DETERMINING THE EFFECT OF POST-EARNINGS-ANNOUNCEMENT DRIFT ON VARYING DEGREES OF EARNINGS SURPRISE MAGNITUDE TOM SCHNEIDER (20157803) Abstract In this paper I explore signal detection theory (SDT) as an explanatory factor for the observed S-curve reaction of abnormal market return to earnings surprise. I hypothesize that post-earnings-announcement drift (PEAD) will be greater for firms with greater absolute magnitudes of earnings surprise if SDT is a factor. I replicate the work of Kinney, Burgstahler and Martin [2002] and extend the time frame of their observations to include a period for PEAD. I find no evidence of greater degrees of PEAD based on earnings surprise and that the S-curve persists over the extended observation period. Thus, I conclude STD is not an explanatory factor for the observed market response. Many thanks to Pat O Brien and Ranjini Sivakumar for their advice and input over the summer and to Sean Spears for his help in data collection.
I - Introduction Two studies, Freeman and Tse [1992] (hereinafter FT) and Kinney, Burgstahler and Martin [2002] (hereinafter KBM), have found that the scatter plot of the market s reaction to earnings surprises, as measured by abnormal stock return, follows an S-curve centred on the origin. Neither study gives a definitive reason for this result, although they do look to earnings persistence and forecast precision as possible reasons. In this paper, I explore the possibility that surprise magnitude is a stand-alone contributing factor in the S-curve reaction to earnings surprise. I look to signal detection theory (SDT) as a basis for hypothesizing that surprises of greater magnitude will have relatively smaller abnormal market returns around the announcement date. To determine whether this could be true, I look for cross-sectional differences in post-earnings-announcement drift (PEAD) between portfolios that are created based on surprise magnitude. If increasing magnitude moderates the market response, market efficiency dictates this should correct itself over time and be observable in PEAD. The hypothesis is that portfolios created with larger surprise magnitude firms will show greater drift than portfolios created with smaller surprise magnitude firms. If this can be observed, it would support the possibility that surprise magnitude is a stand-alone factor in determining the market s reaction to earnings surprise. In the next section of this paper, I discuss FT and KBM, in section III I discuss SDT and how it might apply to earnings surprise. In section IV, I develop the hypothesis to be tested, in section V I present the research design, in section VI the sampling process, in 2
section VII the results, in section VIII a regression analysis and in the final section I present my overall conclusions. II - Background In FT, the authors focus on demonstrating a cross-sectional difference in the response to earnings surprises and that this difference can be attributed to the magnitude of earnings surprise. The result is evident in the better fit of a non-linear S-curve function as opposed to a linear function in modeling abnormal return in relation to earnings surprise. They imply that the S-curve in their data is a function of the earnings persistence of the sample firms earnings. That is, forecast error will increase as earnings persistence is decreased. Thus, the upper and lower tails of the S-curve would be expected to have a higher number of firms with transitory earnings. In the second paper, KBM demonstrate that analysts forecast dispersion is an explanatory factor for the S-curve. If they limit the range of their data to include firms with a higher number of analysts and lower forecast dispersion, the S-curve flattens out to a more linear form. They note that analyst dispersion could be a proxy for other determinants of the surprise/return relation, such as earnings persistence, the precision of the signal that earnings provides about firm value, or both. 1 Thus, these two explanations are not necessarily mutually exclusive as analysts forecast accuracy could be positively correlated with more persistent earnings. Both studies note that the non-linear form in response to earnings surprises should be taken into account when studying the Earnings Response Coefficients. The Earnings 1 KBM [2002], p. 1323 3
