis due to the concern for sample size.
Hypothesis 1: The effect that analysts’ underreactions increasing with timeliness of forecast revision is positively related to volatility and in unfavorable situation with quarterly variability. Due to the change of macroeconomic circumstances, it is plausible to assume that analysts have adapted judging criteria according to volatility, reflecting different levels of underreaction. Loss aversion proved by Prospect Theory is applicable in this case that analysts are more reluctant to announce a negative adjustment, namely lower updated forecast in optimism. Corporation behavior differs quarterly as they often announce earnings, adjust operating target at a predictable time and the new information makes further predictions possible. Analysts might be less aggressive as time approaching the end of year.
Hypothesis 1 is tested in two ways. Firstly, based on the tests of Precondition Hypothesis, comparison among three sample periods will be supportive. Secondly, interpretation of volatility variable in all regressions including Logit Model are relevant to Hypothesis 1.
Hypothesis 2: Timeliness increases the probability that analysts give same sign to forecast revision and error. Logit model can be adapted to estimate the possibility change generated by different factors.
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Hypothesis 2 is tested using Logit Model with a binary dummy of UNDERREACTION as dependent variable.
3
Methodology
Provided certain amount of new information awaiting incorporated to updated forecasts, a portion is contained in forecast revision and the remainder is in forecast error. In the case of optimistic forecast, actual value is lower than the forecast so there is a negative forecast error calculated by actual minus forecast. New information arrives as announcement date approaches. For simplicity, assume that new information reduces uncertainty in the way of reducing forecast error. Revision thus is the adjustment from initial forecast to a lower one, calculated as new minus old, also negative. The revision has a smaller absolute value than previous forecast error, as well as leaves a negative forecast error with smaller
magnitude.
This graph illustrates one possible case of underreaction, as part of forecast error that implied in the information but not included in the latest forecast with revision against last forecast. Note that the Implied Actual is supposed to be the value of EPS based on all things happened till the announcement of forecast. Accumulated implied actual value until the one right before earnings announcement is supposed to be the real earnings per share. Each revised forecast acts as the original forecast for the next revision.
Forecast EPS Original forecast
Revision Revised forecast
Implied actual Underreaction
Time (within a cluster)
Figure 1 Illustration of underreaction in the case of optimistic forecast
3.1
Test procedures and models
Besides correlation test for Hypothesis 1, this research design contains two regression models. Hypothesis 1 is then tested with the first model, while the other hypotheses are tested in both models. Hence, to be brief, the following sections will be organized by models instead of hypotheses.
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3.1.1 Precondition Test
The first test is almost a replication of Mozes (2003)’s Hypothesis 3 test because this research needs to base on empirically confirmed underreaction. Since the First Call Corporation’s historical detailed
database (RTEE) that used by previous work is discontinued, this research firstly redoes the test with data extracted from IBES during the same period 1990-1994. Cluster is constructed to group forecasts and for each cluster size, correlation between revision and consensus forecast error is provided to test
underreaction. In addition, the following Model 1 is identical to Mozes (2003)’s Model 3: 𝐶𝐹𝑂𝑅𝐸𝑅𝑅𝑖𝑗= 𝑏0+ 𝑏1𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏2%𝐹𝑂𝑅𝐸𝐶𝐴𝑆𝑇𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏3𝐴𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏4𝑁𝑈𝑀𝐹𝑂𝐿𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+𝑏5𝐻𝑂𝑅𝐼𝑍𝑂𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+𝑏6𝐷𝑂𝑊𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏7𝑇𝑆𝑉𝐴𝑅𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑒𝑖𝑗 (1.1),
where CFORERR is the error of the consensus forecast divided by price i.e. the mean of all forecasts; REVISION is the difference of cluster mean forecasts;
%FORECAST is the percentage of analysts following the firm who provide a forecast in the cluster. The higher (lower) %FORECAST, the more (less) forecasts have reacted to recent news release;
AREVISION is the absolute value of REVISION, indicating the amount of new information; NUMFOL is the number of analysts following the firm;
HORIZON is a control variable representing the number of days until the end of the fiscal year; DOWN is a dummy variable with a value of 1 when the REVISION is negative;
TSVAR is the time-series variability of the firm’s earnings process calculated as the standard deviation of the first-differenced annual earnings series divided by price. Subscription i denotes clusters and j denotes different observations within the cluster.
The above model uses interacted terms to capture additional relation between the dependent and independent variables. It is crucial to note that the basic relationship between forecast error and revision is theoretically and empirically proven to be negative. Underreaction results in smaller revision than implied by available information, so positive coefficients of interacted terms will support that the factor
contributes to underreaction.
Based on the rationale, 𝑏1 is expected to be negative. The more the original forecast is revised, the closer the updated forecast will be to actual. This indicates a positive relationship between REVISION and forecast accuracy, which is reasonable because previous literature have stated a lot about the
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incentives that trigger analysts to be accurate. However, incentives to underreact imply an increasing positive relationship between forecast error and revision as forecasts are issued more intensively.
