Earnings Surprise Materiality as Measured by Stock Returns

Transcription

1 Journal of Accounting Research Vol. 40 No. 5 December 2002 Printed in U.S.A. Earnings Surprise Materiality as Measured by Stock Returns WILLIAM KINNEY, DAVID BURGSTAHLER, AND ROGER MARTIN Received 3 January 2000; accepted 2 June 2002 ABSTRACT Ranked earnings surprise portfolios formed from First Call files for are used to assess the annual earnings surprise magnitude for an individual firm sufficient to expect a significant market reaction. We find that, for an individual firm, the maximum probability of a gain from trading on prior knowledge of any surprise magnitude is.622. The lack of probable trading gains is due to the S-shaped surprise/return relation and the large variance of returns for a given magnitude of surprise. In turn, we find that the S-shape is related empirically to the dispersion of analyst forecasts. Thus, factors underlying dispersion differences are related to the importance or materiality of earnings surprise as measured by stock returns and explain at least part of the S-shaped surprise/return relation. 1. Introduction On September 28, 1998, Securities and Exchange (SEC) Chairman Arthur Levitt delivered a speech entitled The Numbers Game in which he University of Texas at Austin; University of Washington; Indiana University. Financial support by the Center for Business Measurement and Assurance Services at the University of Texas at Austin, and the Big Five Audit Materiality Task Force is gratefully acknowledged, as are the efforts of Stanley Levine for providing access to the First Call Corporation database, the research assistance of Marcia Weidenmier, and comments from Mary Barth, Bill Beaver, Larry Brown, Dan Collins, Ilia Dichev, Bob Lipe, Jerry Salamon, Terry Shevlin, Abbie Smith, K. R. Subramanyam, Ramu Thiagarajan, and workshop participants at Stanford University, Indiana University, Northwestern University, Emory University, Washington University, University of Washington, University of Minnesota, University of Iowa, University of Notre Dame, and University of Texas at Austin Copyright C, University of Chicago on behalf of the Institute of Professional Accounting, 2002

2 1298 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN lamented the importance to stock prices of meeting analysts consensus forecasts of accounting earnings. He cited a company that missed its numbers by a single penny (i.e., earnings surprise was $.01 per share) and lost 6% of its stock value in a single day (Levitt [1998]). He expressed concern that, to meet consensus forecasts of analysts, some SEC registrants use non- GAAP (generally accepted accounting principles) methods intentionally to manipulate accounting earnings by small amounts, and that this behavior may erode investor perceptions of the quality of the U.S. system of mandated financial reporting. Subsequently, the SEC issued Staff Accounting Bulletin (SAB) No. 99 (SEC [1999]) warning registrants and auditors that, under certain conditions, even small earnings manipulations by registrants may be deemed material accounting misstatements and therefore subject registrants and their auditors to SEC sanctions for improper accounting. One specified condition is a quantitatively small manipulation that hides an earnings surprise expected to have a significant positive or negative market reaction. SAB No. 99 offers no guidance on how to assess expected market reactions to such manipulations. Levitt s speech and SAB No. 99 suggest two related questions: (1) what magnitude of annual earnings surprise is enough to have a significant market reaction, and (2) what magnitude of earnings manipulation that hides a surprise is enough to expect a significant market reaction? In this article we use publicly available data on consensus analyst forecasts, accounting earnings, and stock returns to address the first question by estimating the magnitude of earnings surprise typically necessary to result in a significant market reaction to a firm s annual earnings announcement without regard to the cause of the surprise. We cannot directly address the second question because population data on managements intentional manipulation of GAAP-based assertions to hide a surprise are unobservable ex ante. 1 However, under the assumption that unknown-to-the-market earnings manipulations affect returns approximately the same as other causes of surprise, our data may reasonably estimate market reaction to management s intentional manipulations of earnings that remain unknown to the market. To better assess the possible effects of ex ante uncertainty about earnings on reactions to earnings surprises, we document an empirical association of dispersion of analyst forecasts composing the consensus forecast with the realized surprise magnitude. Finally, we explore dispersion of analyst forecasts as an explanation for the S-shape of the earnings surprise/market return relation. We obtained more than 22,000 annual earnings composite forecasts and reported earnings per share (EPS) for 1992 through The EPS forecasts 1 Ex post data on possible manipulations exist for a small sample comprising SEC allegations of manipulation and misstatements by registrants (e.g., see Committee of Sponsoring Organizations of the Treadway Commission [1999]), and for registrants restating their previously filed 10-Ks or 10-Qs (see Palmrose and Scholz [2001]). Also, Tuttle, Coller, and Plumlee [2002] present laboratory market evidence on security prices conditional on misstatement-free and misstated earnings of various unknown-to-participants magnitudes.

