## impact of firm age on the stock price drift

*Statement of Originality*

This document is written by Yassine Bali (12165867) who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

**JEL Classification: G14**

Academic Year 2020 - 2021

**1. Abstract**

The Post-Earnings-Announcement Effect is a continued upwards (downwards) drift in stock price when a company publishes a substantially positive (negative) earnings report. This paper aims to corroborate previous documented evidence of this market anomaly with a distinct approach to the methodology and to quantify the effect of firm age on the drift. This entails that the benchmark to define normal returns is different from other PEAD research and in this case is defined as the average daily return of the 150 trading days ending 30 days prior to the earnings announcement. After running the appropriate tests to measure for statistically significant results with a data sample from 2010-2019, the figures showed that the models were not successful in identifying a relation between the Cumulative Abnormal Returns and firm characteristics i.e., firm age and firm size. Lastly, this study concludes with a discussion of the aforementioned results and attributes them to the use of methodology and makes recommendations for future research.

**2. Introduction**

The difference between the expected earnings for a quarter by financial analysts compared to the actual reported earnings is known as the earnings surprise or forecast error. The earnings surprise has a well documented effect that influences the stock price based on multiple factors, especially firm size, direction and the magnitude of unexpected earnings (Bernard &

Thomas, 1989), which is known as the post-earnings announcement drift (PEAD from this point onwards). The PEAD implies, in more technical terms, that in the weeks right after the earnings announcement, cumulative abnormal returns are to be made for companies that had a positive earnings surprise when taking a long position in their underlying stocks, as well as for companies that experience a negative earnings surprise when shorted. (Bernard &

Thomas, 1989). How this paper defines abnormal returns will be briefly explored later in this section, and in more depth in the Methodology section, since the benchmark used to

determine how an abnormal return is calculated might differ among different academic articles.

This study will seek to replicate previous studies (Bernard & Thomas, 1989; Foster, Olsen & Shevlin, 1984) that show a persistent stock price effect of the earnings surprise, and if such a relationship is supported by statistical evidence, this paper will research how the PEAD relates to the firm’s age. The expected findings will be reflected on later in this section and certain predictions will be made regarding the outcome of the regression results.

In addition to the aforementioned research objectives it is also worthwhile to mention that this study will contribute to the knowledge base and close the research gap by

investigating a link that had not previously been explored. The methods for this study are largely quantitative, hence the tools used will be highly accurate in quantifying the researched relationship which facilitate the interpretation of the results, provided the tests yield

statistically significant findings.

The implications of finding substantial evidence would corroborate existing literature (Bernard & Thomas, 1989; Foster et al., 1984) suggesting there are abnormal returns to be made trading this market inefficiency, hence if more investors acted upon this price pattern by taking a long or short position depending on the direction and magnitude of the earnings surprise, there are substantial gains to be made (Foster et al., 1984). Research by Ke &

Ramalingegowda (2005) proved that certain institutional investors were already engaging in trades based on the PEAD, yielding them an average annualized return of 22% accounting for transaction costs, however it is not documented if it is a popular trading strategy among retail investors. In the case that the PEAD is not widespread knowledge among retail investors and other institutional investors and it became a popular criteria for entering a trade, the effect of the PEAD could become accentuated, since it would put additional buying (selling) pressure on stocks of firms with a substantial positive (negative) earnings surprise. Furthermore, this entails that the self-fulfilling prophecy will hold, as it has been shown to affect stock price movement in the past (Wan & Yang, 2019), due to all investors having similar expectations of the short-term outcome after an earnings report. These and other implications will be further analyzed in the discussion section, where the empirical results of the event study that this research is attempting to conduct will be examined, as well as the future implications that these results bring about.

