Post-Earnings Announcement Drift in Denmark

Transcription

1 Post-Earnings Announcement Drift in Denmark An efficient stock market should quickly adjust market prices with the release of new information. How will the Danish stock market react with the release of earnings announcements and is there a potential profit? Author: Supervisor: Jeppe Vestrup Skivild MSc (Econ.) Finance and International Business Exam number: Associate Professor, Jan Bartholdy Department of Economics and Business School of Business and Social Sciences Aarhus University November 2013 Word Count: excl. Appendices

2 Abstract The Post-Earnings Announcement Drift (PEAD) has been analysed for many years on the American stock exchanges. However, the amount of European studies is limited. The PEAD is a decisive piece of evidence against an efficient market if found to be significant. This study analyses the PEAD on the Danish stock exchange in the period from The characteristics of this study are that it is performed on a small stock exchange, where generally PEAD studies have been performed on the major stock exchanges. A test on whether the Danish stock exchange reacts to newly released information is also conducted. The main objective of a PEAD study is to test for market efficiency so a market reacts swiftly to the release of new information (e.g. earnings announcements). The methodology is constructed by both older and recent studies on PEAD, where a method of three estimated measures which each captures different parts of the newly released information are ranked into ten portfolios 1. The portfolios abnormal returns are followed over 90 days and tested whether these are significant, especially the cases of extreme bad news and good news portfolios. The event study framework is supported by tests for normality along with four parametric and three non-parametric tests to provide the most reliable results. The Danish stock exchange is found to react significantly to the release of earnings announcements - hence it reacts to new information. This study documents evidence of the existence of PEAD on the Danish stock exchange up till 90 days after an announcement. This result should be taken with caution since this is only found for one of the measures, where the two remaining measures do not show significant evidence of PEAD in either of the tested event windows. These two measures are considered to be of lesser value, because one is too small in sample size and one is capturing too much different information. Therefore, the main conclusion is that PEAD exists on the Danish stock exchange. Several regressions on the above results are performed to provide insights of the causes for PEAD, but the only significant variable is based on past returns, therefore this indicates that past abnormal returns can explain future abnormal returns. The results also undergo several robustness checks, but these do not change the main conclusion. 1 A portfolio refers to a grouping of stocks. Page 2 of 113

3 Table of Contents Part Introduction Research Design What is Post-Earnings Announcement Drift? Motivation Problem Area Problem Statement Methodology Structure Part Literature Review Causes for Post-Earnings Announcement Drift Evidence of Post-Earnings Announcement Drift in European Region United Kingdom Spain Sweden and Finland Germany Belgium and Poland International Studies including European Countries Evidence of Earnings Announcements in Denmark The Efficient Market Theory Part Methodology The Earnings-, Price- and EPS-measure Event Study and T-tests Event Windows The Event Study Model Parametric T-Tests T0: T-test with Crude Dependence Adjustment T1: T-test with Adjusted Cross-Sectional Independence T2: T-test with Standardized Abnormal Return T3: T-test with Adjusted Standardized Abnormal Return Non-Parametric T-Tests Page 3 of 113

4 3.4.1 T4: Rank Test T5: Sign Test T6: Generalised Sign Test Performance of the T-tests and Normality A Test for Reaction to New Information Data Selection Part Empirical Results Descriptive Statistic Empirical Results of Normality Tests Reactions to Earnings Announcements Empirical Results of the Earnings-Measure Empirical Results of the Price-Measure Empirical Results of the EPS-measure Discussion about the Empirical Results Regression Results of the Basis of Portfolios 1 and Robustness Checks Part Final Conclusion Implications and Further Research Part References Appendix Page 4 of 113

5 LIST OF TABLES Table 1 - Test of Earnings Expectation Models Table 2 - Correlation Matrix Table 3 - Descriptive Statistic Table 4 - Normality Test Table 5 - Empirical Results for the Earnings-Measure Table 6 - Empirical Results for the Price-measure Table 7 - Empirical Results for the EPS-measure Table 8 - Regression Results Table 9 - Empirical Results for the Sample Size Check Table 10 - Case Specific Test of PEAD Table 11 - Empirical Results for the Raw Return Check LIST OF FIGURES Figure 1 - Overview of PEAD studies in Europe Own Creation Figure 2 - Efficient Market Theory Own creation Figure 3 - Methodology Overview Own Creation Figure 4 - Overview of the Measure Processes Own Creation Figure 5 - Event Windows Own Creation Figure 6 - The Earnings-measure s sample selection of earnings announcements Figure 7 - The Price-measure s sample selection of earnings announcements Figure 8 - The EPS-measure s sample selection of earnings announcements Figure 9 - Earnings Announcements per month Figure 10 - Q-Q Plots for Normality Figure 11 - Market Reaction to Earnings Announcements Figure 12 - Market Reaction to Earnings Announcements per Quarters Figure 13 - Hedge Graph of the Earnings-measure Figure 14 - Case Specific Test of PEAD CD CONTENT Three folders with ten spreadsheets for each measure. A folder with the spreadsheets for the ranking used for each measure. A spreadsheet with all the earnings announcements dates. A folder with all the results from Eviews. Test results for the Reaction to new information. An overall spreadsheet with all the empirical results. Page 5 of 113

6 PART 1 1. INTRODUCTION The Post-Earnings Announcement Drift (PEAD) was discovered by Ball and Brown in 1968 and it is still one of the most robust discoveries in the financial markets. The phenomenon was discovered when testing for market efficiency. Ball and Brown (1968) were estimating how fast a financial market incorporates new earnings information into the stock prices. They found an upward drift much longer than expected in stock prices after a good news earnings announcement and a similar downward drift for a bad news announcement. At that time they realised they might have discovered one of the most damaging arguments against the efficient market theory and also a possibility for profitable exploitation of this gap in the market. Generally, a study of market efficiency was formed on the idea that the earnings announcement was telling the stock market and that the market should quickly react to this new information. The theoretical conception is that investors should react rationally to new information and therefore the actions after an announcement should be swiftly reflected in the stock prices. However, the real-life picture is different from the theoretical conception, and studies have shown that investors have a tendency to await forecast analysts updates and, therefore miss out on an amount of profit when the information to make a rational decision was available to the investor (Dische, 2002). Another possible explanation is the simple fact that an investor has higher trust in their intuition, and thereby makes an irrational decision (Forner et al. 2009). The studies on PEAD have been repeated several times in the American stock exchanges and these studies showed complimenting results (Foster et al., 1984: Bernard and Thomas, 1989: Chan et al., 1996). The PEAD can be exploited by investors and studies have reported annualized return before transaction costs of 25% (Foster et al., 1984), 19% (Bernard and Thomas, 1989) and 10.8% in the UK (Liu et al., 2003) by forming a hedge strategy 2. However, the questions of why and where the abnormal returns from the PEAD originates are still a puzzle to be solved. 2 Hedge Strategy: This strategy is built on the concept of decreasing the risk, as e.g. a trader will buy an amount of shares of a specific stock and then make a future contract of selling the stocks at a set price, and then the trader will not be influenced by the stock declining, because of the previously agreed selling price in the future contract. In PEAD a trader will buy the good news stock and make contract for a put option to sell the bad news stocks at a set price, therefore when the bad news declines in price, then the trader can sell at the agreed set price. Page 6 of 113

7 Though, there are mainly three groups of explanations: a price delayed response, a risk premium or a behavioural finance perspective of investors not acting rationally. Each explanation has been discussed and investigated several times, but the specific causes are still not agreed upon (Kothari, 2001). The European literature on PEAD is characterized by diversity in conclusions, yet most of them point in the same direction as the American studies. Therefore, there is a need for further research of the European markets on PEAD. There have been several studies on the major stock markets on PEAD, but the literature on small stock exchanges such as the Danish stock exchange is in short supply. The Danish stock exchange is generally considered to be efficient and therefore it should not suffer from PEAD. Hence, the aim of this study is to investigate this assumption by performing a full analysis of the existence of PEAD on the Danish stock exchange RESEARCH DESIGN WHAT IS POST-EARNINGS ANNOUNCEMENT DRIFT? It is central to define what PEAD is, since the scope of the study is to investigate the phenomenon. In the literature different definitions are used to refer to the same phenomenon. Examples are earnings momentum, standardised unexpected earnings (SUE) effect or earnings surprise, all of which have only mild differences. Firstly, I have chosen in this study to use the term PEAD as in Bernard and Thomas (1989), because their study on PEAD in the US market generally is considered an authoritative study on PEAD. Secondly, the PEAD is defined in this study as: Post-Earnings Announcement Drift is the systematic pattern of a stock s abnormal return to drift in the direction of an earnings surprise for a period of time subsequent an earnings announcement. It is implicit in the definition that the earnings surprise is the extreme case of good news or bad news and a period of time referred to is longer than a couple of days MOTIVATION I was first introduced to PEAD in the article by Bernard and Thomas (1989) where they investigated the PEAD on the New York Stock Exchange (NYSE) with the event study framework. The financial literature on this subject is comprehensive, but there is still a lack of a profound investigation of the Danish market and I was motivated to fill this gap in the literature. Former studies within this area in the Danish market are compiled by few studies, which examine the Page 7 of 113

8 information content of annual earnings announcements and how it is incorporated into the stock return in the first couple of days after the announcement (Sponholtz, 2005: Lønroth et al., 2000; Sørensen, 1982). After performing an extensive literature review I have not been able to find a specific study seeking to test for PEAD in Denmark. Therefore, I am inspired to investigate this matter further and both adding to the out-of-sample evidence and the financial literature on PEAD in the small traded Danish stock exchange PROBLEM AREA The financial literature has proven that PEAD is found to be present in a majority of the financial markets. Therefore, I do not expect the Danish market to differ significantly, and in line with my expectations a dissertation by Sponholtz (2005) has concluded that the Danish market is inefficient. This might point in the direction that PEAD could also exist in Denmark. Another Danish study found the market to also be inefficient (Lønroth et al., 2000). Whether the effect of the PEAD will be as significant as in former studies is an open question, and therefore also the question of relevance for whether it could be a profitable phenomenon for investors. Denmark is ranked as number one in E-readiness by the Economist Intelligence Unit and IBM Institute for Business Value, which is the ability to use and process information and communication technologies. This ranking owes to the Danish stock exchange being a highly technologically developed environment and therefore information is provided quickly to the investors without delays. This could raise doubts whether Denmark might be a special case, where information is processed faster into the stock prices. This study will estimate three different measures, which each capture an explicit part of the earnings announcements and thereby the new and unexpected information to the market. The first measure is the standardized unexpected earnings measure 3 (Earnings-measure), which ranks the difference between the actual earnings and expected earnings scaled on their standard deviation of past earnings. The price-measure ranks on the basis of the four days abnormal returns surrounding the earnings announcement and the last measure is based on the analysts forecasts of earnings per share (EPS) ranked according to actual figures scaled by the stock price. This study will also seek to explain if specific factors are influencing positively or negatively on the possible PEAD by regressing on these factors. These are inspired by former papers (Forner et al. 2009; Liu et al. 2003; Bernard and Thomas, 1989; Setterberg, 2007; Jegadeesh and Titman, 1993). 3 In the literature it is commonly referred to as SUE. Page 8 of 113

9 However, there is a problem concerning the information content in the earnings announcements. All of the above measures are estimates based on the earnings information providing new information to the market. Therefore, a Danish earnings announcement might not reveal similar information and it might even reveal more (or less) information to the market. This will complicate the study in making a profound conclusion on PEAD, since each of the announcements should contain new and unexpected information. A test of whether the earnings announcements provide new and unexpected information is also conducted PROBLEM STATEMENT The main objective of this study is to perform: A test for the existence of Post-Earnings Announcement Drift in Denmark To investigate the main objective the following three research questions are constructed: If PEAD exists, then how can PEAD be explained? How robust are the results of the three estimated Earnings-, Price- and EPS-measures? How will the Danish stock market react to earnings announcements depending on the time of the year? METHODOLOGY This study seeks to investigate the relationship between stock returns and unexpected earnings. The existing research on this relationship is extensive. However, I will follow the footsteps of Bernard and Thomas (1989) and Liu et al. (2003) with regards to the significant scientists methodology. The major work by Bernard and Thomas (1989) within this area is considered to be of high methodological value and has been quoted several times 4. Therefore, it will constitute the foundation for the test design of this study. The paper by Bernard and Thomas (1989) estimates the standardized unexpected earnings (SUE) by using a seasonal random walk, where they estimate on the prior quarter s earnings and divide the securities into portfolios according to their SUE. Later research has revealed different methods to examine the relationship. The paper by Liu et al. (2003) uses the above method and adds two different methods. The first is a price-based measure, where the abnormal returns in a four day window is estimated and the 4 In the Social Science Citation Index: Bernard and Thomas (1989) have been quoted 296 times, which is the highest within this specific topic. Page 9 of 113

10 securities are divided into portfolios on this basis. The second is a newer and well-developed method, where the actual earnings per share (EPS) is subtracted from the forecasted earnings per share and divided with the monthly stock price. The latter method has been examined in different papers and is commonly thought to be the best proxy (Bradshaw et al., 2012) for estimating the unexpected earnings on the short horizon window (less than a year), which is the case in this study. Unfortunately, as the data availability of forecasted quarterly EPS are not common on small and medium sized firms and small stock market as the Danish market. This forces the method to only be examined on a yearly basis and with a small sample. The event study framework is performed to test for the existence of PEAD with four parametric and three non-parametric T-tests. The earnings announcement dates have been collected manually from the OMX Nordic Webpage 5, since the data availability of these dates were only collected on an annual basis and often very imprecise in other databases. The dates were collected from 2008 to All of the above methods are explained in-depth in the third part on methodology STRUCTURE This study is structured by six parts. The first part is the introduction and research design of this study. The second is the literature review of past articles on this subject and the presentation of the efficient market theory. The third part is the methodology and sample selection. The fourth part is the empirical results and robustness checks. The fifth part is the conclusion and final remarks. The last part is the list of references and appendices. 5 Page 10 of 113

