Getting Bad News Out Early: Does it Really Help Stock Prices?

Getting Bad News Out Early: Does it Really Help Stock Prices? (cid:3) Chris Downing and Steve Sharpe October 2, 2003 Abstract In this paper, we examine the stock price bene(cid:12)t of meeting or beating earnings expectations. Using a general methodology, we (cid:12)nd no evidence that the timing of earnings news has any bene(cid:12)t for (cid:12)rms’ stock returns. In fact, in many cases we (cid:12)nd (cid:12)rms attempting to engineer positive earnings surprises by beating down expectations onlytodiscoverthattheire(cid:11)ortsarecounterproductive. Ourresultsappeartooverturn the (cid:12)ndings of previous authors who, using less general methodologies, have suggested that (cid:12)rms can boost their stock returns by getting bad news out early. Our results are robust across time periods, for di(cid:11)erent scaling factors on earnings revisions and surprises, when controlling for (cid:12)rm size and growth prospects, and when conditioned on past earnings news. (cid:3) We thank Eli Bartov, Mark Carey, Robert Hauswald, Andreas Lehnert, Michel Robe, and the participants at the 2003 Western Finance Association Meetings for helpful comments and suggestions, and Eric Richards for excellent research assistance. This paper represents the views of the authors and does not necessarily represent the views of the Federal Reserve System or members of its sta(cid:11). Please address correspondence to (Downing): Federal Reserve Board, Mail Stop 89, Washington, DC 20551. Phone: (202) 452-2378. Fax: (202)728-5887. E-Mail: cdowning@frb.gov. (Sharpe): FederalReserveBoard,MailStop89, Washington, DC 20551. Phone: (202) 452-2875. Fax: (202) 728-5887. E-Mail: ssharpe@frb.gov.

1 Introduction Over the last decade, corporate chieftains seem to have become increasingly preoccupied with their quarterly (cid:12)nancial results and whether those results meet their equity analysts’ forecasts. Indeed, both market observers and academic studies have pointed out an apparent tendency for corporate managers to guide analysts’ overly optimistic earnings forecasts downward in advance of the o(cid:14)cial release, so that the (cid:12)rms are able to meet or beat Wall Street expectations on the release date. It is easy to understand management’s obsession with meeting Wall Street estimates in light of the punishment frequently meted out to the stocks of companies whose quarterly results fall short of forecasts. What is more di(cid:14)cult to understand is how (cid:12)rms could bene(cid:12)t from managing down current quarterly forecasts by \preannouncing" bad news several days or weeks before their (cid:12)nal results are released. If, at the end of the day, the total news is the same, then any bene(cid:12)t to the stock price at the earnings announcement should be entirely o(cid:11)set by the earlier negative price impact at the time of the warning, rendering the cumulative return insensitive to the timing of the news. This standard e(cid:14)cient markets view, however, seems at odds with popular perceptions. Moreover, some recent academic studies also conclude that managing expectations down ahead of bad news reduces the total stock price impact of the news. In principle, testing the hypothesis that (cid:12)rms can boost their near-term stock prices by managing expectations should be straightforward. Controlling for the total earnings information revealed over the period in question | the gap between realized earnings and the beginning-of-quarter forecast (the \total forecast error") | one can test whether the timing of information revelation matters for the cumulative stock return over that period. While a number of recent studies have attempted to implement this testing strategy, the results are somewhat contradictory and the methodologies may not be robust. In this paper, we examine the stock price bene(cid:12)t of meeting or beating expectations using a general, yet intuitive, approach. Our methodology most closely parallels Kasznik 1

and McNichols (2002) and Bartov, Givoly and Hayn (2002), both of whom measure interim earnings news using revisions to analyst forecasts. Kasznik and McNichols (2002) gauge the rewards to meeting analysts’ annual earnings forecasts by testing whether meeting (or beating) those forecasts has a positive incremental e(cid:11)ect on stock price, while controlling for the total information revealed over the year. Indeed, they (cid:12)nd a positive incremental e(cid:11)ect of meeting the expectations at the time of the earnings announcement. Bartov et al. (2002) conduct a similar experiment, but focus on quarterly earnings. They also (cid:12)nd that meeting expectations has a bene(cid:12)cial stock price e(cid:11)ect, even after controlling for the total earnings news over the quarter, including the day of the report. A clear implication of these (cid:12)ndings is that earnings news released during the (cid:12)rm’s performance period, that is, during the year or quarter, has a smaller stock price impact than the same news released around the time of the actual report. This suggests that (cid:12)rms can boost their stock prices by releasing negative news early, when price responses are lower, while keeping any good news under wraps until the earnings report, when price responses are larger. Like these and a few other studies that have appeared recently in the literature, in this paper we estimate the e(cid:11)ect of quarterly earnings news on quarterly abnormal stock returns by splitting quarterly total forecast errors into two contiguous pieces: (i) a forecast revision, de(cid:12)ned as the di(cid:11)erence between analysts’ forecasts early in the quarter and their forecasts three days before the earnings announcement; and (ii) an earnings surprise, de(cid:12)ned as the di(cid:11)erence between the three day forecast and actualreported earnings. Wethen estimate the e(cid:11)ects of these forecast revisions and earnings surprises on the cumulative abnormal return over the period. The most important methodological di(cid:11)erence here is our use of nonparametric estimation, which allows for a wide range of abnormal return response functions. Given the potential nonlinearities that might underpin the relation between earnings news and stock returns, we argue that careful consideration should be given to the form of the assumed 2

response function. Most of the previous studies have assumed that the response of stock returns to earnings information is linear, with the possible exception of a discontinuity at an earnings surprise of zero. Indeed, under any number of possible nonlinearities, such regressions would be prone to incorrectly accept the hypothesis of a discontinuity at zero. To estimate the abnormal return function, we employ the locally weighted least squares (loess) method (Cleveland (1979), Cleveland and Devlin (1988)), which allows for a wide range of possible functional forms. Moreover, under standard assumptions on the error term, thestatisticalpropertiesofthelocallyweightedleastsquaresestimatorarewellapproximated by those of the the ordinary least squares estimator. The principal drawback to loess is that it is a computationally and data intensive procedure, but given recent advances in computer speed and our very large dataset, these drawbacks are signi(cid:12)cantly mitigated in our application. We report our results in the formof three-dimensional plots of the abnormal return on the vertical axis against the forecast revision and the surprise on the horizontal axes, thereby allowing one to examine the estimated tradeo(cid:11) that (cid:12)rms face at a variety of points in revision-surprise space. A second important methodological di(cid:11)erence between our study and previous work is that we focus on the econometrician’s choice of the \preannouncement period," and suggest that revisions early in the quarter might reflect the previous quarter’s news. If analysts do not fully incorporate the previous quarter’s earnings announcement into their newly updated or recon(cid:12)rmed forecasts, but the stock price does immediately incorporate the information, then revisions to these early-quarter forecasts might not convey as much information to the market as revisions that follow company guidance later in the quarter. This would create a spurious asymmetry in the magnitude of stock price responses to forecast revisions and earnings surprises. Finally, we examine the choice of the scaling factor applied to the forecast revisions and surprises | a choice that we argue could influence the results. It is conventional in accounting studies to normalize by beginning-of-period stock price, which reduces problems 3

with outliers. We argue that, in theory, expected earnings (or book value) is a preferable measure. We (cid:12)nd that the expected earnings scaling factor produces (cid:12)ts that are slightly superior, in a statistical sense, to the (cid:12)ts produced by the price scaling factor. In contrast to previous studies, we do not (cid:12)nd any short-term stock price bene(cid:12)t to preannouncing bad news. In other words, we (cid:12)nd little or no di(cid:11)erence in the sensitivity of stock returns to early forecast revisions and earnings surprises. This conclusion appears to be robust across practically the entire range of the data. In particular, in most cases we do not even see a bene(cid:12)t from nudging analysts’ forecasts so that the earnings surprise is zero or slightly positive rather than slightly negative. Finally, we look at whether these results obtain when we condition on the size of the (cid:12)rm and on the (cid:12)rm’s growth prospects as measured by analysts’ long-term growth forecasts. While we do (cid:12)nd that the stock prices of high-growth (cid:12)rms, particularly small, high-growth (cid:12)rms, tend to be much more sensitive to quarterly earnings news than those of low-growth (cid:12)rms, we again do not (cid:12)nd any signi(cid:12)cant asymmetries in their sensitivity to news released early versus news released at the earnings report. This paper is organized as follows. In the next section, we provide an overview of this rapidly expanding literature. Section 3 describes the data in detail and discusses our empirical methodology, and section 4 lays out our results. The (cid:12)nal section concludes. 2 Previous Literature Over the past decade, the consensus-meeting game played by corporate management and equity analysts seems to have become a dominant feature of the corporate reporting landscape. In general, (cid:12)rms can meet over-optimistic expectations in one of two ways. They can \manage" their (cid:12)nancials insuch a way as to boost the earnings they actually report, or they can provide guidance to analysts well before earnings are actually reported, causing analysts to immediately mark down their forecasts. Our analysis focuses on the latter behavior. 4