The outlook on possible results of this study regarding the post announcement effect are similar to that of other studies, in the sense that the expectation is to find evidence of abnormal returns, however the research gap relates to the effect of the firm’s age on the CARs and the methodology to determine said CARs. In addition to simply adding to the knowledge base by testing for a previously untested variable that is firm age, the data sampled will be from the time period 2010-2019, while the benchmark papers of this study, such as Bernard & Thomas (1989) and Foster et al. (1984), performed their data analysis on the time period 1974-1986 and 1974-1981 respectively. Last decade has seen substantially above average returns for the S&P 500 index, such that while the 10-year average return sits at 9.2%, the 2010-2020 period saw an average 13.6% annual return (Knueven, 2021). A potential implication for this phenomenon could be the finding of a higher magnitude PEAD for positive earnings surprise, and a less negative PEAD for negative earnings surprise compared to previous research. In essence, this paper brings a slightly different methodology to the table than Bernard & Thomas (1989) in order to test for the PEAD, and is therefore important for two reasons, to corroborate previous findings relating to this market anomaly with a differing approach, and to confirm whether firm age has any influence on the drift. The design of the event study follows a standard procedure, however the main difference with previous PEAD research is the use of the average return during an estimation period as the benchmark of normal returns, while other studies have used the CAPM valuation (Francis et al., 2007) or the equally weighted mean return on the NYSE firm size decile that a firm is a member of (Foster et al., 1984; Bernard & Thomas, 1989; Bernard & Thomas, 1990). The rationale behind the deliberate choice of a simple average over the market model will be further elucidated in the Methodology section.

This research is an event-study that aims to quantify and test the earnings surprise effect, and it will do so by following a standard structure for quantitative research papers. The Literature Review will discuss related papers, gaps in the literature and how this paper

attempts to bridge said gaps by testing multiple hypotheses. In the Data section, the origin of the data used for this study will be described, as well as the sampling method. In addition, all manipulations and transformations to the data will be disclosed to ensure full transparency, as well as the descriptive statistics of the dataset. Next, in the Methodology section, the different variables, such as abnormal returns (ARs) and standardized unexpected earnings (SUE) will be defined with mathematical formulas and a reasoning behind the choice of a certain

benchmark over another (in the case of determining abnormal returns), and lastly, we will go over the design of the event study, by explaining in a detailed manner how we are able to determine abnormal returns were to be made in the period after the event (earnings surprise) took place by running the appropriate regressions.

The Results section is the follow-up of the Methodology, where the output data of the statistical tests to prove abnormal returns could be made will be presented, together with a brief explanation of the figures and tables. The Results section is meant to highlight the most relevant findings that will be interesting for the reader, such as the answer to the question whether age has a significant effect on the PEAD, as well as the most important discoveries made after having applied the right statistical methods. The interpretation and thorough analysis of the figures and tables described in the Results segment, will take place in the Discussion section. In this fragment of the research, the empirical data will be related to the theoretical background and explore whether the results coincided with the expected findings presented in the Introduction, as well as finding out why this was the case. If the research gap has been filled as a consequence of this study, the future implications will be discussed as well as the limitations of the study due to certain assumptions that were made. Lastly, to summarize the findings and in order to provide a clear answer to all the questions posed by the researcher, the Conclusion segment will be the last section that completes this study. In this attempt to round off the research, the potential for further fact-finding to take place on the topic of the PEAD will be discussed, together with a reflection on the subject matter and insights made during the research process.

**3. Literature Review**

Multiple papers studying the PEAD factor in individual characteristics of the firms in the regression equations. The underlying assumption is that these characteristics might have an influence on the Cumulative Abnormal Returns that are to be made trading this market anomaly. The most common firm characteristics analyzed in the literature are liquidity (Chordia, Goyal, Sadka, Sadka, & Shivakumar, 2009) and firm size (Chung & Hrazdil, 2011;

Liang, 2003), however each paper on the topic of PEAD adds other previously untested variables to their respective regression models in an attempt to bridge the research gaps. As was briefly discussed in the Introduction section, the main gap that this research aims to

bridge is that of determining the impact of the firm’s age on the price drift, and it will do so by testing multiple regression models that include age as an independent variable, in addition to a sub-analysis that consists in segregating the data by age and subsequently running the regressions on the subset of the sample. After having run these tests, the answer to the

research question will likely be known and this will add to the current knowledge base on the PEAD.