Response Coefficient (ERC) measures the market response to accounting earnings 2. Easton and Zmijewski [1989] find that ERCs vary cross-sectionally and in a predictable manner. They identify revision parameters as one of the two key factors affecting the ERC (the other key factor being the expected rate of return). The revision parameters they identify are essentially a measure of earnings persistence, based on either a timeseries model (such as Foster s [1977] seasonal first-order autoregressive time series process) or a regression of analysts most recent revision of next quarter s earnings on analysts most recent forecast error. They demonstrate that this revision parameter (or persistence) will vary across firms. If during a specific period these parameters do not change but earnings do in relation to expectations, the change in stock price will be the change in earnings times the ERC. If the revision parameters change, the reaction to changes in earnings would not be linear. They also note that variations in time-series approach can result in different ERCs. Thus the possible form of the reaction to earnings surprise is infinite. In an efficient market, the information imparted in earnings news should be capitalized in a manner that reflects the present value of this information. If FT are correct in their hypothesis that earnings persistence is recognized in the market, then investors are able to differentiate between firms and apply the appropriate ERC to earnings surprises. Teets and Wasley [1996] deal directly with calculating cross-sectional and firm specific ERCs and demonstrate that cross-sectional ERCs are, on average, lower than firm specific ERCs due to over-weighting of the higher magnitude surprises. Thus, if they are to be applied accurately they must be calculated on a firm specific basis. Mendenhall [2002] 2 For a review of ERCs, see Kothari s [2001] review of Capital market research in accounting. 4
and Ball and Bartov [1996] provide empirical evidence that investors do indeed do this. Ball and Bartov also find that even though investors can differentiate between firms, they underestimate the firm specific ERC by one half of its true value. They identify this as the key cause of post earnings announcement drift. Part of my motivation to follow the post earnings announcement drift of various surprise magnitudes is to try and determine whether the firm-specific ERCs are consistently underestimated across all surprise magnitudes. As mentioned earlier, KBM hypothesize that analysts forecast dispersion could be a proxy for persistence and/or precision. The literature discussed here has shown that cross-sectional differences in persistence can create the observed S-curve. The issue of precision was examined by Subramanyam (1996). Subramanyam develops a market model in which uncertainty about the precision of the signal in earnings forecast errors is a sufficient condition to create a non-linear relationship between returns and surprise. The form of this non-linearity would depend on the relation between expected precision and surprise. Subramanyam s model tries to reconcile the two conflicting factors that are: the revaluation of a stock price given a surprise, and the negative relation between absolute returns and absolute surprise. He demonstrates that the only requirement to create an S-curve in the response to earnings surprise is the relaxation of the assumption of constant precision across all surprises. This argument is well supported by the results that come from KBM and FT. 5
Thus, there are currently two suggested contributing factors to the S-curve persistence and precision. I wish to explore one more. Nothing to date addresses the relative magnitude of the surprise as a stand-alone factor for at least part of the observed reaction to earnings surprises. Thus, I am interested in exploring whether, ceteris paribus, the relative magnitude of an earnings surprise is a sufficient condition to cause a non-linear market response. Signal Detection Theory (SDT), as described by Green and Swets [1964], provides a theory that supports the concept that investors reaction to earnings surprise would decrease as its absolute magnitude increases. If this were true, it would create an S-curve in response to earnings surprise magnitude. It would also create a source of market inefficiency. I propose that this inefficiency would correct itself over time and would be observable in the form of PEAD. III - Signal Detection Theory Investors must make buy-sell decisions based on a stream of information that is a combination of public announcements and private information. These decisions are made against a background of noise. The final signal to an investor to buy is made in a haze of macro and micro-economic information. Green and Swets developed Signal Detection Theory (SDT) in the 1960s building on probability theory and statistical decision theory. It is specifically based on the ability of observers to detect a signal and differentiate it from noise. It is structured as an outcome matrix of the four possible situations when signals are, or are not, detected against a background of noise. The four possible outcomes are: A signal is detected as noise (a miss type II error) A signal is detected as a signal (a hit) 6