Early evidence on the asymmetric nature of management disclosures is provided by Skinner (1994), who found that, more than a decade ago, 67 percent of early quarterly disclosures conveyed badnews. Kasznik andLev (1995)show thatthis asymmetry did notmerely reflect the state of forecasts relative to the economy, but a greater propensity by management to divulge signi(cid:12)cant earnings news early when that news was negative. Moreover, the propensity to avoid the negative announcement-day surprises appears to have become increasingly pervasive over the last decade. For instance, Matsumoto (2002) shows that in a large and growing percentage of cases where quarterly reports matched or even beat expectations, those reports were negative surprises relative to where analyst forecasts stood one to two months prior to the report (see also Burgstahler and Eames (2002)). Media reportsoftenpresume that preannouncements areaimedatsoftening theimpact of bad news on stock prices, but the underlying motivation remains a subject of growing debate in the academic literature. Skinner (1994) and other early research on the topic emphasizes that thethreat oflitigationgives rise to anasymmetry inthe penalty forreporting signi(cid:12)cant downside surprises. A number of authors have o(cid:11)ered behavioral rationales, such as the presumption that analysts are more embarrassed when a company that they follow reports a negative surprise than when results top their forecasts. A third type of rationale invokes signaling: Bypreannouncingbadnews, (cid:12)rmsmightsignalthattheyhavesomeunderstanding of the situation. In particular, Liu and Yao (2003) argue that (cid:12)rms preannounce bad news to signal they have better growth prospects than (cid:12)rms that don’t preannounce bad news. This last rationale, if not the others, would seem to suggest that the consensus-meeting game is designed to boost (or perhaps just bolster) the (cid:12)rm’s stock price. Some recent studies propose more insidious motivations. For example, Aboody and Kasznik (2000) o(cid:11)er evidence that managers are motivated to make bad news public or hold back good news prior to receiving installments on executive stock option grants. By moving forward and perhaps exaggerating its negative stock price impact, preannouncing bad news lowers the strike price on newly-granted stock options, thereby raising the potential value 5

of the options to managers. In contrast to previous explanations, this rationale does not imply that prereleasing negative information bene(cid:12)ts the (cid:12)rm’s stock price in the short- or long-run; rather, it merely pulls forward in time any downward price adjustments. In a similar vein, Richardson, Teoh and Wysocki (2003) point out that the window during which insiders can sell shares, and when (cid:12)rms tend to issue shares, usually follows o(cid:14)cial earnings releases. If management believes that the market temporarily overreacts to bad news, or that the market reacts less to bad news when it is disseminated prior to the earnings report, then preannouncing such news well before both the report date and the window for selling shares could bolster the price that managers receive on sales of shares to the public. A similar argument, which may be more easily reconciled with market e(cid:14)ciency, is that preannouncing bad news might simply reduce the variance of the price received on post-report share sales, by providing more time for the information to be digested. While there is little agreement on the primary motivation behind the consensus-beating game, there does appear to be mounting evidence that playing this game has a positive impact on stock prices. Such evidence has taken one of two forms. One approach to gauging that impact is by analyzing valuations (the level of stock prices) to infer whether (cid:12)rms that tend to meet consensus forecasts on the report date also tend to be more highly valued (Chevis, Das and Sivaramakrishnan (2002), Liu and Yao (2003)). This type of evidence, though highly suggestive, must be viewed with at least some skepticism, as it is di(cid:14)cult to control for (cid:12)rm characteristics and insure that the true direction of causation is not the reverse. In particular, it is di(cid:14)cult to control for the likelihood that highly-valued \growth (cid:12)rms" are more prone to play the consensus-beating game. Indeed, those (cid:12)rms should be more motivated to do so if, as suggested by Skinner and Sloan (1999), they are penalized disproportionately when their reported earnings do fall short of consensus forecasts. The most direct evidence on the stock price bene(cid:12)ts of playing the consensus-beating game comes from studies that analyze stock returns. One of the (cid:12)rst studies to try gauging the e(cid:11)ect of company preannouncements on stock prices was Kasznik and Lev (1995), who 6

identify discretionary management disclosures via a NEXIS News search. They analyze fourth-quarter earnings announcements from 1988-1990, focusing only on observations with substantial total forecast errors between actual earnings and forecasts 30 days after the previous quarter’s earnings announcement. Controlling for the total forecast error, they (cid:12)nd no evidence that issuing an early disclosure boosts cumulative returns. In fact, among (cid:12)rms with substantial negative forecast errors, they (cid:12)nd that issuing an early disclosure has a negative e(cid:11)ect on the cumulative returns measured over a narrower window. More recently, So(cid:11)er, Thiagarajan and Walther (2000) analyze the stock returns of companies identi(cid:12)ed by First Call as having issued quantitative preannouncements no earlier than two weeks prior to quarter-end. They (cid:12)nd that, even after controlling for the total forecast error (the di(cid:11)erence between actual earnings and the forecast at the time of the preannouncement), having a negative earnings surprise on the earnings announcement has a negative e(cid:11)ect on total-period stock returns. Moreover, they (cid:12)nd that stock prices are more sensitive to the amount of negative news when it is released at the earnings announcement, suggesting that (cid:12)rms can reduce the impact of negative news by preannouncing it. These ideas are further tested in the study by Bartov et al. (2002), henceforth BGH, who analyze roughly three-month cumulative returns for all (cid:12)rms whose quarterly earnings are forecasted by analysts tracked by Thompson/First Call. Again, controlling for the size of the total forecast error, they test whether cumulative stock returns are a(cid:11)ected by the timing of earnings news. Their methodology is similar in spirit to the analysis of annual earnings surprises by Kasznik and McNichols (2002). In both studies, news is gauged solely by changes in analyst estimates, and in both cases, it is found that the cumulative returns on stocks of (cid:12)rms with bad news (negative forecast errors) are higher when the bad news is reflected in forecasts before the earnings announcement. The implication is that (cid:12)rms can dampen the e(cid:11)ects of bad news by driving down analyst forecasts prior to the earnings report, through preannouncements or quieter means.1 1Firms’ scope for influencing analysts’ forecasts by quieter means was signi(cid:12)cantly limited following October 23, 2000, when the Securities and Exchange Commission adopted Regulation FD (Fair Disclosure) 7

BGH recognize the potential for nonlinearities and provide relatively compelling evidence usingdi(cid:11)erence-in-meanstests. Inparticular,theydivideobservationsintobuckets according to the size of the total forecast error. Among the set of observations falling within any given range of total forecast errors (e.g., -5 to 0 percent), they compare the average abnormal return for observations where there is a negative surprise on the report date to the average return among those where there is a positive surprise. Our approach di(cid:11)ers fromBGHin two potentially important respects. First, our methodology uses a continuous distance metric for de(cid:12)ning which observations are \close" to one another in the sample space. Second, among observations within a given neighborhood, our estimation strategy allows for a slope, as well as an intercept, in estimating the abnormal return function. While this should make our estimates less biased, the potential downside is a loss of precision. Venkatachalam and Wang (2000) recognize a need to allow for nonlinearities, but they estimate anearnings response function thatonly allows for some select breaks inthe linearity assumption, including asymmetries in the response to positive and negative information. Their results partially con(cid:12)rm those of BGH, but suggest a more complicated story in which the bene(cid:12)ts of lowering expectations are not uniform. Still, these inferences may be just as sensitive to their parametric restrictions, which presume linearity over large ranges of the data. Our approach to the question essentially amounts to a generalization of the common hypothesis in these previous studies: Is the size of the cumulative stock return a function of not only the amount of earnings news, but also of the timing of that news? For instance, does bad news have a smaller negative e(cid:11)ect if that news is released some days or weeks ahead of the actual earnings announcement? As in the more recent studies, we use analysts’ earnings forecasts to measure market expectations. Under this approach, current-quarter revisions to analysts’ forecasts are assumed to reflect the timing of earnings news released which addresses selective disclosure. The regulation provides that when an issuer ((cid:12)rm), or person acting on its behalf, discloses material non-public information to securities market professionals and/or holders of the issuer’s securities, it must make public disclosure of that information. 8

by the (cid:12)rm, either publicly or privately. 3 Data and Methodology 3.1 Data Construction and Measurement Issues Our study examines U.S. (cid:12)rms’ quarterly earnings reports from 1987 through 2001. Data on both equity analysts’ forecasts of earnings per share and actual earnings per share (EPS) are drawn from the I/B/E/S history and analyst detail (cid:12)les. For each (cid:12)rm-quarter observation, we compute the average of analysts’ quarterly EPS forecasts, measured in dollars per share, at three points in time: (i) 7 days after the previous quarter’s report (or about twelve weeks beforethecurrent-quarter report date); (ii) 42days (or six weeks), beforethe current-quarter report date; and (iii) 3 days before the report date. To avoid using stale forecasts, average forecasts are computed using only those forecasts that were issued or con(cid:12)rmed after the previous quarter’s earnings report. To (cid:12)lter out observations where information timeliness may be a problem, we exclude (cid:12)rm-quarters in which earnings are not reported within 90 days after quarter-end. In addition, we exclude observations in which the report is not issued between 8 and 16 weeks after the previous quarter’s earnings report (where the mode is about 13 weeks). These data are used to construct our main information variables. We de(cid:12)ne the total forecast error as the di(cid:11)erence between actual quarterly EPS, revealed on the announcement date, and our earliest consensus forecast, F0 in (cid:12)gure 1. Similar to BGH, we split the total forecast error into two components: (i) the surprise, de(cid:12)ned as the di(cid:11)erence between actual earnings and the consensus forecast 3 days earlier, F ; and (ii) the forecast revision, de(cid:12)ned 2 as the di(cid:11)erence between the 3-day forecast, F , and the early-quarter consensus forecast, 2 F . 0 A key methodological question concerns the timing of the early forecast, F : How early 0 should this measurement be taken? BGH measure this as early as 3 days after the previous 9

quarter’s announcement. However, early in the quarter it is possible that analysts have not fullyincorporatedtherami(cid:12)cationsofthepreviousquarter’so(cid:14)cialearningsreleaseintotheir updated or recon(cid:12)rmed forecasts, even if the stock price has incorporated that information. If this were the case, then revisions to these forecasts may not convey as much information to the market (where the news has already been digested) as revisions that follow new company guidance later in the quarter. This would create a spurious asymmetry in the magnitude of stock price responses to forecast revisions and announcement-day surprises. To address this concern, we construct an alternative measure of the initial forecast revision, equal to the average forecast as of six weeks (42 days) prior to the actual earnings announcement, denoted by F in (cid:12)gure 1. In this case, the revision is the di(cid:11)erence between 1 F and F , while the surprise is de(cid:12)ned as before. For the typical (cid:12)rm, F would fall in 1 2 1 the middle of the third month of the quarter, about the time that most managers would have an accurate picture of the (cid:12)rm’s performance over the (cid:12)rst two months of the quarter. Also, most warnings tend to come near the end of the quarter or shortly thereafter, so this more abbreviated forecast revision period should capture most of the information released in pre-announcements (So(cid:11)er et al. (2000)). A second measurement issue that we consider is how to best scale earnings revisions and surprises. The most common scale factor in the literature is the (cid:12)rm’s beginning-of-period stock price. This scale factor is convenient because the stock price is always positive and is rarely small relative to the numerator. From an analytical perspective, however, this approach is less satisfying, and we also argue that this scale factor is likely to distort the relativesizesofearningsrevisionsandsurprises across(cid:12)rms. Inparticular, ithasbeenargued that the stock return of high growth, high price-to-earnings (PE) ratio (cid:12)rms should be more sensitive to any given earnings surprise compared to slower growing, low-PE (cid:12)rms. However, all else equal, scaling earnings revisions by stock prices will make the news on high-price (cid:12)rms appear smaller than the same news on low-price (cid:12)rms. If so, this scaling would induce measurement error that would reduce the apparent explanatory power of earnings news. 10

