Earnings Precision and the Relations Between Earnings and Returns

Transcription

1 Earnings Precision and the Relations Between Earnings and Returns Presented by Dr David Burgstahler Julius A Roller Professor of Accounting University of Washington #2017/18-11 The views and opinions expressed in this working paper are those of the author(s) and not necessarily those of the School of Accountancy, Singapore Management University.

2 Earnings Precision and the Relations Between Earnings and Returns* David Burgstahler Julius A. Roller Professor of Accounting University of Washington Elizabeth Chuk University of California - Irvine September 7, 2017 * We appreciate helpful comments on earlier drafts from Bill Beaver, Darren Bernard, Phil Berger, Sunhwa Choi, Dan Collins, Dan Dhaliwal, Ilia Dichev, Michael Eames, Robert Freeman, Weili Ge, Christi Gleason, Michelle Hanlon, Thomas Hemmer, Frank Hodge, Bill Kinney, Bill Lanen, Roby Lehavy, Christian Leuz, Feng Li, Russell Lundholm, Roger Martin, Dawn Matsumoto, Terry Shevlin, Mark Soliman, K.R. Subramanyam, John Wertz and workshop participants at Santa Clara University, Southern Methodist University, Sungkyunkwan University, University of Technology Sydney, and the Universities of Chicago, Houston, Iowa, Michigan, Tennessee, and Washington.

3 Earnings Precision and the Relations Between Earnings and Returns Abstract The low estimates of earnings response coefficients (hereafter, ERCs) reported in the literature have sometimes been interpreted as indicating that earnings information is relatively unimportant (Beaver, Lambert, and Morse 1980; Lev 1989). Prior literature typically documents ERCs in the range of 1 to 3 (Kothari 2001), which is an order of magnitude lower than theoretically plausible annual earnings capitalization factors (hereafter, ECFs) in the range of 10 to 30. This paper uses a simple Bayesian model to highlight and explain differences between the coefficient relating security returns to observable unexpected earnings (i.e., the ERC) versus the coefficient relating changes in firm value to unobservable revisions in expected earnings (i.e., the ECF). In this model, the ERC is the product of a Bayesian weight and the ECF, which implies that the ERC is lower than the ECF and that variation in the relative precision of the earnings signal translates directly into variation in the ERCs. Results for a large sample of widely followed firms from show that proxies for precision explain a broad empirical range of relations between earnings and returns. In fact, we find that the highest precision subsamples have ERCs in the range of 10 to 30. Thus, our model and results reconcile the large gap between typical empirical estimates of ERCs versus plausible values for ECFs, and suggest that earnings information is much more important than the low ERCs in the prior literature would seem to imply. JEL classification: G14, M40 Key Words: Earnings precision, earnings response coefficients, analyst forecasts, uncertainty

4 1. Introduction The vast literature on earnings response coefficients (hereafter, ERCs) examines the relation between stock returns and current-period earnings (Kothari 2001). The magnitude of the return associated with an earnings signal depends on the importance of the information contained in the earnings signal relative to existing information prior to the signal. If the earnings signal is relatively important, then the earnings signal leads to greater revisions in the market s expectations of future earnings and therefore larger price changes. Prior studies typically document ERCs in the range of 1 to 3 (Kothari 2001), which is an order of magnitude lower than theoretically plausible earnings capitalization factors (hereafter, ECFs) in the range of 10 to 30. The low values of empirical ERCs have sometimes been interpreted as indicating that earnings information is relatively unimportant (Beaver, Lambert, and Morse 1980; Lev 1989; Amir and Lev 1996; Lev and Sougiannis 1996; Aboody and Lev 1998; Lev and Zarowin 1999). The objective of our paper is two-fold. First, we model how the relative importance of new versus prior information affects the magnitude of the ERC, the coefficient relating returns and unexpected earnings. Second, we use the model and empirical proxies for the relative importance of new earnings information to reconcile the order-of-magnitude gap between empirical ERCs (in the range of 1 to 3) and theoretical ECFs (in the range of 10 to 30). To discuss the gap between the ECF and the ERC, we invoke a simple Bayesian model similar to the models in Subramanyam (1996), Holthausen and Verrechia (1988), or DeGroot (1970). In the Bayesian model, revised beliefs about expected future earnings after an earnings announcement can be described as a relative weighting of prior information versus new information in the announcement, where the weight on the new earnings information depends on the precision of the new information relative to the precision of the prior information. We define precision of new information contained in the earnings signal in an equity valuation decision Page 1