Noise is detected as noise (correct identification) Noise is detected as a signal (a false alarm type I error) Karim and Siegel (1998) apply SDT to the detection of fraud during the audit process. They discuss the aspect of increased false alarms if increased vigilance is required in detecting fraud. They question the ability of auditing techniques in place at that time to successfully detect fraud without raising an inordinate amount of false alarms. Raising the bar on fraud detection is a trade-off of efficiency versus effectiveness. In an optimal decision strategy, any given information will be interpreted perfectly. However, this is not always possible against a significant and often confusing background of noise. In a capital markets context, if a particular investor wants to increase the number of hits, the number of false alarms will also go up. Conversely, if the false alarm rate is to go down, the rate of hits will also go down. A conscious or unconscious decision must be made as to what the tolerated false alarm rate will be. A precise ex ante rate cannot be calculated; however, an ex ante rate will be established based on expectations and an investor s willingness to accept the cost of a false alarm. The key measure in SDT is the likelihood ratio (L), the probability of the information being a signal, divided by the probability of the information being noise. Given the cost of a false alarm, the decision maker must make a decision as to what level of L is appropriate. In the case of earnings surprise, I make the assumption that as earnings surprise magnitude increases, the cost of a false alarm increases correspondingly. That is, if the 7
same ERC is applied as surprise magnitude increases, the cost of being wrong will increase. Thus, as the absolute magnitude of an earnings surprise increases, investors will apply a larger L to the underlying information in the surprise and want to lower the ERC to reflect this. If the relative magnitude of the surprise is small, a lower L will apply and investors will be willing to capitalize the change in earnings with a larger ERC. This type of reaction to surprise magnitude would create a market reaction function that is more steeply sloped as earnings surprise approaches zero and would flatten out as surprise magnitude increases. For example, let s assume two surprise magnitudes, 1 percent and 3 percent of share price and an ERC for persistent earnings of 5. The resulting change in price would be 5 percent and 15 percent respectively. However, if only 60 percent of the surprise is persistent, investors will lose more by applying the ERC to the greater magnitude surprise. In the case of the greater magnitude surprise, the error will cost investors 6 percent of the ex ante share price (5x3x0.4). In the case of the lower magnitude surprise, the error will cost investors 2 percent of the ex ante share price (5x1x0.4). This increased cost in applying a consistent ERC across increasing magnitudes of earnings surprise creates a higher cost of false alarm as absolute surprise magnitude increases. SDT suggests that investors would apply a higher likelihood ratio as the absolute surprise magnitude increases to compensate for the increased cost of a false alarm. This would imply a systematic under-estimation of the appropriate firm specific ERC as the absolute magnitude of earnings surprise increases. The resulting market reaction would be concave for positive surprises and convex for negative surprises. This form would occur 8
if the underlying information in the earnings surprises were the same across surprise magnitudes. Thus, barring other factors, such as persistence and precision, SDT implies an S-shaped curve when measuring abnormal returns versus earnings surprises magnitude. If SDT does apply as described here, it would create inefficiency in the market. Assuming that the market is efficient over time, it would correct this inefficiency. Thus, there would be an observable correction as more private and public information about the underlying characteristics of the earnings surprises filters into the market. The result should be varying degrees of post-earnings-announcement drift with varying degrees of surprise magnitude. IV - Hypothesis Development To test for the possibility that earnings surprise magnitude is a sufficient condition to create the non-linear S-curve, I will explore PEAD in relation to various relative magnitudes of earnings surprise. If, ceteris paribus, the market response to varying degrees of surprise magnitude creates systematic differences in the ERC based solely on surprise magnitude and not the underlying value parameters (i.e. earnings persistence and discount rate), then mispricing will occur. Market efficiency dictates that this mispricing should be corrected over time. Thus, I hypothesize that this will be reflected in PEAD. The hypothesis is as follows: 9