Two alternative scale factors that we consider are the level of realized earnings-pershare, which converts the revisions and surprises into percentage terms, and book value per share, which converts them into returns on equity. While these measures might be preferable analytically and theoretically, they produce numerical di(cid:14)culties when earnings or book value are negative or near zero. To implement these scale factors, we use their absolute values, and delete observations for which the value of the scale factor is close to zero. For the EPS scale factor, we omit observations in which actual EPS is 5 cents or less in absolute value, denoting the resulting variable by jEPSj. In the case of book value, we omit observations where the absolute value of the expected quarterly return on equity was greater than 25 percent (an annualized expected return of 100 percent).2 Because the book value scaling factor produced results that were qualitatively indistinguishable from the jEPSj scaling factor, in what follows we discuss only the results based on the jEPSj and price scaling factors. The earnings data are linked with stock price data drawn from CRSP. For each (cid:12)rmquarter, we calculate the cumulative return on the (cid:12)rm’s stock between the day of the initial forecast, F , through the day after the release of the current quarter’s earnings. To compute 0 abnormal returns, we calculate the cumulative return on the S&P500 Composite index over the same period and subtract this from the (cid:12)rm-level return. Although not shown in the paper, we also calculated abnormal returns using estimated betas in a traditional singlefactor market model. However, both the qualitative and quantitative results using these measures were virtually indistinguishable from the results reported here.3 2We drew the book value data from Compustat. 3We constructed betas for each (cid:12)rm-quarterusing daily stock returns for the 250 trading days preceding the (cid:12)rst calculation of the mean EPS forecast for each (cid:12)rm, matched with daily returns on the S&P 500 index (the \market" return) overthe same time period. In other words,for each(cid:12)rm we compute quarterly betasonrollingoneyearsamplesofthe (cid:12)rm’sstockreturnsandS&P500returns. Theprincipalreasonthat beta-adjusted returns do not change our results appears to be the fact that betas contain little predictive power for (cid:12)rm-level returns, particularly for smaller (cid:12)rms. 11

3.2 Sample Statistics After merging the I/B/E/S, CRSP, and Compustat data, constructing the revision, surprise, and abnormal return variables, and applying our data timeliness criteria, we have 134,098 (cid:12)rm-quarter observations (before scaling revisions and surprises). For most of our analysis, wesplit thedataintotwo subsamples, anearlysample spanning 1987-1995,andalatesample spanning 1996-2001. Doing so should provide some indication of any longer-term behavioral changes. Because coverage of smaller (cid:12)rms has expanded over time, there are many more observations per quarter in later years. We apply some additional criteria to eliminate outliers. We remove (cid:12)rm-quarters with a beginning-of-period stock price less than 3 dollars, as such observations are likely to produce very volatile and highly idiosyncratic returns. As mentioned earlier, for the earnings-scaled analysis, we eliminate observations in which quarterly EPS is 5 cents or less in absolute value. Lastly, we trim out observations for which any of the variables (revisions, surprises, or abnormal returns) have extreme values, de(cid:12)ned as values in the top or bottom 2 percent of the variable’s empirical distribution. After these re(cid:12)nements, we are left with a total of 100,437 observations in the sample using the jEPSj scaling factor, and 111,111 observations for the sample using the price scaling factor. Inordertoprovideasense ofsomeofthequalitativefeaturesofourdata,(cid:12)gure2provides scatter plots depicting the joint distribution of \12-week" earnings revisions and earnings surprises, scaled by jEPSj. Panel A depicts the joint distribution over the period 1987-1995, while panel B shows the distribution for the period 1996-2001. In the early period, revisions range from -0.94 to 0.30 (-94 percent to 30 percent), while in the late period, revisions range from -108 percent to 21 percent. The distribution of surprises in the early period is more skewed toward negative surprises than in the late period. These features of the data are suggestive of increased e(cid:11)orts over time on the part of analysts to keep their forecasts current, and/or increased e(cid:11)orts on the part of (cid:12)rms to manage down expectations so as to 12

avoid negative surprises.4 Turning to a quantitative description of the data, table 1 displays univariate statistics for our measures of revisions, surprises, and abnormal returns. The table displays the 25th, 50th, and 75th percentiles for the variables, plus the interquartile ranges, with all values multiplied by 100 (which converts the dependent variable and the jEPSj-scaled revisions and surprises into percent values). Panel A shows statistics for the early and late samples when the revisions and surprises are scaled by jEPSj, while panel B shows sample statistics when we scale by price. The (cid:12)rst column in the upper left box of panel A shows some of the distributional characteristics of abnormal returns, the dependent variable, in the early period for the 12-week revision subsample. As shown, (cid:12)fty percent of the observations on abnormal returns lie between -7.90 percent and 7.43 percent, and the median value is -0.18 th percent. In the late period, abnormal returns appear more volatile, with the 25 percentile th at -13.00 percent and the 75 percentile at 10.17 percent. In both the early and late samples, there is a clear asymmetry in the distribution of revisions, with negative revisions being much larger and more plentiful than positive revisions. In the early sample, the 25 th percentile jEPSj-scaled revision equals -5.15 percent, whereas th the 75 percentile is 1.67 percent. Although the late sample also shows this asymmetry, the distribution is notably tighter, implying that that quarterly forecasts have become more accurate in recent years. Moving down panel A to the statistics for the 6-week forecast revisions, we (cid:12)nd this narrower measure to be much more tightly distributed compared to the 12-week revisions, th with a higher proportionof zeros. The 25 percentiles fall to -1.71percent and-1.14 percent in the early and late periods, respectively, while the median 6-week revision is zero in both subsamples. More obvious here than in the scatterplots is the strong positive skew of surprises, consistent with the (cid:12)ndings of previous studies, such as Richardson et al. (2003), which document 4The striations evident in the data reflect rounding and our cuto(cid:11) on EPS values. We discuss the boxes below. 13

analysts’ generally positive forecast bias that disappears as the earnings announcement date nears. In the early sample, the median surprise is 1.08 percent, while in the late period, it is 2.34 percent. The positive skew in the distribution of surprises is most evident in the late sample, suggesting greater e(cid:11)ort by (cid:12)rms to avoid negative surprises in recent years, consistent with the (cid:12)ndings in Matsumoto (2002). Turning to the price-scaled data in panel B, the qualitative features of the statistics di(cid:11)er only slightly from panel A. The small di(cid:11)erences in the distributions of abnormal returns owe to the (cid:12)ltering out of observations with tiny earnings-per-share values. The partial correlations amongst the variables can be inferred from table 2, which shows the results of simple linear regressions estimated on the various subsamples, with abnormal return as the dependent variable. All three information variables | the two partly overlapping revision variables and the surprise | are included as regressors. The regression R2 values range between 4.8 and 6.2 percent, values comparable to those for similar regressions in previous studies. There appears to be little di(cid:11)erence in qualitative comparisons between the results for the jEPSj-scaled and the analogous price-scaled regressions. Focusing on the jEPSj-scaled regressions, in both the early and late subsamples, all three information variables are signi(cid:12)cant, suggesting that the stock price e(cid:11)ects of late-quarter revisions (those during the last six weeks before report) tend to be larger than the e(cid:11)ects of revisions earlier in the quarter. In the early sample period, the coe(cid:14)cient on the 12-week revision is only 0.05, while the marginal e(cid:11)ect of the 6-week revision is 0.23; this would imply that a revision during the latter six weeks has a total e(cid:11)ect of 0.28 (0.23+0.05). Notably, the coe(cid:14)cient on the surprise is only 0.16, suggesting that surprises have a substantially smaller e(cid:11)ect on returns compared to late-quarter revisions. However, we view these results as at best suggestive; given the potential for nonlinearities in the relationship between returns and revisions and surprises, they may not hold up over key portions of the revision-surprise space. The late period results are similar, though the e(cid:11)ects of our information variables appear 14