5 context, such that a higher-precision signal provides higher-quality and more accurate information about expected future earnings. Higher precision earnings signals provide more information about expected future earnings, leading to a higher Bayesian weight on the new information. As explained in more detail in Section 3, the unobservable revision of expected earnings is the product of the Bayesian weight and the observable difference between realized and expected earnings. As a consequence, the ERC, the coefficient on the observable new earnings information, is the product of (i) the Bayesian weight and (ii) the ECF, the coefficient on the unobservable revision of expected earnings. Thus, our decomposition shows how the gap between the ERC and the ECF depends on the precision of the earnings signal. In summary, we show that earnings information is much more important than the low ERCs in the prior literature would seem to imply. The model and results provide several important contributions to the accounting literature. First, the model and results show that the combination of ex ante and ex post precision proxies explains a more substantial range of relations between earnings and returns than previously documented in the literature. In the model, the coefficient on observable unexpected earnings (the ERC) is a fraction of the coefficient on unobservable earnings revision (the ECF), where the fraction is determined by the relative precision of the earnings signal. Results show that when our two proxies for the statistical precision of earnings are high, accounting quality, which we infer from the ERC, is high and when the proxies for precision are low, accounting quality is low. For instance, for observations where both our ex post and ex ante proxies simultaneously indicate high precision, estimated ERCs range as high as 17 to 27, much higher than the ERCs typically reported in the previous literature. For observations where both proxies indicate low precision, Page 2

6 estimated ERCs are near zero. Thus, precision proxies explain much more variation than other empirical determinants of earnings quality previously considered in the literature. 1 Second, we demonstrate that the substantial range in ERCs that we document (as described above) becomes compressed into a low point estimate by research design choices typically employed in the prior literature. When we apply regression consistent with approaches in prior literature (i.e., using a pooled sample without conditioning on precision), the ERC for our sample is low and consistent with the estimates reported in prior studies. However, we demonstrate how the low ERC for the pooled sample is explained by the mechanics of leastsquares regression combined with the strong inverse relation between the magnitude of unexpected earnings, our ex post proxy for precision, and the Bayesian weight on new earnings information. Third, the Bayesian model provides a framework for conjectures about plausible values for the weights that determine ERCs to explain why ERCs documented in the literature are so low. The weights on new versus prior information are relative, so a high weight on new information implies a low weight on prior information. Because the set of information available prior to the announcement of earnings is almost always rich and broad, the plausible relative weight on new information is almost always far below 100%. For example, we conjecture that even high precision fourth-quarter earnings signals have a relative weight no higher than the weight on the rich set of all prior information, which includes earnings from all previous quarters as well as all previously available non-earnings information. This conjecture implies the relative weights on even high precision earnings signals are likely to be no greater than half (i.e., 50%) and, for lower precision earnings, weights are likely to be far lower than 50%. The weights implied by our 1 For example, Ali and Zarowin 1992; Choi and Jeter 1992; and Wilson 2008 document much smaller ranges of ERCs explained, respectively, by earnings persistence; the issuance of qualified audit reports; and earnings restatements. Page 3

7 empirical results are consistent with these conjectures. For the highest precision subsamples (where estimated ERCs are as high as 17 to 27), we find that the implied relative weight on new earnings information is on the order of 40%. For lower precision subsamples, we find that the implied weights are much lower and, for the lowest precision subsamples the implied weights approach 0%. Thus, the model illustrates how differences in precision lead to a wide range of plausible values for Bayesian weights, which in turn lead to a wide range of ERCs that extend from as high as 40% of theoretical ECFs to as low as the low ERCs consistently documented in prior literature. The paper is organized as follows. Section 2 provides background. Section 3 uses a Bayesian model to characterize the effect of relative precision of the earnings signal on the relation between unexpected earnings and returns. Section 4 develops empirical proxies and predictions. Section 5 provides results and discussion, and Section 6 concludes. 2. Background A variety of models express firm value as a function of the stream of future earnings. 2 It is often further assumed that expectations about the stream of future earnings can be summarized in a scalar expected earnings number where firm value can be expressed as an ECF, c, multiplied by the scalar expected earnings. 3 In these earnings capitalization models, the change in value in response to new information is equal to c times the revision in expected earnings in response to new information. The accounting concept of earnings quality corresponds directly to the statistical concept of precision of the earnings signal. In an equity valuation decision context, earnings quality focuses on the amount of information that current earnings provide about future earnings, and 2 See, for example, Beaver 1968, Kormendi and Lipe 1986, or Ohlson See, for example, Miller and Modigliani 1966, Ramakrishnan and Thomas 1998, or Easton et al Page 4

