Turn of the month anomalies

Transcription

1 MSc Finance & International Business Author: Valdemar Stilling Chistensen Academic advisor: Tom Engsted Turn of the month anomalies - A global research on small, mid and large cap stocks. Aarhus School of Business June 2007

2 Abstract This thesis researches the return of stocks in a 4 day turn of the month (TOM) period, in 9 countries from all over the globe from 988 until 2006, in contrast to the return of the rest of the month (ROM). The data was taken from established indices from Datastream and the Swiss Stock Exchange. The primary object was to prove that the TOM effect exists in the stock markets of the countries. Hence we also examine if the effect is confined to the size of the index capitalization, and if the location of the effect can be restricted to any particular country or region. The empirical research part includes both parametric and non-parametric statistical methods. This increased the robustness of the study, and helped us to avoid data mining. Further it is a reaction to the critique of anomaly studies from authors around the world. The method used in this study consisted of one-way ANOVA analysis, Wilcoxon signed rank test, Tukey s multiple comparison test, Kruskas-Wallis test and Dunn s multiple comparison test. The results show that a 4 day TOM-effect was found in 4 of the 9 countries. However it remains unsolved if the TOM effect exists in the remaining 5 countries. The TOM effect shows excess returns compared to the ROM return. Further we prove that TOM-effect is related to the capitalized indices. The TOM effects are significant different in the small cap indices, than in the mid and large cap indices. The TOM effect of the mid and large cap indices could not be separated. Moreover the TOM effect in the latter group shows excess returns that are higher than in the small cap group. Finally our result showed that no pattern of countries or region could be confined to the TOM effect. The existence and whereabouts of the TOM effect is random.

3 Introduction Objective Problem statement Methodology Structure Delimination Efficient Capital Markets Market efficiency Fama s efficiency definition Literature review of the EMH Anomalies The definition of anomalies Anomaly types and literature review Other anomalies Calendar anomalies The dangers of data mining The best TOM pattern Empirical research Data The definition of index capitalization Data preparation Data Bias The definition of the TOM and ROM Periods Methodology Simple linear regression model of the TOM-effect One-way ANOVA test WSR test of the TOM effect Kruskal-Wallis test Results TOM and ROM Effects The TOM effect in the perspective of capitalization The TOM effect in the perspective of countries Discussion...6

4 5 The TOM effect and the EMH Conclusion TOM anomalies are present today The Efficient market hypothesis and the future of anomalies References...73 Appendices 2

5 Introduction Since Rozeff and Kinney challenged the efficient market theory in 976 by finding the January anomaly, and became recognised for it, many have eagerly contributed to the research of anomalies (Ogden, 990). Either they tried to exploit an anomaly themselves and earn excess return, or they published their results and tried to get the recognition that followed. Despite the many anomalies discovered, there are no known examples of investors who successfully have earned excess return. There are many different types of anomalies: The seasonal anomaly, the size-effect anomaly and the low price to earnings anomaly are just some of them. Calendar anomalies are particular interesting, because they have proved to be one of the most persistent of all anomalies. However, where many calendar studies try to prove anomalies, almost none try to determine the structures and the behaviour of the anomalies on a general scale. Kunkel et. al. (2003) and McGuinness (2006) are some of the authors who have contributed with the most recent and well documented proof of the turn of the month (TOM) effect, which is a calendar anomaly. It is interesting that many authors do not elaborate their work after they have proved the existence of the TOM effect. This paper is an attempt to elaborate on the work done by Kunkel et. al. (2003) and McGuinness (2006), in order to gain more generalised and global knowledge of the behaviour of the TOM effect anomaly.. Objective Kunkel et. al. (2003) presented in his article results that are in agreement with other findings of the TOM effect. However his use of statistical tools created a robustness that overcomes the data mining problems raised by a number of authors in the area of anomalies. Additionally the countries he investigated represent a global selection, thus stating the TOM effect is a global anomaly phenomenon. 3

6 McGuinness (2006) proves that the TOM effect is particularly great in the small cap stock from the Hong Kong exchange. His findings are among the first to describe the structures of the TOM anomaly. Kunkel et. al. and McGuinness articles have lead to this thesis, which is inspired and motivated by the articles mentioned above. The thesis will research the TOM effect on a global scale. McGuinness found evidence that the TOM-effect is correlated with the small cap indices of countries. However some of Kunkel et. al. (2003) findings indicate that the TOM-Effect is also present in large cap stocks. Therefore this paper will seek to reveal the relationship between stock capitalization and TOM effects. Thus to continue the work of McGuinness the samples investigated are small cap, mid cap and large cap indices. Consequently the work in this thesis will be inspired and motivated by the articles above. We will research whether or not the TOM effect is confined to any capitalization size in particular. Further we will discover if the TOM effect is greater in some stock capitalizations than others. Kunkel et. al. (2003) also indicates in his study that some countries contain the TOM effect while others do not. Therefore the authors of this study will analyse the possibilities of a global TOM-pattern, or if a particular region presents a better or worse TOM effect than other regions. The contrary part of this is that the TOM effect is randomly spread across countries and regions. Finally the results of the study are evaluated in the perspective of the efficient capital market theory. Will the research of anomalies change the fundamental theories? Will the efficient market hypothesis (EMH) continue to hold up? Those are some of the questions we will try to answer... Problem statement To research the TOM anomaly on a global scale from , hence an analysis of the TOM effect in the perspective of stock capitalization and the viewpoint of He uses the KFX index of Denmark which is the largest capitalized stocks of Denmark and finds the TOM effect. 4