to be larger. The coe(cid:14)cient on 12-week revisions is substantially larger, at 0.21, perhaps reflecting increased attentiveness toward early-quarter forecasts in more recent years. In this sample, the total estimated e(cid:11)ect of forecast revisions during the second 6-week interval is 0.35 (0.21+0.14). Finally, the coe(cid:14)cient on surprises, at 0.28, is nearly twice as large as in the earlier years. 3.3 Methodology: Locally Weighted Least Squares Our basic regression speci(cid:12)cation is given by: Abnormal Return = f(Revision ;Surprise )+(cid:15) ; (1) n n n n for n = 1;2;:::;N, where N is the number of (cid:12)rm-quarter observations (note that we have pooled the quarterly data and dropped the time subscript for notational ease). The \Abnormal Return" on a (cid:12)rm’s stock is the cumulative return over the roughly 12-week period ending one day after the earnings report, less the cumulative return on the S&P500. The \Revision" and \Surprise" are de(cid:12)ned as described above. 5 The random error (cid:15) is n assumed to be normally distributed with zero mean and constant variance (cid:27)2, and is further assumed to be uncorrelated with revisions and surprises. Theory provides little guidance on the functional form of f((cid:1)), so in order to allow for the greatest range of possible functional forms, we adopt a nonparametric estimation approach. Speci(cid:12)cally, we employ locally weighted least squares (loess) to estimate f((cid:1)) (Cleveland (1979), Cleveland and Devlin (1988), Cleveland, Devlin and Grosse (1988)). Loess is essentially a method for smoothing scatterplots by means of the local (cid:12)tting of low-order polynomials. At a given point in the revision and surprise space, local (cid:12)tting is achieved with a weighting scheme that down-weights data points that are relatively distant from the given (cid:12)tting point. Compared to perhaps more familiar kernel regression techniques, such 5In our notation, we do not explicitly indicate the scaling factor; in the discussion of our results, we will always make clear which scaling factor applies. 15

as the Nadaraya-Watson estimator (Nadaraya (1964), Watson (1964)), loess is typically less biased on the boundaries of the data and in other situations where the data are asymmetrically distributed in the local regression sample (where by local regression sample we mean the points with non-zero weight in the local (cid:12)t | see Hastie and Loader (1993)). Moreover, the estimator enjoys a number of convenient statistical features by virtue of its close association to the ordinary least squares estimator. Animportantelement oftheloessmethodologyisthede(cid:12)nitionoftheweighting function. Following Cleveland (1979), we employ the \tricube" weight function: 8 >>< (1−jxj3)3 for jxj < 1; W(x) = (2) >>: 0 for jxj (cid:21) 1: As shown in Devlin (1986), the tricube weighting function improves certain approximations to the distributions of some of the statistics associated with the loess estimator. Denoting by h the distance from x to its rth nearest neighbor, for each data point n = 1;2;:::;N we i i construct the weights: (cid:18) (cid:19) x −x w (x ) = W n i : (3) n i h i As can be seen by examining equations (2) and (3), the rth nearest neighbor and all points more distant from x receive zero weight. i The estimates (cid:12)^ and (cid:12)^ are computed by minimizing the sum of squared residuals: i;0 i;1 XN w (x )(y −(cid:12) +(cid:12) x ) 2: (4) n i n i;0 i;1 n n=1 More independent variables can, of course, be included in equation (4), if called for in the application at hand. As we move across the (cid:12)tting points x , we re-compute the weights i assigned to each of the data points included in the regression, producing a series of estimates (cid:12)^ and (cid:12)^ for i = 1;2;:::;N. i;0 i;1 Like all other nonparametric techniques, an application of loess requires that the econo- 16

metrician decide onthe degree to which the precision ofthe estimate (bias) is to be tradedo(cid:11) against smoothness (variance). In general, the desired amount of smoothing is applicationspeci(cid:12)c (Mallows (1973)). We based our smoothing parameter selections on two standard selection methods. First, we performed generalized cross-validation (GCV) on each subsample in order to select a smoothing parameter (Ha¨rdle (1990)). Second, we computed M-statistics across a range of smoothing parameter settings. As discussed in Cleveland and Devlin (1988) and summarized in the appendix, the M-statistic is an extension of the C p procedure of Mallows (1973) for choosing a subset of independent variables based on estimates of the mean squared error for each subset. We used graphs of M-statistics (M-plots) to gauge the tradeo(cid:11) between bias and variance embodied in the smoothing parameter selected by GCV. In general, the M-plot analyses con(cid:12)rmed the GCV smoothing parameter settings: the M-plots revealed that the GCV parameters were consistent with a null hypothesis of zero bias. In cases where there was divergence between the GCV parameters and the optimal parameter suggested by the M-plot analysis, we picked the lowest smoothing parameter (least smoothing) that would accept a null hypothesis of zero bias at the traditional 95 percent level, so as to reveal nonlinearities in the abnormal return response function. 4 Empirical Results We begin by estimating the e(cid:11)ects of 12-week forecast revisions and earnings surprises, both scaled by jEPSj, on abnormal returns in the early sample period (1987-1995). Figure 3 shows four sets of estimation results, each based on a di(cid:11)erent smoothing parameter. The upper left plot depicts the estimated surface for a smoothing parameter setting of 0.15, meaning that each local regression uses 15 percent of the available data. At the other extreme, the bottom left plot shows the estimated surface based on a smoothing parameter of 0.75. We display the surfaces over a portion of revision and surprise space that contains most of the data. For this subsample, the displayed surfaces are on a grid of points laid over the box 17

drawn in panel A of (cid:12)gure 2.6 The rest of the surface is omitted because the quality of the (cid:12)t deteriorates as we move toward the fringes of the data. Each surface shows the predicted abnormal return in the relevant revision-surprise space. As one would expect, the surface tends to be highest where both the revision and surprise are positive and relatively large. Casual observation suggests that the predicted abnormal return is an increasing function of the revision and surprise over most of the sample space. But the results also indicate substantial nonlinearities; in particular, the e(cid:11)ect of a change in the revision or surprise appears to be largest when both are close to zero. Of course, the degree of nonlinearity is reduced when the surface is estimated with a high smoothing parameter, but the GCV smoothing parameter for this sample is low, about 0.15. Figure 4 illustrates the results from the same estimation procedures run on the later sample period (1996-2001).7 These surfaces clearly slope upward over the whole range of the data in both the revision and surprise dimensions, and di(cid:11)er from the early sample in two notable respects. First, there appears to be less nonlinearity: changes in either independent variable have a noticeable price impact over the entire range of the independent variables, rather than e(cid:11)ects that are concentrated near (0,0). The optimal smoothing parameter reflects this fact; our selection methodology picked an optimal smoothing parameter of 0.6, much higher than in the early sample. Second, while somewhat di(cid:14)cult to discern, the range of predicted abnormal returns in this sample (the vertical range of the surface) is wider than that in the early sample, implying that the stock price sensitivity to earnings surprises has increased over time. A useful tool for gauging the relative e(cid:11)ects of revisions and surprises is the contour plot, a two-dimensional plot of iso-return lines in revision-surprise space. Figure 5 provides such a contour plot for the early-sample estimates shown in (cid:12)gure 3 (at the optimal smoothing parameter setting of about 0.15). The iso-return lines (the solid curved lines) reflect 1 6In each case, the box over which the surfaces are displayed covers the 4 th through 96 th percentiles in th th the revision dimension and the 6 through 94 percentiles in the surprise dimension. Twenty points in each dimension are plotted, for a total of 400 points on each surface. 7The surfaces are displayed over the box drawn in panel B of (cid:12)gure 2. 18

percentage point steps: moving from one iso-return line to an adjacent line corresponds to a 1 percentage point change in abnormal return. The highest iso-return lines are in the upper right-hand corner, where both the revision and surprise are positive. The distance of the iso-return lines from one another indicates the return gradient in a particular direction; moretightlypacked contour lines indicatea largere(cid:11)ect of earningsinformationonabnormal return. If the timing of information matters, then changing the decomposition of a given total forecast error into surprise versus revision would put one onto a di(cid:11)erent iso-return line. In order to gauge the trade-o(cid:11), we overlay three \iso forecast error" loci, represented by the straight dashed lines. Any given iso-forecast error locus represents the state faced by the (cid:12)rm, characterized by (i) the initial expectations at the beginning of the quarter and (ii) the earnings it will ultimately report. A particular position along that iso-forecast error line represents an informationrelease policy by the (cid:12)rm. For instance, the lowest line, labeled -10 percent, represents the state in which the early-quarter analyst forecast, F0, is 10 percent higher than the actual earnings, which the company will ultimately report in its earnings release after quarter-end. The coordinates (0,-10) on this line represent the outcome in which no information is released early and a -10 percent surprise is revealed on the earnings announcement date. Alternatively, the coordinates (-10,0) represent a -10 percent early revision and zero surprise; here, all of the information was revealed early, perhaps via a preannouncement. Another possible outcome is (-20, 10): overly pessimistic information is preannounced, prompting a -20 percent forecast revision, and actual earnings then exceed the pre-report forecast by 10 percent. The (cid:12)rst key empirical result of our analysis is seen by comparing the slope of the isoforecast error lines with the slopes of the iso-return lines, or \information policy lines." Forecast revisions have smaller price e(cid:11)ects than surprises if the information policy lines are steeper than the iso-return lines. In that case, a (cid:12)rm can achieve a higher return by releasing unfavorable information early, that is, by choosing a point to the northwest on 19