Weighing both concerns, this thesis expects a larger basic effect while trying to capture the second effect by drawing attention on the trend of correlation as cluster size increases, which is shown separately in result section.
Mozes (2003) uses %FORECAST, the ratio of newly issued forecasts in one cluster compared to the total number of analysts following the firm as the proxy of timeliness. A large %𝐹𝑂𝑅𝐸𝐶𝐴𝑆𝑇 means that new information has already be followed a lot, implying high forecast immediacy because analysts are acting fast in response to new information. 𝑏2 is the coefficient of interest that is expected to be positive because given a revision, an increase in forecast immediacy would increase forecast error. A larger forecast error means an actual earning to be higher than positively revised forecasts or to be lower than negatively revised forecasts. Absolute value of forecast revision represents the amount of information.
The number of analysts following a firm indirectly describes analysts’ incentives in giving forecasts. Usually, firms with larger size, better cognition, better profitability and more favorable expectations are possibly followed by more analysts. Meanwhile, analysts often have more access to information of the firms and are more active to conduct research in order to exploit private information. However, as pointed out in Bhushan (1989), a greater analyst following may result from higher forecast difficulty. The
reversed causality provides explanations for both signs. Consistent with Mozes (2003), this thesis weighs more on the second causality and expects a positive coefficient 𝑏4.
Interacted terms of TSVAR, HORIZON, and NUMFOL are used to control underreaction related to uncertainty-generated forecast difficulty. Using time-series variability of earnings as a proxy for macroeconomic volatility, larger TSVAR and longer horizon increase uncertainty and difficulty of forecasting. So, given a revision, the factors lead to lower accuracy and larger forecast error, and 𝑏5, 𝑏7 are expected to be positive.
According to theory of loss aversion, analysts are more reluctant to lower their forecasts than to increase. It is reasonable to assume that this discouragement be more severe faced with bad news. Underreaction can be more significant when it comes to negative revisions. So, the coefficient 𝑏6 of 𝐷𝑂𝑊𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗 is expected to be positive.
𝐶𝐹𝑂𝑅𝐸𝑅𝑅𝑖𝑗= 𝑏0+ 𝑏1∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏2%𝐹𝑂𝑅𝐸𝐶𝐴𝑆𝑇𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏3𝐴𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏4𝑁𝑈𝑀𝐹𝑂𝐿𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+𝑏5𝐻𝑂𝑅𝐼𝑍𝑂𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+𝑏6𝐷𝑂𝑊𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏7𝑇𝑆𝑉𝐴𝑅𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏8FIRST QUARTER ∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+
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𝑏9SECOND QUARTER ∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏10THIRD QUARTER ∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑏11FOURTH QUARTER ∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗+ 𝑒𝑖𝑗 (1.2),
To test quarterly effect on the relationship between forecast error and revision, using the latest sample period, quarter dummies are added to Model 1.1 in terms of interactions with cluster consensus revision, yielding Model 1.2. For convenience to correspond to Model 1.1, REVISION variable is kept, yet 𝑏1 will equal zero because adding interacted quarter factors makes it omitted. For each term, the quarter dummy has value of 1 when announcement date of the forecast lies in respective calendar quarter elsewise zero. As explained above, taking the effect of both sides that forecast revision is intended to make updated forecast closer to actual so the relationship should be nagetive, yet underreaction concerns result in positive correlation between them, coefficients 𝑏8 to 𝑏11 are still expected to be negative around the value of 𝑏1 from Model 1.1 results, and comparisons will be made among them.
3.1.2 Factors that contribute to underreaction
𝑈𝑁𝐷𝐸𝑅𝑅𝐸𝐴𝐶𝑇𝐼𝑂𝑁 = 𝛽0+ 𝛽1𝐼𝑁𝐷𝐼𝑉𝐼𝐷𝑈𝐴𝐿 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+
𝛽2PERCENTAGE OF PREVIOUS FORECAST + 𝛽3𝐴𝐵𝑆𝑂𝐿𝑈𝑇𝐸 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝛽4𝑁𝑈𝑀𝐹𝑂𝐿 + 𝛽5𝑇𝑆𝑉𝐴𝑅 + 𝛽6𝐷𝑂𝑊𝑁 + 𝛽7𝐻𝑂𝑅𝐼𝑍𝑂𝑁 + 𝜖 (2.1),
𝛽1 is expected to be negative because a larger forecast revision incorporates more information and this is defined to be less underreaction. The second independent variable, Percentage of previous forecast, is the indicator of the sequence that a forecast lies in the cluster. A higher value means more forecasts has been issued before in response to the same new information, so a low timeliness. Therefore, a negative 𝛽2 would be consistent with hypothesis. Larger absolute forecast revision contains more information in an update, thus reduces possibility of underreaction and 𝛽3 is expected to be negative. Lower analyst coverage implies small private information discovery, adding motivation to underreaction from uncertainty, thus 𝛽4 is expected to be negative. Long forecast horizon and larger volatility also add to uncertainty and less information available at the time of forecast, so 𝛽5 and 𝛽7 are expected to be positive. Loss aversion predicts positive 𝛽6.