11 PART 2 2. LITERATURE REVIEW This part contains selected research studies about PEAD starting with the first study conducted in the US and continuing with the later conducted studies in relation to the Danish stock exchange and the surrounding European countries. Theories and explanations will also be dealt with in this part. To start this part I have chosen a simple, yet detailed quote about PEAD. An impressive body of theory supports the proposition that capital markets are both efficient and unbiased in that if information is useful in forming capital asset prices, then the market will adjust asset prices to that information quickly and without leaving any opportunity for further abnormal gain. (Ball and Brown, 1968) The quote is from the first paper by Ball and Brown (1968) who discovered PEAD 6 and stated that PEAD would not exist in an efficient market. It simply defines that in efficient markets the PEAD should not exist in theory. The paper has led to numerous studies on their findings. Particularly, in the late 1980s and the early 1990s many papers were published on this specific matter. These papers were written mainly by American professors, who tested the existence of PEAD in numerous US stock markets. The NYSE market is the most liquid in the world 7 and therefore theoretically has the lowest chance of abnormal gains. Bernard and Thomas (1989) found conclusive evidence on PEAD on NYSE firms and further in this literature part, there will be presented newer research evidence on the existence of PEAD today. The following part presents a list of causes and a discussion about the causes concerning PEAD. The discussion about PEAD still continues today after nearly 45 years of research on this matter (Gerard, 2012) CAUSES FOR POST-EARNINGS ANNOUNCEMENT DRIFT A total list of causes for PEAD would be very extensive, therefore I have chosen to present three of the main causes that are commonly repeated and discussed in several of the PEAD articles. The first cause is the conclusive explanation in Bernard and Thomas (1989), where they found the evidence of the PEAD to be a delayed price response. This came from investors not recognising the public available information or the transaction costs were too high to implement 6 Several papers published similar evidence, but it is generally thought to be the first. 7 Page 11 of 113

12 the proposed trading strategy of going long in good news and short 8 in bad news. These transaction costs could consist of bid-ask spread 9, commissions, cost of selling short or the cost of implementing and following this trading strategy. This price delayed response can occur from investors not being unbiased in their estimates of future earnings based on current earnings, therefore they will not realise the potential profit before analysts forecasts are updated or future earnings are earned. Another contribution to this explanation is the study by Brennan et al. (1993), where they proved that if an increasing number of analysts start following a stock then the PEAD effect will decrease, because the price response is not delayed when attention is aimed at the specific stock. This argument could also be support by the fact that other articles have found the PEAD to be less significant for larger stocks, where commonly larger stocks have more public attention directed towards them than small stocks (Liu et al., 2003; Bernard and Thomas, 1989). Another reason for PEAD commonly discussed in the literature is the misspecification question of e.g. the Capital Asset Pricing Model (CAPM). This argument originates from one of the authors that discovered the PEAD, Ray Ball, who later wrote that the capital markets are impeccable examples of competition (Ball, 1988), and therefore could not be as inefficient as the PEAD indicates. The associated betas for the extreme cases could shift upward or downward in the event of an announcement, which would not be captured by the stationary beta estimation. An article by Ball et al. (1988) allowed the betas to shift and found the drift not to be significant. However, the Spanish study by Forner et al. (2009) allowed the betas to shift and found evidence of PEAD. Foster et al. (1984) estimated portfolios on the basis of the past 60 days stock return including the announcement day and found no evidence of PEAD in this approach. Therefore they only found the PEAD to be significant when using the standardized unexpected earnings approach. Foster et al. (1984) further expressed the opinion that the evidence might explain that in using the earnings-measure a researcher would have a higher unknown risk for this higher premium, which is not accounted for in the CAPM. However, Jegadeesh and Titman 8 Short selling or short position: This term refers to trader having the belief that stock will decline in the future and therefore borrows an amount of shares and sells them. The trader is now short an amount of shares, because he has sold something that he did not own. If the shares decline then the trader will buy the shares at a lower price and replaces them with the borrowed shares which give a profit of the difference in price between the borrowed and brought shares. 9 The difference between what a stock s asking price is and what the bid price is. If these were equal then there would not be any transaction costs. Page 12 of 113

13 (1993) contradicted this evidence of misspecification in PEAD studies by estimating on the previous 6 months return and found the PEAD to be significant. This raises the question on the effect for the chosen time horizon. Newer evidence by Fama (1998) reviewed the methodological robustness of different studies of market anomalies. In the study he concluded that PEAD is still unexplained and robust. In line with this is the study by Liu et al. (2003) that examined variables such as market risk, market value and book-to-market and these were found not to be significant in explaining the PEAD in the UK. Other effects were tested for by Liu et al. (2003) in their study such as price, cash earnings-to-price and number of analysts following a particular stock. However, these were also found unlikely to explain PEAD. From the above discussion you could argue that the evidence for methodology misspecification seems to be contradicting each other, therefore leaving the researcher more puzzled than clarified. Bernard and Thomas (1989) estimated on raw returns and thereby omitted the methodology misspecification and found the PEAD to be significant. The last cause which has come to light in newer studies is an explanation based on evidence from the behavioural finance literature. The theory about market efficiency assumes that investors are making rational decisions. However, investors make irrational decisions, and therefore they do not recognise fundamental information in an earnings announcement. Instead, they make a psychologically biased decision based on the information in the earnings announcement, which could come from a mixture of intuition, rumour or recent news about the company. There is a relation between the number of institutional investors following a stock and the effect of PEAD, which are negatively correlated (Bartov et al., 2000). This should implicate that the more sophisticated the investors are the better chances are that the stock will be correctly priced after an earnings announcement (Bartov et al., 2000). These could be plausible examples; Commissions to traders from selling more of a particular stock to another investor or a specific trend occurring as we have seen with the IT stocks in the 1990s and later the goinggreen concept. Ball and Bartov (1996) found systematic underestimation of serial correlation 10 between the quarters. This means that traders rely more on a specific quarters earnings one year ago than the three quarters earnings in between the current. This could be the effect of seasonality, still this was a general finding and not all companies are affected by seasonality in 10 Serial correlation stands means that the quarters are dependent on each other and the information/data in the last quarter can help you understand the current quarter. Page 13 of 113

14 their earnings. There has been evidence that if more financial analysts are following a stock then a lower effect of PEAD which is in line with the conclusion of Bartov et al. (2000) and Brennan et al. (1993). It has been discussed in the financial literature, but not proven yet, that traders are not acting on the specific earnings announcement day for a specific stock, but they are waiting until the analysts forecast is updated before buying or short selling stocks. Mendenhall (2004) tested whether the PEAD was associated with higher arbitrage risk and found it to be significant, therefore investors would not take part in these higher risk stocks. After reviewing the discussion on PEAD and reflecting on the different causes my personal view is, that the behavioural finance perspective can be an important explanation. This perspective has been investigated very scarcely in the studies which focus on PEAD compared to the two other explanations. The biases created by traders acting irrationally could to some degree explain why PEAD exist. Therefore, an expansion of this study would be to include both interviews of traders and stock price data as this would create a study of both qualitative and quantitative aspects, which might provide a more precise answer of what causes PEAD and why it is not arbitraged by traders. To support my personal view, I will quote Bernard (1992) when he reviewed nearly all possible published explanations at that time in 1992 and wrote: we should remain open to unconventional approaches to understanding how prices might deviate from fundamental values in what appear to be extremely competitive markets. Page 14 of 113

15 2.2. EVIDENCE OF POST-EARNINGS ANNOUNCEMENT DRIFT IN EUROPEAN REGION Studies on PEAD in the European region are growing, but the amount is not as extensive as the American studies. In the European countries several articles have been published on a specific country and a few international articles investigating several markets have included some of the European countries. Based on extensive research the figure 1 below is showing the countries where PEAD is found to be significant and the countries where it has not yet been investigated 11. This shows that PEAD is not only an American phenomenon, but an abnormality that exists also on the capital markets in Europe. Figure 1 - Overview of PEAD studies in Europe Own Creation The colour green marks a country where PEAD was found to be significant and the colour white marks a country that has not yet been investigated. In Belgium it was only found to exist for large firms. 11 It should be noted that I have primarily searched for articles in Western Europe Page 15 of 113

16 2.2.1 UNITED KINGDOM In the UK the existence of PEAD was found by Liu et al., (2003). They tested for the existence of PEAD using three different methods, which are similar to those used in this study. They found the UK stock market to be inefficient to publicly available information. They found the pricemeasure to have the strongest drift compared to the analysts forecast and earnings-measure. This study is considered to be one of the important studies to conclude that PEAD exists outside the US. Another example is the international study where it was concluded that the earningsmeasure would generate significant profit in the UK (Hong et al., 2003). A smaller event study in the UK was conducted in the period of with a sample of 206 companies, where they found PEAD to be significant for small and medium sized companies, but not for larger companies (Hew et al., 1996) SPAIN The study by Forner et al. (2009) presented strong Spanish evidence on the existence of PEAD in the Spanish stock market for the earnings-measure and EPS-measure, but not for the pricemeasure. They found an average return for the earnings-measure 12 to be 7.3% for up to 12 months and the EPS-measure was smaller at 3.4% for the same period. In the studies by Forner et al. (2009) and Liu et al. (2003), they made several adjustments to counter the PEAD, but nevertheless they still found evidence of PEAD which strengthens their conclusion on PEAD. In the Spanish study, they also tested for the robustness of the methodology, which has been mentioned as one of the causes for PEAD, however, they let the beta vary over time and still found conclusive evidence of PEAD. When a study lets the beta vary over time, then it is similar to letting the risk associated with the stock vary over time SWEDEN AND FINLAND In the Nordic countries, Sweden was investigated by Setterberg (2007), where she found similar evidence of PEAD in the Swedish stock market. The existence of PEAD in Sweden was found for both earnings and return momentum (Setterberg, 2007). A trading strategy would earn an average of 10.8% per year in the Swedish market. In an earlier study, the negative PEAD was only found to be significant for the Swedish market (Griffin et al., 2006), still as mentioned by Setterberg (2007) curiosity remains about the method used in the international study by Griffin 12 SUE-measure in their paper, but to remain consistent in this paper then the term earnings, price and EPS-measure are used instead of the original names from the papers. Page 16 of 113

17 et al. (2006). In Finland there was found evidence for PEAD for bad news earnings, however, he did not find a similar pattern for good news (Kallunki, 1997). It should be mentioned that short-selling is prohibited in the tested period in Finland, and therefore investors could not take advantage of the bad news announcement as they could with the good news. This negative drift was later confirmed by Vieru et al. (2005) where they measured the SUE on the basis of the abnormal return on the announcement day; however they did not find a positive drift for the good news. This suggests that Finland might be a special case where only negative PEAD exist, since any significant evidence for positive announcements was not found by Kallunki (1997) or Vieru et al. (2005) GERMANY In the German market the study by Burghof and Johannsen (2009) on the Frankfurt Stock exchange supported further the existence of PEAD in the German stock market. They found a trading strategy with a long position in good news and short position in bad news announcements to generate about 3% to 6% of abnormal return for up to 109 days after the earnings announcement. An international study by Hong et al. (2003) also concluded that the German market yielded significant drift for the earnings-measure. Another international study by Griffin et al. (2006) did not find the German market to have a significant PEAD at the 5% significance level, but was estimated on the difference between the actual earnings and average forecast from the Institutional Brokers' Estimate System (I/B/E/S) which is divided by the price. This method is not commonly used, since it is more common to scale by the standard deviation than the stock price, which questions the comparability with other studies BELGIUM AND POLAND A study by Van Huffel et al. (1996) on the Brussels Stock Exchange in Belgium concluded that PEAD was not found to exist in the period They used two models in their study, the market model and the size-adjusted returns, and neither presented evidence of PEAD. If they distinguished between large and small firms, then they found evidence of PEAD for large firms, but not for small firms. Furthermore, they found the market model to be misspecified for a small stock exchange. In Poland on the Warsaw Stock Exchange Szyszka (2002) estimated the earnings measure as Foster et al. (1984) and found a drift for the bad news announcements on -12.5% from 2 to 60 days after the announcement. He finally concludes that Polish investors could not take advantage of these results since short-selling is prohibited in Poland. Page 17 of 113

18 2.2.6 INTERNATIONAL STUDIES INCLUDING EUROPEAN COUNTRIES The international studies can provide clarification on the remaining western countries. Hong et al. (2003) concluded that France, UK and Germany have significant drift based on the earningsmeasure and also based on the price-measure. These are the most liquid markets in the European region. For the earnings-measure it was found to be profitable for all countries. A hedge strategy of good news versus bad news in France would give a significant return of 0.95%. The return for this hedge in Germany would be 0.90% and in the UK it was 1.11%. For the price-measure they found significantly higher returns with a hedge strategy for France to profit 1.33%, Germany were 0.88% and the UK was 1.32%. In another international study by Griffin et al. (2006) they estimated portfolios on the basis of analysts forecasts derived from I/B/E/S for a period of 2 to 126 days after the announcement and scaled by the price. They used a period of years from 1994 to Contrary to the above presented studies concluding the existence of PEAD in their investigated country, then Griffin et al. (2006) did not find significant evidence of PEAD in Germany, UK, Finland or Poland. They concluded by finding significant evidence of PEAD for neither good, bad or both types of announcements in Sweden, Spain, France, Switzerland, Netherlands, Italy, and Turkey. The countries where PEAD was found not to exist besides Germany, UK, Finland and Poland were Austria, Belgium, Denmark, Portugal, Norway (Griffin et al., 2006). However, the credibility of the results in the article is vague, since five independent country specific articles concluded the presence of PEAD where Griffin et al. (2006) did not come to the same conclusion. Therefore I have chosen to interpret this article with circumspection. Lastly, a test on a large sample of European firms conducted by Gerard (2012) provided evidence of the existence on PEAD in the European region over a 14-year period. He used the FTSE 13 All-World Developed Europe Index from 1997 to There are many papers on PEAD that studies different variables, methods and measures, but the above have been selected, since they are directly testing for PEAD in a specific European country and following more or less in the footsteps of the American studies. These European studies are also testing new methods and controlling for more variables, but they are still finding evidence of PEAD in the European region. The evidence for PEAD is different in Europe, since the drift is mostly found for bad news announcements. For good news announcements the PEAD is not 13 Financial Times Stock Exchange Page 18 of 113