3 EARNINGS SURPRISE MATERIALITY 1299 are the last composite forecast of earnings reported by First Call Corporation before the announcement of annual earnings, and the difference between the actual and forecast earnings is denoted earnings surprise. The First Call file also contains the range, standard deviation, and number of analyst forecasts that form the composite. Related market-adjusted stock returns were obtained from the Center for Research in Security Prices (CRSP) and accumulated for a 22-day period beginning 20 days before and ending 1 day after the final earnings announcement dates. Portfolios of 500 observations each were formed on ranked earnings surprise scaled by fiscal year-end price, with distributions of market-adjusted stock returns tabulated for each portfolio. Plots of the portfolio means, medians, and 33.3 and 66.7 percentiles exhibit an S-shaped relation between earnings surprise and stock returns that is steeply sloped for small absolute surprises and approximately flat for large absolute surprises, consistent with the findings of Freeman and Tse [1992] and others. Thus, large absolute surprises yield smaller market reactions per unit of surprise than do small absolute surprises, or the incremental response to an additional unit of surprise is greater near zero, other things equal. Data plots show that the means and medians of the return distributions are reliably positive for positive earnings surprise portfolios and reliably negative for negative earnings surprise portfolios, even for earnings surprises very near zero. However, within each portfolio, many firms returns and surprises are of opposite signs. Over all earnings surprise portfolios, the minimum proportion of firms with negative returns is.378, and the minimum proportion of firms with positive returns is Thus, for an individual security, there is no magnitude of earnings surprise that is material to investors in the sense that prior knowledge of its magnitude alone allows probable (or statistically significant) trading gains at a likelihood of.622 or higher. The lack of significant market reaction or probable trading gains from prior knowledge of earnings surprise magnitude implies that surprise magnitude alone is not a reliable indicator of market reaction to earnings announcements of a single firm. The lack of reliability at the firm level is due to two characteristics of the data: (1) the S-shape of the distribution of returns given earnings surprise, and (2) large return variation around the mean response for each level of surprise. The first dampens the absolute reaction to large absolute surprises, and the second requires a large surprise to yield probable trading gains, other things equal. Empirically, firms with small earnings surprises tend to have low dispersion among analysts forecasts, whereas firms with large surprises tend to have high forecast dispersion. That is, small absolute surprises tend to arise ex post for firms with low ex ante uncertainty or dispersion, whereas large surprises arise for firms with high ex ante dispersion. Also empirically, per unit 2 The same results hold approximately for asset-scaled portfolios and for portfolios grouped by cents per share of earnings surprise.

4 1300 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN of surprise, small surprises tend to have large return reactions relative to those of large surprises, resulting in the S-shaped surprise/return relation. Thus, the observed combinations of surprise, return reaction, and dispersion among analysts are consistent with a Bayesian view of ex ante dispersion and ex post surprise in which prices respond to the relative surprise (surprise conditioned by ex ante uncertainty about current and possibly future earnings or its components), in addition to the magnitude of surprise. To quantify the effects of the shape and variation of price response and to allow more direct comparison with the prior accounting literature on market response to earnings announcements, we use linear regression to estimate the slope of the earnings surprise/return relation (the earnings response coefficient, or ERC) over various ranges centered on zero earnings surprise. We find a statistically significant positive linear relation for surprises over the broad range ±.02 (relative to price), and the relation s slope becomes progressively (and substantially) steeper as the range is progressively restricted to the narrowest range of to (relative to price). Thus, inclusion of large absolute surprises yields smaller linear response coefficients (i.e., smaller returns per unit of surprise) than do small absolute surprises. Using two times out of three or p =.667 to define probable, we calculate, over various ranges of surprise the.667 probability (one-sided) prediction interval on return reaction conditional on surprise. 3 We find that prediction intervals for return reaction almost always include zero, implying that the probability of gains from trading on advance knowledge of a single firm s surprise magnitude is almost always less than.667. Specifically, the upper prediction interval on return is above zero for all earnings surprise ranges, and the lower prediction interval is below zero for all but the widest ranges of positive surprise. Thus, results using regression analysis are essentially consistent with the frequency-based portfolio analyses. To test statistically whether incorporating analyst forecast dispersion improves estimation, we sort consensus forecasts into three equally sized groups based on ranked forecast dispersion. We find the earnings surprise/return relation is more nearly linear within dispersion groups and significantly steeper for the low-dispersion group in which the slope coefficient approaches typical price-to-earnings (P/E) ratios. Also, for about 1.5% of firmyear observations in the extreme tails of the widest earnings surprise ranges of the low- and moderate-dispersion groups, the.667 one-sided prediction interval on market reaction excludes zero, indicating material surprises. Although this percentage is small, it is more than twice the percentage (.7%) for the same observations without incorporating dispersion. Thus, the earnings surprise magnitude deemed material using stock returns for a particular firm may depend on firm-specific factors related empirically to 3 A.667 one-sided prediction interval for a random variable such as return conditional on surprise is analogous to a.667 one-sided confidence interval on a parameter such as a mean or regression coefficient (see Neter, Wasserman, and Kutner [1990, pp ]).