𝑈𝑁𝐷𝐸𝑅𝑅𝐸𝐴𝐶𝑇𝐼𝑂𝑁𝑘 = 𝛽0+ 𝛽1𝐼𝑁𝐷𝐼𝑉𝐼𝐷𝑈𝐴𝐿 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝛽2Percentage of previous forecasts𝑘+ 𝛽3𝐴𝐵𝑆𝑂𝐿𝑈𝑇𝐸 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝛽4𝑁𝑈𝑀𝐹𝑂𝐿𝑘+ 𝛽5𝑇𝑆𝑉𝐴𝑅𝑘+ 𝛽6𝐷𝑂𝑊𝑁𝑘+ 𝛽7𝐻𝑂𝑅𝐼𝑍𝑂𝑁𝑘+
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𝐼𝑁𝐷𝐼𝑉𝐼𝐷𝑈𝐴𝐿 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝛽10THIRD QUARTER ∗ 𝐼𝑁𝐷𝐼𝑉𝐼𝐷𝑈𝐴𝐿 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝛽11FOURTH QUARTER ∗ 𝐼𝑁𝐷𝐼𝑉𝐼𝐷𝑈𝐴𝐿 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑘+ 𝜖 (2.2),
Similar to precondition test, quarterly effect is also tested by replacing INDIVIDUAL REVISION in Model 2.1 by four interacted terms. Coefficients 𝛽8 to 𝛽11 are expected to be negative around the value of 𝛽 from Model 2.1 results. Subscription k is to identify different individual values, regardless of their clusters.
3.2
Variable Construction
3.2.1 Cluster
Forecast cluster is a concept constructed in Mozes and Williams (1999), then adopted in Mozes (2003). Information content is supposed to be abstract and sophisticated to quantify. By sectionalizing time between announcements, it becomes more plausible to argue that information content can be controlled. The flexibility of cluster setting makes it even possible to relax the assumption to a wider range of new information arrival.
A forecast cluster contains several forecasts of a firm for a certain forecast period, and the forecasts are issued intensively. By assigning forecasts to clusters, information content is controlled with assumption to be the same among forecasts in a cluster. In practice, by calculating the time difference between consequent forecasts of a firm for the same forecast period, observations that are separated from each other for more than three calendar days are assigned to two successive clusters.
Therefore, it is plausible to conclude that in Mozes’s three-day cluster setting, closely successive cluster may reflect the same information release, while if two successive clusters are separated by many days without any forecasts, they may reflect different information set.
Mozes (2003)’s three-day condition is replicated in the first precondition test, while further tests will use a longer condition of more than six days to cover a whole week, assuming seven days as the longest period for an analyst to process new information. This longer cluster separation setting is also more appropriate for the second proxy of timeliness that is the percentage of previous forecasts in a cluster, because as the cluster separation condition increases, some clusters with separation more than three says but less than six days are combined, resulting in longer clusters. Longer clusters have higher possibilities to contain more forecasts and more variations of timeliness, which makes the tests explicit. So,
1990-15
1994 sample period is tested for both cluster setting, similarly to robustness requirement, with three-day cluster to meet Mozes (2003)’s methodology and six-day cluster to be comparable with following tests.
Empirically, cluster is constructed by numbering observations that are not intensively published. Firstly, I sort forecasts in groups of the same firm and same forecast period, and number them in the order of announcement. Secondly, I take the difference of successive announcements date. Finally, forecasts with more than six-day difference from the previous one will be assigned to different cluster by numbering, and those with less difference will be in the same cluster as the previous forecast.
3.2.2 %FORECAST and Percentage of previous forecasts
%FORECAST is the percentage of analysts following the firm who provide a forecast in the cluster, while 𝑁𝑈𝑀𝐴𝑁𝑆𝑖 is the number of analysts following the firm in cluster i, and it varies annually and 𝑁𝑈𝑀𝐹𝑂𝐿𝑖 is the number of forecasts in cluster i.
%𝐹𝑂𝑅𝐸𝐶𝐴𝑆𝑇𝑖 =
𝑁𝑈𝑀𝐴𝑁𝑆𝑖 𝑁𝑈𝑀𝐹𝑂𝐿𝑖
Mozes (2003) supposes that larger information arrival would appeal for more responses. With a little complexity to understand, 𝐴𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗∗ 𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗 is a control variable about whether under adjustment is proportional to total revision and a coefficient 𝑏3 insignificantly differs from zero is expected. From the perspective of this research, this Forecast Immediacy measure has at least three drawbacks. First of all, %FORECAST measure assumes that there are several clusters when forecasts are revised intensively following a major information announcement. Hence, it is plausible to assume a fixed number of forecasts that have been and will be revised for certain new information, possibly limited to the number of analysts following the firm. Thus, a greater %FORECAST in a cluster means that previous clusters have less revisions, which is similar to the statement in the original paper that “the lower the number of forecasts that have already followed the most recent information release”. Analysts are reacting mainly in a later cluster instead of an earlier one. Nevertheless, it is not intuitive to believe so.