8 hence about firm value. 4 For example, Dechow and Schrand (2004, Chapter 2) define earnings quality in terms of how well current earnings represents the scalar expected earnings: "We define earnings to be of high quality when the earnings number accurately annuitizes the intrinsic value of the firm." In a more abstract model of the relation between an accounting signal and prices, Holthausen and Verrecchia (1988, p. 83) characterize the "quality" of the signal in terms of the variance of the error in the signal (the inverse of its precision): "The potential usefulness of the information is determined, in part, by the variance of its error term (its 'quality')." Earnings quality is determined by both the accounting processes used to measure earnings and by the fundamental economics of earnings processes. Accounting measures that capture more persistent (or more permanent) components of earnings result in a more informative signal about future earnings. 5 In contrast, transitory components of the economic earnings process (such as temporary fluctuations in input or output prices or other non-recurring events such as one-time gains and losses) and transitory components of the accounting measurement process (such as random accounting errors) make current earnings less informative about future earnings and hence less informative about firm value. Despite the theoretical importance of earnings information in determining firm value, the ERC estimates documented in the prior literature appear to suggest that current-period earnings innovations contain little relevant information to market participants. Our study offers a modelbased reconciliation of the inconsistency between the theoretical versus empirical importance of earnings information. The reconciliation hinges on the conceptual distinction between two related 4 Dechow, Ge, and Schrand (2010) provide a comprehensive review of the recent literature on earnings quality. DGS summarize evidence on ten proxies for, and eighteen determinants of, earnings quality in a variety of decision contexts. Earnings response coefficients are directly related to one of these decision contexts, equity valuation decisions. 5 Kormendi and Lipe (1987) develop and test the hypothesis that the coefficient relating earnings to returns is related to persistence assessed based on the parameters from a moving-average time-series model. While they find a statistically significant relation between time-series properties and the magnitude of ERCs, their estimated ERCs remain far below the range of plausible earnings capitalization factors. Page 5

9 concepts. First, the ECF relates firm value to the theoretical construct of expected future earnings, and changes in firm value to changes in expected future earnings. Second, the ERC relates changes in firm value to empirical measures of unexpected earnings. There is an order-ofmagnitude gap between plausible values for the ECF, in the range of 10 to 30, versus empirical estimates of the ERC, which have frequently been in the range of 1 to 3. 6 In the model discussed in Section 3 below, the key insight into why the large gap exists relies the conceptual distinction between the ECF and the ERC, where the ERC can be decomposed into (i) a Bayesian weight and (ii) the ECF Model In this section, we interpret the typical operationalization of the empirical ERC model in the framework of the theoretical Bayesian model of belief revision. Consider a Bayesian model of the revision of beliefs about annuitized future earnings in response to the announcement of earnings. 8 Let pre-announcement beliefs about future earnings be summarized by the mean, m', of a normal prior distribution with precision I', where precision is the inverse of the variance of the prior distribution over firm value. Let the earnings signal, m, be generated by a normal distribution with known precision I, the inverse of the noise component of the signal that current earnings provides about expected future earnings. The predictive distribution for m is normal with expectation equal to the prior expectation of firm value, m', and variance equal to the sum of the variances of the prior distribution and the distribution of the earnings signal. 6 See Kothari and Sloan (1992, p. 144) or Kothari (2001) section for a more extensive review and discussion. 7 Another consideration, explained in more detail later, is that the ECF also depends on the length of the period over which earnings are measured. For example, in the absence of seasonality or other complicating factors, the ECF for quarterly earnings should be roughly four times as large as for annual earnings. As a result, the ERC for unexpected quarterly earnings should be on the order of 4 times larger than the ERC for unexpected earnings for a full year. 8 We use a generic Bayesian revision mechanism and notation from Winkler (1972, pp ) but the model is also consistent with DeGroot (1970) Section 9.5 and other similar discussions of Bayesian revision. Page 6

10 Post-announcement beliefs about annuitized future earnings are described by the posterior distribution, where the posterior mean, m", is a weighted average of the prior mean, m', and the signal, m, where the weight reflects the relative precisions of the prior and the signal: 9 m" (I m I' m') (I I'). (3.1) Equation (3.1) implies the revision in beliefs due to the earnings signal (i.e., the change from the prior belief m' to the posterior belief m") is m" m' I (I I') (m m. (3.2) The revision is the product of two terms: 1) a weight, defined as w = I / (I+I'), and 2) the difference between the realized earnings signal and its expectation (m m'). To convert equation (3.2) from units of expected and realized earnings to units of firm value, each term is multiplied by the ECF, c. The left side becomes the change in market value due to belief revision while the right side is the product of the weight, the ECF, and the deviation of the realized signal from its expectation. 10 cm" cm = w c (m m ). (3.3) 3.1 ERC operationalization of the Bayesian model The standard ERC regression model can be interpreted as an empirical version of the theoretical Bayesian revision represented in equation (3.3). First, divide both sides by market value prior to the announcement of earnings, cm. The left side becomes the return attributable to the earnings signal, operationalized as the announcement period return. The right side becomes the product of w, c, and the deviation of the signal from its expectation scaled by prior market value. This scaled deviation is operationalized as the standard ERC unexpected earnings variable, 9 Equations (3.1) and (3.2) also correspond to equations for the revision of price in period 1 in the model of Holthausen and Verrecchi (1988, pp ). 10 This operation assumes the announcement of earnings does not result in a change in the ECF, c. Page 7