5 EARNINGS SURPRISE MATERIALITY 1301 forecast dispersion, such as the precision of the signal that current earnings provides about firm value or the persistence of earnings. Overall, we find limited evidence that earnings surprise magnitude alone reliably indicates a significant positive or negative market price reaction due to the relation s S-shape and wide variance. Thus, if SAB No. 99 criteria are to be applied by registrants and auditors, more guidance is needed. Our results also imply that the surprise/return relation s shape and variance may warrant consideration by regulators, practitioners, analysts, and researchers wishing to address information and disclosure questions at the firm level. The next section reviews SEC officials concerns and accounting and auditing aspects of materiality, and defines market-price-based earnings surprise materiality. Section 3 describes our sample, section 4 presents results of descriptive and statistical analyses, and section 5 provides a summary and conclusions. 2. Market-Based Measures of Materiality and Earnings Surprise According to auditing standards, financial statements are materially misstated when they contain accounting misstatements whose effect is important enough to cause them not to be presented fairly... in conformity with generally accepted accounting principles (AICPA [1983, para ]). In turn, standards setters for GAAP define materiality as follows: The magnitude of an omission or misstatement of accounting information that, in the light of surrounding circumstances, makes it probable that the judgment of a reasonable person relying on the information would have been changed or influenced by the omission or misstatement. (FASB [1980]) The SEC s Regulation S-X (Rule 1 02) is similar and focuses on matters about which an average prudent investor ought reasonably to be informed. A stock price change following the disclosure of information is an indication that investors judgments about a firm s value have changed and suggests one measure of the importance or materiality of the information. Stock price reaction has been considered by standards-setting bodies, scholars, and courts (e.g., see FASB [1980], O Connor and Collins [1974], Newman, Herrmann, and Ritts [1995]). However, the FASB [1980] rejected stock price reaction as too blunt an instrument for measuring materiality. Also, before SAB No. 99, SEC guidance did not specify possible market reaction as an ex ante criterion for registrant management or auditors to consider when determining materiality for financial reporting purposes. The use of the earnings surprise/stock return relation to judge the importance or materiality of earnings manipulation originated in a section of Levitt s [1998] The Numbers Game speech. He raised questions about immaterial misapplications of accounting principles, in which managers use non-gaap methods intentionally to manipulate earnings by small amounts, but their auditors do not require correction because the amounts are within traditionally accepted limits of quantitative materiality

6 1302 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN for accounting such as less than 5% of earnings. 4 Levitt suggested that there is not a bright line cutoff of three or five percent of pre-tax earnings in determining whether an accounting misstatement is material for financial reporting purposes and therefore should be corrected for an unqualified audit opinion. 5 To clarify the SEC s position, the SEC issued SAB No. 99 (August 12, 1999) that lists nine qualitative factors that might make misstatements of less than 5% of earnings material. Included is whether the misstatement hides a failure to meet analysts consensus expectations for the enterprise. SAB No. 99 acknowledges the FASB s view that potential market reaction is, by itself, too blunt an instrument on which to depend in assessing materiality, but it also requires that market reaction be considered under some circumstances. Specifically, it states that when management or the independent auditor expects (based, for example, on a pattern of market performance) that a known misstatement may result in a significant positive or negative market reaction, that expected reaction should be taken into account when considering whether a misstatement is material. Although SAB No. 99 requires consideration of qualitative factors that might make quantitatively small or immaterial misstatements qualitatively important or material, no further guidance is given regarding how a pattern of market performance is to be determined. Both Levitt s 1998 speech and SAB No. 99 express concern about the capability of earnings surprise to move stock prices significantly, with particular concern for surprise due to management s use of non-gaap methods to hide a surprise. 6 And although comprehensive data on manipulations, management s intent to hide a surprise, and related stock prices are not available, one can assess the importance or materiality of earnings surprise as measured by stock returns. This assessment may also serve as a measure of the effect of unknown-to-the-market accounting manipulations. In this article, a given magnitude of earnings surprise is deemed important, or the earnings surprise is defined as material, if it is associated with (statistically) significant market reaction at the individual firm level. We 4 Shortly after the Levitt address, SEC Chief Accountant Lynn Turner [1998] wrote a letter to the American Institute of Certified Public Accountants (AICPA) echoing many of the concerns expressed by Chairman Levitt, and outlining an action plan. 5 In an experiment conducted before issuance of SAB No. 99, Libby and Kinney [2000] document audit managers beliefs that an auditor-detected misstatement of 3% of earnings is not likely to be corrected if correction would cause a missed consensus forecast. However, registrants would be more likely to correct if correction would not lower earnings below the consensus forecast. 6 Accounting manipulation through use of non-gaap methods or misstated amounts is only one possible cause of earnings surprise. Others include: systematically poor forecasts by analysts, events that could not be anticipated, management of information released to analysts, (unintentional) accounting errors, and management of earnings within GAAP (through timing of transactions, biased accounting estimates, and accounting method changes).