the information policy line. Indeed, this is what we (cid:12)nd in the region near (0,0), where the data concentration is highest. Thus our initial set of estimates are consistent with previous results suggesting that (cid:12)rms might be able to engineer higher returns by beating down expectations early on and then releasing good news to the market on the announcement date. In particular, this result is consistent with the (cid:12)ndings of Bartov et al. (2002) who use di(cid:11)erence-in-means tests on a similar sample and similar de(cid:12)nitions of revisions and surprises. Figure 6 depicts the contour plot that results from running the same estimation procedure on the late sample, spanning the period 1996-2001. Here, we are led to the opposite conclusion. The picture shows that the (cid:12)rm’s information policy lines either run parallel to the iso-return lines or even, in some data-rich areas of the design space, at a shallower slope. For instance, the zero-percent forecast error line crosses over to lower iso-return lines when moving northwest from (0,0) to (-10, 10). Before speculating on why the two time periods might di(cid:11)er, we examine the sensitivity of the results to our de(cid:12)nition of the forecast revision period. As noted earlier, there tend to be relatively few earnings preannouncments early in the quarter (subsequent to the previous quarter’s report). Hence a measure of the forecast revision based on early-quarter forecasts could produce a downwardly biased estimate of the stock price e(cid:11)ects of analyst revisions induced by preannouncments. To eliminate this potential source of bias, we re-estimate the return response surfaces using the 6-week forecast revision in place of the 12-week revision. Figures 7 and 8 show the contour diagrams with the results for the early and late sample periods, respectively. Here, in both samples, we (cid:12)nd no evidence of a favorable tradeo(cid:11) from releasing negative information early. In fact, the iso-return contours in both cases tend to be a bit shallower than the information policy lines, which implies that the total e(cid:11)ect of earnings news on returns may even be smaller in cases where (cid:12)rms kept the negative information under wraps until the earnings announcement. Clearly, the estimates using the 6-week forecast revision produce no evidence to suggest 20

that (cid:12)rms can bolster their stock prices by preannouncing bad earnings news early in order to meet or beat expectations when the earnings report is released. How do we reconcile these results and the somewhat ambiguous conclusions drawn based on the 12-week revision? First, as argued earlier, early-quarter forecasts by analysts may not reflect all of the information revealed to the market in the previous quarter’s (cid:12)nancial report. With similar e(cid:11)ect, even if investors have not re(cid:12)ned their own views on current-quarter earnings, they still might heavily discount analysts’ early-quarter forecasts. Either way, movements in analyst estimates earlier in the quarter might not accurately reflect investor convictions. Still, there remains the question of why the earlier 12-week revisions appear to have had more price impact in recent years, as implied in Figure 6. This might be rationalized by the observation that analysts’ earnings forecasts have garnered increased attention over the 1990s, evidenced for instance by the increased use of analysts’ forecast revisions as a factor in stock selection during this period (Kirschner and Bernstein (2003)). As their forecast revisions have garnered more attention in recent years, analysts presumably felt stronger incentives to exert greater e(cid:11)ort in calibrating their early-quarter forecasts. 4.1 Standard Errors The statistical precision of our conclusions is perhaps best cast in terms of the accuracy with which we can resolve the location of the contour lines on our contour plots. Hence, in terms of statistical precision, we are primarily concerned with the standard errors on the (cid:12)tted values (the distribution of the standardized residuals) as opposed to the individual coe(cid:14)cient estimates. Under the loess theory, the distribution of the standardized residuals is well approximated by a t-distribution. However, calculation of the degrees of freedom is computationally expensive (see Cleveland et al. (1988)), requiring the inversion of a matrix with rows and columns equal to the number of observations. Moreover, this matrix must be built up one row at a time because, in essence, there is a di(cid:11)erent set of regression coe(cid:14)cients at each 21

(cid:12)tted point. To make these calculations we developed specialized software based on the Scalapack software library.8 Table 3 provides calculations of the precision of our (cid:12)t for the late sample period.9 We display the width of 95 percent con(cid:12)dence intervals around the (cid:12)tted values at various points on the solution surface. Panel A displays the con(cid:12)dence interval widths when we use the 12-week revision. As can be seen, in the center of the data (near the point where both the revision and surprise are zero), the con(cid:12)dence intervals have a width of about 1.3 percentage points of abnormal return. When we move to the outer fringes of the data, where the observations are far less concentrated, the con(cid:12)dence interval widths range from 2.1 to 3.7 percentage points. Comparing these results to those in Panel B, we (cid:12)nd that the widths of the con(cid:12)dence intervals in the center of the data are comparable when we use the 6-week revision, but at the fringes the con(cid:12)dence intervals are somewhat wider. Taken together, these results indicate that a two percentage point move, that is, a move across two contour lines, is a statistically signi(cid:12)cant move in the area where the data is densely distributed. This suggets that, in (cid:12)gures 6, 7, and 8, the perverse tradeo(cid:11)s that we (cid:12)nd for (cid:12)rms moving along their information policy lines are only statistically signi(cid:12)cant for fairly sizable moves, if at all. Our results on statistical precision also indicate that, as one moves further away from the center of the data, the contours are not resolved with as much statistical precision, suggesting some cautionis required in interpreting the shape of the contours in regions where the data are relatively sparse. 4.2 Robustness and Sub-Sample Analysis This section explores the robustness of our qualitative results, focusing in particular on the (cid:12)ndings for the 6-week revision period. As discussed earlier, our main concern is the sensitivity of the results to the choice of the scaling factor for the earnings news. To examine 8The Scalapack library contains pre-programmed Fortran and C routines for carrying out basic linear algebra computations on a network of workstations. 9Calculations for our other (cid:12)ts reveal similar degrees of precision, and are omitted. 22

this issue, we re-estimate the early- and late-period contours with the revision and surprise variables scaled by price. The results are shown in Figures 9 and 10. The optimal smoothing parameters used to estimate these contours are low, particularly the 0.10 used for the early period, which compares to the value of 0.15 used in the earnings denominator speci(cid:12)cation. Consistent with the low smoothing parameter, the contours for the early sample suggest a high degree of nonlinearity, with a large portion of the vertical climb being concentrated around the zero-surprise line. In contrast, the contours for the late-period are much more evenly spaced, suggesting less nonlinearity. While the evidence of nonlinearities seems clear, we (cid:12)nd no substantive evidence of any bene(cid:12)t from getting bad news out early. This is most obvious in the late-sample estimates. In the early-sample estimates, this judgment requires more careful scrutiny. As shown in (cid:12)gure 9, there appears to be no net bene(cid:12)t from moving along the -.002 forecast-error locus, for instance, from the zero revision to the zero surprise point. While moving further up the locus (into negative revision and positive surprise territory) does appear to produce some bene(cid:12)t, the gain is small and statistically insigni(cid:12)cant. Finally, we note that, as shown in the appendix, the jEPSj scaling factor produces somewhat better (cid:12)ts to the data, at least as judged using the Akaike Information Criterion (AIC) values for the jEPSj-scaled (cid:12)ts compared to the (cid:12)ts scaled by price. So far, the analysis ignores any potential role of heterogeneity, that is, the likelihood that sensitivity to earnings news di(cid:11)ers systematically across (cid:12)rms. This may be particularly important if such di(cid:11)erences induce substantial variation in the propensity to play the consensus-meeting game. Forinstance, Skinner andSloan(1999)provideevidence suggesting that stocks of high-growth (cid:12)rms are more vulnerable to negative earnings surprises, due to their high valuations being so dependent upon investors’ optimistic expectations for earnings growth. If so, these (cid:12)rms might be more prone to prerelease bad news thanlow-growth (cid:12)rms. Moreover, investor awareness of such di(cid:11)erent propensities might influence how the market reacts to news. In particular, (cid:12)rms that habitually warn and then meet or beat expectations 23

or those that have not met expectations in recent quarters might face a di(cid:11)erent tradeo(cid:11) in the current quarter than (cid:12)rms that recently reported negative surprises. While it is unclear how such heterogeneity might bias our conclusions, we can examine the robustness of our results by splitting the sample along some potentially important dimensions. This approach is used principally because computational and data constraints limit our ability to expand the dimensionality of the estimation, although it does have the advantage of allowing for very general qualitative comparisons. Two (cid:12)rm characteristics that we consider are: (i) (cid:12)rm size, gauged by market value; and (ii) (cid:12)rm growth prospects, gauged by the median of analysts’ long-term growth forecasts. Firm size may be an important factor because, all else equal, larger (cid:12)rms tend to have more predictable earnings. Moreover, such (cid:12)rms have a broader following in the investment community, and analysts may do a better job of forecasting their earnings. Casual observation of press reports suggests that the very largest (cid:12)rms devote a relatively high level of resources toward managing market expectations. As mentioned earlier, (cid:12)rm growth prospects have been shown to correlate with the sensitivity of stock price to earnings news. 10 Weperformatwo-by-two sample split alongthe(cid:12)rmsize andgrowthdimensions, producingfoursubsamples: large/highgrowth, large/lowgrowth, small/highgrowth, andsmall/low growth. The size split is based on beginning-of-quarter market value. A (cid:12)rm is assigned to the large-(cid:12)rm subsample if its market value is above the median (cid:12)rm’s market value in the same quarter. This produces a split that is balanced over time; the small-(cid:12)rm group does not shrink over time due to the upward trend in nominal (cid:12)rm valuations. The growth split is based on the sample median growth forecast. A (cid:12)rm is assigned to the high-growth subsample if its analysts’ average long-term growth forecasts are above the sample median. Figure 11 displays (cid:12)tted surfaces for the four subsamples based on their optimal smoothing parameters. Noting that the vertical axes di(cid:11)er markedly across the subsamples, the 10We have explored whether the number of analysts following a (cid:12)rm a(cid:11)ects our results. Speci(cid:12)cally, we imposed a lower limit on the number of analysts tracking a (cid:12)rm in order for the (cid:12)rm to be included in the sample, and re-ran all of our calculations. Our results were not a(cid:11)ected in a material way by this type of restriction. 24