H 1 : Firms with earnings surprises of greater relative magnitude experience higher degrees of post-earnings-announcement drift. The returns window used by KBM is from trading day 20 to +1 relative to day 0, the day of the announcement. The window used by FT starts two days after the previous quarter s earnings announcement and ends one day after the current period s announcement. Bernard and Thomas [1990] find that the majority of PEAD occurs within the first 3 months of earnings announcements. Thus, I examine the effect of extending the window used by KBM over the three months following the earnings announcement to look for a relative difference in abnormal market returns between firms that have different magnitudes of earnings surprise. My methodology follows that of KBM to provide comparability of their S-curve. Since I want to follow the abnormal return over the three months after the announcement date I use an extended observation window including 60 trading days after day 0. Findings that flatten out the observed S-curve in the KBM would mean that at least some of the observed variation in market response to different magnitudes of earnings surprises is the result of the surprise magnitude itself. It would imply that the market increases its underestimation of the appropriate ERC that should be applied to earnings surprises as the absolute magnitude increases. Thus, SDT would not be rejected as a causal factor in the non-linear S-curve reaction to earnings surprises. 10
V - Research Design KBM get their data from First Call, Compustat and CRSP, for the period from January 1 st, 1992 to December 31 st, 1997. I will replicate their sample for comparability. KBM measure earnings surprise as actual reported EPS minus the most recent First Call consensus forecast prior to the announcement date, scaled by year-end share price. KBM calculate the returns associated with each earnings announcement as the raw return minus the value-weighted market return accumulated over a 22-day window extending from 20 days in advance to one day after the earnings announcement. I will replicate this return calculation, and will examine an extended window of 60 days after the earnings announcement 3. The 60-day time frame after the announcement is meant to capture the three calendar months after the announcement date and the majority of the PEAD as per Bernard and Thomas [1990]. Thus, including the replication, the observation windows will be 22 and 81 days, all observations starting 20 days before the earnings announcement. 3 I also replicate all of the analysis using windows including the 20 and 40 days after the earnings announcement. The qualitative results and conclusions are consistent with those found using the extended window of 60 days after the announcement. 11
VI - Sample The purpose of the sample is to capture year-end annual earnings announcement dates and measure the response to earnings surprise in relation to that date. All firm-years with a fiscal year end between January 1, 1992 and December 31, 1997 with reported actual earnings per share (EPS) were selected from the First Call Historical Database (FCHD). This resulted in a total of 32,441 observations. To eliminate earnings re-statements, I only use the first announcement for each firm-year. The sample is further reduced if required data fields to calculate earnings surprise and abnormal return are not available. The required data fields are mean consensus forecast from the FCHD, daily returns data from CRSP, and fiscal year-end stock price from Compustat. A significant number of fiscal year-end announcements on the FCHD have announcements on days well ahead of actual fiscal period end. As described in the FCHD Users guide, The Actuals table contains the actual per share numbers reported by the companies following a fiscal period end. 4 To avoid this anomaly, any observations with reported announcement dates ahead of the fiscal period were eliminated. As per KBM, the sample is then limited to observations with ES (earnings surprise scaled by price) within +/- 0.02. The sample selection process is described in Table 1. KBM s limited sample resulted in 19,383 observation or 88% of the unrestricted sample. In applying the same restriction to my sample, 87% of the observations are retained (16,831 observations). 4 First Call Historical Database User Guide, page 9. 12
Table 1 - Sample Selection Process Step Process Remaining Observations 1 Select all EPS announcements reported on the actuals table 32,441 in the FCHD 2 Eliminate observations that are not related to the first 30,937 announcement (eliminates most re-statements) 3 Eliminate observations for which no CUSIP is found in the 26,285 summary table of the FCHD 4 Eliminate observations where the values are not available 25,314 and the default value is in the mean forecast cell 5 Eliminate observations where CUSIP cannot be found on the 22,889 CRSP database 6 Eliminate observations where null observation has been 21,992 picked up by CRSP (-99) 7 Eliminate observations where CUSIP cannot be found on 21,154 Compustat 8 Eliminate observations for which the null default is in the 20,998 Compustat data item 199 cell (year end stock price) 9 A number of fiscal year end announcements on the FCHD 19,707 have announcements on days well ahead of actual fiscal period end. All observations with announcement dates in advance of the fiscal period end were eliminated. 10 Eliminate any announcements that are more than 120 days 19,301 after the fiscal period end. 11 Calculate raw ES and scaled ES 19,301 12 Sort step 11 by ES and limit sample to +/-.02 (using 9 decimal places) 16,831 (87% of step 11) The univariate descriptive statistics of this sample, along with those for KBM, are presented in Table 2. The sample shows most of the characteristics of KBM. The size measures are similar, with the means greater than the 75 th percentile for all four measures. The number of observations increases over the sample period, approximately doubling. This is consistent with KBM. The decrease in negative and increase in positive earnings surprises over the period is also consistent with KBM. They point out that this may be consistent with increased earnings management over the period. 13