Concentrating on one certain cluster, a higher %FORECAST directly stands for active response by all analysts. The alternative explanation might lead to the complexity understanding the rationale.
In addition, this preconditional assumption ignores the possibility that information environment be dynamic so that new information induced by major announcements may follow, such as responding comments from informed people or reactions taken by peer companies. In other words, it is not reasonable to assume that all clusters between two major information announcements share the same
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information content. Secondly, forecasts in one cluster is considered to represent the general behavior of all analysts compared to other clusters following the same new information. However, this combination eliminates some information about different behavior among analysts following the same firm forecasting the same period but revising with different incentives. Underreaction is a concept considering human behavioral, so it would be better to study individual observations to keep the most possible variety in drawing conclusion. Thirdly, an analyst might issue more than one forecasts even in a short cluster if new information is uncertain, so the calculation using number of updated forecasts as nominator is not
accurate.
Inspired by Mozes (2003), this research creates a different variable as proxy for timeliness. Within a cluster of with N forecasts (N actually equals the cluster size), a certain forecast will have a sequence, noted as X, then 1 ≤ 𝑋 ≤ 𝑁. There will be 𝑋 − 1 forecasts before the forecast in this cluster. Percentage of previous forecast is the indicator of the sequence a forecast lies in the cluster i, calculated by
𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠𝑖 =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑏𝑒𝑓𝑜𝑟𝑒 𝑎 𝑐𝑒𝑛𝑡𝑎𝑖𝑛 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 𝑖𝑛 𝑡ℎ𝑒 𝑐𝑙𝑢𝑠𝑡𝑒𝑟𝑖 ×100% =
𝑋−1
𝑁 ×100%. As all forecasts in one cluster reflect the same set of information, the percentage of forecasts before a certain forecast, can be interpreted as a proxy of timeliness that when a forecast is issued
relatively late in the cluster, X and 𝑋 − 1 is large, then the percentage will be large. In other words, this percentage is an inverse measure, representing high timeliness when the percentage value is low.
%FORECAST is a proxy from the perspective of all forecasts in a cluster and is confusing. The percentage of all forecasts to all analysts following is the same to all observations in a cluster, and the difference of timeliness is measured between clusters. While 𝑃𝑒𝑟𝑐𝑒𝑛𝑡𝑎𝑔𝑒 𝑜𝑓 𝑝𝑟𝑒𝑣𝑖𝑜𝑢𝑠 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑠 bases the idea on individual forecasts, believing that each revision is the result of an independent decision process.
3.2.3 Other variables
𝐶𝐹𝑂𝑅𝐸𝑅𝑅𝑖𝑗 is the error of the consensus forecast of cluster i, divided by forecast j’s corresponding 𝑃𝑟𝑖𝑐𝑒𝑖𝑗. Subscription j denotes different individual actual and price values in cluster i.
𝐶𝐹𝑂𝑅𝐸𝑅𝑅𝑖𝑗=
𝐴𝑐𝑡𝑢𝑎𝑙𝑖𝑗− 𝐶𝑙𝑢𝑠𝑡𝑒𝑟 𝑀𝑒𝑎𝑛 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖 𝑃𝑟𝑖𝑐𝑒𝑖𝑗
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Consensus forecast errors are intended to decrease forecast deviations around the same information set during the same period, so consensus reduces analyst-specific characteristics that are persistent in all decision processes but irrelevant to underreaction. This design supposes that the judging rules an analyst applies to all forecasts under any circumstances suggests a persistent bias comparing to objective information content as though the inertia as a metaphor.
Individual Forecast Error is the difference of actual and individual forecast, divided by price.
𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗 is the current cluster i’s consensus forecast minus the previous cluster 𝑖 − 1’s consensus forecast, divided by individual 𝑃𝑟𝑖𝑐𝑒𝑖𝑗. Subscript i denotes cluster. Consensus revision is not simply the mean of all revisions in the cluster but calculated firstly by taking the average forecast among successive cluster then take the difference, which is regarded as better reflection of the part of new information reflected as market expectation without noisy behavior volatility.
𝑅𝐸𝑉𝐼𝑆𝐼𝑂𝑁𝑖𝑗 =
𝑀𝑒𝑎𝑛 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖− 𝑀𝑒𝑎𝑛 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡𝑖−1 𝑃𝑟𝑖𝑐𝑒𝑖𝑗
×100%
Individual forecast revision is the difference between successive forecasts issued by the same analyst of a firm for the same forecast period, divided by price.
Models based on Mozes (2003)’s Model 3 are using cluster consensus variables, namely mean values throughout all forecasts in the cluster, because the model is using the first timeliness measure that has the same value across the cluster. Logit models are using forecast error revisions on individual level because individual motivations are the focus.