estimated surfaces for high growth (cid:12)rms (the two bottom (cid:12)gures) are much steeper than those for the set of low-growth (cid:12)rms (the two top (cid:12)gures). This indicates that earnings news can explain more stock return variance for high-growth (cid:12)rms than for low-growth (cid:12)rms. Moreover, since the horizontal axes for the high- and low-growth results cover similar ranges, thesteeper slopealso implies thata givenmagnitude ofearningsnews tends tohave a larger impact on high-growth (cid:12)rms’ stock prices. In contrast, comparing the small and large samples while holding the growth class constant, it appears that smaller (cid:12)rms experience a wider range of earnings news; in particular, they experience more extreme negative surprises and revisions than large (cid:12)rms. The associated contours are shown in (cid:12)gure 12. The top row of (cid:12)gures again displays the contours for the low-growth (cid:12)rms, small and large. As in the overall sample, bringing out bad news early does not appear to produce any net bene(cid:12)t for those (cid:12)rms, and in many instances appears to be counter-productive. However, this (cid:12)nding is a bit more nuanced for at least one of the subsamples. Consider the large low-growth (cid:12)rm contours. Moving along the negative -0.10 (negative 10 percent) forecast error locus, from zero revision (0, -0.10) to zero surprise (-0.10, 0) appears to reduce stock returns on average by 2 percent. However, the concave-shaped contours imply that this is the worst place to be. Moving up from (-0.10, 0) to (-0.25, 0.15) appears to boost return 2 percent, which suggests that it may be better to exaggerate the possible shortfall than to warn and then just meet revised expectations, at least in this case. The results for the other three subsamples suggest that the trade-o(cid:11) from preannouncing news is at best neutral over the vast majority of the surprise/revision space. This result comes through quite clearly in the case of large high-growth (cid:12)rms. This is the group of (cid:12)rms that is probably most prone to playing the consensus-meeting game, and, as evidenced by their more tightly-packed contours, their stock prices are much more sensitive to earnings news compared to their low-growth counterparts discussed above. The most interesting group, however, may be the small high-growth (cid:12)rms. For these (cid:12)rms, the (cid:12)gure shows 25

about 35 contour lines (35percentage points ofreturn variation), which implies that earnings forecasterrorsexplainalargerangeofabnormalreturns. Thecontoursalsorevealsubstantial nonlinearity; the tightly packed lines in the region just to the southwest of (0,0) indicate that relatively small negative revisions as well as small negative surprises have particularly strong, albeit symmetric, e(cid:11)ects on stock returns. We end our search for the timing e(cid:11)ect by conditioning our sample split on (cid:12)rms’ recent surprise histories. In one group, we include only (cid:12)rms that did not have a negative surprise in either of the two preceding quarters; the second group contains all other (cid:12)rms, that is, (cid:12)rms with one or two negative surprises in the previous two quarters. As shown in panels A and B of (cid:12)gure 13, this sample split again con(cid:12)rms the robustness of our earlier results. The scale ranges on the surprise axis of the contours do indicate that (cid:12)rms with a recent negative surprise are more prone to issue a negative surprise again. However, we (cid:12)nd that neither group of (cid:12)rms appears to bene(cid:12)t by preannouncing negative news in order to meet expectations at the time of report. 5 Conclusion In this paper, we examined the stock price bene(cid:12)t of meeting or beating earnings expectations. We estimated the e(cid:11)ect of quarterly earnings news on quarterly stock returns by splitting analysts’ total forecast errors into a forecast revision and an earnings surprise. We then estimated the e(cid:11)ects of these forecast revisions andearnings surprises onthe cumulative abnormal return over the period. The most important methodological di(cid:11)erence between our study and previous studies is our use of loess, a nonparametric estimation technique that allows for a wide range of functionsthatmapearningsnewsintoabnormalreturns. Asecondimportantmethodological considerationinouranalysisistheeconometrician’schoiceofthe\preannouncement period." We conjecture that revisions early in the quarter might be contaminated by the previous 26

quarter’s news, which could create a spurious asymmetry in the magnitude of stock price responses to forecast revisions and earnings surprises. Finally, we examined the choice of the scaling factor applied to the forecast revisions and surprises. In contrast to previous studies, we did not (cid:12)nd persuasive evidence of a short-term stock price bene(cid:12)t to preannouncing bad news; that is to say, we found little or no di(cid:11)erence in the sensitivity of stock returns to early forecast revisions and earnings surprises. Our nonparametric approach does uncover signi(cid:12)cant and fairly interesting nonlinearities. In particular, we (cid:12)nd that the sensitivity of returns to earnings news tends to get stronger when the news is close to zero. Moreover, this would appear to be true regardless of whether the news is reflected in revisions or surprises. There is one notable case where we do (cid:12)nd evidence consistent with the hypothesis that (cid:12)rms bene(cid:12)t by getting bad news out early. When we estimate the response function using the longer revision period, on the 1987-1995 subsample, surprises appear to have a larger e(cid:11)ect on returns than revisions over an important part of the sample space. However, when the model is estimated using a shorter (6-week) revision period, when more of the revisions are presumably driven by preannouncements, the asymmetric response disappears. Moreover, when we estimate the response function on the post-1995 sample, this result is again reversed, regardless of the de(cid:12)nition employed for the revision period. An appealing interpretation that reconciles these results is that, in earlier years, equity analysts may not have been particularly diligent about reworking their quarterly earnings forecasts following previous-quarter announcements. If so, then revisions over the earlier part of the quarter would have partly reflected information that may have already been incorporated into stock prices. However, as quarterly earnings forecasts garnered increasing attention during the 1990s, analysts may have become more assiduous about updating their current-quarter estimates. We further examined the issue by splitting the sample into subgroups by size and earnings prospects. Again, we found little evidence of an asymmetric stock return response to 27

the timing of news. However, for large, low-growth (cid:12)rms, it does appear to be better to exaggerate any possible earnings shortfalls than to warn and just meet expectations. Finally, we conditioned on (cid:12)rms’ recent surprise histories to see if (cid:12)rms with a track record of negative surprises, or a track record of meeting expectations, might face asymmetric stock return responses. Again we found no evidence of an asymmetric response. Theabsenceofanyshort-termstockpricebene(cid:12)tfromgettingbadnewsoutearlybegsthe question: Why do (cid:12)rms manage their news releases? A de(cid:12)nitive answer is beyond the scope of this paper, but a few comments are in order. First, it is possible that individual managers might believe that such actions will produce a near-term bene(cid:12)t to their stock price even if, on average, this is not the case. Indeed, if researchers in possession of the comprehensive data can not agree on the stock price bene(cid:12)ts, should we expect managers, focused largely on their own (cid:12)rm’s experience, to know the average e(cid:11)ect? Second, the absence of any clear short-term bene(cid:12)t does not rule out the possibility of a longer-term reputational bene(cid:12)t. As pointed out earlier, both Chevis et al. (2002) and Liu and Yao (2003) provide evidence to suggest that (cid:12)rms that habitually meet expectations tend to be more highly valued, that is, have a higher stock price level given fundamentals. A comparison of short run returns probably has little power as a test of such longer-term valuation bene(cid:12)ts. In closing, it is worth reemphasizing that a variety of rationales that do not presuppose any bene(cid:12)t to quarterly stock returns have been proposed to explain this behavior. In fact, the hypothesis of Aboody and Kasznik (2000), that management is motivated to warn by the desire to receive stock option grants when their stock price is relatively low, is perhaps even more plausible inlight of our (cid:12)ndings. Furthermore, managers that intend to sell shares after the end of a \quiet period" might also bene(cid:12)t directly by shifting the timing of bad news and the associated volatility along the lines suggested by Richardson et al. (2003). Finally, the traditional rationale for the early release of bad news | that management is striving to mitigate the risk of securities litigation | does not presuppose any short-term stock price bene(cid:12)t. 28

Table 1: Univariate Statistics Thetabledisplaysunivariatestatisticsforrevisions,surprises,andabnormalreturns. Thetable displaysthe 25 th , 50 th , and 75 th percentiles for the variables, plus the interquartile ranges (labeled 75−25), with all values multiplied by 100. Panel A: jEPSj scaling factor 1987-1995 1996-2001 Abnormal Abnormal Percentile return Revision Surprise return Revision Surprise 12-week revision, N=22,987 N=42,424 25 -7.90 -5.15 -5.86 -13.0 -3.37 -1.19 50 -0.18 -0.27 1.08 -0.90 0.00 2.34 75 7.43 1.67 7.14 10.17 0.50 8.33 75-25 15.33 6.82 13.00 23.21 3.87 9.52 6-week revision, N=49,041 N=51,396 25 -8.17 -1.71 -8.64 -13.00 -1.14 -1.40 50 -0.31 0.00 0.54 -1.05 0.00 2.36 75 7.39 0.12 7.69 10.04 0.00 8.61 75-25 15.56 1.83 16.33 23.08 1.14 10.01 Panel B: Price scaling factor 1987-1995 1996-2001 Abnormal Abnormal Percentile return Revision Surprise return Revision Surprise 12-week revision, N=25,029 N=46,986 25 -8.35 -0.10 -0.12 -13.9 -0.06 -0.02 50 -0.49 -0.01 0.01 -1.24 0.00 0.03 75 7.38 0.03 0.12 10.15 0.01 0.12 75-25 15.73 0.12 0.23 24.00 0.06 0.14 6-week revision, N=54,005 N=57,106 25 -8.77 -0.03 -0.18 -14.0 -0.02 -0.03 50 -0.67 0.00 0.00 -1.43 0.00 0.03 75 7.24 0.00 0.13 9.99 0.00 0.12 75-25 16.01 0.03 0.31 23.95 0.02 0.15 29