11 announced earnings minus forecast earnings scaled by beginning market value, denoted below by UE. Finally, adding an intercept term, β0, to allow for the possibility of a non-zero expected return during the announcement period and an error term, eit, to allow for the effects of non-earnings information related to firm i during the announcement period, we have the familiar ERC relation for firm i during earnings announcement period t: Rit = β0 + wit c UEit + eit. (3.4) The key insight from Equation (3.4) is that the ERC can be decomposed into two individual components: (i) the Bayesian weight, w, and (ii) the ECF, c. The weight is less than or equal to one and varies with the precision of the earnings signal relative to the precision of the prior information. Consequently, the ERC, the coefficient on UE in (3.4), is a fraction of the ECF, where the fraction is the Bayesian relative weight. The ERC is near zero when the precision of the earnings signal is low relative to the precision of the prior (where the weight is near zero) and increases as the precision of the earnings signal relative to the precision of the prior increases. The low ERCs previously reported in the literature might seem to imply that the weights on new information are consistently small across all observations. However, the results below show that proxies for precision explain substantial empirical variation in ERCs. Specifically, the results suggest that while there are some observations where the weights on new earnings information and the corresponding ERCs are low, there are even more observations for which the weights on new earnings information and the corresponding ERCs are remarkably high. 3.2 Numeric example to illustrate the effect of the Bayesian weight on the ECF Equation (3.4) defines the ERC as the product of a weight and the ECF. In this section, we illustrate the weights implied by ERC estimates for a stylized example assuming an annual ECF common to all observations equal to 15, which 1) is approximately the long-run average priceearnings ratio for the S&P 500 and 2) provides a convenient, round parameter for the numerical Page 8

12 example that illustrates the weights. 11 In the absence of seasonality in earnings, the quarterly ECF is about four times the annual ECF so the assumed annual ECF of 15 translates into a quarterly ECF of 60. The following example illustrates the intuition for the implied weights. Consider a firm with expected annual earnings of $4.00 per share (i.e., expected quarterly earnings of $1.00 per share, assuming no seasonality in earnings) and an annual ECF of 15 (i.e., a quarterly ECF of 60, again assuming no seasonality), which implies a pre-announcement market value of $60.00 per share. 12 Assume announced fourth quarter earnings is $1.50. The $.50 surprise can be variously interpreted as 50% of expected fourth quarter earnings of $1.00 or as 12.5% of expected annual earnings of $ The posterior price, after the announcement of earnings, is the product of the ECF and the posterior belief about expected future earnings, which in turn depends on the relative weight on new earnings information. Therefore, the price, return, and ERC that result from the $.50 surprise also depend on the relative weight. The table below illustrates the posterior beliefs, prices, returns, and ERCs that correspond to five examples of weights in Column II, which range between the extremes of 0% and 100%. Note that the weight on new information in Column II and the weight on prior information in Column III are relative, such that they always add to 100%. At one extreme where the weight on new earnings information is 0% (in the first row), posterior beliefs are unchanged from the prior 11 The assumption of a single ECF common to all observations ignores any inter-temporal or cross-sectional variation in the ECF. However, it is easy to extend the example to consider variation in ECFs and the weight we derive for an assumed ECF of 15 can be easily converted to the weight for alternative values of the ECF. For example, doubling the assumed ECF to 30 implies half the weight implied by an ECF of 15 while cutting the assumed ECF in half to 7.5 implies a weight double the weight implied by an ECF of This example is constructed so that expected quarterly earnings of $1.00 serves as a convenient numeraire. However, conclusions do not depend on the per share amounts the substance of the example is no different when the example is rescaled for expected quarterly earnings equal to $.10 per share, $10.00 per share, or any positive amount per share. 13 To place this example in the context of price-scaled earnings surprise reported later in Table 3 (the scaling that is also frequently used in the previous literature), the implied $.50 earnings surprise represents of market value of $60, which falls in the middle ES magnitude range of ±.01 in Table 3. Page 9

13 beliefs of $1.00 (Column IV) and the posterior price is unchanged from the prior price of $60.00 (Column VII). At the other extreme where the weight on new earnings information is 100% (in the last row), posterior beliefs effectively ignore prior information and are revised completely to the new earnings information, or $1.50 (Column IV), and the posterior price is revised to $90.00 (Column VII). Between these two extremes, the three examples of weights on new information of 20%, 50%, and 80% (in the second, third, and fourth rows, respectively) illustrate cases that result in posterior beliefs between the prior beliefs and the new information. (I) (II) (III) (IV) (V) (VI) (VII) (VIII) (IX) ECF Weight on new information Weight on prior information Posterior expected quarterly earnings % change in expected earnings Prior price Posterior price Return ERC % 100.0% % % % 80.0% % % % 50.0% % % % 20.0% % % % 0.0% % % 60 Columns VII, VIII, and IX of the table summarize how the revision of beliefs translates into price, return, and the ERC. The posterior prices (Column VII) translate into announcement returns that correspond exactly to the percentage change in expected future earnings (Column V), ranging from 0% to 50%. The returns translate into ERCs ranging from 0 (for a weight on new information of 0% in the first row) to 60, the ECF (for a weight on new information of 100% in the last row). Thus, consistent with equation (3.4), the ERC is the product of (i) the quarterly ECF in Column I and (ii) the weight on new information in Column II). In the example, the weight (Column II) determines the posterior expected earnings (Column IV) which, together with the ECF (Column I), implies the posterior price (Column VII) and return (Column VIII). In empirical applications, we use the observed price and return together Page 10