𝐻𝑂𝑅𝐼𝑍𝑂𝑁𝑘 is the number of days until the forecast period end date, noted that all the forecasts are one-year ahead quarterly values. Subscription denotes the sequence of the observation.
𝑇𝑆𝑉𝐴𝑅𝑘 is the time-series variability of the firm’s quarterly actual earnings, calculated as the standard deviation of the first-differenced earnings series, divided by price.
𝐷𝑂𝑊𝑁𝑘 is a binary dummy variable with a value of 1 if individual revision is negative.
𝑈𝑁𝐷𝐸𝑅𝑅𝐸𝐴𝐶𝑇𝐼𝑂𝑁𝑘 is the indicator of possible underreaction. For each individual forecast and the corresponding revision that it generates against previous forecast by the same analyst for the same company’s same forecast period:
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When Signal is positive, revision and forecast error has the same direction, indicating that the revision is not enough to cover all the error, thus 𝑈𝑁𝐷𝐸𝑅𝑅𝐸𝐴𝐶𝑇𝐼𝑂𝑁𝑘 equals 1.
𝑈𝑁𝐷𝐸𝑅𝑅𝐸𝐴𝐶𝑇𝐼𝑂𝑁𝑘= {
1, 𝑆𝑖𝑔𝑛𝑎𝑙𝑘 > 0 0, 𝑆𝑖𝑔𝑛𝑎𝑙𝑘 < 0
To explicitly illustrate UNDERREACTION, the following Table 1 presents all six possible outcomes considering a simple case of one original forecast followed by one revision, among which the first outcome is depicted in Figure 1. Higher horizontal position represents higher value. 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑒𝑟𝑟𝑜𝑟 = 𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝑎𝑐𝑡𝑢𝑎𝑙 − 𝑅𝑒𝑣𝑖𝑠𝑒𝑑 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡, 𝐹𝑜𝑟𝑒𝑐𝑎𝑠𝑡 𝑟𝑒𝑣𝑖𝑠𝑖𝑜𝑛 = 𝑅𝑒𝑣𝑖𝑠𝑒𝑑 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡 − 𝑂𝑟𝑖𝑔𝑖𝑛𝑎𝑙 𝑓𝑜𝑟𝑒𝑐𝑎𝑠𝑡.
Table 1 Possible outcomes of a forecast revision
Table 1 presents magnitude relation with positions. Column 2 are two-dimension graphs describing the change of forecasts as time goes by. Column 4 and 5 indicate the sign of variables calculated later value minus previous value.
𝑇1 𝑇2 𝑇3 Forecast revision Forecast error Analyst behavior
1 Original forecast Negative Negative Underreaction Revised forecast Implied actual 2 Implied actual Positive Positive Revised forecast Original forecast 3 Revised forecast Positive Negative Overreaction Implied actual Original forecast 4 Original forecast Negative Positive Implied actual Revised forecast 5 Implied actual Negative Positive Wrong revision Original forecast Revised forecast 6 Revised forecast Positive Negative Original forecast Implied actual
From Table 1, it seems plausible to give UNDERREACTION the value of one when forecast error and revision have the same signs. All six situations are grouped in to three types of behavior, but it is
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important to emphasize that these are only behavior tendency. It is not about a individual revising behavior to be underreacting, but about how important the incentives are to financial analysts during forecast decision process.
3.3
Data
Forecast data are extracted from IBES Academic Detail History’s Detail dataset. Actual earnings per share are extracted from IBES Academic Detail History’s Actuals dataset. Price data are extracted from CRSP quarterly-updated Monthly Stock dataset. Three sample periods are separately extracted:1990-1994 to testify Mozes (2003)’s results, 2006-2010 to observe crisis effect, and 2011-2015. Each sample period contains five calendar years and the recent two are successive. The main reason for using separate samples is that financial analysts’ forecast behaviors have heterogeneity when macro economy changes a lot and when financial techniques improves a lot. Although the essence about incorporating information and reflecting market expectation remain the same, it is reasonable to test them separately rather than a combined sample.
When merging the dataset, IBES Ticker is the primary indicator, while CUSIP, Official Ticker, and company names are also applied to ensure the most results. Individual and cluster-consensus forecast errors, forecast revisions, and volatility variable TSVAR that suffer from possible extreme values are winsorized by replacing 2nd and 98th percentile values. Companies are kept in the sample with a
minimum of analyst following of 5 to avoid extreme value of volatility. Forecasts from the same analysts within three days are excluded from sample because short intervals may violate the implies assumption about new information available before later forecast. Some analysts revise forecasts every day. Even if short intervals do reflect new information, as the decision process might be different from less frequent revisions, it is reasonable to exclude those observations, assuming that most information can still be reflected from the difference of forecasts three-day-apart. This thesis will compare coefficients from different sample periods. To ensure the comparability, data collection method of the database should be consistent.