However, they also show a shift to zero earnings surprise from negative earnings surprise, whereas my sample has a relatively constant percentage of observations falling in the zero earnings surprise category. In general, my sample has more positive earnings surprises, more zero earnings surprises and fewer negative earnings surprises than KBM This may be a result of the different number of observations being used in the restricted sample (16,831 versus 19,383) and may reflect some non-random characteristics of the firm-years eliminated in the sampling process. Median forecast age decreases by 4 days over the 6 years of the sample period, whereas KBM forecast age decreases by 17 days (I calculate forecast age by calendar year and assume that KBM do the same, although they do not define this). The change in KBM can be attributed to one year over year change. Between 1995 and 1996 their median forecast age declines from 35 days to 13 days and holds at the same age for 1997. This further indicates potential differences in the two data sets. To calculate the scaled earnings surprise, the different methodology for handling stock splits of First Call and Compustat must be reconciled. To adjust for the stock splits that are reflected on the FCHD, I multiply all the reported EPS on the FCHD and the related mean forecasts by stock split factors reported on the FCHD split table. This is different from KBM, who adjust the Compustat year-end stock price for stock splits. However, the resulting earnings surprise is the same. 14
Table 2 Descriptive Statistics for Observations with Earnings Surprise (ES) scaled by price within +/- 0.02 Panel A: Size Measures Percentiles n Mean Standard Deviation 1 25 50 75 99 KBM KBM KBM KBM KBM KBM KBM KBM Revenues 16673 19383 1875.7 1802.8 6256.4 6711.5 1.1 2.1 88.7 80.2 292.8 260.6 1105.3 970.1 25478.6 25438.0 Assets 16696 19383 4020.2 3973.7 18089.6 19232.6 15.1 13.6 107.1 102.4 380.9 366.6 1670.2 1512.1 72385.0 74438.0 Book Value 16689 19133 778.7 756.6 2214.6 2345.2 (12.2) 7.7 53.3 51.5 144.3 137.8 509.1 458.9 10959.0 10836.0 Market Value 16668 19383 2181.2 2028.2 7436.1 7291.1 20.0 17.4 128.4 115.2 371.5 331.1 1287.3 1117.0 33463.4 31680.8 Panel B: Descriptive Statistics Year 1992 1993 1994 1995 1996 1997 All Years KBM KBM KBM KBM KBM KBM KBM ES (n) 1,717 2,041 2,251 2,739 2,530 3,136 2,997 3,347 3,513 4,061 3,823 4,059 16,831 19,383 Mean (0.000) (0.001) (0.000) (0.001) (0.000) (0.000) (0.000) (0.000) 0.000 (0.000) (0.000) (0.000) (0.000) (0.000) Median 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Percent firms by surprise Year 1992 1993 1994 1995 1996 1997 All Years KBM KBM KBM KBM KBM KBM KBM Negative 41.9% 45.3% 39.7% 44.0% 34.8% 39.4% 34.1% 40.4% 33.4% 38.3% 32.1% 35.6% 35.1% 39.8% None 17.4% 11.9% 16.6% 12.2% 16.3% 12.1% 18.0% 12.6% 17.3% 17.3% 17.3% 16.1% 17.2% 14.1% Positive 40.7% 42.8% 43.7% 43.7% 48.9% 48.5% 47.9% 47.0% 49.4% 44.4% 50.6% 48.3% 47.7% 46.1%
Mean 22-day window return by surprise 1992 1993 1994 1995 1996 1997 All Years KBM KBM KBM KBM KBM KBM KBM Negative (0.0014) 0.0022 (0.0053) (0.0014) (0.0164) (0.0121) (0.0219) (0.0166) (0.0178) (0.0210) (0.0248) (0.0152) (0.0159) (0.0119) None 0.0084 (0.0050) 0.0155 0.0244 0.0076 0.0024 (0.0025) 0.0031 (0.0085) (0.0065) (0.0130) 0.0065 0.0037 0.0034 Positive 0.0257 0.0299 0.0172 0.0269 0.0105 0.0156 0.0195 0.0214 0.0118 0.0203 0.0049 0.0287 0.0173 0.0234 All 0.0113 0.0137 0.0080 0.0139 0.0007 0.0031 0.0014 0.0037 (0.0016) (0.0002) 0.0046 0.0095 0.0033 0.0065 Mean 81-day window return by surprise 1992 1993 1994 1995 1996 1997 All Years Negative (0.0001) (0.0103) (0.0308) (0.0019) (0.0565) (0.0519) (0.0284) None 0.0245 0.0217 0.0104 0.0392 (0.0437) (0.0257) 0.0102 Positive 0.0580 0.0379 0.0180 0.0693 (0.0135) 0.0079 0.0316 All 0.0278 0.0161 (0.0002) 0.0396 (0.0331) 0.0077 0.0068 1992 1993 1994 1995 1996 1997 All Years Forecast Age (n) KBM KBM KBM KBM KBM KBM KBM 1,717 2,041 2,251 2,739 2,530 3,136 2,997 3,347 3,513 4,061 3,823 4,059 16,831 19,383 Mean 61 61 62 61 64 62 55 59 57 28 57 28 59 47 Median 46 40 45 40 47 38 39 35 38 13 42 13 42 23 No. of Analysts 1992 1993 1994 1995 1996 1997 All Years KBM KBM KBM KBM KBM KBM KBM Mean 4.7 6.1 4.9 6.1 4.8 6.3 5.0 6.2 4.8 6.4 4.9 6.4 4.9 6.3 Median 3 4 3 4 3 4 3 4 3 5.0 3 5.0 3 4 16