7 EARNINGS SURPRISE MATERIALITY 1303 interpret a reaction as statistically significant at a probability level of p if an investor trading solely on prior knowledge of the magnitude of surprise for an individual firm would earn an abnormal return with a likelihood p or greater. Consistent with general findings of behavioral research on interpretation of subjective uncertainty expressions in accounting contexts, we interpret probable to mean two times out of three, or p =.667 or greater Sample A sample of 22,023 firm-years for the six years preceding Levitt s 1998 speech was obtained from the intersection of the First Call, Compustat, and CRSP databases. First Call analyst forecast observations consist of U.S. firms that have at least one forecast and associated EPS reported for annual earnings amounts for fiscal years ending from January 1, 1992, through December 31, 1997 (file dated March 31, 1998). Accounting and stock return data are from Compustat and CRSP. Earnings surprise is measured as actual EPS reported by First Call minus the consensus forecast as of the last First Call update before announcement of earnings for the year. The dispersion of analyst forecasts is measured as the standard deviation of First Call s analyst forecasts. Returns associated with the earnings announcement are measured as the raw return minus the value-weighted market return accumulated over a 22-day window extending from day 20 through day +1 relative to day 0, the day of the announcement of earnings. 8 Table 1 presents univariate descriptive statistics for the sample observations where earnings surprise scaled by price per share is between and This restricted range of earnings surprise reduces the influence of outliers and forms the basis for our primary analyses. 10 As in many accounting populations, the size measure distributions shown in panel A are skewed, with the means greater than the 75th percentiles for all four size measures. Table 1, panel B indicates considerable changes in the characteristics of First Call s earnings forecast composites over the six-year period. The number of observations available each year increased consistently, almost 7 For example, Amer, Hackenbrack, and Nelson [1995] summarize several surveys of auditors, managers, bankers, and investors and find.69 is the average judgment about the lower boundary of the likelihood deemed to be probable when evaluating risk in financial statement disclosures. 8 Our rationale for the 22-day return window is further discussed later. We also calculated results using returns accumulated over a shorter 7-day window surrounding the earnings announcement, extending from days 3 to +3 (some results for the shorter window are described in more detail later). Also, the analyses were repeated using raw returns, equally weighted market-adjusted returns, and risk-adjusted returns using both the value-weighted and equally weighted returns. Results were qualitatively similar. 9 Results using earnings surprise scaled by total assets are qualitatively similar. 10 This range includes about 88% of all earnings surprise observations in the database.

8 Panel A: Size Measures b TABLE 1 Descriptive Statistics for Observations with Earnings Surprise (ES) Scaled by Price Within ±0.02 a Percentiles n Mean Std. Dev Revenues 19,383 1, , ,438.0 Assets 19,383 3, , , ,483.0 Book value 19, , ,836.0 Market value 19,383 2, , , ,680.8 Panel B: Descriptive Measures c Year d All Measure Years ES (n) 2,041 2,739 3,136 3,347 4,061 4,059 19,383 Mean Median Percent firms by surprise Negative None Positive Mean 22-day window returns, by surprise Negative None Positive All Forecast age (n) 2,041 2,739 3,136 3,347 4,061 4,059 19,383 Mean Median W. KINNEY, D. BURGSTAHLER, AND R. MARTIN

9 No. of Analysts (n) 2,041 2,739 3,136 3,347 4,061 4,059 19,383 Mean Median Forecast dispersion (n) 1,645 2,221 2,602 2,780 3,806 3,774 16,828 Mean Median a Observations consist of the intersection of the First Call, Compustat, and CRSP databases. Observations from First Call consist of U.S. firms that have at least one forecast and associated actual earnings per share reported for annual earnings amounts for fiscal years ending from January 1, 1992, through December 31, 1997 (file dated March 31, 1998). Accounting and stock return data are from Compustat and CRSP for the relevant period. Observations are included in this table if ES is within ±0.02, where ES is defined as the annual per share earnings surprise divided by fiscal year-end price per share. Limiting observations for this table to ES within ±0.02 reduces the number of observations from 22,023 to 19,383. Earnings surprise is the actual EPS reported by First Call less the average per share forecast as of the last First Call update before the announcement of earnings for the year. Price per share is Compustat data item 199 (fiscal year-end price). b Size measures are defined as: Revenues Compustat data item 12, Assets Compustat data item 6, Book Value Compustat data item 60, and Market Value Compustat data item 199 (fiscal year-end price) times Compustat data item 54 (common shares used to calculate primary EPS). c Variables are defined as follows. ES is the annual per share earnings surprise divided by fiscal year-end price per share. Earnings surprise is the actual EPS reported by First Call less the average forecast as of the last First Call update before the announcement of earnings for the year. Price per share is Compustat data item 199 (fiscal year-end price). Percent firms, by surprise is the percentage of firms with negative, none, or positive surprise, where surprise is negative for firms if the forecast mean exceeds actual earnings, positive for firms if actual earnings exceed the forecast mean, and none if actual earnings and the forecast mean are equal. Mean 22-day window returns, by surprise is the average cumulative 22-day return, adjusted for a value-weighted market index, for the period beginning 20 days before and ending 1 day after the First Call database earnings announcement date, by surprise category. Forecast age is the number of days between the date of the last First Call forecast update before the announcement of earnings and the earnings announcement date, both from the First Call database. No. of analysts is the number of forecasts in the First Call database as of the date of the last forecast update before the announcement of earnings. Forecast dispersion is the standard deviation of the forecasts in the First Call Database as of the date of the last forecast update, scaled by fiscal year-end price per share (Compustat data item 199). This variable is defined only if the number of forecasts is greater than one. d Years are defined as fiscal year-ends from January 1 to December 31 of the referenced year. EARNINGS SURPRISE MATERIALITY 1305