Table 2: Regressions of Abnormal Returns on Scaled Revisions and Surprises The table displays linear regressionresults for four variations of the basic speci(cid:12)cation Abnormal return=(cid:12) 0+(cid:12) 1(12-week revision)+(cid:12) 2(6-week revision)+(cid:12) 3(Surprise)+(cid:15); with the revisions and surprises as de(cid:12)ned in the main text. The regressionis repeated for each scale factor over each sample period. The early subsample coversthe period 1987-1995,while the late subsample covers the period 1996-2001. The sampling frequency is quarterly. The t-values displayed beneath each estimate are based on heteroscedasticity-robuststandard errors. The sample sizes are smaller than those displayed in table 1 owing to the inclusion of both revisionvariables;observations missing either variable are dropped from the regression. Normalization Period (cid:12) 0 (cid:12) 1 (cid:12) 2 (cid:12) 3 N R 2 jEPSj Early 0.00 0.05 0.23 0.16 19,259 0.060 3.48 4.12 11.79 25.22 Late -0.02 0.21 0.14 0.28 35,825 0.048 -16.94 12.42 5.99 26.49 Price Early 0.00 2.91 14.43 9.34 20,971 0.062 0.12 4.94 13.25 26.87 Late -0.02 14.17 9.80 17.83 39,605 0.051 -19.37 13.91 6.92 28.60 30

Table 3: Width of 95 Percent Con(cid:12)dence Intervals across Solution Surface The table displays the widths of 95 percent con(cid:12)dence intervals at the indicated points on the solution surface. For example, in panel A, when the 12-week revision is -0.05 (-5 percent) and the surprise is -0.05, the width ofthe 95 percentcon(cid:12)dence intervalaroundthe (cid:12)tted value is 0.024(2.4 percentagepoints wide). The width of the con(cid:12)dence intervals across the solution space indicates the degree to which the contours shown on the relevant contour plot can be di(cid:11)erentiated. The con(cid:12)dence intervals are for the late sample period (1996-2001) using the jEPSj scaling factor; the widths of the con(cid:12)dence intervals for our other (cid:12)ts are similar in magnitude. Panel A: 12-week revision Revision Surprise -0.05 0.00 0.05 0.05 0.024 0.014 0.027 0.00 0.021 0.013 0.034 -0.05 0.024 0.020 0.037 Panel B: 6-week revision Revision Surprise -0.05 0.00 0.05 0.05 0.030 0.014 0.037 0.00 0.026 0.012 0.048 -0.05 0.027 0.017 0.052 31

Figure 1: Decomposition of Total Forecast Error into Revision and Surprise TFE z }| { 12-week revision Surprise z }| {z }| { 7 days t t t t t t t - Beginning of Previous quarter End of Current quarter F F F quarter EPS report 0 1 quarter 2 EPS report | {z } 6-week revision 32

Figure 2: Scatterplots of 12-Week Revisions and Surprises Panel A of the (cid:12)gure displays a scatterplot of revisions against surprises for the early period (1987-1995). The data are scaled by jEPSj and reflect our other data (cid:12)lters discussed in the main text. Panel B displays a scatter of revisions against surprises for the late period (1996-2001). The boxes in panels A and B show the regions plotted in (cid:12)gures 3 and 4, respectively. Panel A: Early Period (1987-1995) 0.2 0 -0.2 -0.4 -0.6 -0.8 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 esirpruS Revision Displayed surface Panel B: Late Period (1996-2001) 0.4 0.3 0.2 0.1 0 -0.1 -0.2 -0.3 -0.4 -0.5 -1 -0.8 -0.6 -0.4 -0.2 0 0.2 esirpruS Revision Displayed surface 33

Figure 3: Fitted Surfaces for 1987-1995 Period, jEPSj Scaling Factor The (cid:12)gure displays (cid:12)tted surfaces for the early period subsample using the jEPSj scaling factor and the 12 weekrevision. The(cid:12)tting methodis locallyweightedleastsquares,witheachsurfacedepictingthe (cid:12)tatthe indicated smoothing parameter. The sample size is 22,987. Smoothing parameter = 0.15 Smoothing parameter = 0.25 Excess return Excess return 0.06 0.06 0.04 0.04 0.02 0.02 0 0 -0.02 -0.02 -0.04 -0.04 -0.06 -0.06 -0.08 -0.08 -0.1 -0.1 0.2 0.2 0 0 -0.5 -0.4 R -0 e . v 3 isi - o 0 n .2 -0.1 0 0.1 -0.6 -0.4 -0.2 Surprise -0.5 -0.4 R -0 e . v 3 isi - o 0 n .2 -0.1 0 0.1 -0.6 -0.4 -0.2 Surprise Smoothing parameter = 0.75 Smoothing parameter = 0.50 Excess return Excess return 0.08 0.06 0.06 0.04 0.04 0.02 0.02 0 -0.02 0 -0.02 -0.04 -0.04 -0.06 -0.06 -0.08 -0.08 -0.1 -0.1 0.2 0.2 0 0 -0.5 -0.4 R -0 e . v 3 isi - o 0 n .2 -0.1 0 0.1 -0.6 -0.4 -0.2 Surprise -0.5 -0.4 R -0 e . v 3 isi - o 0 n .2 -0.1 0 0.1 -0.6 -0.4 -0.2 Surprise 34

Figure 4: Fitted Surfaces for 1996-2001 Period, jEPSj Scaling Factor The (cid:12)gure displays (cid:12)tted surfaces for the late period subsample using the jEPSj scaling factor and the 12 weekrevision. The(cid:12)tting methodis locallyweightedleastsquares,witheachsurfacedepictingthe (cid:12)tatthe indicated smoothing parameter. The sample size is 42,424. Smoothing parameter = 0.15 Smoothing parameter = 0.25 Excess return Excess return 0.1 0.1 0.05 0.05 0 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.15 -0.2 -0.2 0.3 0.3 0.2 0.2 0.1 0.1 -0.6 -0.5 R -0 e . v 4 is - i 0 o . n 3 -0.2 -0.1 0 0.1 -0.3 -0.2 -0.1 0 Surprise -0.6 -0.5 R -0 e . v 4 is - i 0 o . n 3 -0.2 -0.1 0 0.1 -0.3 -0.2 -0.1 0 Surprise Smoothing parameter = 0.75 Smoothing parameter = 0.50 Excess return Excess return 0.1 0.1 0.05 0.05 0 0 -0.05 -0.05 -0.1 -0.1 -0.15 -0.15 -0.2 -0.2 0.3 0.3 0.2 0.2 0.1 0.1 -0.6 -0.5 R -0 e . v 4 is - i 0 o . n 3 -0.2 -0.1 0 0.1 -0.3 -0.2 -0.1 0 Surprise -0.6 -0.5 R -0 e . v 4 is - i 0 o . n 3 -0.2 -0.1 0 0.1 -0.3 -0.2 -0.1 0 Surprise 35

Figure 5: Iso-Return Contours for 1987-1995 Period, jEPSj Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on early-period data and the jEPSj scaling factor, and the revision is measured over a 12 week interval. The sample size is 22,987(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.15615,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.20 0.00 -0.20 -0.40 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 36

Figure 6: Iso-Return Contours for 1996-2001 Period, jEPSj Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on late-period data and the jEPSj scaling factor, and the revision is measured over a 12 week interval. The sample size is 42,424(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.62499,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.30 0.20 0.10 0.00 -0.10 -0.20 -0.30 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 0.10 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 37

Figure 7: Iso-Return Contours for 1987-1995 Period, 6-Week Revision, jEPSj Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on early-period data and the jEPSj scaling factor, and the revision is measured over a 6 week interval. The sample size is 49,041(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.15619,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.20 0.00 -0.20 -0.40 -0.60 -0.80 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 38

Figure 8: Iso-Return Contours for 1996-2001 Period, 6-Week Revision, jEPSj Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on early-period data and the jEPSj scaling factor, and the revision is measured over a 12 week interval. The sample size is 51,396(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.15623,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.30 0.20 0.10 0.00 -0.10 -0.20 -0.30 -0.40 -0.40 -0.30 -0.20 -0.10 0.00 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 39

Figure 9: Iso-Return Contours for 1987-1995 Period, 6-Week Revision, Price Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on early-period data and the price scaling factor, and the revision is measured over a 6 week interval. The sample size is 54,005(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.10670,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.005 0.000 -0.005 -0.010 -0.015 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001 esirpruS Revision Contours TFE = -0.001 TFE = 0.000 TFE = -0.002 40

Figure 10: Iso-Return Contours for 1996-2001 Period, 6-Week Revision, Price Scaling Factor The (cid:12)gure displays iso-return contours and three information policy lines. The (cid:12)t is based on late-period data and the jEPSj scaling factor, and the revision is measured over a 12 week interval. The sample size is 57,106(cid:12)rm-quarterobservationsandtheoptimalsmoothingparameteris0.15628,determinedbygeneralized cross-validation. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for total forecasterrors(TFE) of 0, -5, and -10 percent. Movement along an information policy line represents an information release policy by the (cid:12)rm in terms of the timing of information release. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.006 0.004 0.002 0.000 -0.002 -0.004 -0.006 -0.006 -0.005 -0.004 -0.003 -0.002 -0.001 0.000 0.001 esirpruS Revision Contours TFE = -0.001 TFE = 0.000 TFE = -0.002 41

Figure 11: Fitted Surfaces for 1996-2001 Period, 6-Week Revision, Large and Small, Highand Low-Growth Firms, jEPSj Scaling Factor The (cid:12)gure displays (cid:12)tted surfaces for (cid:12)rms split into subsamples based on size and growthprospects, where size is measured by market value and growth prospects by analysts’ long-term growth forecasts. A (cid:12)rm is classi(cid:12)ed as large if its market value is above the median (cid:12)rm market value for the given quarter. A (cid:12)rm is classi(cid:12)edas high-growthif its consensus long-termgrowth forecastis above the sample median consensus long-term growth forecast. The upper two panels display the surfaces for small and large low-growth(cid:12)rms, respectively. The lower two panels display the surfaces for small and large high-growth (cid:12)rms, respectively. The samples sizes and smoothing parameters used for each (cid:12)t are shown in the appendix. Small, Low-Growth Firms Large, Low-Growth Firms Excess return Excess return 0.10 0.10 0.05 0.00 0.00 -0.10 -0.05 -0.20 -0.10 0.40 0.30 0.20 0.20 0.00 0.10 -0.60-0.50-0. R 4 e 0 v i 0 s . i 3 o 0 n -0.20-0.10 0.00 0.10-0.8 - 0 0.6 - 0 0.4 - 0 0.20 Surprise -0.40 -0.30 Re v 0 i . s 2 i 0 on -0.10 0.00 0.10-0.3 - 0 0.2 - 0 0.1 0 0.00 Surprise Small, High-Growth Firms Large, High-Growth Firms Excess return Excess return 0.10 0.20 0.00 0.10 -0.10 0.00 -0.20 -0.30 -0.10 -0.40 -0.20 0.40 0.30 0.20 0.20 -0.80 0.00 -0.30 0.10 -0.60 -0.20 Surprise -0.20 0.00 Surprise -0.40 -0.20 -0.40 -0.10 -0.10 Revision 0.00 0.20-0.60 Revision 0.00 0.10-0.20 42