14 with the assumed ECF to infer the posterior expected earnings and the weight on new earnings information. Using the numbers from the second row of the table to illustrate the inference, an observed return of 10% (Column VIII) implies a weight on the new earnings information of 20% (Column II), which is the ratio of the ERC (Column IX) to the quarterly ECF (Column I) Empirical Proxies In this section, we develop proxies for precision based on two conjectures: (1) lower precision earnings processes tend to generate larger magnitude unexpected earnings and (2) lower precision earnings processes tend to be accompanied by greater dispersion among analyst forecasts. These two conjectures lead to proxies based on either (1) realized deviations of earnings from expectations, or (2) variation among analyst earnings forecasts. The first conjecture is consistent with both prior empirical evidence and with formal models. There is a long stream of empirical evidence showing an S-shaped aggregate relation between unexpected earnings and security market returns, consistent with a negative relation between the magnitude of unexpected earnings and precision. Beaver, Clarke, and Wright (1979) report an S-shaped relation for the average returns for portfolios formed on the magnitude of unexpected annual earnings. Freeman and Tse (1992) examine the relation for unexpected quarterly earnings and fit an S-shaped functional form based on the arctangent function. Kinney, Burgstahler, and Martin (2002) use a portfolio approach that extends the original Beaver, Clarke, and Wright methodology, and also report strong visual and statistical evidence of the S-shape. The formal model in Subramanyam (1996) illustrates how precision of the earnings signal is inferred from the magnitude of unexpected earnings, which leads to an S-shaped relation that is more steeply-sloped for smaller magnitude unexpected earnings and flatter for larger magnitude 14 The weight of 20% can also be interpreted as the ratio 10%/50%, i.e., the ratio of the percentage revision of expected quarterly earnings (10%) divided by the earnings surprise as a percentage of expected quarterly earnings, 50% (=$.50/$1.00) Page 11

15 unexpected earnings. Subramanyam (1996) outlines reasons to believe that precision is inferred from the magnitude of unexpected earnings: (A)n examination of institutional features and the information environment reveals that the market is unlikely to have perfect knowledge of the signal precision ex ante. For example, in the case of an earnings announcement, a number of the determinants of information accuracy--such as the proportion of transitory cash flows and other non-recurring items, and the effect of changes in accounting methods--are specific to each announcement, and the market is unlikely to have perfect a priori knowledge of them. In addition, accrual earnings incorporates estimates of future events, but managers rarely report the precision of those estimates. Therefore, a descriptively richer analysis is one which incorporates ex ante uncertainty regarding signal precision. Note that uncertain precision does not imply that the market has no ex ante information regarding signal quality, it merely implies that the market does not have perfect ex ante information. (p. 208) The second conjecture is based on evidence in Kinney, Burgstahler, and Martin (2002, hereafter KBM) for a sample of First Call forecasts from 1992 through The results show that the S-shape relation between returns and magnitude of unexpected earnings is steeper and more pronounced among observations with lower forecast dispersion and flatter and more nearly linear among observations with higher dispersion, consistent with the conjecture that forecast dispersion is inversely related to relative precision of the earnings signal. However, forecast dispersion is affected by a number of factors other than precision, and these factors potentially affect dispersion as a proxy for precision. For example, dispersion reflects differences in analysts priors that result from heterogeneity of information or information processing skill among analysts (Barron et al. 1998) and analysts incentives to herd (Trueman 1994), so forecast dispersion may include noise unrelated to precision. Dieter, Malloy, and Scherbina (2002) consider a variety of possible interpretations for forecast dispersion. They conclude that dispersion is a proxy for differences in opinion among investors, though differences of opinion might also result from other factors that have little or nothing to do with relative precision. Finally, Yeung (2009) suggests forecast dispersion could be positively related to the relative precision of the current earnings signal if higher forecast dispersion proxies for lower Page 12

16 precision of prior information. In sum, the KBM conjecture that lower forecast dispersion may proxy for higher precision of the earnings signal remains an open empirical question. Based on these two conjectures, we develop the following proxies for precision: 1. Magnitude of current unexpected earnings: The first proxy, the magnitude of current unexpected earnings, is only observable ex post (i.e., after realization of the earnings signal). The ex post proxy is based on extensive empirical evidence of an S-shaped relation between unexpected earning and returns and on the theoretical model in Subramanyam (1996). 2. Dispersion of current analyst forecasts: The second proxy, analyst forecast dispersion, is observable ex ante (i.e., prior to realization of the earnings signal). The ex ante proxy is motivated by the empirical evidence and conjecture in KBM and by the Dieter, Malloy, and Scherbina (2002) conjecture that dispersion may proxy for differences in opinion among investors. In order to have meaningful measures of standard deviation, the analysis based on this proxy is restricted to observations where there are four or more analyst forecasts. In the next section, we present evidence on the relations between these proxies and the relation between the proxies and ERCs. Our predictions are as follows. First, we expect a positive relation between precision and ERCs, as higher-precision earnings information is expected to lead to larger revisions in beliefs about firm value. 15 Second, because the ex ante and ex post proxies are separate measures of precision, they potentially each provide incremental information about ERCs. For example, holding the value of the ex post proxy constant, subsamples with higher ex ante precision are likely to have higher ERCs than subsamples with lower ex ante precision. Third, because both are proxies for the same construct (i.e., precision), we expect them to be positively correlated. Finally, to the extent that precision is a stable characteristic resulting from the accounting and economic processes that create earnings quality, we also expect the proxies to be positively autocorrelated. 15 Statements about the relation can be confusing because lower values of the precision proxies (i.e., smaller magnitude unexpected earnings or smaller forecast dispersion) indicate higher precision. To minimize the potential for confusion, we refer to the theoretical construct as precision and each empirical measure as a precision proxy. Using this terminological convention, we expect a positive relation between precision and ERCs but a negative relation between each precision proxy and ERCs. Page 13