10 1306 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN doubling by the end of 1997, as First Call expanded coverage by adding progressively smaller firms to its database. Other changes are consistent with more accurate forecasting by analysts, increased management of earnings and forecasts, or both. 11 From 1992 to 1997, average forecast dispersion (measured by standard deviation across analysts) decreased by 33% and the average age of forecasts at the annual earnings release date decreased by 54% (median decrease 68%), with most of the decrease in 1996 and The proportion of firms with zero earnings surprise increased from 12% in 1992 to 16% in 1997, whereas the proportion with negative surprises decreased from 45% to 36%, consistent with increased efforts by managers to avoid negative earnings surprises. For each observation of earnings surprise, we accumulated returns over a 22-day window surrounding the associated earnings announcement date, extending from trading day 20 through day +1 relative to day 0, the day of announcement of earnings. The 22-day return accumulation window is used rather than a shorter window concentrated at the earnings announcement date for three reasons. 12 First, table 1 shows that the median date of the composite forecast is 23 calendar days before the announcement. A return-accumulation period starting about 28 calendar days (20 trading days) before the announcement date reduces the risk of missing the price reaction to measured earnings surprise incorporated into price before the beginning of a shorter window (the stale forecast problem). Second, information about realized earnings may leak into stock prices before the announcement date (e.g., through earnings pre-announcements; see Soffer, Thiagarajan, and Walther [2000]) and the longer window reduces the risk of omitting any portion because of leakage before the beginning of a shorter window return period. Third, the 22-day window includes most of the period for which Skinner and Sloan [2001] show significant return effects in a study of quarterly earnings surprise and firm growth. 4. Results and Analysis 4.1 EARNINGS SURPRISE AND STOCK PRICE RESPONSES DESCRIPTIVE STATISTICS To summarize the relation between a given magnitude of earnings surprise and returns, nonzero earnings surprises scaled by price are ranked and formed into portfolios of 500 earnings surprise observations of similar magnitude. That is, the 500 smallest positive earnings surprises scaled by price are included in the first positive portfolio, the 500 next smallest 11 Burgstahler and Eames [1999] provide evidence that earnings are managed upward toward forecasts and forecasts are managed downward toward earnings to avoid negative earnings surprises. 12 We also considered but rejected a return-accumulation period starting at the literal forecast date, which would result in a broad range of different length accumulation periods for different earnings surprise observations, with resulting accumulated returns that are highly heteroskedastic.

11 EARNINGS SURPRISE MATERIALITY Abnormal Stock Returns Median return Mean return 33.3 and 66.7 percentiles Earnings Surprise Scaled by Price FIG. 1. Distributions of returns for price-scaled earnings surprise portfolios of 500 observations. positive surprises are in the second positive portfolio, and so on. All zeroearnings-surprise firms are included in a single portfolio of 2,736 firm-year observations. For each portfolio comprising 500 approximately equal-magnitude earnings surprises, there is an associated distribution of 500 abnormal returns. Figure 1 presents the mean, median, and 33.3 and 66.7 percentiles of the distributions of returns for portfolios formed on earnings surprise scaled by price. For all four descriptive statistics, the relation between earnings surprise and returns is relatively steeply sloped in the immediate vicinity of zero and flattens for more extreme values of earnings surprise. Thus, consistent with previous evidence reported in Freeman and Tse [1992] and others on mean responses, the overall relations are S-shaped. Figure 1 also suggests that the relation between earnings surprise and returns is relatively symmetric around zero earnings surprise. Evidence of strong negative reactions to small negative earnings surprises is accompanied by evidence of correspondingly strong positive reactions to small

12 1308 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN positive earnings surprises. That is, although it is clear that there are a fairly large number of observations exhibiting a substantial negative return to just missing a forecast, there is an approximately equal and symmetric positive return to just beating a forecast. 13 The price-scaled relation plotted in figure 1 also suggests that the distribution of returns associated with zero earnings surprise fits with the more or less continuous overall relation, even though zero surprises might be expected to differ from surrounding nonzero surprises if zero earnings surprises are often attained through earnings management or forecast management (see Burgstahler and Eames [1999]). This conclusion is further supported by results of regression tests described in section Finally, because SEC officials and the financial press often refer to earnings surprises of a single penny or a few pennies (e.g., see Morgenson [1999]), we reformed the earnings surprise portfolios by grouping unscaled earnings surprises measured in fractions of dollars per share. The number of observations with earnings surprise of a given amount per share declines rapidly with the magnitude of the surprise. 15 Therefore, to avoid very small portfolio sizes for more extreme surprises, portfolios were formed by penny per share for ES < 0.10, by nickel per share for 0.10 < ES 0.30, and dime per share for 0.30 < ES. Focusing on the positive surprises as an example, there are nine penny-per-share-based portfolios comprising surprises between.01 and.09 per share (ranging in size from 221 to 2,366 observations), four nickel-per-share-based portfolios comprising surprises from.10 to.14,.15 to.19,.20 to.24, and.25 to.29 (ranging in size from 153 to 679 observations), and two dime-per-share-based portfolios comprising surprises from.30 to.39 and.40 to.49 (ranging in size from 80 to 158 observations). Figure 2 plots the distribution for each of these portfolios by midpoint of the earnings surprise range for the portfolio and shows that the overall mean, median, and 33.3 and 66.7 percentile results are qualitatively similar to those of the earnings surprise scaled by price Returns for positive versus negative earnings surprise portfolios in figure 1 exhibit differential skewness as reflected in the relation between the mean and median. For positive surprises, the mean is always greater than the median, reflecting upward skewness; that is, the distributions contain relatively more positive extreme values than negative extreme values. In contrast, for negative surprises, the mean is usually (but not always) less than the median, reflecting downward skewness; that is, the distributions contain relatively more negative extreme values than positive extreme values. 14 Specifically, inclusion of the zero earnings surprise observations does not have significant effects on the estimated regression intercepts or slopes reported in table Although there are more than 500 observations for each of the values of earnings surprise between.04 and +.05 per share (all decimal numbers are in dollars), the number of surprises of exactly.10 (.10) per share is only 177 (247), the number of surprises of.30 (.30) per share is only 17 (54), and the number of surprises of.50 (.50) is only 9 (17). 16 First Call (and I/B/E/S) retroactively adjust analyst forecast and earnings data for stock splits in periods after the reporting period, and the resulting restated data are rounded to two digits. Thus, an earnings surprise of $0.01 reported in a year before a 4-for-1 split could represent an original earnings surprise ranging from $0.02 to $0.05. Baber and Kang [2002] and Payne