In order to gain a complete understanding of the PEAD effect and the relationship with firm age, it is paramount to discuss the multiple factors that have an influence on said link. Firstly, a wealth of research has been conducted relating a firm’s age and its

performance, such as the paper by Loderer & Waelchli (2010), and while some academics have found evidence for a negative relationship between the two variables, as is the case with the aforementioned paper, such that an increase in age would in turn lead to lower

performance, a literature review by Rossi (2016) claimed that these results have been contested by other professionals in the field. Assuming that the inverse relationship holds, a negative earnings surprise could be accentuated as a function of age, such that the older the firm, the lower the cumulative abnormal returns when a negative earnings surprise has been established. The expectations would also hold for a positive earnings surprise, entailing that the younger the firm, the higher the cumulative abnormal returns when a firm experiences a positive earnings surprise. In second place, a factor that has been found to have an influence on the drift is the arbitrage risk, which Mendenhall (2004) defines as “the idiosyncratic part of a stock’s volatility that arbitrageurs cannot avoid by holding offsetting positions in other stocks or indexes” (p. 876). That same article concluded that there is a strong association between the arbitrage risk and the magnitude of the drift, which supports the underreaction hypothesis as a possible explanation for the PEAD, which will be further discussed in this section. Nevertheless, in response to Mendenhall (2004), the findings by Barinov, Park &

Yildizhan (2016) directly contradict what previous papers had uncovered regarding arbitrage risk. Barinov et al. (2016) concluded that for the same level of earnings surprise,

conglomerate or complex structure firms had a larger PEAD than simpler or single-segment firms, which in turn opposes the idea of limits-to-arbitrage since conglomerates tend to be larger on average than simple firms. Despite this contradiction, both ideas still share the idea that these theories are rooted in the underreaction hypothesis. Specifically, it is more

complicated to comprehend firm specific earnings from conglomerates, thus leading to slower information processing and an underreaction to the surprise in earnings (Barinov et al., 2016).

The relevance of investigating a link between the drift and firm specific

characteristics is not overshadowed by the potential gains that are to be made if an investor decided to actively trade this market phenomenon, and hence before moving to the

explanations for the drift, the firm specific factor of size, commonly measured by total assets under the company’s control or market value of common equity (Bernard & Thomas, 1989), will be further discussed. Predicting the Cumulative Abnormal Returns with a regression model and assessing which variables included in the analysis yield the most explanatory power is a solid manner of uncovering how and why the PEAD effect persists. In the

literature around this topic, firm size is commonly used as a control variable (Barinov et al., 2016; Ng, Rusticus & Verdi, 2008; Bhushan, 1994) and it has also been found to have an inverse relationship with the stock price drift. The implication is therefore that taking a long position in small firms that had a large positive earnings surprise and a short position in those small firms that experienced a large negative earnings surprise would yield an investor an abnormal return of 5.3% in the 60 days after the announcement date, while the same strategy for medium-sized companies averaged around 4.5% and only 2.8% for large firms (Bernard

& Thomas, 1989). In essence, firm size is seen as a strong predictor of Cumulative Abnormal Returns in the PEAD literature.

A wide variety of hypotheses exist surrounding the true drivers of the PEAD, and while they all make a compelling case, a realistic presupposition is that they might all contribute to the drift of the stock price after an earnings surprise. Therefore, it is of high relevance to discuss the main hypotheses in order to further give a solid theoretical base to this study:

1. Naive Expectations: Bernard & Thomas (1990) concluded in their research that naive expectations were likely one of the reasons for the existence of the PEAD, since investors believe that future earnings will be equal for the same quarter of the previous year.

2. Underreaction: Multiple papers seem to point towards the underreaction hypothesis as the best explanation for the stock price drift after a significant earnings surprise. This hypothesis explores the possibility that the market fails to acknowledge all the implications of the current earnings for future earnings (Bernard & Thomas, 1989).

As was previously discussed, researchers aiming to analyze what variables influence the direction and magnitude of the drift also found evidence of alternative

explanations surrounding the PEAD that reinforce this underreaction hypothesis (Barinov et al., 2016; Mendenhall, 2004). In an effort to fully comprehend this explanation, Choi & Kim (2001) researched the relationship between the level of saliency of the news and the drift, to which they found that news that was not clear or salient accentuated the PEAD effect since it caused an underreaction due to investors not fully understanding the implications of the news piece. The perceived clearness of news could hence be a major factor that fuels the underreaction by market participants as a result of their own interpretations of said news pieces (Choi & Kim, 2001).

3. Transaction costs: While transaction costs are not included in the main analysis of many papers, they are of high relevance when it comes to actually designing a profitable trading strategy that aims to exploit the PEAD. The results of the paper by Ng et al. (2008) concluded that when accounting for these costs, the abnormal returns are significantly reduced, and that transaction costs not only explain the persistence of the PEAD, but likely also its existence.