19 always found to be significant. This might be a difference between the American and European studies EVIDENCE OF EARNINGS ANNOUNCEMENTS IN DENMARK The studies on earnings announcements with relation to market efficiency performed on the Danish stock exchange 14 are limited. Earlier published event study on market efficiency in Denmark was published by Sørensen (1982) which found evidence that the market adjusted within a few weeks to new information released in earnings announcements. Sørensen (1982) stated that the Danish market is efficient. The next published paper on PEAD was by Lønroth et al. (2000) which found the Danish market adjust more quickly to new information from earnings announcement within 4 days, but they concluded the Danish market to not be as efficient as the American markets. The last article is a dissertation by Sponholtz (2005), which seeks to study the information content in earnings announcements. She finds evidence that the Danish market reacts slowly to new information, and therefore concludes the Danish market to be inefficient. In an international study, Denmark was included and was not found to be significant in either of the two studies based on analysts forecasts (Griffin et al., 2006; Griffin et al., 2010); however the method used are different from the common approach in PEAD studies as mentioned in the above section on international studies in Europe. It is important to notice, that the above studies are not testing for a longer period than a couple of weeks and are not testing directly for PEAD. Therefore this study will help fill this void in the Danish financial literature by testing for up to 90 days after earnings announcement. It will also bring further out-of-sample evidence on PEAD in Europe THE EFFICIENT MARKET THEORY The theoretical approach in this study is the efficient market theory, which was first developed by Fama (1965) 15. It states that in an efficient capital market all prices fully reflect all available information. If a trader buys a stock, then the price will reflect all available information both public and private concerning the firm. If a market always has prices reflecting the fully available information, then it ought to be efficient. 14 I chose to use the term the Danish stock exchange, since the Copenhagen Stock Exchange changed named to NASDAQ OMX Nordic, which consists of all the listed stocks in Denmark, Norway and Sweden. 15 There are some discussions in the literature which specific article was the first on this theory, however mostly it is consider to be the one by Fama (1965) Page 19 of 113

20 In this study, the purpose is to test whether PEAD exists in Denmark, but at the same time it is also to test the efficiency in the Danish stock exchange as these two go hand in hand. Therefore, the efficiency perspective is the key to detect the existence of PEAD in Denmark, since if new information is released as an earnings announcement to the market then the stock price should adjust quickly and shift without creating an upward or downward drift. It would not be possible to arbitrage on this change. In the Figure 2 below there is the depiction of the three different actions the market can shift to in theory. It can create an abnormal gain bigger than zero or an abnormal loss lower than zero, which both implies an inefficient market. These two reactions will generate space for PEAD to exist; however, if the market does not experience a gain or a loss, then the market would be in equilibrium and therefore considered to be efficient. Figure 2 - Efficient Market Theory Own creation Page 20 of 113

21 When reflecting on the term efficient it is not a one-sided term, because there are different degrees of efficiency. In order to better understand how a market is efficient these three forms of market efficiency were developed by Fama (1965): Weak Form of Efficiency; the current market prices capture all available information in the past stock prices and volume data. In this form, analysts use different technical analysis 16 methods to beat the market, because the current prices do not reflect the fair value. Valuation of stocks can be done by using all available financial data. This form is not affected by news statements, but is purely numerical based. Semi-Strong Form Efficiency; the current market prices capture all publicly available information. Prices adjust quickly to new publicly information and the only option to beat the market is by insider trading. This is the common form in the real-life capital market and this PEAD study is testing on the efficiency in this form. Strong Form Efficiency; the current market prices capture all available information both the public and private information. The form is unique, since all information is reflected in the stock prices; therefore it is not possible to beat the market by using a fundamental analysis 17 where several aspects of the business is analyzed. There are other variations of the efficiency where a market might have a combination of the above forms. This could be seen in markets where the highest market capital stocks fully reflect all publicly available information, but smaller and less traded stocks might not reflect all publicly available information. In relation to the objective of this study, then it should be the middle case for the Danish stock exchange of semi-strong efficiency. This study will test this theory by using the PEAD methodology. Fama is also one of the authors behind event studies, which will also be used in this study. Event studies have been one of the main sources to bring forward the evidence not supporting the efficient market theory. Here is a short presentation of the anomalies against the above theory, which I will not go into further depth with: 16 I define a technical analysis as a study of stock prices and volumes. Purpose is to look for trends or cycles. 17 I define a fundamental analysis as a study of financial statements, future prospects, management, the macro environment and news about the business. Page 21 of 113

22 The January Effect; it has been found that there are higher returns compared to the rest of the year. (Rozeff and Kinney, 1976) The Monday Effect; it was proven that returns are highest on Friday and lowest on Mondays, and even the returns on Mondays were often negative. (French, 1980) This evidence does not fully collapse the Efficient Market theory (Fama, 1998), but it may challenge the preciseness. The defense for the theory is that many of the above anomalies are only seen under specific circumstances or time periods. However, Fama (1998) concludes in his paper that the PEAD is above suspicion and have survived several robustness checks. The discussion of validity of efficient market theory still continues today. I have chosen to use the efficient market theory as the main theoretical approach in this study, because it is difficult to imagine markets today not being efficient with the massive amount of information publicly available at any time at any location in the world. The evidence against the efficient market theory is strong in some cases and difficult to overlook, but there has not been developed a more precise and accurate theory to overtake it. There have been developments in behavioral finance theories, however, they only seem to be able to explain some of the abnormalities, but Fama (1998) does not find them suitable for all abnormalities. Therefore, this will still be the main theoretical foundation in this study. Page 22 of 113

23 PART 3 3. METHODOLOGY This part comprises the methodology of this study, where the methods, techniques and calculations used in this study are explained in depth. The results are included on the CD, where all the portfolio formations calculations and T-tests are found in their respective spreadsheets. There are three spreadsheets that show the ranking into portfolios for each measure on the CD. PEAD studies have been performed for many years, but unfortunately the vast numbers of articles on PEAD have not developed the perfect methodology to test for PEAD. Several different approaches have been used in the literature, but overall the strongest methodological approach is by applying the earnings-, price- and EPS-measures in a PEAD study (Foster et al., 1984; Bernard and Thomas, 1989; Chan et al., 1996; Liu et al., 2003). These three measures are explained in depth later in this part. The specific measure whether it is price, earnings or EPS will determine which portfolio each stock is divided into and afterwards each portfolio is followed for up to a number of days, months or years See figure 3. Figure 3 - Methodology Overview Own Creation Sample Ranking T-tests Three different samples of data are extracted for each of the measures. The specific measure is estimated for each stock and ranked according to each stock in the sample, and then sorted into portfolios. In total thirty portfolios for all three measures. For each portfolio seven different T-tests are estimated with event windows of 10, 20, 30, 60 and 90 days. PEAD? The results are investigated and discussed to provide a profound conclusion of the presence of PEAD in Denmark This study will follow the stock returns for 90 days after portfolio formation, since it was found that most of the drift occurs within 90 days (Bernard and Thomas, 1989). In line with this, the section on event studies will contain a discussion on the length of the event windows. I have Page 23 of 113

24 chosen 7 different T-tests 18, where 4 of them are parametric and 3 are non-parametric. Former studies on PEAD have as a standard used one parametric T-test, but these studies had samples of above 1000 to around of stocks which increased the power and robustness of the used parametric T-test (Foster et al., 1984; Bernard and Thomas, 1989; Burghof and Johannsen, 2009; Liu et al., 2003). This is not the case in this study, where the sample sizes are smaller and therefore several T-tests are required in order to make a profound conclusions based on them. The T-tests are used to test the significance of the abnormal returns being different from zero, if they are significantly different from zero, then this will lead to a conclusion on the existence of PEAD in Denmark. Mixtures of both parametric and non-parametric tests have been proven to be more reliable in order to make profound conclusions in event studies (Corrado, 2011) THE EARNINGS-, PRICE- AND EPS-MEASURE The first method in this study is adopted from Foster et al. (1984) and later by Bernard and Thomas (1989), which is considered to be of high methodological value (Setterberg, 2007) and also the most quoted study in the literature of PEAD 19. It is a univariate time series model called an autoregressive model (Model 1) with a seasonal random walk. It is used to forecast on the prior quarterly earnings, and the equation estimated as follows: (Eq. 1) There are other models mentioned in the literature, therefore I conducted a trial and error test to select the best fit for the sample of earnings data for this specific study (See table 1 below). The results were the same as concluded by Foster (1977) that Model 1 20 is the best fit for predicting future earnings based on past earnings. The was significantly higher between Model 1 and Model 3, which was not similar to the results by Foster (1977),where he found it to 18 A T-test generally refers to a statically test where the null hypothesis stated as the mean not being different from zero is tested. In this study I will also use the term as referring to the 7 tests used in this study. See the below section on T-tests. 19 In the Social Science Citation Index: Bernard and Thomas (1989) have been quoted 296 times, which is the highest within this specific topic of PEAD. 20 In his article Foster (1977) the model was named Model 5 Page 24 of 113

25 have little or no difference between these models. The possible weakness of the chosen Model 1 is based on the assumption that all firms are described on the basis of their fourth differences over time 21, which is a strong assumption to make for all firms - hence not all current firms earnings can be explained by what happened four quarters ago. Table 1 - Test of Earnings Expectation Models A Test for the best fit model Average Model 1: 32% Model 2: 17% Model 3: 17% Model 4: 19% Note: R-Squared ( ) indicates the correlation between two datasets and provides a correlation coefficient from 0% to 100%, where 100% is considered to be the perfect model. Source: See the CD Content. The difference between the actual and the forecasted quarterly earnings is scaled on the standard deviation of the prior quarterly earnings ( ) See equation 2. This is commonly known as the standardized unexpected earnings (SUE) with a slight difference, since the standard deviation (deflator) is estimated from the previous quarterly earnings and not the forecast errors as used by Bernard and Thomas (1989). In the article by Foster et al. (1984) the absolute value of the series in their Model 1 was used for the denominator and still found evidence of PEAD. The SUE is defined similarly in this study as in Jegadeesh and Titman s research (2011) and therefore I name it the earnings-measure throughout the remaining study. The reason why I am not following the path of Bernard and Thomas (1989) is the forced reduction in the sample size in order to estimate the standard deviation from the forecast errors, because it would 21 E.g. the model assumes a company s earnings can better be explained by what happened in last year s quarter, than the previous quarter. If a company is very dependent on the previous quarter s earnings, then the model will be a poor fit for this company. Page 25 of 113

26 require at least 20 quarters of earnings data, which is not possible to find for Danish stock exchange data 22. Therefore, I have chosen to define the earnings-measure as follows: (Eq. 2) Where the deflator ( ) is estimated from a minimum starting point of 8 prior quarterly earnings up to 27 quarterly earnings at the end of the estimation year Other studies have used the price as the deflator (Griffin et al., 2006; Griffin et al., 2010), but their findings were questioned compared to other studies as mentioned in the literature review part of this paper. Another way of thinking about this deflator is that by taking the difference between the actual earnings and the expected earnings scaled by the standard deviation it will give a better impression of when it is a surprise than by scaling on the stock price. This owes to that the standard deviation incorporates the past volatility for this particular stock rather than a value as the stock price. The second price-measure uses the abnormal returns in a four day window around the earnings announcement date to estimate the portfolio ranking. This method was used by both Liu et al. (2003) in their UK study on PEAD and by Chan et al. (1996) which examined different momentum strategies. (Eq. 3) The abnormal return ( ) is the abnormal gain calculated as Equation 6 as in the below section on the event study model. This method is slightly different than Liu et al. (2003), where they use buy and hold abnormal returns and compound these for the four day period. I have chosen to sum the abnormal returns; since this method matches the later used Cumulative Average Residual (CAR), where each abnormal return is summed up in the specific event windows. This will keep the method straightforward instead of mixing different methods. The third method is the analysts forecasted measure (EPS-measure), which is based on the difference between the actual earnings per share (EPS) and the analysts forecasted earnings per share divided with the monthly stock price. This measure is newer and seems to be gaining considerable recognition among researchers which cannot overlook the fact of superiority of analysts forecasts in the ranking method in these studies (Bradshaw, 2011; Livnat & Mendenhall 22 As mentioned before the data availability is very limited before The investigated sources are all licensed fee financial databases at ASB and CBS including help from the ASB library. Page 26 of 113

27 2005). However, in this study the availability of EPS is very limited, which has reduced the sample size substantially for the Danish stock exchange. The EPS-measure is defined as follows: (Eq. 4) o o o The data availability of the analysts forecast on quarterly EPS is lacking and therefore it is only possible to study this method on an annual basis, whereas the two above methods are studied on a quarterly basis 23. To test the correlation between the measures I performed a correlation matrix to see whether the measures might be identical - See table 2 where a perfect correlation is one. Table 2 - Correlation Matrix Source: See the CD Content under the folder Eviews The EPS versus earnings-measure is not correlated with the lowest correlation of the three measures. The earnings-measure versus price-measure is only slightly correlated. The EPS versus price-measure seems to have the opposite correlation, but are the most correlated measures. However, the conclusion of this correlation matrix is that each measure tells its own story. I would have expected the EPS and earnings-measure to be more correlated, since both measures are based on the earnings. The reason for this difference could be that the analysts are incorporating much more than quantitative information into the forecasts of EPS, than a technical analysis of pure earnings as the earnings-measure. Therefore, it is fairly reasonable to state from this matrix that each measure captures its own part of information. 23 After searching for several months I was not successful in finding the forecasted quarterly EPS for stocks listed on Danish Stock Exchange, only a 12 month forward EPS. Page 27 of 113

28 Overall, the above explained methods are only different in the measures estimates, whether it is earnings, price or EPS-measure. In figure 4 an overview of the processes is shown and it shows the consistency and focus on the different methods. The ranking procedure into portfolios and the T-tests are similar for all three measures. The measures are estimated and ranked into ten portfolios on the basis their measure. Figure 4 - Overview of the Measure Processes Own Creation All of the stocks that are ranked as thirds are allocated into the portfolio number three and together with all the stocks ranked as thirds from the first quarter of 2008 to the last quarter of 2011 for each of the measures. This creates ten overall portfolios which are used in the later explained T-tests. This means that a stock e.g. Novozymes can be put into the same portfolio several times if it is ranked similar in two or more of the quarters. This will not cause a bias, since the stocks are measured at different time periods. Afterwards, the returns are measured by the CAR for over 90 days after the formation. The significance of the CAR is tested in the latter explained seven T-tests. Page 28 of 113