17 5. Data and Results We obtain data from the IBES database for the 23-year period We measure the following variables from IBES: earnings surprise (defined as actual EPS minus the consensus forecast as of the last update before the announcement of earnings for the year, where the consensus forecast serves as the measure of expected earnings), the number of analyst forecasts used in computing the consensus forecast, and forecast dispersion (defined as the standard deviation of analyst forecasts). 16 Accounting and stock return data are obtained from Compustat and CRSP. We measure announcement period returns as raw return minus the value-weighted market return accumulated over a 22-day window extending from day -20 to +1 relative to the day of the announcement of earnings. 17 We scale earnings surprise and forecast dispersion by price at the end of the fiscal year (Compustat data item PRCC_F), which is typically shortly before the beginning of the return period. Table 1 provides descriptive statistics for the final sample of firm-years with the necessary IBES analyst forecast, accounting, and stock return data and where price-scaled earnings surprise is in the range between and The descriptive statistics are generally comparable to the older and smaller sample in KBM. Panel A shows that all four size measures have rightskewed distributions with means greater than the 75 th percentile. Panel B provides descriptive 16 Payne and Thomas (2003) report that versions of IBES data adjusted for stock splits and then rounded to the nearest penny sometimes incorrectly include zero forecast error for firms with stock splits even when the actual forecast error is non-zero. Also, the standard deviation of analyst forecasts computed using the split-adjusted and rounded forecasts is mechanically reduced for firms with stock splits. However, because we use the unadjusted IBES data, our measures of earnings surprise and dispersion of analyst forecasts should not be affected by these issues. 17 We also computed our primary results 1) using raw returns minus the equally-weighted market return, and 2) using a shorter 3-day return window extending only from day -1 to +1. Results using the equally-weighted market return are similar to those reported here. Results using 3-day returns are similar to the reported results except that the magnitude of the return reactions and the associated ERCs are reduced by as much as 50% for the 3-day return window, consistent with previous evidence that a substantial portion of earnings information "leaks" to market participants during days -20 to -2 prior to the actual announcement. 18 Although the range in figures later in the paper is similarly restricted to the range between -.02 and +.02, subsequent tables generally include results for the entire unrestricted range of earnings surprise. Page 14

18 statistics showing some changes in sample properties over time such as growth in the number of analyst forecast observations available and decreases in the mean and median forecast dispersion. The statistics do not highlight any important differences from samples commonly used to examine the relation between returns and earnings. Similar to many previous ERC samples, this sample should not be construed as representative of the entire population of Compustat firms because it is conditioned on analyst coverage and specifically excludes firms not covered by analysts. At the same time, this conditional sample covers a large proportion of the total market value of firms in the entire Compustat population, as shown in the last few lines of Panel B. In most years, the proportion of market value represented by firms followed by 2 or more analysts is between 72% and 81% of the total market value of the population of firms on Compustat and the proportion represented by firms followed by 4 or more analysts is between 56% and 72% of total market value. 5.1 Effect of Ex Post Proxy Figure 1 plots statistics describing the distribution of returns corresponding to portfolios of 1,000 observations formed on the ex post proxy, magnitude of earnings surprise. Consistent with previous results in KBM (2002), Freeman and Tse (1992), and Beaver, Clarke, and Wright (1979), and consistent with the Subramanyam (1996) model where the magnitude of earnings surprise proxies for precision of the earnings signal, the relation exhibits a pronounced S-shape. 19 This S- shape is reflected in all of the return distribution statistics (mean, median, 25 th, and 75 th percentile 19 For earnings surprise beyond the range plotted in Figure 1, the S-shape turns back toward zero for more extreme earnings surprise, consistent with the Subramanyam model. Note also that there is no evidence in Figure 1 (nor later in Figure 3) of an asymmetrically larger effect for slightly negative earnings surprise than for slightly positive earnings surprise. In fact, unreported statistical tests suggest that the coefficient on small positive earnings surprise is usually significantly larger than the coefficient on small negative earnings surprise. Thus, the "torpedo effect" reported in Skinner and Sloan (2002) for a subsample of high growth firms does not generalize to our broad sample of firms. Page 15