a: Observations come from an intersection of First Call, Compustat and CRSP databases. All firms with reported actual EPS on the First Call Historical Database serve as the starting point for the sample. Accounting and Stock Return data comes from Compustat and CRSP over the relevant period. Observations without data in the required field, announcements more than 120 days after the fiscal period end dates and second EPS announcements (I.e. restatements) on First Call are eliminated from the sample. The result is 19,301 observations. As per KBM, observations included in this table are included for ES +/- 0.02. ES is defined as the annual per share earnings surprise divided by fiscal year-end price per share. This scaling includes 16,831 observations from the unrestricted sample of 19,301 (87%). Earnings Surprise is the actual reported EPS by First Call less the most recent average analysts forecast. Price per share is Compustat data item 199 (fiscal year-end price). b: As per KBM, size measures are defined as: Revenues Compustat data item 12, Assets Compustat data item 6, Book Value Compustat data item 199 (fiscal year-end price) times Compustat data item 54 (common shares used to calculate primary EPS). c: As per KBM,. 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, 41, 61 and 81-day window returns, by surprise is the average cumulative 22, 41, 61 and 81-day return, adjusted for the value-weighted market index, for the period 20 days before and ending 1,20,40 and 60 days after the First Call Historical database earnings announcement date. Forecast age is not defined by KBM, I calculate forecast age as number of calendar days between the announcement date and the most recent update of the mean forecast (both as reported on the FCHD). No. of Analysts is the reported number of forecasts on the FCHD as of the day of the most recent update. d: As per KBM, Years are defined as fiscal year-ends from January 1 to December 31 of the referenced year. 17
VII - Results As per KBM, the firm-years with zero earnings surprise are broken out into one portfolio. Then portfolios of 500 firm-years are created from the 500 smallest negative earnings surprises, the next 500 smallest earnings surprise and so on. The same process is done with the positive earnings surprises. The zero earnings surprise portfolio is made up of a portfolio of 2,893 firm year observations. Thus, for each portfolio of similar earnings surprises, there are two distributions of abnormal earnings one for each of the returns windows. Figure 1 presents the mean, median, 33.3 percentile and 66.7 percentile of the 22-day returns window. Figure 1-22-day Window Return 0.08 0.06 Abnormal Stock Return 0.04 0.02 0-0.02-0.01 0 0.01 0.02-0.02-0.04 Mean Median 33.3 66.7-0.06-0.08 ES Scaled by Price
Figure 1 shows the same qualitative results as KBM. The results are relatively symmetric around zero with a steeper slope closer to the origin and a flattening out as the absolute magnitude of the earnings surprise increases. Thus, although some of the descriptive statistics in the samples differ, the overall resulting S-curve is similar. Figure 2 presents the mean, median, 33.3 percentile and 66.7 percentile of the 81-day returns window. Table 2 presents a comparison of the mean and median abnormal returns of the 22-day and 81-day returns windows and Figure 3 presents the mean comparisons in graph form. Figure 2-81-day Return 0.15 0.1 Abnormal Stock Return 0.05 0-0.02-0.01 0 0.01 0.02-0.05-0.1 Mean Median 33.3 66.7-0.15-0.2 ES Scaled by Price 19
Table 2: 22-day vs. 81-day Returns by Portfolio Mean Median Mean ES 22-day 81-day 22-day 81-day -0.0169-0.0132-0.0293-0.0187-0.0428-0.0120-0.0208-0.0387-0.0142-0.0585-0.0087-0.0164-0.0151-0.0236-0.0333-0.0064-0.0212-0.0312-0.0232-0.0571-0.0046-0.0233-0.0244-0.0232-0.0278-0.0034-0.0181-0.0178-0.0206-0.0236-0.0026-0.0106-0.0260-0.0191-0.0304-0.0019-0.0131-0.0261-0.0156-0.0239-0.0014-0.0122-0.0301-0.0112-0.0368-0.0010-0.0143-0.0273-0.0124-0.0248-0.0007-0.0140-0.0262-0.0142-0.0186-0.0004-0.0120-0.0502-0.0106-0.0404 0.0000 0.0037 0.0103-0.0014-0.0057 0.0003-0.0002-0.0252-0.0046-0.0252 0.0005 0.0020 0.0011-0.0015-0.0015 0.0007 0.0112 0.0199 0.0059 0.0047 0.0008 0.0083-0.0002 0.0026-0.0006 0.0010 0.0152 0.0329 0.0109 0.0195 0.0013 0.0084 0.0163 0.0028 0.0039 0.0015 0.0194 0.0423 0.0134 0.0197 0.0018 0.0202 0.0446 0.0045 0.0289 0.0021 0.0196 0.0423 0.0080 0.0269 0.0025 0.0192 0.0328 0.0040 0.0165 0.0031 0.0205 0.0426 0.0096 0.0269 0.0039 0.0297 0.0586 0.0170 0.0239 0.0049 0.0235 0.0484 0.0129 0.0359 0.0064 0.0355 0.0721 0.0106 0.0390 0.0089 0.0156 0.0367 0.0065 0.0060 0.0143 0.0282 0.0425 0.0120 0.0022 20
Figure 3-22-day vs. 81 day window (mean) 0.08 Abnormal Stock Return 0.06 0.04 0.02 0-0.02-0.01 0 0.01 0.02-0.02-0.04 22-day 81-day -0.06 ES scaled by price Figure 2 shows that the S-curve is still evident three months after the earnings announcement. Thus, based on Figure 2, the hypothesis that PEAD occurs at a greater rate for firms with earnings surprises of greater absolute magnitude can be rejected and STD can be discounted as a contributing factor to the S-curve. Overall, the portfolios do show PEAD in the three months after the announcement date. The exceptions to this are the portfolios just over zero (mean and median) and the third largest negative surprise portfolio (mean only). Three of the four smallest positive surprise portfolios show decline between the 22-day window and the 81-day window 21