29 3.2. EVENT STUDY AND T-TESTS This study uses an event study framework to test the main objective. An event study investigates a specific event for a stock (i.e. merger, stock split, or earning s release) and compares the returns after the event with the forecasted returns which are estimated on historical returns, thereby indicating what the return should have been in theory had the event not occurred. The event day is important to identify accurately since all the returns before the event are used to estimate the beta and alpha for the stock and as well the abnormal returns after the event had occurred. This is also referred to as the estimation period. The event window consists of the event day and the following days after. This study undertakes the tests under the assumption that there are efficient markets. The estimation period is defined as -200 trading days before the event day. I have chosen not to use the commonly -250 trading days (approximately a year excluding weekends and holidays) since the post-earnings announcement drift is commonly found within 3 months after the earnings announcement. So by not including this potential former drift in the linear regression of each stock I have limited the estimation period to -200 days. The trade-off is to find the correct balance between not including former drifts and not limiting the estimation period, which can cause misspecification of the alpha and beta for each stock EVENT WINDOWS The post-event windows 24 are identified as day 0 to day +10, +20, +30, +60 and +90 after the estimation period See figure 5. Figure 5 - Event Windows Own Creation The main focus of an event study is to see if the company gains abnormal return after the event. It is difficult to estimate when these abnormal gains will occur, since some events has effects for only a day, where PEAD is considered to be a longer effect (thereby the name drift) and 24 In the remaining referred to as event windows. Page 29 of 113

30 therefore a 90 trading day s window is necessary to detect its plausible existence. The problem with this decision on the event window is the power and robustness of the T-tests used in event studies. There are short-term (< 1 year) and long-term studies (> 1 year) and the methodology used in these studies are different. The short-term studies are often used for +/- 1 day event windows, but they can be extended to be used with 90 days event windows by the use of averages and adjustments to the standard deviation. As shown in appendix 3 the power of a sample size of 100 for a one day event window is very strong (100%) but for an event window over 6 months it is fairly low (approx. 40%) (Kothari, 2007). This fact has also been the basis for not extending my window further than 90 days and at the same time making a trade-off between capturing the PEAD with robust and powerful results from the conducted T-tests and still have a well-specified event study framework. Another reason for not conducting long-term studies is the use of tests such as bootstrapping and pseudo portfolios which are considered to be the proxy for long-run studies. The bootstrapping methodology is also questioned by Mitchell and Stafford (2000) as not adequate for long-term studies, but still it is one of the more popular methods for long-term studies. Kothari (2007) expressed in his article on the matter of long-term studies that: The methodological research in the area is important because it demonstrates how easy it is to conclude there is abnormal performance when none exists. (Kothari, p. 21, 2007). The correct methodology for long-term studies is difficult and filled with traps, which could easily distort the results and limit the usability of this study. Further the PEADs articles used in this study are conducted as short-term event studies with event windows at commonly 10 to 120 days THE EVENT STUDY MODEL I have chosen to use the market model 25 approach from MacKinlay (1997). The market model uses a chosen stock and a relevant market index to estimate the expected return if the event had not occurred. The market index used in this study is the All-Share Morgan Stanley Index (MSCI Denmark 158 stock included), which is similar to the former KAX Index 26. The use of a 25 Other models used in event studies are the CAPM, mean adjustment, market adjustment, and Fama & French s three factor model, Carhart s four-factor model. These have been test and have not been proven to be significantly better than the chosen market model. (Fama, 1998; Kothari, 2007) 26 This was an index of all the stocks in Denmark. Page 30 of 113

31 market index is common and the MSCI Country Index for Denmark is an equally weighted mean return index and a similar Country Index is also used in other studies (Bernard and Thomas, 1989; Foster et al., 1984; Chan et al., 1996). The market model is defined as follows: (Eq. 5) Where is expected return on stock i at time t and is the return m on the MSCI Denmark at time t. The day to day return for both the stock and market are calculated as follows: (Eq. 6) The day to day returns are used with the natural logarithmic to make the return distribution converge to normality and the elimination of negative values. Corrado and Truong (2008) found that the logarithmic return provided better test specification in event studies and later a test for normality is conducted. The parameters are obtained from the ordinary least squares method 27 estimated from the stock and market index. The alpha ( ) and beta ( ) are the risk adjustments compared to the market, therefore a high will give a higher expected return because of the higher the risk compared to the market. The event window is not included in order to avoid biases in the parameter estimates (MacKinlay, 1997). The market model assumes a linear relationship between the stock and market index. The error term is set equal to zero. A problem of the market model is the calculation of expected returns for smaller stocks, because the risk adjustment in the market model is expected to produce false results (Fama, 1998). A mixture of small, medium and big stocks are used in this study, therefore this should help overcome the problem. The effect of the announcement is measured as the abnormal return arising after the event. This states that the abnormal return is the actual stock return i at time t subtracted the expected return on stock i at time t if the event had not occurred. The abnormal return is defined as follows: (Eq. 7) 27 The Excel function =Intercept and =Slope have provided the parameters. Page 31 of 113

32 Where and are the alpha calculated as the intercept between the stock return and market return and the beta are calculated as the linear relationship between the stock return and the market return. Each abnormal return is seen as part of the portfolio, therefore they are all averaged with the number of stocks N included in the portfolio. This is also referred to as cross-sectional averages and the average abnormal returns in the event window is defined as follows: (Eq. 8) The average abnormal return is useful for a single day event window, but this study is testing over a multiday period. Therefore, the commonly used CAR method is used and it is recommended in the article by Kothari (2007) on econometrics in event studies and also Fama (1998) argues to use this measure. A critique of the CAR measure is that it does not accurately measure investors return over time (Fama, 1998). To develop on the average abnormal return equation defined above, the CAR becomes: (Eq. 9) Where the and are the starting and ending day of the event window. Another measure of the abnormal return is the Buy-and-Hold Abnormal Returns (BHAR). This measure requires the use of specific benchmarks portfolios or matching of stocks that have not experienced the particular event. The matching approach is impossible, since most of the stocks listed on the Danish stock exchange are obligated to present an earnings announcement every quarter, where smaller firms are obligated to do it yearly. Therefore the matching of firms is not possible, because all listed firms produce at least one earnings announcement a year and thereby they will experience the same event as the tested stocks. Benchmarks portfolios are difficult for a small stock exchange as the Danish stock exchange, because most of the stocks are included in the sample and therefore they cannot be in the benchmark portfolio, since that would create a bias. On the American stock exchanges it is easier, since there are numerous stocks to pick from when conducting an event study for the benchmark portfolio. The last argument relies on the comparability with former PEAD studies that have used the CAR measure (Bernard and Thomas, 1989; Burghof and Johannsen., 2009; Liu et al., 2003; Foster et al., 1984; Forner et al., 2009; Gerard, 2012; Setterberg, 2007; Sadka, 2006; Sadka and Sadka, 2003). This is the reason behind my decision to use the CAR measure. The CARs are used in T-tests to test the hypothesis of the Page 32 of 113

33 abnormal returns being equal to zero and the implicitly alternative hypothesis of the abnormal returns being not equal to zero. (Eq. 10) The T-tests are based on both parametric and non-parametric tests. The T-tests used in this study are presented below. The first four T-tests are parametric tests, which have resemblances among each other, but each of them is adjusted to solve a possible problem within the sample. This is explained further under each test. The last three are non-parametric tests PARAMETRIC T-TESTS In this study a combination of both parametric and non-parametric tests are used to cope with the possible violation of the assumption of normality and to improve robustness to the tested results by using a variety of tests. In general, a non-parametric test makes fewer assumptions than a parametric test, but then why would a researcher not always use non-parametric tests, since they are easier to work with? A non-parametric test is less powerful if the data is approximately normal distributed and these test results are more difficult to interpret than parametric tests. The parametric tests use more of the information in the data sample by estimating on the mean rather than the median as in non-parametric tests, therefore you could draw more conclusions on parametric test results where non-parametric test results are simpler T0: T-TEST WITH CRUDE DEPENDENCE ADJUSTMENT This T-test is adopted from the paper by Brown and Warner (1985) and the formulas are adopted from Campbell et al. (2010). It adjusts for cross-sectional dependence across the data by calculating the standard deviation using the sample s mean returns from the estimation period. The performance of the test has been proven to be fairly strong in shorter windows (Brown and Warner, 1985). In longer event windows this test loses considerable power to estimate whether the test statistics are significant. The test is distributed as the Student t-test and is approximately standard normal under the null hypothesis. The formulas for this test statistic and the standard deviation are presented in appendix T1: T-TEST WITH ADJUSTED CROSS-SECTIONAL INDEPENDENCE This T-test performs the opposite actions of the T0, since it adjusts for independence across stocks on the event day. This test can be strengthened by the use of the Patell s Adjustment (Brown and Warner, 1985; Patell, 1976). This adjustment is made in order to avoid the variance fluctuations in thinly traded stocks. The test is distributed approximately standard normal under Page 33 of 113

34 the null hypothesis; therefore the normal distribution is chosen. The event window is formulated in line with the article by Bartholdy et al. (2011), but expanded to fit the chosen event windows in this study. The formulas for this test statistic and the standard deviation are presented in appendix T2: T-TEST WITH STANDARDIZED ABNORMAL RETURN The third T-test standardizes each abnormal return by its own standard deviation. This will decrease the forecast errors and normalise each stock returns compared to the estimation period. The test is distributed approximately standard normal under the null hypothesis; therefore the normal distribution is chosen. The daily standardized abnormal returns are cumulated for each day and added together depending on the event window being tested. The standardization incorporates the standard deviation and therefore by multiplying the number of days in the event window with the number of firms in the sample, then this becomes equal to estimating on the averages in the event window(s) as performed in the above T-tests. This test is adopt from Bartholdy et al. (2011). The formulas for this test statistic and the standard deviation are presented in appendix T3: T-TEST WITH ADJUSTED STANDARDIZED ABNORMAL RETURN This test incorporates the Patell s Adjustment into the standardization of the abnormal returns. In the article by Campbell et al. (2010), he uses this method for a multiday event window in his multi-country event study. This test is a combination of T1 and T2, where both adjustments are incorporated into the test statistic. The test is distributed approximately as standard normal under the null hypothesis; therefore the normal distribution is chosen. For each of the event windows 10, 20, 30, 60 and 90 days there are calculated a specific standard deviation, since lengthening of the event windows demands re-calculation of the standard deviation in order to achieve a correct T-value for each event window. These re-calculated standard deviations incorporate the number of announcements and number of days in the event window, so the T- statistic is estimated on averages similar to the above T-tests. The formulas for this test statistic and the standard deviation are presented in appendix NON-PARAMETRIC T-TESTS The main difference between these tests is the assumption of normality in the sample. However, most of the financial studies examine different events as in this case, earnings announcements, where the assumption of normality can easily be invalid. Therefore, a non- Page 34 of 113

35 parametric test would be stronger, since it considers no form of distribution. In the paper by Corrado (2011), he reviews different test statistics used in event studies and concludes the rank and sign test to be well-specified in most situations and from the study by Bartholdy et al. (2011) on the Danish Stock Exchange the Rank test, Sign test and Generalised Sign test are the best specified tests for portfolio of either 25 or 50 stocks with induced return T4: RANK TEST The T4 Rank test performed in this study is replicated from the article by Cowan (1992), where he used an 11 day event window which is expanded to suit the 10, 20, 30, 60 and 90 day event windows in this study. The test unites with the standard normal distribution. Each abnormal return is ranked according to each other with the highest rank being equal to highest abnormal return and then it is estimated whether the highest ranks are part of the event windows. The formulas for this test statistic and the standard deviation are presented in appendix T5: SIGN TEST The Sign test assigns a number of 1, 0, -1 to each of the abnormal returns whether it is positive, zero or negative and then it is estimated whether the number of positive is higher than the number of negative returns or vice versa. This test is adopted from the Corrado and Zivney (1992). The expected number for the difference between positive and negative returns in this test are zero. The formulas for this test statistic and the standard deviation are presented in appendix T6: GENERALISED SIGN TEST The final test is the generalised sign test, which is a further development of the sign test. Each of the abnormal returns are assigned a 1, 0,-1, but instead of the expected number of positive or negative signs being equal to zero as with the above sign test. This test estimated the number of expected signs from the estimation period. This test is adopted from Cowan (1992) where he used an 11 day event window, which is expanded to suit the event windows in this study. The formulas for this test statistic and the standard deviation are presented in appendix PERFORMANCE OF THE T-TESTS AND NORMALITY There are several studies on the performance of T-tests (Bartholdy et al., 2011; Ahern, 2009; Corrado, 2011; Brown and Warner, 1985; Corrado, 1989; Corrado and Zivney, 1992; Cowan, 1992; Patell, 1976), where the strengths and weaknesses are tested to find the best performing T-test. However, the obvious choice is the article by Bartholdy et al. (2011) where a battery of T- Page 35 of 113

36 tests are performed on the Danish Stock Exchange, where the Rank test, Sign test and Generalised Sign Test seems to be well-specified for this study. However, as also concluded in the paper: A researcher can use a variety of parametric and nonparametric tests to detect abnormal performance. If all tests agree, the researcher can be fairly confident of results. (Bartholdy et al., 2011) A common mistake in event studies is to neglect the fact of non-normality in the sample, which causes a Type 1 error, where a researcher wrongly rejects the hypothesis of an existence of abnormal returns where none exists. The parametric T-tests rely on the assumption of normality in the independent abnormal returns for each stock. Generally, an event study with large samples can rely on the central limit theorem that states: the sum of a large number of independent random variables has a distribution that is approximately normal (Ross, 2000) Unfortunately, the sample size in this study is not sufficient to make the same assumption and therefore in this study a visual interpretation of Q-Q plots and four tests for normality is conducted to assure a profound conclusion based on the above explained T-tests. This method is conducted with help from the statistical program Eviews and the results are presented in the section four A TEST FOR REACTION TO NEW INFORMATION The above tests cannot be used to test for the market s reaction on whether the information in earnings announcements is new and unexpected and therefore a different parametric test is conducted. The reason is that the positive and negative abnormal returns that are estimated in the market model will offset each other. A test where the positive and negative abnormal returns are divided into two groups is not useful for the purpose of measuring the market reaction to new information unconditionally of it being a bad news or good news announcement. I have chosen to develop the test statistic from Lønroth et al. (2000) with close similarities with Sponholtz (2005) where a test of the squared abnormal returns is estimated. In Lønroth et al. (2000) there is estimated two other tests, but they show very similar results so on the basis of this discovery I will not include other tests. When squaring the abnormal returns, the bad news versus good news is ignored. This test is also suitable for visual presentation. I assume the abnormal returns are independent and normally distributed. The estimation and Page 36 of 113

37 calculations for this test can be found on the CD and the main results are presented in the in Empirical results section. The formulas for this test statistic and the standard deviation are presented in appendix 2. Page 37 of 113