Figure 12: Iso-Return Contours for 1996-2001 Period, 6-Week Revision, Large and Small, High- and Low-Growth Firms, jEPSj Scaling Factor The (cid:12)gure displays the iso-return contours for the four surfaces shown in (cid:12)gure 11 above. The upper two panels display the contours for small and large low-growth(cid:12)rms, respectively. The lower two panels display the contours for small and large high-growth (cid:12)rms, respectively. Note that the vertical and horizontal axes all vary. The samples sizes and smoothing parameters used for each (cid:12)t are shown in the appendix. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a pointonanadjacentcontourrepresentsaonepercentagepointchangeinabnormalreturn. The information policy lines are for total forecast errors (TFE) of 0, -5, and -10 percent. Movement along an information policy line representsaninformationreleasepolicy bythe (cid:12)rmin termsof the timing ofinformationrelease. Points to the northwest on a policy line represent a policy of releasing bad news in the revision period and good news in the surprise period. 0.20 0.00 -0.20 -0.40 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 esirpruS Small, Low-Growth Firms Large, Low-Growth Firms 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.20 -0.35 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 Contours TFE = -0.05 Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 TFE = 0.00 TFE = -0.10 0.30 0.20 0.10 0.00 -0.10 -0.20 -0.30 -0.40 -0.50 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 esirpruS Small, High-Growth Firms Large, High-Growth Firms 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 Revision Revision Contours TFE = -0.05 Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 TFE = 0.00 TFE = -0.10 43

Figure 13: Iso-Return Contours for 1996-2001 Period, 6-Week Revision, Sample Split on Lagged Surprises, jEPSj Scaling Factor The (cid:12)gure displays the iso-return contours for (cid:12)ts based on late-period data and the jEPSj scaling factor. The revisionis measuredoverthe six week interval. PanelA displaysthe (cid:12)t for the subsample of (cid:12)rms with at least 1 lagged negative surprise; Panel B shows the (cid:12)t for the subsample of all other (cid:12)rms. The sample sizes and smoothing parameters used for each (cid:12)t are shown in the appendix. The iso-return contours are spaced at one percentage point intervals; moving from a point on one contour to a point on an adjacent contour represents a one percentage point change in abnormal return. The information policy lines are for totalforecasterrors(TFE)of0,-5,and-10percent. Movementalonganinformationpolicylinerepresentsan informationrelease policy by the (cid:12)rm in terms of the timing of informationrelease. Points to the northwest onapolicy line representa policyofreleasingbadnews inthe revisionperiodandgoodnews inthe surprise period. Panel A: Firms with at least 1 lagged negative surprise 0.30 0.20 0.10 0.00 -0.10 -0.20 -0.30 -0.40 -0.50 -0.60 -0.50 -0.40 -0.30 -0.20 -0.10 0.00 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 Panel B: All other (cid:12)rms 0.25 0.20 0.15 0.10 0.05 0.00 -0.05 -0.10 -0.15 -0.30 -0.25 -0.20 -0.15 -0.10 -0.05 0.00 0.05 esirpruS Revision Contours TFE = -0.05 TFE = 0.00 TFE = -0.10 44

A Smoothing Parameter Selection Following Cleveland and Devlin (1988), the expected mean squared error of the loess estimator, given by " # (cid:16) (cid:17) PN 2 E f^ (x )−f(x ) h i i i=1 M = ; (5) h (cid:27)2 canbedecomposedintoatermrepresentingthecontributionofbias,B ,andthecontribution h of variance, V , to the overall mean squared error. Here we have subscripted M and f^ by h, h to emphasize that the calculations are conditional on the degree of smoothing. A larger h is analogous to a wider bandwidth in kernel regression, implying a lower variance estimate at the risk of potentially greater bias.11 Denoting the residual sum of squares by RSS , the h estimated error variance by (cid:27)^2, and by L the matrix such that y^ = L y, it can be shown h h h that:12 M = B +V ; where (6) h h h RSS B = h −tr[(I −L )(I −L ) 0 ]; and (7) h (cid:27)^2 h h V = tr[L L0 ]; (8) h h h where I is the identity matrix. As shown in Cleveland and Devlin (1988)it isstraightforward to compute an estimate M^ of M . Moreover, it is possible (albeit highly computationally h h intensive) to compute approximations to the distribution of M^ under the null hypothesis of h zero bias. The M-plot is a graph of M^ against V for a range of values of h. The basic idea is to h h consider a range of smoothing parameters running from the standard OLS (cid:12)t (including all 11The term V h is often referred to as the \equivalent number of parameters". This is an intuitive label because, under ordinary least squares, V h is equal to the trace of the projection matrix, which in turn is equaltothenumberofparametersbeingestimated. Whiletheloessoperatorisnotaprojectionmatrix,itis neverthelessthe casethatV h increasesas hdecreases{less smoothingresults inahigher equivalentnumber of parameters,and vice-versa. 12An estimate of (cid:27)2 is obtained from the residuals of a (cid:12)t with very small h { a highly localized (cid:12)t. 45

of the data in each local regression) to very localized (cid:12)ts in order to see how the contribution of bias changes as the degree of smoothing is varied. Figure A1 presents a representative set of estimates of M-statistics at di(cid:11)erent degrees of smoothing and their associated con(cid:12)dence intervals under the null hypothesis of zero bias for the late period jEPSj-scaled dataset using the 12-week revision.13 The points on the plot show the estimated M-statistic values. The 45-degree line through the origin and the rightmost M-statistic value show the values of the M-statistics that are expected under the null hypothesis. The vertical lines show the 95 percent con(cid:12)dence bands, while the ’x’ symbols on the vertical lines indicate the 90 percent con(cid:12)dence bands. The leftmost point - at an equivalent number of parameters equal to 3 - gives the M-statistic at the OLS (cid:12)t. It is clear from the plot that the OLS (cid:12)t is heavily biased - the null hypothesis of zero bias is soundly rejected. As the equivalent number of parameters rises, the estimated M-statistics fall. For an equivalent number of parameters equal between nine and twelve, we cannot reject the null hypothesis of zero bias. As we increase the number of parameters from twelve, the bias again rises, suggesting that the optimal smoothing parameter is the one that uses approximately 60 percent of the data. It should also be noted that this (cid:12)t is the one that is selected with the generalized crossvalidation procedure for these data. Inordertoconserve space, wedonotdisplayalloftheM-plotsforourvarioussubsamples. Table A1 displays the smoothing parameters selected by the generalized cross-validation technique. In general, our M-plot analyses con(cid:12)rmed these settings. 13These calculations were made on a random sample of 2,500 points from the overalldataset. The calculation of the M-statistics on the full dataset is computationally infeasible. 46

Figure A1: M-Plot, 12-Week Revision, jEPSj Scaling Factor 50 40 30 20 10 0 -10 0 5 10 15 20 25 30 35 40 45 50 citsitatS-M Late Period Sample, N=2,500 M-Statistic 95% Confidence Interval 90% Confidence Interval Equivalent Number of Parameters 47

Table A1: Generalized Cross-Validation Results The table displays the sample size (N), the generalizedcross-validationobjective function value (GCV), the AkaikeInformationCriterion(AIC),andthe optimalsmoothingparameterforallofthe estimates discussed in the main text. Panel A displays the main sample splits on sample period, scaling factor, and revision de(cid:12)nition. Panel B displays the sample splits on (cid:12)rm growth and size, and Panel C displays the split on recent earnings news. Panel A: Sample Period, Scaling Factor, and Revision Sample Splits Sample Scaling Smoothing period factor N Revision GCV AIC parameter All (cid:12)rms Early jEPSj 22,987 F −F 6.248e-07 -3.24309 0.15615 0 2 49,041 F −F 3.063e-07 -3.19828 0.15619 1 2 Price 54,005 F −F 2.978e-07 -3.12987 0.10670 1 2 Late jEPSj 42,424 F −F 9.043e-07 -2.26050 0.62499 0 2 51,396 F −F 7.418e-07 -2.26679 0.15623 1 2 Price 57,106 F −F 7.172e-07 -2.19526 0.15628 1 2 Panel B: Late Period, jEPSj Scaling Factor, F −F Revision, Growth and Size Sample 1 2 Splits Growth Size Smoothing Class Class N GCV AIC Parameter Low Small 15,918 2.18e-06 -2.36219 0.22355 Low Large 14,968 1.08e-06 -3.12539 0.31217 High Small 10,460 7.34e-06 -1.56637 0.15626 High Large 10,079 4.81e-06 -2.02729 0.62452 Panel C: Late Period, jEPSj Scaling Factor, F −F Revision, Previous Earnings Surprise 1 2 Sample Split Smoothing Surprise History N GCV AIC Parameter No recent negative surprises 16,709 5.464e-07 -3.34235 0.15627 A negative surprise in previous 2 quarters 15,638 1.040e-07 -3.38635 0.61745 48

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