One of the hypotheses to explain the PEAD that was not discussed was quite an intuitive one, which is that of individual investors having an influence on the drift, nevertheless this theory was disproved by Hirshleifer, Myers, J. N., Myers, L. A., & Teoh

(2008) in their exhaustive research which concluded that individual investors were actually net buyers after both a positive and negative earnings surprise. A common critique to the PEAD is its violation of the strong, or at least semi-strong form of the efficient market hypothesis, which entails that the stock prices should experience a quick reaction to any new information publicly available to investors (Mendenhall, 2004). By the aforementioned definition, an earnings surprise ought to classify as an event that should undergo a price correction quasi-instantaneously, nevertheless evidence points towards the drift continuing weeks or even months after the earnings announcement (Livnat & Mendenhall, 2006;

Bernard & Thomas, 1990).

**4. Data**

The data employed by this study is a randomized sample of 254 firms that have reported quarterly earnings in the period 2010-2019, ranging from small to high market capitalization companies, extracted from the CRSP, COMPU-STAT, I/B/E/S and Factset databases.

After polishing the data and eliminating incomplete data points surrounding the events, 152 firms remained, for a total of 635 events of interest, the latter being an event which classifies as the lowest or highest decile ranking by the key variable called Standardized Unexpected Earnings (SUEs).

The specific variables of interest that are necessary to run the tests are daily returns of the given stock. Next, the earnings announcements had to be obtained, and matched with the analysts earnings forecasts. This data was later converted into SUEs , which will be covered in the next segment. Subsequently, other firm specific characteristics are gathered that will be used in the regression analysis:

1. Firm age: In order to run the regression, we need at least one independent variable which we believe has an effect on our dependent variable, the abnormal returns.

2. Firm size: This control variable is meant to capture differences in returns that might have been generated by the fact that a firm is larger/smaller.

3. SUE ranking: This variable is needed to divide the data in order to test for abnormal returns, and ranges from 1 to 10, however only the values 1 and 10 are of interest to this study.

All of the previously mentioned data that was gathered, was compiled with a Python script into an excel sheet for clear visualization of the data points and further statistical tests. Next, the descriptive statistics are discussed.

**4.1 Descriptive statistics**

The descriptive statistics of the variables for the sample used are the following: The dependent variable for the regressions analyses which were conducted , Cumulative

Abnormal Returns (M = -.0082, SD = .2576), had a median value of -.0030, a range of

2.3268 and a sum equalling 5.2197. For the independent variables, the results were as

follows: Standardized Unexpected Earnings (M = -14. 52, SD = 17.41) had a median value of -20.99, a range of 96.59 and a sum of -9217.48; Firm Size (M = 1086932, SD = 1208628) had a median of 627374, a range of 7723695 and a sum of 6.9E+08; and lastly Firm Age (M

= 33.26, SD = 27.75) had a median value of 26, range of 155 and a sum of 21121. All the previous variables mentioned had a count of 635 entries, meaning that there is no incomplete data on the firms in the sample, since the companies that had missing data were left out from the statistical analyses. The descriptive statistics are summarized in table 1.

**5. Methodology**

As was previously mentioned in the structure segment of the Introduction section, the

Methodology aims to explain the methods used in order to test the hypotheses presented. It is a detailed guide that could be used by other researchers to replicate the results of this study, as well as for readers to assess the validity of the (mathematical) tools employed to obtain said results. In this section we will define the variables that are included in our statistical analysis, and subsequently we will tie all the elements in together and dive into the process of establishing abnormal returns for this specific event-study.

**5.1 Estimation Procedures**

There exists a wide array of methods of defining abnormal returns, however they all boil down to a simple subtraction: The actual returns on a given day (as reported in the gathered data) minus the expected return for that same day. Where studies differ, is in

estimating what consists a reasonable expectation of a daily return for a particular stock, and while some studies use the market return of the day, or the CAPM valuation(Francis, Lafond, Olsson & Schipper, 2007)which takes the market return of the day, the beta, alpha, and risk-free rate as inputs, this research will use the average return over an estimation period as the benchmark return. The choice of the average market return of a stock as the benchmark relates to the nature of scientific research itself, which aims to empirically test previously untested hypotheses. In this case, this paper’s goal is to make use of a benchmark that is not common in PEAD literature and to assess whether this PEAD effect is still found to be statistically significant with this new definition of normal returns. In addition, a small

quantity of papers such asKim, D., & Kim, M. (2003)have claimed that the PEAD is a result of the choice of methodology and that there is no evidence of abnormal returns to be made, and hence opting for the same methodology used by Foster et al. (1984) and Bernard &