38 3.6. DATA SELECTION In this study I have collected earnings announcements from two different databases in order to test for the existence of PEAD with the three different methods. There are a limited number of databases that contain both earnings announcements dates, actual quarterly earnings, EPS and the stock prices for the Danish stocks. Previous studies on PEAD in Sweden, Germany and UK have encountered similar problems with finding quarterly data when conducting PEAD studies in Europe (Setterberg, 2007; Burghof and Johanssen, 2009; Liu et al., 2003). They were required to use multiple databases or limit their study to only include yearly or half-yearly earnings announcements. The first database extraction for the earnings-measure of earnings announcements are from CompuStat Global which contain the quarterly earnings as Income before Extraordinary Items 28, but the announcement dates are the quarterly ending dates (e.g x) and not the official announcement dates of the actual earnings announcement. This extraction resulted in 3525 quarterly earnings announcements for Danish listed firms, which was reduced to 1572 See figure 6. Figure 6 - The Earnings-measure s sample selection of earnings announcements For an earnings announcement to be included in the sample it had to have quarterly information from at least the first quarter of 2006 to the last quarter of 2011 where the majority of the announcements in first extraction sample did not have from the first quarter of 2004 as shown 28 In the remaining referred to as quarterly earnings Page 38 of 113

39 in figure 6 (1649). Former studies by Foster et al. (1984) and Bernard and Thomas (1989) included up to 20 prior quarterly earnings for the American studies to estimate the earningsmeasure, but Liu et al. (2003) included up to 9 prior quarterly earnings for the UK study which did not cause significant problems. I have chosen to include up to last 8 quarters of earnings before estimating the earnings-measure in order not to decrease the sample size substantially. In the final sample 6 announcements are included which only had the prior 8 quarters of earnings 29, and therefore the majority of the sample had above 8 quarters as in the Liu et al. (2003) study. A sample of the 1572 including historical earnings from 2004 was used to estimate each earnings-measure for each announcement in the period 2008 to From this estimation 832 earnings announcements were ranked into the ten portfolios. The data extraction from Datastream for 832 announcements revealed 130 missing stock prices or thin trading which reduced the final sample to 702. The second extraction for the price-measure was conducted manually from the news section on the OMX Nordic Webpage (See appendix 1), which also is the official webpage of Danish Stock Exchange. I have copy-pasted each date, headline and link to the specific announcement into Excel 30. This procedure should increase the precision of the dates, since a stock listed on the Danish Stock Exchange is obligated to report stock related news to the Danish Stock Exchange, which is first presented on their webpage news section where the extraction have been performed 31. The dates were collected from 2008 to 2011, which resulted in 5299 earnings announcements on the Danish Stock Exchange See figure The final sample is found in Excel Spread sheet Earnings-measure on PEAD 30 A screen print of the webpage can be found in Appendix 1 31 After a phone conversation with a NASDAQ OMX Customer Service it was confirmed that all news are first published here. Page 39 of 113

40 Figure 7 - The Price-measure s sample selection of earnings announcements This first extraction have been sorted for financial firms 32, duplicates of the same announcement, annual meeting announcements instead of earnings announcement, English and Danish announcements for the same announcement, delisted firms and excluding non-danish firms. This resulted in a sample of This sample was used to extract several variables from Datastream 33 : - Price Index per stock from 365 days prior and after the announcement date (PI) - The 12-months forward EPS, which were on an annual basis (EPS1FD12) - The number of shares (WC05191) - The annual net income to calculate the actual EPS (WC01751) - Turnover by volume, where this is used to adjust for thin trading (VO) - The Morgan Stanley Denmark Index, which is used to estimate the market model (MSM) - Market value of common equity (MV) 32 The accounting principles and standards are different; therefore the earnings and so forth have a different interpretation. However, a study with the EPS-measure was conducted including financial firms. It did not show different results than the EPS-measure excluding financial firms See the content on the CD under EPS-measure. 33 DataStream s mnemonics are in brackets () Page 40 of 113

41 From this extraction from Datastream several of the announcements had to be excluded (475), because of either thin trading (<80%) or missing stock price data. The final sample used in the T- tests is 870 earnings announcements. The third extraction for the EPS-measure from Datastream was 337 annual earnings announcements See figure 8. The data availability is limited on the Danish stock exchange and therefore the sample was reduced considerable (161). Further, there was some missing stock data which reduced the final sample to 162. Figure 8 - The EPS-measure s sample selection of earnings announcements The above extraction procedures impose some problems for the further analysis of PEAD. Firstly, the three collected samples are not equal in size or firms. This is mainly determined on how much data is available for each announcement and measure. This will not influence the testing considerably, but it might strengthen this study if all of the above measures prove similar results. Second, the sample sizes range from 162 to 870 where a higher sample size would increase the power of the tests used to test if the existence of PEAD is significant. This is not possible until more data is collected and stored and this might not be the case in the future, since the Danish law only allows for online storage of data up to 5 years. Page 41 of 113

42 Thirdly, from the below figure 9 the earnings announcement seems to be peaking in specific months, where months as June and July are very low on announcements, and then August is the overall winner of announcements in the period. Figure 9 - Earnings Announcements per month All of earnings announcements depicted by the price-measure sample of 1345 in the period Source: See the CD Content. This spread among the announcement makes it more difficult as a researcher to capture the effect. This is because not all firms publish on the 31.xx.xx each quarter end, but on very different dates during the quarter. A similar problem was encountered in a German study and they estimated that each firm would have published their announcement within 80 days after the quarter have started, so they followed the stocks from day 80 and onwards (Burghof and Johannsen, 2009). I chose to follow this logic and therefore examine the stock returns after the quarter have ended hence from the xx, xx, xx, xx. By using this logic, it is possible to estimate whether this would be a possible real-life investment strategy. For the price- and EPS-measures the official earnings announcement date is known and therefore each stocks measures is estimated and ranked on the specific date, but the stock price is not followed before the quarter have ended in order to make it possible to implement in real-life. This will propose a problem for stocks that announces early in quarter, since the PEAD might have happened, but it would not be captured in this study s method. However, this method is possible to implement in real-life and I chose to value that as an important part for this study, since one of the critiques of PEAD is that is not possible to implement in real-life. In the study by Burghof and Johannsen (2009) a case specific test for PEAD is conducted to overcome the above Page 42 of 113

43 mentioned problem where the stocks are measured exactly from each of their earnings announcements dates. This study is also conducted for the earnings-measure with portfolio 10 and 1. The results are only possible to achieve by insider trading and not valid as a real-life trading strategy and therefore consider this test in theory. The results are presented in the robustness check section in part four. Page 43 of 113

44 PART 4 4. EMPIRICAL RESULTS This part consists of the descriptive statistic and normality tests for the performed studies, which will lead to an analysis of the overall results for all three measures used in the T-tests. A comparison with previous research in Europe and US, and also the possible explanations for PEAD will be presented. Several robustness checks are performed to increase credibility of the results and these will also be presented and discussed DESCRIPTIVE STATISTIC The descriptive statistic (see table 3 below) for the earnings-measure reveals a slightly different expectation of Portfolio 1 (P1), since the average mean is positive (0.03%), which would be expected to be negative in order to prove PEAD. However, the Portfolio 10 (P10) is positive by (0.05%) and therefore a higher average which supports a hedge strategy of going long in P10 and short in P1. In general all portfolios have a slightly positive mean (0.01%), which is a sign of a positive stock market during the tested period from 2008 to The study by Setterberg (2007) encountered the same problem with all the means being slightly positive for all portfolios, but still found evidence of PEAD. The assumption for normality in the tests might be too harsh, since the skewness deviates marginally from zero and the kurtosis is very high for all portfolios. From these results I cannot assume that the central limit theorem is valid argument for the samples to be normally distributed. The normality tests are presented after this section. The average standard deviation is fairly high for all samples for all three measures indicating that possibly there are some outliers in the sample or the deviation of the observations is very disparate. For every researcher in statistic it is always a question of whether you should remove the outliers from the samples, however, in this test I chose not to remove the outliers. In the robustness section about regression on possible explanatory variables the dependent variable CAR is examined by excluding or including the outliers to see if these can explain the abnormal returns. Page 44 of 113

45 Table 3 - Descriptive Statistic The first column for the descriptive statistic is the number of earnings announcements included in each portfolio over the tested period from 2008 to The next five columns are the mean, median, standard deviation, skewness and kurtosis based on the abnormal returns. The last column is the beta between the stock price and the market index. Source: See the CD Content. Page 45 of 113

46 4.2. EMPIRICAL RESULTS OF NORMALITY TESTS The earnings-, price- and EPS-measure and raw return samples abnormal returns and all the CARs from day 0 to day 90 are depicted in Q-Q plots below - See figure 10. Four out of five graphs shows an S shape which are indicating a heavy tail in the data and therefore these are deviating from the normal distribution. These visual results with the descriptive statistic in table 3 indicate that the central limit theorem is not valid for this data. However, the last graph of the CAR values shows very small deviations from normality and could therefore be an approximation to the normal distribution. Figure 10 - Q-Q Plots for Normality Page 46 of 113

47 Here are presented five quantile-quantile (Q-Q) plots of the Earnings-, price- and EPS-measure s samples. The last two are the CAR values from day 0 to 90 from the above samples and the raw returns without the market model. The red line indicates the theoretical density line for a normal distribution. A deviation from the line indicates that the data is not normally distributed. Four tests are conducted on each of the samples, but specifically to answer whether the CAR values are normally distributed. The tests shows very similar results 34, however, only the Anderson-Darling test is presented in the below table 4, since it is concluded to have a very good performance overall compared to the other tests (Stephens, 1974). Table 4 - Normality Test Test Sample Anderson-Darling Test Earnings-Measure 6920,3 Price-Measure 8497,1 EPS-Measure 1183,8 Raw Returns 1170,5 CAR Values 6,7 Significance Level at 5% is equal to a critical value of 2,492. From the table is it clear that all of the tests for normality are rejected and also the test on the CAR values. The non-normality in the samples makes it essential for the parametric tests to be supported by non-parametric tests to make any profound conclusion of the parametric results. 34 See Appendix 15 for all four tests results conducted in Eviews. Page 47 of 113

48 T-Value 4.3. REACTIONS TO EARNINGS ANNOUNCEMENTS For the PEAD to have significant influence an earnings announcement should contain new information for the market. This information will make the stocks react by either adjusting the prices up or down. I adopt a test for the market efficiency from the Danish article by Lønroth et al. (2000). Firstly, a test for all of the earnings announcements in this study in the period from 2008 to 2011 See figure 11 below. The red line indicates a significance level of 5% with the day 0 being the official earnings announcement date. From the figure it can be concluded that the announcements contain new and unexpected information to the market and therefore creates an significant reaction for a period of 2 trading days (Shown in the figure 11), where after the stocks adjusts to below the 5% significance level indicating that the Danish stock exchange is slowly efficient. These results are different than the results by Lønroth et al. (2000), where they found the market to have a slower reaction over 4 trading days. The article by Sponholtz (2005) found the Danish Stock market to be even slower with a period of 6-7 trading days. The methodology used in the article by Lønroth et al. (2000) and Sponholtz (2005) are comparable to this study, which indicates that the Danish stock market is more efficient now than before. Figure 11 - Market Reaction to Earnings Announcements All Quarters from 2008 to ,13 α-level at 5% 2, Trading Days In the below figure 12 the same test is conducted for each quarter to test whether the reaction to the earnings announcement might be different. The three graphs for the first, second and fourth quarters shows the same conclusion as overall with a 2 trading day reaction. The third quarters are different with a reaction period of 4 trading days. This could be that nearly all of the third quarter announcements are gathered in the same month (August See figure 9) and not split over 2-3 months as commonly for the other quarters, which means that the market might become overload with new information which reflects that the stocks prices does not react as quickly as other quarters. Besides the third quarter the Danish stock market can be concluded to Page 48 of 113

49 be fairly efficient. Therefore, it is unlikely that there is room for the existence of PEAD, since the prices seems to adjust fairly fast to new information and they do not reflect evidence for an possible future drift of the stocks. It should be mentioned that the American stocks on the NYSE is known to adjust within minutes of an earnings announcements and abnormal return are found to exist until the next opening day after an earnings announcement (Patell and Wolfson, 1984) and therefore the conclusion is that it is fairly efficient and should not be interpreted as a fully efficient market. In newer research on market reactions it have been proven that a positive analytical stock report on the American TV channel CNBC are fully incorporated into the stock price within one minute (Busse and Green, 2002). Figure 12 - Market Reaction to Earnings Announcements per Quarters Page 49 of 113

50 4.3.1 EMPIRICAL RESULTS OF THE EARNINGS-MEASURE The next three sections are the main results of this study. The first is the empirical results for the earnings-measure See table 5. The earnings-measure s portfolio 1 is significant up to 30 days, however, these results show positive CAR values which was not expected before conducting these tests and only in the event window up to 60 days after event date the CAR is neutral (0,0%), but not significant. These are general strong results support by two of parametric tests and two of the non-parametric (see appendix 7). The CAR 0 is not explicitly displayed in the below main results tables, since this day is the portfolio formation day and also the quarter end day, where the official earnings announcements have happen before this CAR 0. This is performed to make it a possible real-life investment strategy, since one of the arguments against PEAD is that it only exists in the financial literature and not in real-life. Table 5 - Empirical Results for the Earnings-Measure The table contains the main results with the event date set at the end of each quarter for the tested period The firms are ranked into 10 portfolios at each quarter end on the basis of the Earnings-measure. The Earnings-measure is estimated as the difference between the actual earnings and the expected earnings scaled on the standard deviation of past earnings. The abnormal returns are estimated by the market model and followed for up to 90 days after portfolio formation. The first 10 columns contains the results for each portfolio and the last column contains the results from an hedging strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 trading days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T-values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T-values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content folder on the Earnings-measure. Significance under a two-tailed test is indicated as follows: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. The next two portfolios 2 and 3 are both significant and negative at the event period of 60 days, and these two portfolios are showing more similar signs towards former studies on PEAD with aggregated negative values. The middle portfolios 4, 5, and 6 are showing no significant signs of either positive or negative CAR values, which was expected. Portfolio 7, 8 are showing significant Page 50 of 113