based on mean and all four based on median 5. In general, the negative quadrant shows a flattening out of the response to earnings surprise. In the positive quadrant, larger earnings surprises do show larger drift, particularly considering the negative drift of the small positive surprises. VIII - Regression Analysis To further match with the KBM study, cumulative abnormal returns (CAR) as a function of earnings surprise are explored. Given the observed S-curve, it would be expected that a regression of CAR on smaller and smaller +/- return windows would yield larger slope coefficients on ES. This result is found by KBM and is generally the case in Tables 3 and 4 (presented below). However, the smallest window seems to be affected by the decline of the observations with small positive surprises. Table 3 presents the regression including the zero surprise portfolio and Table 4 presents the regression without the zero surprise portfolio included. KBM s results are presented in both cases for comparison. Table 3: Results of CAR on Earnings Surprise Scaled by Price Panel A: 22-Day Window +/- Range of ES n ßo t o p-value ß1 t 1 p-value adjusted R 2 All Observations (Including zero earnings surprise) Unrestricted 19301 0.0017 1.779 0.075 0.0247 3.27 0.0011 0.0005 0.02 16831 0.0035 3.581 0.000 2.3711 13.07 0.0000 0.0100 0.01 15272 0.0027 2.741 0.006 4.1875 13.85 0.0000 0.0123 0.005 13057 0.0017 1.597 0.110 6.9051 12.69 0.0000 0.0121 0.0025 10297 0.0012 1.037 0.300 8.7912 8.31 0.0000 0.0066 0.00125 7194 0.0000-0.026 0.980 13.1260 5.65 0.0000 0.0043 0.000625 4700 0.0003 0.153 0.879 16.3050 2.65 0.0081 0.0013 0.0003125 3248 0.0026 1.249 0.212-9.0617-0.36 0.7169-0.0003 5 As a follow-up to the exploration of the characteristics of the returns portfolios, I explore firm size characteristics across the portfolios (not presented). The results show that the portfolios with the largest average size statistics are closest to the zero earnings surprise. 22
Panel B: KBM 22-Day Window for comparison +/- Range of ES n ßo t o p-value ß1 t 1 p-value adjusted R 2 All Observations (Including zero earnings surprise) Unrestricted 22023 0.0100 2.19 0.0029 0.11 0.0000 0.02 19383 0.0076 8.69 2.6801 15.96 0.0129 0.01 17717 0.0069 7.71 4.2647 14.99 0.0125 0.005 15422 0.0054 5.83 7.5858 15.00 0.0142 0.0025 12519 0.0047 4.56 11.6682 12.10 0.0115 0.00125 9310 0.0032 2.77 16.8585 8.58 0.0077 0.000625 6183 0.0018 1.26 24.4251 5.30 0.0044 0.0003125 3783 0.0018 0.93 37.9551 2.54 0.0014 Panel C: 81-Day Window +/- Range of ES n ßo t o p-value ß1 t 1 p-value adjusted R 2 All Observations (Including zero earnings surprise) Unrestricted 19301 0.0052 2.8082 0.0050 0.087 5.99 0.0000 0.0018 0.02 16831 0.0071 3.7455 0.0002 4.122 11.56 0.0000 0.0078 0.01 15272 0.0064 3.2494 0.0012 6.971 11.63 0.0000 0.0087 0.005 13057 0.0027 1.3013 0.1932 12.652 11.83 0.0000 0.0105 0.0025 10297-0.0009-0.4043 0.6860 19.297 9.31 0.0000 0.0082 0.00125 7194-0.0036-1.3349 0.1820 25.237 5.57 0.0000 0.0042 0.000625 4700-0.0034-1.0196 0.3080 26.324 2.19 0.0288 0.0008 0.0003125 3248 0.0047 1.1333 0.2572-31.895-0.64 0.5215-0.0002 Table 4: Results of CAR on Earnings Surprise Scaled by Price (No Zeroes) Panel A: 22-Day Window (No Zeroes) +/- Range of ES n ßo t o p-value ß1 t 1 p- value adjusted R 2 All Observations (Not including zero earnings surprise) Unrestricted 16,407 0.00137 1.284 0.199 0.02448 3.19 0.001 0.0006 0.02 13,937 0.00342 3.192 0.001 2.37100 12.98 0.000 0.0119 0.01 12,378 0.00250 2.2534 0.024 4.19270 13.84 0.000 0.0152 0.005 10,163 0.00109 0.91465 0.360 6.95090 12.82 0.000 0.0158 0.0025 7,403 0.00019 0.13742 0.891 8.99050 8.55 0.000 0.0096 0.00125 4,300-0.00272-1.5766 0.115 13.98400 6.22 0.000 0.0087 0.000625 1,806-0.00565-2.2666 0.024 19.65500 3.51 0.001 0.0062 0.0003125 354-0.00686-1.502 0.134-1.63550-0.09 0.928-0.0028 23
Panel B: KBM 22-Day Window for comparison (No Zeroes) +/- Range of ES n ßo t o p-value ß1 t 1 p- value adjusted R 2 All Observations (Not including zero earnings surprise) Unrestricted 19287 0.01100 2.10 0.00340 0.12-0.0001 0.02 16647 0.00820 8.83 2.69050 16.09 0.0153 0.01 14981 0.00750 7.82 4.26540 15.14 0.0151 0.005 12686 0.00590 5.82 7.57000 15.24 0.0179 0.0025 9783 0.00500 4.46 11.62370 12.39 0.0154 0.00125 6574 0.00320 2.39 16.88030 9.05 0.0122 0.000625 3447 0.00050 0.27 25.12230 6.09 0.0104 0.0003125 1047-0.00270-0.95 42.09670 3.55 0.0110 Panel C: 84-Day Window (No Zeroes) +/- Range of ES n ßo t o p-value ß1 t 1 p- value adjusted R 2 All Observations (Not including zero earnings surprise) Unrestricted 16,407 0.00435 2.124 0.034 0.08651 5.88 0.000 0.0020 0.02 13,937 0.00649 3.082 0.002 4.12050 11.49 0.000 0.0093 0.01 12,378 0.00551 2.505 0.012 6.99080 11.62 0.000 0.0107 0.005 10,163 0.00048 0.207 0.836 12.82300 12.03 0.000 0.0140 0.0025 7,403-0.00560-2.067 0.039 20.19400 9.82 0.000 0.0127 0.00125 4,300-0.01348-4.052 0.000 28.40300 6.54 0.000 0.010 0.000625 1,806-0.02669-5.600 0.000 39.54600 3.69 0.000 0.007 0.0003125 354-0.04246-4.093 0.000 5.11410 0.12 0.901-0.003 If the hypothesis regarding PEAD on varying degrees of ES is not to be rejected, the slope coefficients for the 81-day returns window should show a flatter trend line than that for 22-day returns as the range of earnings surprise is decreased. A comparison of the slope coefficients from Table 3 that are significant at greater than the 0.05 level is presented in Table 5 and presented graphically in Figure 4. The same is done for Table 4 in Table 6 and Figure 7. 24