Thomas (1989) would not add any new results to the current knowledge base. Nevertheless, by selecting this distinct benchmark we can investigate whether the PEAD effect persists with the alternate methodology. Consequently, the estimation period for determining normal returns will be a 150-day timespan ending 30 trading days prior to the event date, when the earnings surprise is announced. The post-event window where the performance of the stock will be monitored is 60 trading days after the event date, not including the day itself since it is not clear whether the announcement was made before, during or after the market activity for said day. Abnormal returns are defined as follows:

where

*The return on day t of firm i.*

𝑅 𝑖,𝑡 =

*= The average return of firm i during the 150-day estimation period ending 30*
𝑅 𝑖

days prior to the event.

Once we have calculated abnormal returns (ARs) for each of the 60 days after the event, the Cumulative Abnormal Returns (CARs) will simply be the addition of all the individual ARs, hence:

where

= Time period of the event window, in this case 0 and 60 respectively 𝑡 1, 𝑡

2

The null hypothesis hence for this experiment is captured in the following simple equations based on the SUE ranking:

where

= Cumulative abnormal returns for the bad news decile, i.e. lowest 𝐶𝐴𝑅𝑠 𝑑𝑒𝑐𝑖𝑙𝑒 1

decile of the SUE ranking

= Cumulative abnormal returns for the good news decile, i.e. highest 𝐶𝐴𝑅𝑠

𝑑𝑒𝑐𝑖𝑙𝑒 10

decile of the SUE ranking

Lastly, the SUEs, which is the most popular measure and proxy for an earnings surprise, and in this study is calculated as the difference between the actual earnings and the forecasted earnings, measured by EPS, divided by the standard deviation of the forecast errors. In the case that there is more than one forecast for a quarterly earnings report, the average of all the earnings forecasts will constitute the variable of forecasted earnings.

Hence, the equation is as follows:

**5.2 Event study design**

First and foremost, in order to prove the alternative hypothesis to the null hypothesis presented above, an independent sample T-test is run to provide statistical evidence that the CARs are significantly different from zero.

If the CARs are found to be statistically significant, it would be possible to build a portfolio by splitting the firm in one of ten deciles ranked by SUE that holds an

equally-weighted long position in the first decile of stocks, and an equally-weighted short position in the last decile, which would be held for 60 trading days from the event day. In order to qualify as an event that will be analyzed, daily return data must be available for the 180 days prior to the event day until 60 days after said date to calculate ARs, as well as the SUE of that quarter, in addition to the firm’s individual characteristics. Only when all of this data is gathered, it is possible to properly construct the event.

**5.3 Regression Models**

After designing the event-study and extracting the relevant CAR data for the targeted time frame, multiple regression will be run with firm age and SUE as the independent variables, firm size as a control variable, and CARs as the dependent variable, with the null hypothesis being that firm age has no effect on the CARs. The regressions will take place in

two steps: the first step will regress a short model (only firm size and firm age as independent variables) (6) and a long model (7) which also includes SUEs. The multivariate regression equations are the following:

where

= Intercept or constant β 0

SIZE = Firm size, calculated as the market capitalization as of 2015

AGE = Firm age, calculated as the difference between 2015 and the founding year of the firm

= Error term ϵ

The second step is to split the data into young and old firms. The firm’s age is sorted in ascending order from young to old, and the first half qualifies under young, while the second half qualifies under the dummy variable old. Consequently, the long regression model will be applied to both splits of the data in an attempt to find evidence of statistically

significant results.

The interpretation of the regression models are an important aspect that ought to be tackled before proceeding to the Results section. The x-on-y effects are straightforward to interpret, due to the fact that no logarithmic manipulations to the data took place (which would result in the interpretation being in percentage points). Thus, if the model is found to be significant, the values of the beta coefficients of the IVs (Age, Size & SUE) in each regression model indicate the average change in the DV (CAR) for a single unit variation of said IVs, holding the other variables constant. As for the diagnostics checking of the

regressions, the standard assumption of independence, normality, homoscedasticity and linearity hold. The problem of outliers was first thought to pose a threat to the validity of the study, however there was only presence of weak outliers (defined as a value between 1.5 and 3 times the interquartile range plus the third quartile value; and a strong outlier being a value that exceeds 3 times the IQR plus the third quartile) in the dataset used for the regression analysis. Lastly, the assumptions relating to the error term are that its mean is zero and that it has no correlation with the IVs. Furthermore, a result for the error term should not be able to predict the next error term, and it also must have constant variance. There are no indications to assume that any of these assumptions are violated in the regression models constructed and hence do not pose a threat to the internal validity of the paper.