As mentioned in Mozes (2003), this research might suffer survivorship bias, especially during the second test period covering crisis, because when actuals are less than forecast, the company is believed to perform worse than expectation and finally has lower possibility to survive until sample period end. Since forecast revision instead of forecasted value itself is the object of the research, observation is counted only when an analyst gives at least two forecasts for the same forecast period of a certain firm. A lot of data are dropped because single forecast. Moreover, I/B/E/S offers relatively less data for 1990-1993 than
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1994, resulting in that effective observations of the first sample period appear to be late. That is, the condition of five-year period according to the original paper does not work well, which might lead to poor results in the first sample period.
4
Empirical Results
This section firstly provides descriptive statistics of all variables in two main models. The second part presents correlation table and figure as evidence for Hypothesis 1, using %FORECAST proxy. The third part provide regression results for two main models respectively.
4.1
Descriptive Statistics
Using the method to construct six-day clusters, there are 177 clusters. On average, there are 3 forecasts in a cluster, and half of all clusters have no more than 2 forecasts, while the largest cluster has 39
forecasts, after adjusting for sequent forecasting behavior.
Table 2 Descriptive statistics for three datasets
Table 2 reports simple descriptive statistics for three different datasets using three-day-apart clusters. %FORECAST is the ratio of number of forecasts to number of analysts following in a cluster.
Variables Number of Observations 1990- Mean Standard Deviation
1994 2006-2010 2011-2015 1990-1994 2010 2006- 2011-2015 1990-1994 2006-2010 2011-2015 Individual forecast error 210 69,427 104,079 -0.2542 -2.8152 -1.2769 1.0118 10.2844 4.2643 Consensus forecast error 210 69,427 104,079 -0.2538 -2.7947 -1.2769 1.0088 10.1178 4.2062 Individual forecast revision 210 69,427 104,079 -0.0708 -0.2722 -0.1638 0.2844 1.1506 0.7723 Cluster consensus revision 210 69,427 104,079 -0.0792 -0.1643 -0.0745 0.3595 1.2076 0.8164 Absolute individual revision 210 69,427 104,079 0.1329 0.4909 0.3402 0.2611 1.0756 0.7124 Cluster absolute revision 210 69,427 104,079 0.1461 0.5591 0.4043 0.3378 1.0829 0.7248 %FORECAST 210 69,427 104,079 0.1903 0.2631 0.2596 0.0984 0.2225 0.3674 Percentage of previous forecasts 210 69,427 104,079 0.0262 0.1494 0.1697 0.1090 0.2292 0.2478 Number of analysts following 210 69,427 104,079 7.93 14.08 16.44 2.32 7.29 8.27 Time-series variability 210 69,397 104,046 0.3407 3.7850 1.6054 0.5950 11.1726 3.2132 Negative revision 210 69,427 104,079 0.5857 0.5737 0.5542 0.4938 0.4945 0.4971 Forecast horizon 210 69,427 104,079 372.13 364.51 364.81 25.0523 39.9567 26.2525 UNDERREACTION 191 66,925 100,717 0.6126 0.5642 0.5451 0.4884 0.4959 0.4980
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Some regressions use six-day cluster, yet the differences of descriptive statistics from three-day setting are quite small so ignored. After applying several sample selection criteria, 1990-1994 sample has few observations. A possible reason might be the IBES database used in this research collect less data in that period, compared to the RTEE database used in the original paper.
The original data for 1990-1004 period contains only 7,781 observations because many sample firms did not report forecasts to I/B/E/S until 1994. To control the number of analysts following a company to be at least 6, 5742 observations are dropped, which results in a very small final sample for 1990-1994.
Later sample period contains more observations. Forecast errors and forecast revisions are generally negative. 2006-2010 period reports much higher volatilities, with largest absolute values of all error and revision variables. The most recent sample period 2011-2015 are selected to further test hypothesis 2.
In general, consensus forecast errors and revisions have smaller absolute value than individual observations. The error and revision mean values are quite small because they are standardized by price. For example, the mean individual forecast error of 2006-2010 should be interpreted as -2.8152% of the year-end trading price. Two timeliness proxies, %FORECAST and Percentage of Previous Forecasts are interpreted as around 26% and 16%. Number of analysts following a company increase throughout recent years. The possibility of providing a negative revision, denoted by DOWN, is more than 50% in all three periods, decreasing slightly. The HORIZON is a little smaller than 365 days showing that the average forecast date is right around one-year ahead and is reasonable. The underreaction indicator, actually the possibility of giving the same direction to revision and forecast error is more than 50% in all three periods.
4.2
Correlation
Cluster size is NUMANS, the number of forecasts in the cluster. After grouping clusters by size, correlation between forecast error and corresponding revision is calculated and reported.
Table 5 The correlation between revision and forecast error
This table shows the correlation between cluster consensus revision and cluster consensus forecast error when there are more than 300 clusters with the size. Cluster size is the number of forecasts in a cluster.