13 EARNINGS SURPRISE MATERIALITY Abnormal Stock Returns Median return Mean return 33.3 and 66.7 percentiles Dollars of Earnings Surprise FIG.2. Distributions of returns for unscaled earnings surprise per share portfolios formed on cents per share ( ES <.10), nickels per share (.10 ES <.30), or dimes per share (.30 ES ) of earnings surprise. 4.2 EARNINGS SURPRISE MATERIALITY AS MEASURED BY STOCK RETURNS FREQUENCY ANALYSIS Regarding Levitt s anecdote about the firm that missed its consensus forecast by one penny and lost 6% of its value, figure 2 shows that 33.3% of firms with earnings surprise of $.01 lose more than 3.75% of their value at announcement. However, it also shows that the mean loss is only about 0.3% and that 33.3% gain more than 3% in value. Further analysis of the firms and Thomas [2002] explore how the restated data might influence results of prior studies. We gathered First Call data from data files dated March 31, 1998, which minimizes the number of splits, and we used split-adjusted prices. To examine the potential impact of restated forecast and earnings data, we deleted all observations with nonzero split factors (approximately 22% of observations). The main results reported in section 4 hold even after deleting these split observations, and none of our interpretations or conclusions differ for the restricted sample.

14 1310 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN missing by a penny shows that 25% have market losses of 6% or greater and that 22% have market gains of 6% or greater. Thus, a one-penny shortfall has widely varying consequences, apparently depending on widely varying surrounding circumstances. The frequencies in figures 1 and 2 can be used to quantify the significance of market reaction to earnings surprise by evaluating whether it is probable at a likelihood of.667 or greater that an investor trading on prior knowledge of surprise magnitude for a particular firm would earn an abnormal return. For example, would an investor with prior knowledge of a particular firm selected at random from the portfolio of firms that will report earnings 1 cent greater than (less than) the last composite forecast, be able, at probability.667 or greater, to earn an abnormal profit by buying (selling short) the firm s stock? Similarly, would an investor, with knowledge of a firm selected at random from the portfolio of firms that will report 2 cents or, say, 50 cents above (below) forecast, expect with probability.667 or greater, to earn a profit by buying (selling short) the security? The 33.3 and 66.7 percentiles in figures 1 and 2 provide a possible answer. If the 66.7 percentile for a negative surprise magnitude is greater than zero, the probability of earning a profit by selling short a randomly selected firm is less than.667, and if the 33.3 percentile for a positive surprise magnitude is less than zero, the probability of profit by buying a randomly selected firm is less than.667. The plots in figures 1 and 2 show that all negative surprise portfolios have 66.7 percentiles (the upper limit of the p =.667 range) that exceed zero, and all positive surprise portfolios have 33.3 percentiles (the lower limit of the p =.667 range for positive surprise) that are below zero. We also calculated for each return portfolio the percentages of observations with positive and negative returns. For price-scaled earnings surprises, the maximum percentage of negative returns for negative surprise portfolios is 57.8% (for surprises ranging from to ), and the maximum percentage of positive returns for positive surprise portfolios is 62.2% (for surprises ranging from to ). For surprises in dollars per share, the minimum percentage of positive returns for negative surprise portfolios is 41.1% (for surprises per share ranging from $0.14 to $0.10), and the maximum percentage for positive surprise portfolios is 66% (for surprises per share ranging from $0.25 to $0.29). If we interpret significant or probable to mean a likelihood of.667 or greater, prior knowledge that a firm is in a particular earnings surprise portfolio is not significant because it would not, by itself, allow probable trading gains based on a simple strategy of buying or selling short the firm s stock. Thus, an investor who trades a security based solely on foreknowledge of the magnitude of the firm s earnings surprise has a less than two-thirds chance of a profit. If one uses the probability of obtaining a positive or negative stock return to assess materiality, no amount of earnings surprise (in isolation) is material. Therefore, frequency analyses show that foreknowledge of earnings surprise alone is not important or material to an investor for an individual security, using our stock-price-based materiality definition.