**6. Results**

The Results section is the segment of the research where the figures corresponding to the statistical tests explained in the Methodology are presented. The tests and data handling were conducted rigorously to avoid any possible problem stemming from the misuse of the figures.

The results will be presented in three segments: evidence of CARs, testing two regression models and age-based regression.

**6.1 Evidence of CARs**

Two independent-samples t-tests were run with the goal to examine whether the CARs in each decile group were significantly different from zero. For the decile 1 t-test, there was no significant difference with zero (M = .003862, SD = .1247), with the conditions: t(df

= 369) =.5958, and two-tailed p-value = .5517 , and hence the null hypothesis for equation 3 cannot be rejected. The second test was based on decile 10, and there was also not sufficient statistical evidence to reject the null hypothesis (M = -.02477, SD = .3696), with the

conditions: t(265) = -1.0926, p = .2756. These conclusions suggest that engaging in a trading strategy based around the PEAD that would short the lowest decile and long the highest decile in the SUE ranking would not yield any abnormal returns different from zero. Initially, these findings put in doubt previous research regarding the PEAD effect such as Bernard &

Thomas (1989). These results can be examined in table 3.

**6.2 Testing two regression models**

The results for the short model (N = 635, df = 634) yielded an R Square value of .0013, however the model did not result in any statistically significant results since F = .4148, and its significance value was .6607. The individual components of the multivariate

regression also did not yield statistically significant results, since Firm Size had a t Stat of .3428, p = .7319, and Firm Age had a t = -.8876, p = .3751, both with 95% confidence. The conclusion is therefore that the short model was not able to explain any relationship with

CARs, with the figures summarized in table 3. These results imply that based on this model, the stock price drift does not vary with the age or size of the firm. The results for the variable Size match those found by Liang (2003), which also found no evidence of a significant effect of firm size on the CARs. Nevertheless, these findings do contradict the conclusions of Bernard & Thomas (1989) which defended that the drift and firm size have a significant inverse relationship, which was discussed in the Literature Review section.

The results for the long model (N = 635, df = 634) yielded an R Square value of .0043, however the long model did also not result in any statistically significant results since F = .9119, and its significance value was .4348. The individual components of the

multivariate regression also did not yield statistically significant results, since Firm Size had a t = .1443, p = .8853, Firm Age had a t = -1.1876, p = .2354, and SUE had a t = -1.3802, p = .1680, all with 95% confidence. The conclusion is therefore that the long model was also not able to explain any relationship with CARs, with the figures summarized in table 4. In economics terms, after factoring in multiple variables, the earnings surprise was not able to predict the Cumulative Abnormal Returns, indicating that the PEAD effect is not present in this dataset.Zhang, Cai & Keasey (2014) found that under specific conditions this PEAD effect persists, however when other factors such as transaction costs where included, the event-study approach used by the aforementioned paper concluded that the abnormal returns were illusionary, which was also the case when the regression of the long model was run.

**6.3 Age-based regression**

For the following regressions, the data was separated in half into a young and an old group. The results for the long model of the old half of the sample (N = 317, df = 316) yielded an R Square value of .01667, and however this sub-analysis regression did not result in any statistically significant results since F = 1.7677, and its significance value was .1532, it was the model that was the closest to achieving significance of the four regressions that were run. As for the individual components of the multivariate regression, two variables yielded no statistically significant results, since Firm Size had a t = -.9771, p = .3293, Firm Age had a t =

-.9616, p = .3370, however the SUE was significant at the p < .10 level, and it had a t = -1.8650, p = .0631 and a beta coefficient of -.0011. The conclusion is therefore that the long model for the old sample was also not able to explain any relationship with CARs for the model as whole, however for the SUE component it can be concluded that for a one full point increase in the SUE score, the CARs ought to reduce by .0011, with the figures summarized in table 5. Interestingly enough, while SUEs were not deemed as a reliable predictor of CARs in the simple long model, it did yield significant results when only the older half of the sample was taken into account, which entails that the relationship between SUEs and CARs is moderated by the firm’s age.