Cluster size Correlation Observation
1 0.1103 33,104
2 0.1880 16,588
22 4 0.2636 7,600 5 0.2164 5,760 6 0.2426 4,638 7 0.4313 3,703 8 0.2621 3,080 9 0.4577 2,160 10 0.1001 2,260 11 0.4231 1,573 12 0.5525 1,476 13 0.3355 1,417 14 0.3829 1,330 15 0.7189 1,110 16 0.3569 800 17 0.3544 782 18 -0.5423 882 19 0.5029 665 20 0.8072 520 21 0.7387 525 22 0.6295 396 23 0.5822 391
Figure 1 Correlation and trendline between revision and forecast error
Figure 1 illustrates the relationship between forecast error and revision as the cluster size goes larger, and offers a trend line suggested by correlation points.
-0.60 -0.40 -0.20 0.00 0.20 0.40 0.60 0.80 1.00 0 5 10 15 20 25 Co rrelati on Cluster Size
23
Cluster size is independent of the time that the cluster lies, with a larger value happens when revised forecasts are issued more intensive. As cluster size increases, number of cluster with that many forecasts decreases as the third Column Observation presents. Cluster size 1 has the most observations, indicating that throughout whole sample period 2011-2015, it happens most frequently that one forecast revision is separated from an earlier one and a later one both for more than six days. A possible speculation is that the forecast is updated because the analyst finds private clue for future earnings. This figure shows a general increasing trend on the correlation between cluster consensus forecast error and revision. The result is roughly consistent to Mozes (2003)’s Table 5 Panel A. The more intensive forecast revisions are issued in a short time, the less time took to process information. If there was no underreaction, forecast error represented only the difference between actual value implied by the information available at that time and the final actual, namely was not controllable at the time of revision, therefore should have been independent of forecast revision. Yet, data performs higher correlation when cluster size is larger, suggesting that forecast error contains information available but left out of market expectation
intentionally or not. Provided that forecast revision proxies the information incorporated, the increasing correlation when revised forecasts are issued more intensively supports the hypothesis that timeliness intensifies underreaction.
4.3
Association
As explained above, there are two main models in this research and each model are tested with and without quarter dummy interactions. To explicitly present the results, precondition test results and hypotheses test results are consolidated by models.
4.3.1 Results of Mozes (2003)-based Model
Table 3 Association between underreaction and timeliness
Table 3 shows results from OLS regressions of Model 1.1 and 1.2 using three sample periods: 1990-1994, 2006-2010, and 2011-2015. Column 1 uses Mozes (2003)’s three-day cluster, while Column 2 uses six-day setting on the same sample period. Column 3 and 4 also use six-day cluster setting to test on later sample periods. Column 5 replaces REVISION by four REVISION terms interacted with quarter dummies. Dependent variable is cluster consensus forecast error. REVISION is cluster consensus revision, and other variables are interacted with REVISION. Statistical significance at the 1%, 5%, and 10% level is indicated by ***, **, and *, respectively.
Dependent Variable:
Consensus Forecast Error (1) (2) (3) (4) (5)
24 REVISION -7.374 -7.866 -8.610*** -4.398*** (5.672) (4.769) (0.588) (0.490) %FORECAST*REVISION -1.900 4.173** 2.322*** 0.285*** 0.238*** (2.397) (1.680) (0.214) (0.0791) (0.0818) AREVISION*REVISION 1.393** 0.590 1.395*** 1.499*** 1.491*** (0.655) (0.640) (0.0541) (0.0397) (0.0396) NUMFOL*REVISION -0.0768 0.110 0.0604*** 0.0188*** 0.0200*** (0.150) (0.0975) (0.0129) (0.00532) (0.00531) HORIZON*REVISION 0.0158 0.00831 0.00229 0.00123 -0.00182 (0.0125) (0.0114) (0.00146) (0.00134) (0.00148) DOWN*REVISION 0.820 1.999 2.160*** 0.790*** 0.772*** (1.559) (1.434) (0.192) (0.0896) (0.0894) TSVAR*REVISION 0.370 0.736** 0.0263*** -0.00643 -0.00798 (0.331) (0.333) (0.00394) (0.00827) (0.00826) First Quarter*REVISION -3.555*** (0.524) Second Quarter*REVISION -3.345*** (0.555) Third Quarter*REVISION -3.294*** (0.556) Fourth Quarter*REVISION -2.891*** (0.564) Constant -0.164*** -0.123** -2.084*** -1.008*** -1.007*** (0.0621) (0.0519) (0.0356) (0.0117) (0.0116) Observations 210 210 69,397 104,046 104,046 R-squared 0.427 0.459 0.233 0.200 0.202
Column 1 and 2 roughly support Mozes (2003)’s Table 5 Panel B to the extent of the sign and
significance, while Column 2 uses six-day clusters instead of three-day setting in original paper and yields a more significantly positive coefficient on the key variable %FORECAST*REVISION. That is, Column 1 is the only test in this research to use three-day cluster.