15 EARNINGS SURPRISE MATERIALITY EARNINGS SURPRISE MATERIALITY AS MEASURED BY STOCK RETURNS REGRESSION ANALYSIS In section 4.2 we find that, using frequency analysis and portfolios, no level of earnings surprise is material at the individual firm level, in the sense that prior knowledge of the surprise allows probable trading gains. This result is due, in part, to the S-shape of the earnings surprise/return relation and, in part, to the large standard deviation of return response for each level of earnings surprise. In this section, we estimate the average linear relation of returns to earnings surprise across various ranges of surprise and calculate statistical prediction intervals on returns based on the relation. The frequency-based portfolio approach to evaluating the probability of trading gains in section 4.2 allowed the functional form of the surprise/response relation to vary by portfolios across the range of surprise. An alternative is to assume linearity throughout a given range of surprises and estimate the average surprise/response relation using linear regression. The resulting regression coefficients are consistent with the ERC approach widely used in accounting research. Linear regression also allows calculation of.667 one-sided prediction intervals for firm-year returns to assess significant market reaction. The visual evidence in figures 1 and 2 suggests that the relation between earnings surprise and returns becomes increasingly steeply sloped as earnings surprises approach zero. To quantify this visual evidence, table 2 presents estimates of the coefficients from the following equation representing regressions of abnormal returns on earnings surprise (scaled by price) fitted over progressively narrower ranges of earnings surprise around zero: CAR = β 0 + β 1 ES + ε, (1) where CAR is the 22-day cumulative market-adjusted return and ES is annual earnings surprise scaled by price. Panel A shows results for all observations, and panel B shows results with zero earnings surprise observations omitted. In both panels of table 2, the estimated slope (ERC) is statistically and practically indistinguishable from zero when the range of surprise is unrestricted. 17 When the range is restricted to surprises smaller in absolute value than 2% of price, 18 the slope increases to approximately 2.7 and is significantly greater than zero. As the range is further restricted, the slopes continue to increase substantially, with each 50% reduction in the range resulting in a 45% to 78% increase in estimated slope. As the surprise range is narrowed, the slope rises progressively to 38.0 when zero earnings surprises are included and to 42.1 when zero surprises are excluded. The slopes 17 Note that for all ranges the adjusted R 2 is small, typically on the order of.005 to.015, consistent with the conclusion in the previous section that the effect of earnings during the announcement period is small relative to the effects of nonearnings information. 18 Recall that these represent about 88% of all observations.

16 1312 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN TABLE 2 Results of Regressions of CAR on Earnings Surprise Scaled by Price (ES) a CAR = β 0 + β 1 ES + ε Pred. Interval b ±Range of Root Adjusted ES < 0 ES > 0 ES n β 0 t 0 β 1 t 1 MSE R 2 UPI.67 LPI.67 Panel A: All Observations (including zero earnings surprises) Unrestricted 22, , , , , , , , Panel B: Observations Excluding Zero Earnings Surprises Unrestricted 19, , , , , , , , a CAR is the 22-day return, adjusted for the value-weighted market index, for the period beginning 20 days before through 1 day after the First Call database earnings announcement date. ES is the annual per share earnings surprise divided by price per share. Regressions are shown for increasingly narrow ranges of earnings surprise around zero, with zero earnings surprise observations included in the regressions in panel Aandexcluded in panel B. b UPI.67 and LPI.67 denote one-sided upper and lower prediction interval for CAR for a single observation at the extreme point of the ES estimation range (e.g., ES =.02 or ES =.02), such that the probability of an abnormal return above UPI for ES < 0 is less than or equal to.33, or the probability of an abnormal return below LPI for ES > 0 is less than or equal to.33. remain significantly different from zero for earnings surprises as small as ±.03125% of price despite declining sample sizes. 19 Prediction intervals for return conditioned on surprise for a particular security are used rather than a t-test or confidence interval on a parameter because we wish to assess the interval within which a random variable (return) is expected to lie (see Neter, Wasserman, and Kutner [1990]). Because of the large sample sizes, the approximate upper (lower) prediction interval 19 Results for a 7-day window extending from day 3today+3 and corresponding to those reported in the figures and tables show that slopes accumulated over the shorter period are consistently lower and about 80% of the slopes for 22-day returns, suggesting that the 7-day window omits a portion of the relevant return. However, the t-statistics and levels of significance using 7-day returns are generally comparable to those for 22-day returns, presumably because additional response incorporated in the longer period is offset by more noise or variation in prices unrelated to the surprise. Also, because panel B results (with ES = 0 excluded) are qualitatively similar to those for panel A, subsequent discussion and analysis include zero ES firm-years.