51 signs at the 10 days window, and further on in the 30 days event window the CAR is higher and still significant. The portfolio 9 is the black sheep of the family, because it displays negative CAR values; however these are not supported by the non-parametric T-tests. This could be an indication of outliers affecting the results. This is a sign opposing the PEAD-effect, since in order to prove PEAD the good news" portfolios as 9 and 10 should show significant, positive CAR values. The last portfolio 10 shows significant positive values in all event windows and ends at a high CAR value (4.4%). These results are supported by the non-parametric tests except from the last 90 day event window (see appendix 8). The last column in table 5 above shows the hedge strategy for portfolio 10 and 1 which display the same picture as other studies on PEAD, where this strategy would earn up to significant profit of 2.7% for the 60 day event window and for 90 days with a profit of 1.5% and both event windows are support by the non-parametric T-tests. In figure 13 the CAR values are displayed over the 90 day period, and if this should be a perfect case of PEAD then the blue line would be portfolio 10 increasing and the red line would be portfolio 1 declining, but this is not the case when comparing with the famous graph by Foster et al. (1984) of US stocks going up to 60 days (see appendix 9), however the hedge is still positive from day 30 and onwards. Figure 13 - Hedge Graph of the Earnings-measure A focus on Portfolio 1 (P1) the CAR 0 to 30 shows that there might be a problem with the portfolio formation being set at the quarter end, since the effect of the earnings announcements have occurred and instead started to recover with positive abnormal returns. However, from CAR days 30 to 60 the abnormal returns are negative and therefore I assume that new announcements have happened and therefore the negative drop. This assumption is Page 51 of 113

52 based on a comparison with the former figure 9 under the data selection section, where it is clear that most of the announcements occurred within month two of a quarter which is approximately 30 trading days after CAR 0. Further, in the article by Bernard and Thomas (1989) they found a three quarters negative correlations, which means that one bad news announcement is followed by two more bad news announcements before these will turn to good news in the fourth quarter. In the robustness checks section the case specific test is conducted from the exact earnings announcements date and not at the quarter end as these main results. Comparison with former studies for the Earnings-measure I chose to start the comparison with former studies by the study that inspired me to investigate PEAD in Denmark just as it has been for many of the later studies on PEAD in US and Europe. The study by Bernard and Thomas (1989) discovered that for small and medium sized firms, which are similar with most of the firm sizes on the Danish stock exchange, the drift was only significant up to about 60 days after the announcement for the highest SUE, where in this study it is significant up to 90 days after. The bad news firms were significant in their study for up to 240 days after the announcement with negative CAR values, which are opposite this study s CAR values where nearly all the CARs are positive for the bad news, but only significant up to 30 days after formation. When comparing these results the bad news firms are recovering much faster and do not display the same drift as in the American study. However, for the comparison between good news then the Danish firms have higher CAR values and longer drifts than the US firms. Looking at European studies for a comparison, then the Swedish study by Setterberg (2007) concludes that there is PEAD in Sweden; however it might not be very robust. Overall, the stocks in her study are all positive CAR values with the lowest at 2.8% for bad news and 10.9% for good news and are significant for up to 180 days after portfolio formation. Setterberg (2007) also brings out the possibility of the sample size being too small to detect conclusive evidence of PEAD, since small extreme stocks can influence the specific portfolio heavily if extreme maximum or minimum abnormal returns are observed as discussed the problem with outliers. This might be the case of the portfolio 9 in the results (see table 5), where it stands out with negative values compared to 7, 8 and 10, however the sample sizes were down to 4 in her study (Setterberg, 2007), where it is down to minimum 67 for this earnings-measure. In the UK study by Liu et al. (2003), they found conclusive evidence of PEAD with a hedge portfolio earning up to 10.8% in profit. The bad news portfolio also produced Page 52 of 113

53 positive CAR values as in this study for up to 12.7% after 12 months; however the good news firms earned up to 23.5% after 12 months. In a study by Liu et al. (2003) it was estimated that the event period of 90 days would earn up to 5.4% for good news and 2.5% for bad news. Compared to this study s results of 4.4% for 90 days and 2.7% for 60 days, then the effect seems rather similar for the Danish and UK market. In the Germany study by Burghof and Johannsen (2009) on the Frankfurt Stock Exchange they found evidence for PEAD up to 60 days after formation for a hedge portfolio earning approximately 3%. A surprising result in the study by Burghof and Johannsen (2009) is that the bad news portfolio is not significant in either of the event periods; therefore it seems that most of the drift is carried by the good news portfolio, which is similar to the results in this study. A combined comparison of this study with the three European studies (Liu et al., 2003; Setterberg, 2007; Burghof and Johannsen, 2009) shows that the good news portfolio is generating the highest profits and therefore is outperforming the bad news portfolio. This is the opposite result compared to the US study (Bernard and Thomas, 1989), where the bad news portfolio generates the highest profits for a hedge strategy. This could be an indication that it is better to invest in the good news announcements than the bad news announcements in Europe; therefore the implicit hedge strategy in PEAD studies would generate a profit by the opposite way of the US hedge. This is a surprising finding. Overall, the earnings-measure is following the path of former European studies and therefore I can conclude that on the basis of the earnings-measure that PEAD exist on the Danish stock exchange. The drift for a hedge strategy seems to take a little longer before setting in and Burghof and Johannsen (2009) discovered the same in their German study, however it only took 10 days before the drift was significant, whether the PEAD will last for longer than 90 days on the Danish stock exchange is a possible expansion for future researchers. Page 53 of 113

54 4.3.2 EMPIRICAL RESULTS OF THE PRICE-MEASURE The price-measure shows diverging results and conclusion compared to the above analysis of the earnings-measure See table 6. The same result with Portfolio 1 (Also see appendix 10) producing significantly positive results for most of the period. However, these results are not as strong, because it is only found in the parametric tests, where none of non-parametric supports these results. Table 6 - Empirical Results for the Price-measure The table contains the main results with the event date set at the end of each quarter for the tested period The firms are ranked into 10 portfolios on the basis of the Price-measure, which is the four day abnormal returns surrounding the earnings announcements. The abnormal returns are estimated by the market model and followed for up to 90 days after portfolio formation. The first 10 columns contains the results for each portfolio and the last column contains the results from an hedging strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 trading days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T-values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T-values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content folder on the Price-measure. Significance under a two-tailed test is indicated as follows: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. Portfolio 2, 3 and 4 are following this path of positive results, however they are mostly significant in the first 30 days after formation. Portfolio 5, 6 and 7 are showing slightly neutral results, therefore neither producing significant high nor low CARs, which was expected for these specific portfolios and were the same results for the earnings-measure. For the last portfolios 8, 9 and 10 the results are not in line with the earnings-measure and actually portfolio 10 are insignificant for all the conducted T-tests (See appendix 11). The CAR values for portfolio 8 and 9 are producing significant negative CAR values. The results are quite strong here and do not suggest this phenomenon. The hedge strategy would generate negative CAR values in all event windows from 10 to 90 days. The measure is Page 54 of 113

55 developed by Liu et al. (2003) in their study on the UK market, therefore with the UK being the neighboring country, and then my expectation is a similar result as they found, but the conclusion on the price-measure is that the PEAD does not exist on the Danish stock exchange. Comparison with former studies for the Price-measure A comparison with former studies on the price-measure, then Liu et al. (2003) found negative CAR values for the bad news for up to -1.1% and positive for the good news for up to 2.5%. This measure was also the most profitable for a hedge strategy in the UK study compared to the two other used measures in their paper. For a European study by Gerard (2012) he ranks the stocks with the same approach as the price-measure and finds significant CAR values both negative and positive for up to 60 days after formation. The estimated hedge will generate a significant profit of 1.7% for the 60 day event window in his study. In the Germany study by Burghof and Johanssen (2009), they estimated based on the prior 40 days of abnormal returns, which are more in line with a price-momentum strategy. In order to precisely measure the earnings announcement impact on the stock price, then prior 40 days does not capture this effect, since their measure does not precisely estimate on the announcement day, but on the past changes of the stock price. However, there are similarities between this study s measure and their measure. A significant hedge strategy for up to 109 days after formation was found by Burghof and Johannsen (2009). Now changing the perspective to the American studies, then Foster et al. (1984) estimated two models based on the abnormal returns surrounding the announcement day, which is similar to the price-measure in this study. They found no significant values in any of the ten portfolios for both models. Actually, their study experienced the same trend with the bad news portfolios being slightly positive and the good news being more negative as in this study. The last comparison is with the study by Chan et al. (1996), which measures the prior 2 days and first day s abnormal gain surrounding the announcement. They found significant CAR values for both the bad news and good news. There are some diverging results here, where this study is supported by a study that have shown comparable results of no existence of PEAD and then there is the results from the other studies where this measure is showing conclusive results of PEAD. The reasons for these diverging results could be the use of a small stock exchange, and therefore the announcement is not captured within the four days surrounding, because of lower trading volumes or fewer traders or investors following the stocks. Therefore, the event window should be either longer to capture the effect of an earnings announcement as with the study by Burghof and Johannsen (2009) or the fact that this Page 55 of 113

56 measure might not be useful for a small stock exchange where trading volumes generally are lower. If we are jumping the gun of the regression part, then we see the coefficient of momentum for the -90 or -200 days trading days before announcement abnormal returns being a significant factor in explaining the CAR values in portfolio 1 and 10. This could be an argument to expand the event window, however expanding the window too much would form this study into a price momentum study rather than an earnings momentum study, where former returns can explain future returns and the main point of this study is using the information created by the earnings announcement to explain future returns EMPIRICAL RESULTS OF THE EPS-MEASURE The EPS-measure is only estimated per year and with lower sample sizes, since the amount of analysts following these stocks per year is highly concentrated around a small amount of large stocks. Table 7 - Empirical Results for the EPS-measure The table contains the main results with the event date set at the end of the year for the tested period The firms are ranked into 10 portfolios at each year end on the basis of the EPS-measure. This measure is estimated as the difference between the actual EPS and the average analysts expected EPS scaled by the stock price. The abnormal returns are estimated by the market model and followed for up to 90 days after portfolio formation. The first 10 columns contains the results for each portfolio and the last column contains the results from an hedging strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 trading days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T-values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T-values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content folder on the EPS-measure. Significance under a two-tailed test is indicated as follows: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. In table 7 the Portfolio 1 shows significantly high positive CAR values (see also appendix 12), which are in line with the earnings- and price-measure, however portfolio 10 (see also appendix 13) in this EPS-measure is not showing higher or significant CAR values. Therefore, we see the Page 56 of 113

57 same picture as with the price-measure that a hedge strategy would not generate a profit. For the portfolios 2, 3 and 4 there are also positive CAR values with few of them being significant. The middle portfolios 5 and 6 are fairly neutral and not significant. The top portfolios 7, 8 and 9 shows positive CAR values in the 7 and 9 which are significant up to 30 days, however portfolio 8 show insignificant negative CAR values. Comparison with former studies on EPS-measure Turning the perspective onto studies using analysts forecast in Europe, then the first is the study by Liu et al. (2003) where their EPS-measure shows positive CAR values for a 90 day window in all portfolios and a hedge would generate 3.5% on average. The same measure was used by Forner et al. (2009) and proved a significant positive hedge strategy of 0.47% for a 90 day window. An American study by Chan et al. (1996) also showed positive CAR values in all portfolios for this measure. The Polish study of PEAD used the analysts forecast to form portfolios, and found significant positive CAR values in both the first and third month after formation for up to 2.9% in profit for this hedge strategy (Dische, 2002). An international study by Hong et al. (2003) used the last six month average of analysts forecast to form portfolios and tested a hedge strategy of good news versus bad news. This proved significant positive CAR values in Australia, Canada, France, Germany, Hong Kong and UK, however Japan, Korea, Malaysia, Singapore and Taiwan showed insignificant and some negative CAR values for this strategy. A difference between the measures used in other studies is the length of the estimated average, where this study used the last 30 days up to the announcement and other studies used 3 or 6 months averages to form their portfolios. This could be a liability on the measure and the results might have been different if a longer estimation period was used. However, the fact that this study is performed on a small stock exchange might also influence the accuracy of the EPSmeasure, since the number of analysts following the stocks is small and focused on the major stocks compared to other stock markets. Therefore, my conclusion on the EPS-measure is that the PEAD does not exist on the Danish stock exchange. However, this conclusion on the EPSmeasure should be taken with caution, because of the above mentioned complications with this measure in this study DISCUSSION ABOUT THE EMPIRICAL RESULTS The overall conclusion on PEAD based on these measures is challenging. Each of the measures are showing different results, however mainly the earnings-measure is producing significant related PEAD results as in other studies for the 60 and 90 day event windows. The earnings- Page 57 of 113

58 measure is known as the most used measure in the literature to prove PEAD. The price-measure seems to capture either too much information surrounding the earnings announcement or too little with the event window being set for 4 days. A visual interpretation sums up the differences by assessing a hedge strategy for each measure (See appendix 5). Here the earnings-measure graph shows positive CAR values after 30 days and a peak point at day 55 with approximately 3.5%. The EPS-measure shows a small positive return after approximately 60 day, but it ends below zero. The main objective was to test for the existence of PEAD in the Danish stock market. My conclusion of the above empirical results point to the existence of PEAD in Danish stock exchange and therefore PEAD is a phenomenon in Denmark and in line with this conclusion the Danish stock exchange can be considered to be slow in processing new information REGRESSION RESULTS OF THE BASIS OF PORTFOLIOS 1 AND 10 In this part a regression is performed on the earnings- and price-measure to seek answers for why the PEAD occurs or what characteristic could explain its presence. The EPS-measure was considered to be too small in sample size in order to bring forward valid results based on a regression and is therefore not investigated further in this section. The two extreme portfolios 10 and 1 are chosen to be regressed upon, since these are the key to determine whether PEAD exists and what might be causing it. In table 8 below the two measures are presented along with dependent variable the CAR values in the five event windows. The independent variables ASSETS and MARKETCAP are tested, since they bear close similarity to the Fama-French three factor model (Fama and French, 1993) and therefore might bring insight to the discussion on the PEAD only being significant for large stocks. The EPS variable is tested to seek a relationship between the CAR values and the earnings per share. The BETA variable is tested to see if higher and more risky stocks or less risky stocks could explain the drift inspired by Bernard and Thomas (1989). The MOMENTUM90 and MOMENTUM200 are included, because of the article by Jegadeesh and Titman (1993), where the past return from 3 to 12 months before an event could explain future returns. The last variable is the ABNORMALITY, where it is a test to see if other events in the period could affect the results hence if the sample was influenced by outliers. The error term is assumed as normally distributed and the expected value is zero. The variance of the error term is constant for all the values of the independent variables and the independent variables are uncorrelated with this term. The regression is estimated in Eviews and the results from all the regressions can Page 58 of 113