Lastly, the results for the long model of the young half of the sample (N = 318, df = 317) yielded an R Square value of .0069, however this long model did also not result in any statistically significant results either since F = .7255, and its significance value was .5374.

The individual components of the multivariate regression also did not yield statistically significant results, since Firm Size had a t = .9725, p = .3315, Firm Age had a t = -.9520, p = .3419, and SUE had a t = -.5460, p = .5854, all with 95% confidence. The conclusion is henceforth that the long model of the young half of the sample was also not able to explain any relationship with CARs, with the figures summarized in table 6. These results still support the fact that there is a moderation effect taking place, however it is only significant with a higher value for the firm’s age.

The correlation matrix of all the independent variables yielded no correlations and hence no potential multicollinearity issues. This would have been the case if the SUE Ranking variable was also included, since the SUE score directly influenced what decile the firm would be part of, and hence have a high correlation.

**7. Discussion**

After having performed all necessary statistical tests in order to properly analyze the data compiled for this study and presented said figures in the Results section, the interpretation of these numbers are part of this Discussion section. However, not only the interpretation will be discussed in this segment, but also the implications of these results, and make appropriate comments relating to the findings.

During the sub-analysis in the form of a regression with only the older half of the sample, there was evidence of significance for SUEs at the p < .10 level. This paper makes a distinction between three possible significance levels, p < .01, p < .05 and p < .10, and the validity of the results increase with the lower p values, however this result is still considered significant. The implicit conclusion of these figures is that there might be a non-linear relationship between SUEs and CARs, as a function of age. This entails that the PEAD is exitstant only for older established firms, and not for younger firms, because in contrast, the p value for SUEs in the young sample was far from significant at p = .3419. A possible

explanation could be that young firms don’t have as predictable earnings as firms which have existed for a substantial amount of time since they are still trying to find their place in the market, as well as the difficulty for analysts to forecast the earnings properly due to the fact that a young firm has published only a handful of quarterly earnings. However, since most results for the statistical analyses yielded no significant results, the reasons behind these findings will be discussed in more depth.

A possible first line of reasoning for why there was hardly any evidence of a positive or negative relationship between SUEs and CARs could have to do with the dataset used because the tests were run on data from 2015 to 2019, which is a different timespan used by the benchmark papers of this study. Nevertheless, a better backed reasoning path is that of the differences in methodology between previous studies. Even though there was no test that resulted in a statistically significant result, it is notable that the average of the CARs or CAAR resulted in the contrary of what the hypotheses stated in the introduction were aiming at proving. This was in the form of a negative CAAR for the good news decile, and positive CAAR for the bad news decile, and is most likely to be explained due to the fact that the price movement of an earnings surprise is not only present in the post-event window, however it is also quite relevant in the time period that this paper used as the estimation period for calculating normal returns, as can be seen in the graph presented in Foster et al.

(1984, p. 589) of the drift before and after the event. In said graph, it is clear that not only is there some price action before the event, but that most ARs are realized before the event itself, a phenomenon that could be linked to insider trading since the management has information on the earnings report before it is in fact published.

Since for decile 10 SUE ranking firm-quarters the market already expected a positive surprise, the normal returns calculated in the estimation period were overestimated, and since the abnormal returns were calculated as the actual returns minus the normal returns, the

CAAR was negative for firm-quarters that fell into the aforementioned category due to the overestimation being as substantial as it was. In order for this reasoning to be correct, we would expect similar results for decile 1 SUE ranking firm-quarters that experienced an extremely negative earnings surprise. As was presented in the Results section of this research, the CAAR of holding a stock in the decile 1 portfolio for 60 trading days was in fact positive, as opposed to prior expectations. The rationale behind these results are equivalent to as to why the CARs were negative for holding the decile 10 portfolio, nevertheless in the case of the decile 1 portfolio, the normal returns were considerably lower in the estimation period since the negative drift had already commenced, and said drift continued after the event, however not at the same rate. The result of this was that normal returns were largely negative, and as was mentioned the formula for abnormal returns subtracts normal returns from actual returns, hence resulting in positive CARs. For the sake of scientific accuracy, it is reiterated that the t-tests delivered no significant results, and these lines of reasoning are based simply on the CAAR values from the data sample.