17 EARNINGS SURPRISE MATERIALITY 1313 for a given earnings surprise is the expected CAR estimated via equation (1) plus (minus) Z.667 times the regression s root mean square error. Interpretation of the prediction intervals is as follows. For a negative ES, an upper prediction interval that includes zero (i.e., upper prediction interval >0) ES would indicate that prior knowledge of surprise for an individual firm at that ES would not allow probable short-selling trading gains at probability of.667 or greater and thus would be unimportant or immaterial given our materiality criterion for earnings surprise using stock prices. Similarly, for a positive ES, a lower prediction interval that includes zero would not allow probable gains from buying on positive surprise foreknowledge. The two right-most columns of table 2 show one-sided (p =.667) prediction intervals for returns of a single firm at the end points of the respective ranges of ES used in the estimation. The upper interval is reported for surprises less than zero, and the lower interval is reported for surprises greater than zero. Consistent with the frequency-based plots in figure 1, all of the negative surprise upper prediction intervals include zero. Furthermore, all of the positive surprise lower prediction intervals include zero except for the broadest range of surprise (±.02) in panel A and the two broadest ranges (±.02 and ±.01) in panel B where zero surprises are excluded. Thus, based on linear regression, the probability of observing a negative return in response to a negative surprise is never as large as.667, and the probability of a positive return to a positive surprise is less than.667 for all except the upper tail of surprises. The prediction intervals calculated at the endpoints of ES for an estimation range do not show the point at which ES is equal to materiality. The just material magnitude of ES can be calculated by determining the value of ES for which the product of Z.667 and the root mean square error equals the expected CAR via equation (1). This calculated amount provides an implicit materiality estimate. The estimated price-scaled ES at which the lower limit for the ±.02 ES range equals zero in table 2, panel A (i.e., the implicit materiality estimate) is.016. There are 138 firm-year observations (of 19,383, or 0.7% of the observations in this estimation range) that had ES greater than this material level. 20 Thus, there are relatively few observations in the aggregated data that exceed the implicit materiality estimate. 4.4 RELATION TO PRIOR STUDIES OF THE S-SHAPE In this section, we explore possible explanations of the S-shape that might lead to improved measures of materiality using stock returns and to better 20 For the 135 observations in this range with nonzero forecasts the median ES (in dollars per share) divided by forecasted earnings is.235, or 23.5%, which is well above traditional levels for quantitative materiality for accounting such as 5% of current earnings. These results are also consistent with findings based on market prices observed in the laboratory. Tuttle, Coller, and Plumlee [2002] conducted laboratory market experiments of pricing of securities without misstatements of information and with misstatements of various magnitudes. They find no evidence of significant laboratory market reactions to misstatements of 10% of current earnings or less.

18 1314 W. KINNEY, D. BURGSTAHLER, AND R. MARTIN understanding of price response to surprises. The possibilities include dispersion of analysts forecasts as a proxy for determinants of the slope of the surprise/return relation. Taken as a whole, the relations plotted in figure 1 and the regression results in table 2 show that the average stock price response to larger magnitude earnings surprises is proportionately much smaller than the response to smaller magnitude earnings surprises. 21 These results suggest that expected future earnings are revised proportionately less in response to larger magnitude earnings surprises than to smaller surprises, other things equal. This conclusion is consistent with empirical results in prior studies that find the relation between unexpected earnings and returns to be nonlinear and, in particular, S-shaped. For example, an early study by Beaver, Clarke, and Wright [1979] reports an S-shaped relation between unexpected earnings and portfolio mean and median returns, especially for more extreme unexpected earnings. More recently, Freeman and Tse [1992] show that an ad hoc S-shaped function, the arctan, fits the mean earnings/return relation significantly better than a simple linear relation, and results in Lipe, Bryant, and Widener [1998] also provide empirical support for the S-shape. Several analytical models include factors that result in differences in the slope of the earnings surprise/return relation. For example, Lipe [1990] develops a model in which the slope of the earnings surprise/return relation is increasing in the predictability of future earnings and in the persistence of earnings. Also, Abarbanell, Lanen, and Verrecchia [1995] develop a pure exchange model in which the earnings/price response coefficient (β 1 in equation (1)) is increasing in the precision of the next future-period announcement of earnings 22 and decreasing in the dispersion of analyst forecasts when information acquisition is endogenous. 23 Consistent with these models, Imhoff and Lobo [1992] report evidence from an earlier period that the ERC is decreasing in dispersion of pre-announcement forecasts. At an operational level, a negative relation between analyst forecast dispersion and the earnings/price response coefficient is expected if analyst forecast dispersion is negatively related to the informativeness of current earnings about future earnings, and thus equity value (see Beaver [1989, ch. 4], Freeman and Tse [1992]). Subramanyam [1996] develops a model that incorporates Bayesian probability revision and the assumption that market participants infer the precision of earnings information from the magnitude of an earnings surprise. In his model, greater precision of the signal that earnings provides about firm value implies a larger price reaction to unexpected earnings. An 21 To assess possible changes in the relation between returns and earnings surprise from 1992 through 1997, we also tested whether the slope of the relation has increased over time. Partitioning the data into three consecutive two-year periods, we found no evidence of systematic changes in the estimated slope or intercept across the three periods. 22 See Abarbanell, Lanen, and Verrecchia [1995, eq. (3)]). 23 See Abarbanell, Lanen, and Verrecchia s [1995] Table 5 and surrounding discussion.