19 returns) so the S-shape reflects broad distributional effects, and not the influence of a few unusual observations ERC Estimates We next turn to estimated ERCs and tests of statistical significance corresponding to Figure 1. Table 2 shows estimates of the ERC, β1, for different values of the ex post proxy, beginning with the estimate for unrestricted magnitude of earnings surprise, followed successively by estimates for earnings surprise restricted to the ranges ±.02, ±.01, ±.005, and finally ± Panel A provides results for the total sample of 96,745 observations while Panels B and C provide results for two subsamples. Panel B comprises observations with 4 or more analyst forecasts (for which our ex ante proxy is defined) and Panel C includes the remaining observations with less than 4 analyst forecasts. For the total sample in Panel A, the ERC, corresponding to witc in equation (3.4), for the unrestricted range of earnings surprise is essentially zero. However, as ex post precision increases (i.e., as the magnitude of earnings surprise decreases), the estimated ERCs grow. When the magnitude of earnings surprise is limited to the range ±.02, the ERC increases to about 3 and when the magnitude is successively cut in half to ±.01, then ±.005, and finally ±.0025, the ERC increases to about 5, then 8, and finally Successive narrowing of the included range of earnings surprise reduces the sample size but even the narrowest range includes almost half (about 46%) of the original entire sample in Panel A and more than half (about 60%) of the original defined-dispersion subsample in Panel B. 20 The results reported here are qualitatively consistent with the results for the smaller sample in KBM except 1) the rate of increase in the ERC as the range of earnings surprise is narrowed is smaller for our larger, more recent sample, and 2) KBM report continued substantial increases in ERCs as the range is narrowed even further than ± We do not report results for the much narrower ranges considered in KBM because these ranges comprise smaller and smaller subsets of the overall sample as well as smaller and smaller surprises. For our sample, unreported results show a continued increase in ERCs for the next narrower range of earnings surprise (.00125) though the increase is smaller than in KBM. Page 16

20 The product of an earnings surprise and the corresponding estimated ERC implies a predicted percentage return and percentage revision in expected earnings. 21 For example, a surprise equal to.0025 multiplied by the corresponding ERC of implies a predicted return and percentage revision in expected earnings of.0025 x = 3.30%. However, because the ERC is smaller for larger surprises, larger surprises do not imply proportionally higher revisions in expected earnings. For example, a surprise that is twice as large, equal to.005, multiplied by the smaller ERC of for these smaller surprises implies a predicted return and percentage revision in expected earnings that is less than twice as large, namely.005 x = 4.15%. Further doubling of the magnitude, for surprises equal to.01 or.02, similarly imply predicted returns (and percentage revisions in expected earnings) that do not increase proportional to the surprise, but instead increase to only 5.11% or 6.25%, respectively. Thus, because the ERC decreases as the largest earnings surprise in each successive range doubles, the corresponding return and percentage revision in expected earnings does not double, but rather increases at a much slower rate. Returning to the numeric example in Section 3.2, we can calculate the weight implied by the ratio of the ERC and the assumed quarterly ECF of 60 for any of the earnings surprise ranges in Table 2 Panel A. For example, the ERC for the unrestricted range implies a weight of approximately 0% =.001/60. As precision increases for increasingly narrow ranges of earnings surprise, the implied weight increases to 5.2% = 3.126/60, then 8.5% = 5.111/60, then 13.8% = 8.303/60, and finally, for surprises in the narrowest range ±.0025, to 22% = / Thus, the ex post precision proxy by itself identifies substantial variation in the ERC and in the implied 21 The equivalence of the percentage return and percentage revision in expected earnings follows from the assumption that equity value is the product of expected earnings and the ECF combined with the assumption that the ECF is not affected by the earnings announcement. 22 While the narrowest range of earnings surprise appears numerically small, it 1) includes a large proportion (44,416 / 96,475 = 46%) of all observations, and 2) is not limited to only trivial earnings surprises it includes surprises up to 15% of expected quarterly earnings. Page 17

21 weight on new earnings information. Results in Section 5.2 below show that by partitioning on both the ex post proxy and an ex ante proxy, we can identify subsamples with even higher precision and larger implied weights on new earnings information Evidence of another proxy for precision: analyst coverage Finally, before we turn to exploration of the role of specific ex ante proxies for precision, the results in Table 2 Panels B and C provide evidence of another variable related to precision: analyst coverage. There is evidence in the literature that analysts are less likely to cover firms with earnings that are more difficult to forecast (Stickel 1992 and Mikhail, Walther, and Willis 1999). As a result, analyst coverage may be another ex ante proxy for precision, i.e., firms covered by fewer analysts may have lower precision than firms covered by more analysts. The results in Table 2 are consistent with this conjecture. The ERCs (and the implied weights on new information) for the subsample of 52,388 observations with 4 or more analyst forecasts in Panel B are generally substantially larger than the corresponding ERCs for the subsample of 44,357 observations with fewer than 4 forecasts in Panel C. For each of the restricted ranges of earnings surprise, the ERCs in Panel B range from 56% to 82% larger than in Panel C. For the unrestricted range of earnings surprise, the relative difference is even larger, as the ERC for the subsample covered by more analysts is several hundred percent larger. 5.2 Effect of Specific Ex Ante Proxies We next evaluate the incremental effect of an ex ante proxy relative to the ex post proxy, to examine whether the ex ante proxy provides incremental information about ERCs. In Sections through 5.2.4, we focus on the ex ante proxy defined in Section 4. Then, in Section we present results for two alternative ex ante proxies Incremental Effect of the Ex Ante Proxy To condition on precision using the ex ante proxy, we sort observations with at least four analyst forecasts into three approximately equal-sized subsets based on the price-scaled standard Page 18