59 be found in the appendix 14 and the regression equation is shown in appendix 6. For Portfolio 1 the earnings-measure the MOMENTUM200 is the most significant variable and therefore an important part of the results in the CAR values. The 90 day event window displays other significant coefficients as ASSETS, MARKETCAP, BETA and the intercept term and this sum to a term of 30%, which is fairly high. The regression based on Portfolio 10 for the earningsmeasure shows the MOMENTUM200 being the most significant in all event windows with an term explaining up to 45% of the CAR values in the 90 day event window. In the study by Setterberg (2007), she does not find the Fama-French three factor variables to be significant; however the study by Foster et al. (1984) found the firm size to explain 66% of the variation in the CAR values. Therefore, there is some unexplained difference in whether the firm size has an effect or not. The price-measure displays significant coefficients (ASSETS, MARKETCAP, EPS and BETA) in the last two event windows of 60 and 90 days, however besides the BETA then the actually effect by these variables are fairly low. The two momentum variables are significant in all periods. The term is explaining up to 28% for portfolio 1. The portfolio 10 regression shows a similar picture, but with an ending term of up to 56%, which is considered to be high for the 90 day window. Generally, the former abnormal return seems to be the best indicator of future CAR values, therefore if this study was based on sorting and ranking the stocks based on the MOMENTUM200 variable, it would probably have been possible to reach similar or even higher CAR values for the price-measure than the four day event window that is used in this study. Comparing with former studies, then the regression based on a similar measure for the Foster et al. (1984) study found none of the comparable size variables ASSETS or MARKETCAP to be significant to explain the variation in the CAR values. From the above analysis on the regression results, this does not bring further light to the discussion on what causes the PEAD or why does it exist. The only significant measure in the majority of the regression is the momentum variable, where it states that former return can predict future returns. The earnings-measure is estimated on a quarterly basis, but it could be sought from these results that the stock prices are already showing similar direction as the earnings-measure for a stock. Therefore, it could be stated that past abnormal returns before an earnings announcement could be an indicator of future returns. The BETA variable is a sign of the riskiness of each stock and for the 90 day CARs the BETA is significant, which is indicating that the higher the BETA the higher the CARs and this support the CAPM, where an investor will receive a premium for the higher risk. Page 59 of 113

60 Table 8 - Regression Results The table reports the regression results on the CAR values for the portfolio 1 and 10. The first column is the CAR values from 0 to 10, 20, 30, 60 and 90 days. The next eight columns are the independent variables, where the ASSETS is the book value for each stock in DKK. The MARKETCAP is the market value in millions of DKK. The EPS is the actual earnings per share for each stock. The BETA is the correlation between the stock and the market index. The MOMENTUM90 and MOMENTUM200 are the CAR values for each stock for hence -90 trading days and -200 trading days before the event date CAR 0. The ABNORMALITY is a dummy variable for outliers where one if the abnormal return for each stock is greater than five times the standard deviation for the whole sample or zero otherwise. The last variable is the intercept and the column is the R 2 indicating how much of the dependent variable can be explained by the independent variables. Source: See appendices 14 and 6. Page 60 of 113

61 4.5. ROBUSTNESS CHECKS In this section three different robustness tests are conducted to either support and dismiss the main empirical results and brief discussion on the tested period. Sample Size test The above test results could be influenced by the sample sizes being too small and therefore a chance for generalizing the PEAD when it does not exist. Therefore, I turned the 10 portfolios into 3 portfolios as the study by Setterberg (2003) and Forner et al. (2009) with the aim of investigating if the results were still valid. In table 9 the results are replicated and the results are no different from the former conclusions in this paper. The earnings-measure hedge is not significant in all event windows, however the CAR for the 60 and 90 day windows are highly significant. The price-measure behaves in the similar pattern with the bad news portfolio 1-3 producing higher positive CAR values than the good news portfolio 8-10, which leads to highly negative significant CAR values for the hedge. The EPS-measure also replicates the same conclusion. From these results I can conclude that the above mentioned results are not sensitive to the sample size, since the same conclusion would have been reached by ranking into 3 portfolios instead of 10 portfolios. A discussion on the tested period Another robustness check for the particular sample was the tested period, since the period from 2008 to 2011 is influenced by the financial crisis. It reached its highest point in the year of 2008 and could have a high impact on the results, because of the size of the abnormality. However, a visual interpretation of the produced CAR values in the appendix 4 shows the first two years of the average CAR being negative for nearly all event windows in 2008 and 2009, but the average CAR values are significantly higher in the period 2010 and 2011 and therefore producing positive values. The results could have been higher if the period had been limited to only include 2010 and 2011, but this is also a sign of the PEAD being strong enough to survive a bigger abnormality than itself the financial crisis. The price-measure was also interpreted visually, but in this chart we do see the average CAR values being highly influenced by the financial crisis in Therefore, this could be the reason behind the difference in results compared to former studies, because Chan et al. (1996) and Liu et al. (2003) both tested in periods where the general economy was strong and not influenced by such a big negative abnormality as the financial crisis. Therefore, the figures are an indication that the chosen period might explain some of the Page 61 of 113

62 existence of PEAD. However, this is not investigated further and a possible extension for future research. Table 9 - Empirical Results for the Sample Size Check The table contains the main results with the event date set at the end of each quarter for the tested period The firms are ranked into 10 portfolios at each quarter end on the basis of a measure except for the yearly EPS-measure. The Earnings-measure is estimated as the difference between the actual earnings and the expected earnings scaled on the standard deviation of past earnings. The Price-measure is the four day abnormal returns surrounding the earnings announcements. The EPS-measure is estimated as the difference between the actual EPS and the average analysts expected EPS scaled by the stock price. The abnormal returns are estimated by the market model and followed for up to 90 days after portfolio formation. The first 10 columns contains the results for each portfolio and the last column contains the results from an hedging strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 trading days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T-values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T-values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content folder for under each measure. Significance under a two-tailed test: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. Page 62 of 113

63 Case Specific Test of PEAD In the main empirical results it is chosen that the PEAD should be possible to implement in reallife and therefore the CAR 0 is the portfolio formation day and the quarter end day, however this choice delays the reaction to the PEAD, because the earnings announcements effects are not measured before the quartered have ended. In the below figure the CARs are displayed over the 90 day event window to see the effect if all information is available before the announcement and therefore possible to form the portfolios on the exact earnings announcements dates. This PEAD strategy is only possible to implement with insider information. In this graph the PEAD in Denmark is put on equal footing with former studies on PEAD and especially with the Foster Graph (appendix 9), there is a clear positive effect for portfolio 10 and vice versa for portfolio 1, which generates a very profitable hedge portfolio ending at 9%. Figure 14 - Case Specific Test of PEAD A test of whether these figures CARs are significant is conducted and the results are presented in table 10. The portfolio 1 is revealing significantly negative CARs in nearly all of the event windows and support by the non-parametric tests. The portfolio 10 is displaying positive values in all of the event windows, however only the middle event windows from 20 to 60 days are support by a rejection by the non-parametric tests. For the hedge strategy the results are highly significant and positive for the CARs in all of the event windows and fully supported by the nonparametric tests. This is clear sign of PEAD when measuring from the official earnings Page 63 of 113

64 announcement day and further support to the main empirical results on the existence of PEAD in Denmark. Table 10 - Case Specific Test of PEAD The table contains the results with the event date set at official earnings announcement date for the tested period The firms are ranked into 10 portfolios on the basis of the Earnings-measure. The Earnings-measure is estimated as the difference between the actual earnings and the expected earnings scaled on the standard deviation of past earnings. The abnormal returns are followed for up to 90 days after portfolio formation. The first two columns contains the results for each portfolio and the last column contains the results from an hedge strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T- values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T-values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content under folder Earnings-Measure. Significance under a two-tailed test: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. Page 64 of 113

65 A test with Raw Returns The final robustness check is performed (See table 11 below), since a lot of the discussion on the causes of PEAD is based in the model specification. Therefore, as in the study by Bernard and Thomas (1989) the estimates are based on the specific stock return minus the market return. The procedure leaves out all the model estimation and it is considered as being a process of estimating pure raw returns that a real-life investor would experience. This is only based on the earnings-measure, since it was the only measure to show significant signs of PEAD. The results are even more conclusive than the former results with a hedge strategy for 60 days having a significant profit of 6.4%. A surprise in the CAR values is the sudden change of positive values in the portfolio 1 to high negative values in the 60 and 90 day windows. Therefore, I can conclude on the basis of these results that the results are robust and that the reason for the model being misspecified does not seem valid and this conclusion supports the conclusion Bernard and Thomas (1989). Table 11 - Empirical Results for the Raw Return Check The table contains the results with the event date set at the end of each quarter for the tested period The firms are ranked into 10 portfolios at each quarter end on the basis of the Earnings-measure. The Earnings-measure is estimated as the difference between the actual earnings and the expected earnings scaled on the standard deviation of past earnings. The raw returns (stock return subtracted market return) are followed for up to 90 days after portfolio formation. The first two columns contains the results for each portfolio and the last column contains the results from an hedge strategy of going long in portfolio 10 and short in portfolio 1. The rows are the event windows of 10, 20, 30, 60 and 90 days after formation. These are supplied with their %-Cumulative Average Residual (CAR) and the T-values is displayed in brackets. The T-values are the T3 - Adjusted Standardized Abnormal Return with Patell's Adjustment, if shaded then either the Rank test, Sign Test or Generalized Sign Test supports the rejection. The T- values in the last column are estimated in Eviews and if shaded then the Rank test or Sign test supports this rejection. Source: See the CD Content under folder Earnings-Measure. Significance under a two-tailed test: (*) = significant at 10%, (**) = significant at 5%, (***) = significant at 1%. Page 65 of 113

66 PART 5 5. FINAL CONCLUSION One of the most damaging arguments against the efficient market theory was discovered for 45 years ago and was named Post-Earnings Announcement Drift. During the course of the years several studies have confirmed this phenomenon in the US. The main objective for this study has been to examine whether the abnormal phenomenon is a valid discovery for a small Danish stock exchange? The Danish stock market in general is considered to be an efficient market. However, this study finds the PEAD to be a significant discovery for the Danish stock exchange. It should be emphasized that this statement should be taken with some reservation. The earnings-measure displays significant signs of PEAD after 60 and 90 days of formation supported by both parametric and non-parametric T-tests, however both the price-measure and EPS-measure does not display significant signs of PEAD at any point in time during the tested period. Despite this, my general conclusion is that PEAD exist on the Danish stock exchange, because the earningsmeasure is based on purely past earnings. This makes it a stronger indicator than both the priceand EPS-measure which both capture more and different information surrounding the announcement. The earnings-measure is also the most used measure in the literature on PEAD and whereas the price- and EPS-measure have been developed over time to test if a comparable measure could display a similar result. It should be mentioned that newer research is claiming the EPS-measure to be stronger, but this study was too affected by both a small sample size and only annual announcements to make such a profound conclusion on this measure. This general conclusion therefore supports the conclusion by Sponholtz (2005) that the Danish stock exchange is inefficient and that the top ranking as the highest in the ability to use and process information in E-readiness is not enough to make the PEAD insignificant. But the high ranking might be the source of the lower return comparing with former studies. The PEAD was found to peak between 50 to 60 days for the earnings-measure with the first positive hedge profit of above 1% from day 40 until day 90 (See appendix 5). The EPS-measure also displayed a hedge coming close to a positive profit between 50 to 60 days. A different discovery in this study in line with other European studies is the fact that the good news portfolio produces the highest abnormal returns. This contrasts with the American Page 66 of 113

67 studies where the bad news portfolio produces the highest return for a hedge strategy. A hedge strategy on the Danish stock exchange would on average generate a significant abnormal return of 2.7% after 60 days of portfolio formation. If comparing with former studies of PEAD then these abnormal returns are lower, which makes a hedge strategy not as profitable as in other countries, and also the transaction costs for maintaining a portfolio strategy as the PEAD will diminish over time. How robust are the results of the three estimated Earnings-, Price- and EPS-measure? The empirical results were subjected to several robustness checks; however none of these robustness checks displayed different results, if anything they strengthened the conclusion on PEAD to exist on the Danish stock exchange for the earnings-measure. The robustness test on the methodology was conducted with purely raw return and here an investor would experience a significant abnormal return of 6.4% after 60 days of portfolio formation. Therefore, the discussed reason that the methodology could be the cause of the existence of PEAD is found not to be valid. The correlation between the measures was found to be very low and therefore providing evidence that these measures are not comparable as each of them captures very different parts of the newly released information to the market. The ranking was changed from ten portfolios to three and the same conclusion was still reached. The samples were tested for normality, which showed non-normality and therefore a crucial support by non-parametric T- tests to make a valid conclusion and the results were supported. Finally, the earnings announcements were measured from the official date and these results showed very strong evidence of the existence of PEAD in Denmark. How will the Danish stock market react on an earnings announcement depending on the time of the year? A test on the market reaction on earnings announcements generating new information was found to be significant within 2 trading days for all of the earnings announcements. As expected an earnings announcement contains new information that will make the stock prices adjust either up or down. Generally, the same reaction was found for each of the quarters with a small except for the third quarter where the reaction was slightly longer. The Danish stock exchange is concluded to be slowly efficient based on this test. If PEAD exists, then how can PEAD be explained? The regression results did not provide significant evidence to indicate the causes of the PEAD or its origin. The variable MOMENTUM200 was found to be significant for the majority of the Page 67 of 113

68 regressions results at each event window. Therefore, the past abnormal returns can explain between 28-56% of the future abnormal returns. The remaining variables that were found to be significant had smaller coefficients which would make them explain a minor part of the abnormal returns. Therefore this study supports the conclusion of Kothari (2001, p. 194) about the causality of PEAD: The profession has subjected the drift anomaly to a battery of tests, but a rational, economic explanation for the drift remains elusive IMPLICATIONS AND FURTHER RESEARCH Implications in this study The first implication of the study is found in the data collection process, where the data availability limited the amount of announcements possible to include in the sample as well as it considerably decreased the validity of the EPS-measure. The second is the chosen country market index, since all stocks are matched against this index, then if the index is underperforming then it will be possible to find significant abnormal returns when none exists. This is also one of the arguments against the use of the market model, and other studies have shown the benchmark portfolio method to be stronger and for further research an inclusion of all the Nordic countries could help make this method possible for the study of PEAD in the Nordic countries, since only using the Danish stock exchange is too small for this method. Finally, the third implication is the use of a short-term event window of 90 days, where research on event study s methodology has shown that the power considerably decreases by lengthening the event window by more than a month. This could be overcome by the use of long-term studies, but as mentioned earlier in the methodology part, a long-term study have a high risk of making false conclusions, but the use of bigger sample sizes could help overcome this risk and possible provide more insights to PEAD on the Danish stock exchange. Again, in relation to the other implications this could be possible by expanding this study to the Nordic countries. Further Research In relation to the quote by Kothari (2001) a rational explanation seems yet again to remain undiscovered also for this study on the PEAD. I had hoped that this study would provide further evidence on the root cause of PEAD, but it does not have the capability to make a profound conclusion on this part. However, it does provide evidence that PEAD seems to be a global phenomenon and the answer for its origin is not found only in the quantitative research. Page 68 of 113