Finding substantial evidence for the existence of the stock price drift could in fact be dependent on the benchmark used by the researcher, and since abnormal returns are quite relative to their respective benchmark, this could introduce a bias for any researcher that is actively investigating the existence of abnormal returns PEAD. The implicit desire of most researchers is to find statistical evidence for their hypotheses, however if this leads to said individuals and teams to only make use of the data and specific benchmarks in an attempt to achieve this at all costs, the validity of the studies surrounding this topic could be put in jeopardy. The most common types of benchmarks used to define normal returns are the equally weighted mean return on the NYSE firm size decile that a firm is a member of (Foster et al., 1984; Bernard & Thomas, 1989; Bernard & Thomas, 1990) and the CAPM valuation(Francis et al., 2007), as well as the three-factor model as described by Fama and French (1993). To further back the claim that the choice of methodology influences whether the researcher is able to find evidence of CARs, the paper byKim, D., & Kim, M. (2003) used the three-factor model and added a risk factor to explain the PEAD, to which they concluded that a majority of significant PEAD results from previous papers were the consequence of using misspecified models and not properly adjusting for risk.Next, the limitations of this research approach will be discussed.

The biggest threat to the internal validity of this study is that of the hindsight bias while testing for abnormal returns, such that the portfolio assignment is based on data that was not yet available at the time of the earnings announcement. In order to mitigate this highly relevant threat, certain measures had to be taken before running the appropriate

regressions. As was mentioned in the Data section, the time horizon of the sample used spans from January 2010 until December 2019. This data however was separated into a training set, consisting of earnings announcements and their respectively calculated SUEs from 2010 up until 2015 amounting to 50% of all the earnings announcements; and a test set, with the remaining data points from 2015 until 2019. From this point, the assumption is that the portfolio is being constructed in the year 2015 based on the previous 5 years of SUEs. The SUEs of the training set are placed in ascending order and separated into deciles, while noting

the exact cut-off value for each decile, hence knowing under what decile ranking (1 to 10) each SUE of the test data would fall under. This is necessary because the aim of the portfolio that is constructed is to long (short) the decile with the highest (lowest) SUEs.

After having knowledge of the medium to avoid this hindsight bias, the next step was simply to iterate through the test data, and as was previously mentioned, assign the SUE ranking based on the training data decile cut-off values. In other words, our hypothetical investor would only base his/her decision on data that was available at the time of entering the trade, and these cut-off values were not adjusted as the time passed in an effort to simplify the trading strategy and to avoid constant recalculation of SUE deciles, that way matching the realistic actions of the average investor.

Another limitation was the incomplete data that was downloaded from the CRSP and I/B/E/S databases, from which daily return data and certain earning announcements were missing respectively. To solve this issue, firm data from which there was unavailable

information was eliminated from the excel file containing all the figures. In addition, an event consists of an earnings announcement in the 1 or 10 decile ranking, as well as data of the daily returns on the 180 days prior until 60 days after the announcement. Hence, if information of only one of these variables was missing, it would not be used for the calculation of CARs. In total, 635 events were identified that qualified under these strict criteria. With these details in mind, we can proceed to the Conclusion section to finalize the discussion with future implications of the finding in this study.

**8. Conclusion**

This quantitative research conducted by this paper has resulted in more questions than answers, and for this not to be the case for future studies, it is recommendable for future PEAD researchers to agree on a benchmark that does not overstate or understate the true returns that could be made by exploiting this market anomaly. In addition, this paper

recommends and encourages more research in the form of a comparison of a wide variety of (substantially different) benchmarks for normal returns, to observe whether the PEAD is still significant across all these methodology options.

The models used for the regressions did not deliver significant evidence for the drift of the stock price in the aftermath of a large positive or negative earnings surprise, yet it raised many interesting questions regarding the shortcomings of certain methodologies used and the possible selection bias of the researchers in question. Nevertheless, as was mentioned in the discussion, this is not the first study to pose critical questions relating to the true reason for the existence of an observable price drift. This however does not invalidate all previous studies that claim abnormal returns are to be made, it merely entails that more research is always welcome in order to get a complete picture of all the intricacies surrounding the Post-Earnings-Announcement Effect. Notwithstanding, for the time being controversy is bound to persist.

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