Table 5 - Comparison of slope coefficients across return windows* (with zeroes) n 22-day 81-day Unrestricted 19,301 0.02469 0.0870 0.02 16,831 2.37110 4.1221 0.01 15,272 4.18750 6.9707 0.005 13,057 6.90510 12.6520 0.0025 10,297 8.79120 19.2970 0.00125 7,194 13.126 25.237 0.000625 4,700 16.305 26.324 * Significant at the 5% or greater level ß1 ß1 Slope coefficient of CAR on ES (with zeroes) 30.00000 25.00000 20.00000 15.00000 22-day 81-day 10.00000 5.00000 - Unrestricted 0.02 0.01 0.005 0.0025 0.00125 0.000625 25
Table 6 - Comparison of slope coefficients across return windows* ß1 ß1 n 22-day 81-day Unrestricted 16,407 0.02448 0.0865 0.02 13,937 2.37100 4.1205 0.01 12,378 4.19270 6.9908 0.005 10,163 6.95090 12.8230 0.0025 7,403 8.99050 20.1940 0.00125 4,300 13.984 28.403 0.000625 1,806 19.655 39.546 * Significant at the 5% or greater level Figure 5 - Slope coefficient of CAR on ES (no zeroes) 45.00000 40.00000 35.00000 30.00000 25.00000 20.00000 22-day 81-day 15.00000 10.00000 5.00000 - Unrestricted 0.02 0.01 0.005 0.0025 0.00125 0.000625 As can be seen in figure 4 and particularly in figure 5, there is no flattening of the increase in slopes when the returns window is extended to 81-day. Thus, this regression analysis does not provide any evidence to support the hypothesis. 26
IX - Conclusions The evidence presented in this paper rejects the hypothesis that post-earningsannouncement drift occurs at a greater rate for stocks with earnings surprises of a larger relative magnitude than those with earnings surprises of a smaller relative magnitude. Thus, my conclusion is that SDT does not play a role in the observed S-curve reaction of abnormal stock returns to scaled earnings surprise. Although further pursuing SDT as a factor in the market would not be worthwhile, further study of the relative degrees of PEAD of portfolios based on ES is of interest. The decline of the portfolios just above and below zero raises some questions as to why this occurred in my sample. Thus, looking at the specific underlying characteristics of these portfolios and the specific firms that make them up might help to explain this. 27
References Ball, R., and E. Bartov. How Naïve is the Stock Market s use of Earnings Information? Journal of Accounting and Economics. 21 (1996): 319-37. Bernard, V.L., and J.K. Thomas. Evidence that Stock Prices Do Not Fully Reflect the Implications of Current Earnings for Future Earnings. Journal of Accounting and Economics. 13 (1990): 305-40. Easton, Peter D., and Mark E. Zmijewski. Cross-Sectional Variation in the Stock Market Response to Accounting Earnings Announcements. Journal of Accounting and Economics. Amsterdam: Jul 1989. Vol. 11, Iss. 2,3: 117 142. Foster, G. Quarterly Accounting Data: Time-Series Properties and Predictive Ability Results. The Accounting Review.Vol.52, No. 1 (Jan., 1977): 1-21. Freeman, R.N., and S.Y. Tse. A Non-Linear Model of Security Price Response to Unexpected Earnings. Journal of Accounting Research (Autumn 1992): 185-209. Green, D.M. and Swets, J.A. (1964). Signal Detection Theory and Psychophysics. John Wiley & Sons Inc., New York, NY. Kahneman, D., and A. Tversky. Prospect Theory: An Analysis of Decision under Risk. Econometrica, Vol. 47, No. 2 (Mar., 1979), 263-292. Karim, Khondkar E., and Philip H. Siegel. A signal detection theory approach to analyzing the efficiency and effectiveness of auditing to detect management fraud. Managerial Auditing Journal. 13 (6): 367-375 Kinney, W., D. Burgstahler, and R. Martin. Earnings Surprise Materiality as Measured by Stock Returns. Journal of Accounting Research (December 2002): 1297-329. Kothari, S.P., and R.G. Sloan. Information in Prices About Future Earnings: Implications for Earnings Response Coefficients. Journal of Accounting and Economics, (June/September 1992): 143-71. Kothari, S.P. Capital markets research in accounting. Journal of Accounting and Economics. 31 (2001). 105-231. Mendenhall, R. How Naïve is the Market s Use of Firm-Specific Earnings Information? Journal of Accounting Research (June 2002): 841-63. Subramanyam, K.R. Uncertain Precision and Price Reactions to Information. The Accounting Review (April 1996): 207-20. 28
Teets, W.R., and C.E. Wasley. Estimated earnings response coefficients: Pooled versus firm specific models. Journal of Accounting and Economics, Vol 21, 1996): 279-95. 29