22 deviation of contemporaneous analyst forecasts. The three subsets comprise 17,464 high precision observations, 17,458 medium precision observations, and 17,466 low precision observations. Figure 2 provides evidence on the relation between the ex ante proxy and the ex post proxy by plotting distributions of price-scaled earnings surprise for subsets defined by low, medium, and high forecast dispersion. The low dispersion subset includes mainly small magnitude earnings surprise, tightly concentrated around zero. As we move to higher dispersion subsets, the proportion of larger magnitude earnings surprise increases. 23 Thus, Figure 2 illustrates two important facts: First, the ex post and ex ante precision proxies are strongly positively correlated, as expected if the proxies measure the same construct. 24 Second, because the correlation between the two proxies is less than perfect, there is the potential for the proxies to be empirical complements, where each proxy may provide information incremental to the other. We next depict the relation between returns and earnings surprise within each of the ex ante precision groups, using an approach that corresponds to Figure 1. For each of the three forecast dispersion subsets, Figure 3 shows a plot of the return distribution statistics for portfolios of 500 observations formed on scaled earnings surprise. Lower dispersion observations are predicted to have higher ERCs due to higher precision and the resulting higher weight on the current earnings signal. Consistent with this prediction, the slope of the relation is much steeper for the low dispersion subset in Panel A than for the high dispersion subset in Panel C, with the slope for the medium dispersion subset in Panel B falling between the slopes for the low and high dispersion subsets. 23 The vertical bars at the endpoints of the earnings surprise axis represent the combined frequency of all observations that fall beyond the limits of the horizontal axis. For instance, in the high dispersion subset, the height of the bar at the extreme earnings surprise of indicates there are more than 2,000 observations with earnings surprise less than In each histogram, the checkered bar represents the frequency of exact zero earnings surprise. Also note that each histogram exhibits a pronounced discontinuity at zero earnings surprise, consistent with prior research (e.g., Burgstahler and Eames 2006). 24 The Spearman (Pearson) correlation coefficient between the two proxies is 0.60 (0.54), where the Pearson correlation is computed after winsorizing at the 1 st and 99 th percentiles. Page 19

23 Within each of the subsets conditioned on forecast dispersion, the overall relation is also more nearly linear than in the unconditional relation in Figure 1, as expected if the partitioning based on forecast dispersion yields subsets where precision is more homogeneous within each precision group than in the three groups combined. 25 The conditional relations for the subsets in the three panels also provide a visual explanation as to how the more pronounced S-shape arises in the unconditional relation in Figure 1. Because of the strong correlation between forecast dispersion and earnings surprise magnitude shown in Figure 2, most of the small magnitude earnings surprise observations correspond to the more-steeply-sloped relation in Figure 3 Panel A, forming the more-steeply-sloped center of the S-shape, while most of the large magnitude earnings surprise observations correspond to the less-steeply-sloped relation in Panel C, forming the lesssteeply-sloped tails of the S-shape ERC Estimates and Tests of Significance Table 3 reports estimated ERCs and tests of statistical significance. The ex ante precision proxy based on the dispersion of contemporaneous analyst forecasts has significant explanatory power, both by itself and incremental to the ex post proxy. By itself, the ex ante proxy has significant explanatory power. Comparing ERCs without taking the ex post proxy into account (i.e. comparing results for the unrestricted range of earnings surprise across the three panels), the ERC for the high ex ante precision group is significantly higher than the ERC for either the medium or low precision group. Incremental to the ex post proxy, the ex ante proxy again has 25 Unless precision within each subset is strictly homogeneous, the earnings-return relations within the three ex ante precision subsets are expected to be more linear but still S-shaped. The individual precision subsets are not likely to reflect strictly homogeneous precision, both because the partitioning variable is subject to proxy error and because each of the three partitions includes a range, rather than a single value, of the precision proxy. 26 Note that Figure 1 is not simply the aggregation of the 52,388 observations represented in the three panels of Figure 3 because Figure 1 includes an additional 44,357 undefined dispersion observations with three or fewer analyst forecasts. The decision by analysts to produce forecasts for a firm is not random, so undefined dispersion observations are likely to differ systematically from defined dispersion observations, as noted in the discussion of Table 2 above. Page 20