Interpreting the results requires the idea that basic relationship between forecast error and revision is negative, while factors that motivate underreaction will narrow the effect. From the perspective of statistics, the coefficients for REVISION and quarter-REVISION interactions should be negative, corresponding to the first line reported in Column 1 to 4 and the four quarter interactions in Column 5. Coefficients of factor-REVISION interactions as additional relationship should be positive as long as the factors strengthen incentives to underreact, corresponding to the second till the sixth line.
All coefficients of REVISION are negative. Column 1 was supposed to be identical to Mozes (2003)’s Table 5 Panel B, but is actually insignificant. After extending cluster separation time to at least seven days, the coefficient of interest performs better and matches the original significantly positive result. The
25
divergence possibly suggests that I/B/E/S sample from 1990-1994 is too small to adopt small clusters. Using three-day separation cluster might result in too many clusters with only one revised forecast, therefore %FORECAST will have too many extremely small values. Column 3 and 4 report the interested coefficients of %FORECAST*REVISION as positive and significant at 1% level. Contradictory to original paper, the coefficients of AREVISION*REVISION are generally different from zero, suggesting that under adjustment is not proportional to REVISION.
Comparing results of columns 2, 3 and 4 yields support for Hypothesis 1. Higher volatility due to 2008 financial crisis covered in Column 3 leads to obvious larger and more significant coefficients
for %FORECAST*REVISION and TSVAR*REVISION than other two sample periods. Column 3 and 4 of sample period 2006-2010, 2011-2015 report positive coefficients of
DOWN*REVISION at the 1% significance. The effect is much stronger during crisis period. Analysts perform stronger underreaction when issuing negative forecast revisions.
Replacing cluster consensus revision variable with four interacted terms of quarter dummies and revision yields Column 5 of Table 3. The significantly negative coefficient for REVISION is now broken down to four significant negative terms with decreasing absolute coefficients from the first quarter to the last. Surprisingly, all four quarterly coefficients have smaller absolute values than homologous coefficient of REVISION in Column 4, while coefficients of other variables only change slightly. Yet, it seems evident to conclude that forecast revisions perform quarterly variability. A less negative coefficient stands for more upwards correction added to original negative correlation between forecast error and revisions, which can be interpreted as more underreaction. Hence, the decreasing absolute coefficients show that underreaction is stronger at the end of a year than the beginning. Hypothesis 1 about quarterly effect is justified in the direction of more underreaction in the fourth quarter.
In conclusion, results in Table 3 generally support the hypotheses tested. Column 1 and 2 test the and the availability of alternative longer cluster separation setting. Column 1, 2, 3 and 4 support Precondition Hypothesis about empirical existence of underreaction, larger forecast immediacy generating greater analysts under adjustment, with the adoption of I/B/E/S database. Column 2, 3 and 4 support Hypothesis 1 about volatility-triggered underreaction by reporting larger and more significant coefficient of time-series earnings variability factor during 2006-2010. Column 3 and 4 support Hypothesis 1 about loss-aversion-triggered underreaction by reporting significantly positive coefficients of the factor indicating negative revision. Column 5 supports Hypothesis 2.
26 4.3.2 Results of Logit Model
Table 4 Logit Model Results
Independent variable of interest is individual forecast revision. Based on the results of Column 1, Column 2 reports marginal effects after Logit at the mean of relevant independent variables. Statistical significance at the 1%, 5%, and 10% level is indicated by ***, **, and *, respectively.
Dependent Variable: UNDERREACTION (1) MFX (2) (3)
Individual Revision -0.875*** -0.217***
(0.0231) (0.0057)
Percentage of previous forecasts 0.105*** 0.026*** 0.102*** (0.0280) (0.0070) (0.0281)
Absolute Revision -0.578*** -0.143*** -0.578***
(0.0262) (0.0065) (0.0263) Number of analysts following -0.000398 -0.000099 -0.000448
(0.000825) (0.0002) (0.000826) Time-series variability of earnings 0.0109*** 0.0027*** 0.0108***
(0.00325) (0.0008) (0.00326) Dummy of Negative Revision 0.587*** 0.145*** 0.586***
(0.0156) (0.0038) (0.0156) Forecast Horizon -0.000898*** -0.000222*** -0.00104***
(0.000260) (0.00006) (0.000261)
First Quarter*Individual Revision -0.789***
(0.0272)
Second Quarter* Individual Revision -0.908***
(0.0379)
Third Quarter* Individual Revision -0.852***
(0.0324)
Fourth Quarter* Individual Revision -0.979***
(0.0304)
Constant 0.208** 0.260***
(0.0966) (0.0971)
Observations 100,694 100,694
Despite that sign and magnitude of revisions are respectively tested as dummy DOWN and variable Absolute Individual Revision, the first independent variable Individual Revision is not omitted but even having significantly negative coefficient. Results in Column 1 and 2 indicate that on the average level of individual forecast revision at -0.17%, one percent increase in forecast revision, indicating more of new information incorporated to updated forecast, the possibility of underreaction decreases for 0.21%. Absolute Revision captures the amount of information content. The more information incorporated, the lower possibility of underreaction. At the average absolute revision of 0.3468%, one percent increase will