69 A valuable consideration for further research can be to consider the path of qualitative research. In the discussion in part 2 on the possible causes for PEAD, the behavioural finance was discussed. This aspect might help find stronger explanations for the causes of PEAD, especially in the conception of an earnings announcement. The mind-set of a trader, investor or shareholder is essential to understanding, what the re-action to the new information is? An example here could the very low correlation between the earnings- and EPS-measure, where both of the measures builds upon the same basis, but as concluded are very different. The earningsmeasure is purely based on technical analysis, where the EPS-measures could carry emotions such as intuition, recent news, R&D expectations and many more different aspects that the earnings-measure does not capture. However, this study did not have the objective to investigate the irrational explanations towards PEAD, and therefore I leave it to future PEAD researchers. Page 69 of 113

70 PART 6 6. REFERENCES Ahern, Kenneth R. (2009): Sample selection and event study estimation. Journal of Empirical Finance 16. Page Ball, Ray (1988): What do we know about stock market efficiency?. Managerial Economics Research Center. Ball, Ray and Bartov, Eli (1996): How naïve is the stock market s use of earnings information?. Journal of Accounting and Economics 21. Page Ball, Ray and Philip, Brown (1968): An Empirical Evaluation of Accounting Income Numbers. Journal of Accounting Research. Ball, Ray, Kothari, S.P. and Watts, Ross L. (1988): Economic Determinants of the Relation Between Earnings Changes and Stock Returns. Electronic Copy is available at eid=6636 Bartholdy, Jan, Olson, Dennis and Peare, Paula (2011): Conducting Event Studies on a Small Stock Exchange. The European Journal of Finance. 13:3, February. Bartov, Eli, Radhakrishnan, Suresh and Krinsky, Itzhak (2000): Investor Sophistication and Patterns in Stock returns after Earnings announcements. The Accounting Review. Volume 75. No. 1. Page Bernard, Victor L. (1992): Stock Price Reactions to Earnings Announcements: A summary of Recent Anomalous Evidence and Possible Explanations. Working Paper #703. Division of Research. Bernard, Victor L. and Thomas, Jacob K. (1989): Post-Earnings-Announcement Drift: Delayed Price Response or Risk Premium?. Journal of Accounting Research. Volume 27. Bradshaw, Mark T. (2011): Analysts Forecasts: What do we know after Decades of Work? Electronic copy available at: Page 70 of 113

71 Bradshaw, Mark T., Drake, Michael S., Myers, James N. and Myers, Linda A. (2012): A Reexamination of Analysts Superiority over Time-series Forecasts of Annual Earnings. Rev Account Stud. Volume February. Brennan, Michael J., Jegadeesh, Narasimhan and Swaminathan, Baskaran (1993): Investment Analysis and the Adjustment of Stock Prices to Common Information. The Review of Financial Studies Winter 1993 Vol. 6, No. 4, pp Brown, Stephen J. and Warner, Jerold B. (1985): Using Daily Stock Returns. Journal of Financial Economics. Volume August. Burghof, Hans-Peter and Johannsen Matthias (2009): Risk Effect versus Delayed Price Response: The case of Post-Earnings Announcement Drift in Germany. Kredit und Kapital. Volume January. Busse, Jeffrey A. and Green, T. Clifton (2002): Market efficiency in real time. Journal of Financial Economics. Vol. 65. Page Campbell, Cynthia J., Cowan, Arnold R. and Salotti, Valentina (2010): Multi-country event-study methods. Journal of Banking and Finance. Volume July. Chan, Louis K. C., Jegadeesh, Narasimhan and Lakonishok, Josef (1996): Momentum Strategies. The Journal of Finance. Volume LI. NO. 5. December. Corrado, Charles J and Truong, Cameron (2008): Conducting event studies with Asia-Pacific security market data. Pacific-Basin Finance Journal, Volume 16, Issue 5, Page Corrado, Charles J. (1989): A nonparametric test for abnormal security-price performance in Event Studies. Journal of Financial Economics 23. Page Corrado, Charles J. (2011): Event Studies: A Methodology Review. Accounting and Finance. Volume July. Corrado, Charles J. and Zivney, Terry L. (1992): The Specification and Power of the Sign Test in Event Study Hypothesis Tests Using Daily Stock Returns. Journal of Financial and Quantitative Analysis, Volume 27. No. 3 September Cowan, Arnold Richard (1992): Nonparametric Event Study Tests. Review of Quantitative Finance and Accounting 2. Page Kluwer. Academic Publishers. Page 71 of 113

72 Dische, Andreas (2002): Dispersion in Analyst Forecasts and the Profitability of Earnings Momentum Strategies. European Financial Management. Volume 8. No. 2. Page Fama, Eugene F. (1965): Tomorrow on The New York Stock Exchange. Journal of Business. Fama, Eugene F. (1998): Market efficiency, long-term returns, and behavioural finance. Journal of Financial Economics 49. Page Fama, Eugene F. and French, Kenneth R: (1993): Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, Volume 33, Issue 1, Page Forner, Carlos, Sanabria, Sonia and Marhuenda, Joaquín (2009): Post-earnings announcement drift: Spanish Evidence. Span Econ Rev. Volume October. Foster, George (1977): Quarterly Accounting Data: Time-Series Properties and Predictive Ability Results. The Accounting Review. Volume LII. No. 1. Foster, George, Olsen, Chris and Shevlin, Terry (1984): Earnings Releases, Anomalies, and the Behavior of Security Returns. The Accounting Review. Volume LIX. No. 4. October. French, Kenneth R. (1980): Stock Returns and the weekend effect. Journal of Financial Economics 8. Page North-Holland Publishing Company. Gerard, Xavier (2012): Information Uncertainty and the Post-Earnings Announcement Drift in Europe. Financial Analysts Journal. Volume 68. No. 2. Griffin, John M., Kelly, Patrick J. and Nardari, Federic (2006): Measuring Short-term International Stock Market Efficiency.Electronic copy available at Griffin, John M., Kelly, Patrick J. and Nardari, Federic (2010): Do Market Efficiency Measures Yield Correct Inferences? A Comparison of Developed and Emerging Markets.Oxford Unversity Press. The Society for Financial Studies. Hew, Denis, Skerratt, Strong, Norman and Walker, Martin (1996): Post-earnings-announcement Drift: Some Preliminary Evidence for the UK. Accounting and Business Research 26. No. 4. Page 283. Hong, Dong, Lee, Charles and Swaminathan, Bhaskaran (2003):Earnings Momentum in International Markets. Cornell University. Page 72 of 113

73 Jegadeesh, Narasimhan and Titman, Sheridan (1993): Returns to Buying Winners and Selling Losers: Implications for Stock Market Efficiency. The Journal of Finance. Volume XLVIII. No. 1. March. Jegadeesh, Narasimhan and Titman, Sheridan (2011): Momentum. Annu. Rev. Financ. Econo. Volume August. Kallunki, Juha-Pekka (1997): Handling missing prices in a thinly traded stock market: implications for the specification of event study methods. European Journal of Operational Research 103. Page Kothari, S.P. (2001): Capital markets research in accounting. Journal of Accounting and Economics 31. Page Kothari, S.P. and Warner, Jerold B. (2007): Econometrics of Event Studies. Handbook of Corporate Finance. Volume 1. Liu, Weimin, Strong, Norman and Xu, Xinzhong (2003): Post-earnings Announcement Drift in the UK. European Financial Management. Volume 9. No Livnat, Joshua and Mendenhall, Richard R. (2005): Comparing the Post-Earnings Announcement Drift for Surprises Calculated from Analyst and Time Series Forecasts. Journal of Accounting Research. Volume 44. No. 1. March. Lønroth, Helle L., Møller, Peder Fredslund and Thinggard, Frank (2000): Annual Earnings Announcements and Market Reaction: The case of a Small Capital Market. The Aarhus School of Business. Department of Accounting. MacKinlay, A. Craig (1997): Event Studies in Economics and Finance. Journal of Economic Literature. Volume 35. No. 1. March. Mendenhall, Richard R. (2004): Arbitrage Risk and Post-Earnings-Announcement Drift. Journal of Business. Volume 77. No. 4. Mitchell, Mark L. and Stafford, Erik (2000): Managerial Decisions and Long-term stock Price Performance. Journal of Business. Volume 73. No. 3. Patell, James M. (1976): Corporate Forecasts of Earnings Per Share and Stock Price Behavior: Empirical Test. Journal of Accounting Research. Volume 14. No. 2. Page Page 73 of 113

74 Patell, James M. and Wolfson, Mark A. (1984): The intraday speed of adjustment of stock prices to earnings and dividend announcements. Journal of Financial Economics. Vol 13. Page North-Holland Ross, Sheldon M. (2010): A first course in Probability.8 th Edition. ISBN-13: Pearson Education. Rozeff, Michael S. and Kinney, William R. (1976): Capital Market Seasonality: The Case of Stock returns. Journal of Financial Economics 3. Page Sadka, Gil and Sadka, Ronnie (2003): The Post-Earnings-Announcement Drift and Liquidity Risk. Electronic copy available at Sadka, Ronnie (2006): Momentum and post-earnings-announcement drift anomalies: The role of liquidity risk. Journal of Financial Economics 80. Page Setterberg, Hanna (2007): Swedish Post-Earnings Announcement Drift and Momentum Return. Center for Financial Analysis and Managerial Economics in Accounting. Forth Draft. August. Sørensen, Bjarne Graabech (1982): Regnskabsinformation og aktiemarkedets effektivitet: En empirisk analyse. Nationaløkonomisk Tidsskrift, Nr. 2, s Sponholtz, Carina (2005): Essays on Empirical Corporate Finance. A dissertation submitted to Doctor of Philosophy in Economics and Management. University of Aarhus. Denmark. Stephens, M. A. (1974): EDF Statistics for Goodness of Fit and Some Comparisons. Journal of the American Statistical Association. Vol. 69. No Page Szyszka, Adam (2002): Quarterly Financial reports and the stock price reaction at The Warsaw Stock Exchange. Van Huffel, Gert, Joos, Philip and Ooghe, Hubert (1996): Semi-annual earnings announcements and market reactions: some recent findings for a small capital market. The European Accounting Review. Volume 4. No. 4. Page Vieru, Markku, Perttunen, Jukka and Schadewitz, Hannu (2005): Impact of Investors trading activity to Post-earnings Announcement Drift. Electronic Copy available at Page 74 of 113

75 7. APPENDIX Appendix 1 Extraction Procedure for Announcements Dates Appendix 2 The Mathematical Expressions for the T-tests Appendix 3 T-Tests Power Interval Appendix 4 - CAR Values per Year for Test Period Appendix 5 Hedge Graphs Appendix 6 - Regression Equation Appendix 7 - Earnings-Measure Portfolio Appendix 8 Earnings-Measure Portfolio Appendix 9 Foster Graph Appendix 10 Price-measure Portfolio Appendix 11 Price-measure Portfolio Appendix 12 EPS-measure Portfolio Appendix 13 EPS-measure Portfolio Appendix 14 Regression Results Appendix 15 Normality Tests Page 75 of 113

76 Appendix 1 Extraction Procedure for Announcements Dates Screen Print of the extraction procedure from the official webpage of Danish Stock Exchange. Page 76 of 113

77 Appendix 2 The Mathematical Expressions for the T-tests The market model, abnormal returns and the CARs are explained in depth in the section The below is short summary to help the understanding of the formulas used in the T-tests. The market model is defined as follows: Where is expected return on stock i at time t and is the return m on the MSCI Denmark at time t. Where the alpha and beta are estimated by the least squares method. The day to day return for both the stock and market are calculated as follows: The abnormal return is defined as follows: The cross-sectional averages and the average abnormal returns in the event window are defined as follows: The CAR is defined as: T0: T-TEST WITH CRUDE DEPENDENCE ADJUSTMENT For this T-test the T-value for the event window is defined as: Where the beginning are the ending day of the event periods, which are defined as event windows of 10, 20, 30, 60 and 90 days. Page 77 of 113

78 The Standard deviation is defined as: T1: T-TEST WITH ADJUSTED CROSS-SECTIONAL INDEPENDENCE For this T-test the T-value for the event window is defined as: The Standard deviation is defined as: Where the is the number of observation in the estimation period for each stock. T2: T-TEST WITH STANDARDIZED ABNORMAL RETURN Each abnormal return is calculated as follows: Where is the standardized abnormal return, is the abnormal return calculated from the market model and is the specific stock i own estimated standard deviation. The T-value for each event windows is Page 78 of 113

79 The Standard deviation is defined as: T3: T-TEST WITH ADJUSTED STANDARDIZED ABNOR MAL RETURN T-test is performed as follows Where is the abnormal return estimated by the market model, is the standard deviation and is the adjusted standardized abnormal return. Where the test statistic is calculated as The Standard deviation is defined as: T4: RANK TEST Each abnormal return is ranked according to each other. Where. The estimation period is from -200 up to day zero and the event windows are similar to formerly explained. Each is standardized by the number of missing observations. Page 79 of 113

80 The average value of is ½, because the sum of the values of is therefore the average value of is Therefore, the test statistics for the event windows are Where N is number of stocks used in the sample and is the standard deviation. T5: SIGN TEST The expected value of is zero under the null hypothesis. The test statistic is given by The Standard deviation is defined as: T6: GENERALISED SIGN TEST For multiday event window, the test statistic is as follows Page 80 of 113

81 The test statistic uses a normal approximation of a binomial distribution. stocks in the event windows where CAR ( ) are positive (Cowan, 1992). is the number of Where T-TEST FOR REACTION TO NEW INFORMATION The reaction is measured as: The average reactions are measured as: 5 ; 90] trading days, N is the number of earnings announcements, is the number of stock quotes in the estimation period [-200 ; -5 ], is the squared abnormal return for stock i at time t (t = trading day) in the event window 5 ; 90]. - Where are the estimated abnormal returns in the estimation period [-200 ; -5]. Page 81 of 113

82 Appendix 3 T-Tests Power Interval This is a screenshots from the article by Kothari (2007): Econometrics on Event Studies. Page 82 of 113