7 countries or regions. The results will conclusively be discussed in the context of the efficient capital market..2 Methodology The method is motivated by the procedure from the article by Kunkel et. al. (2003), in which the results are robust and persistent enough to overcome the critics of data mining. This will create the desired level of creditworthiness. The countries selected to investigate will be similar to the ones Kunkel et. al. (2003) investigated. The reason for this is to narrow the subject down to countries where the TOM effects are known to exist before. Further the investigation of structures in terms of small cap, mid cap and large cap only has relevance in countries where the TOM effect appears. This will increase the relevance of the result and decrease the amount of obsolete results in terms of countries with no TOM Effect. The empirical methodology is elaborated further in chapter 4..3 Structure The initial part will give a theory review from the conception of the efficient market hypothesis and forward. This is followed by a review of the anomaly area. The overview of these subjects is necessary in order to understand the choice of statistical tools and analytical approach in the thesis. The empirical part will detailed describe the data collect and methodology. Further the statistical processing will be described and carried out. Moreover the results will be presented and discussed. The core robustness of the empirical research will be consisting of parametric and non parametric statistical methods. Finally the findings will be evaluated in the context of the problem statement and in the broad perspective of efficient capital market..4 Delimination The background of the efficient market hypothesis and anomalies will not be subject to a thorough research, because this would be a thesis in itself. The countries 5

8 investigated are relative few, compared to the many stock markets around the world. This limitation is caused due to the vast amount of data, an additional country would cause. This has to be weighted to the size of this paper. We have limited the thesis from creating the appropriate capitalized indices. Instead indices which have already been created by other entities have been used in this study. 6

9 2 Efficient Capital Markets The definition of the EMH was first made by Eugene Fama in his famous paper from 970 where he states the three market forms weak, semi strong and strong capital markets. However the reason for calling it the EMH was that the paper was based on reviews of theory and statistical empirical work, where hypothesis are used frequently (Fama, E. 970). Though the name of this area is still known as the efficient market hypothesis, others have started to use the more meaningful name efficient capital markets. (Copeland et. al., 2005). Both terms are widely used, and we will use both of them in this study, however the meaning of the expressions is the same. We use both terms because the expressions are used in different context and in particular it varies over time from article to article. It would make sense to use only one expression and hereby increase the understanding of the paper, but the contrary is believed to happen. A unified substitution will confuse the readers understanding instead of simplifying it. 2. Market efficiency According to theory a market is said to be perfect if (Copeland et. al., 2005): The markets are frictionless, meaning that there is no transaction cost, all assets are perfectly visible, and there are no constraining regulations. Perfect competition exists in the markets. This means that all security market participants are price takers. Markets are informational efficient: This means that all information is received simultaneously and is costless. All individuals are rational expected utility maximizers. A market that satisfies this is efficient, but it is also very restrictive, in fact perfect markets do not exist. But a market can be efficient without being perfect. In other words, the efficiency does not correlate with the notion of perfect markets. A market is always efficient if a market is perfect, but it can also be perfect even when the requirements for a perfect market are not fulfilled (Fama, 970). 7

10 2.. Fama s efficiency definition In practise markets are never perfect, therefore Fama used the perfect market theory as inspiration to model a better notion of market efficiency that complies better with the markets in practise. The notion defines three type of market efficiency (Fama, E., 970). Weak market efficiency The weak market efficiency is apparent, when it is impossible to develop a trading strategy, based on historical prices, which earns excess returns. Semi-strong market efficiency. The semi strong markets are apparent when the stock prices fully reflect all obviously publicly available information. Strong market efficiency Strong efficient capital markets are apparent when all available information is fully reflected in the stock prices. This means that no investor has monopolistic access to information, which enables him to earn a higher expected profit than other investors. Empirical tests on the weak form of efficiency are usually a test of the random walk. If the stock prices move randomly, then they are not correlated with the historical prices. The majority of studies in this area prove that the prices do indeed follow a random walk, or a random walk with a positive component, thus proving the existence of the weak form of efficiency (Pilbeam, 998). When testing the semi strong efficiency, the amount of available data increases considerably, from historical stock prices to all public available information. Examples of this information could be news paper articles, announcements, economical key figures, changes in dividend policy etc. This also increases the risk of bias, and the uncertainty of the models used for testing the semi-strong form of efficiency. Event studies are one of the most used means of testing, an example could be to analyse the impact of announcements on the stock price and how quickly it is 8

11 absorbed by the share price (Pilbeam, 998). Most anomalies studies are event studies, see section Generally no market is said to be strong efficient. Many studies have underlined this, by proving the existing of insider information. In 974 Jaffa collected data on insider trading on 86 observations in the 960s. The excess returns were statistically significant and greater than the transaction cost. His conclusion was that investors using insider information do earn positive abnormal returns, thus rejecting the strong form hypothesis. Finerty did an even more comprehensive study in 976 including insider transactions, and the conclusions were in line with Jaffa (Copeland et. al. 2005). 2.2 Literature review of the EMH After the conception of the efficient market hypothesis in the 970, many academics continued their work on the theory, and a vast amount of new empirical findings emerged. The worlds centre for academic finance moved to the University of Chicago, where the conception of the EMH was conceived (Sleifer, 2000). The studies conducted in the 70 s was aimed at the EMH in all three levels, however by the end of the decade, the strong efficient form was only thought of as utopia, whereas the semi strong form of efficiency was becoming the generally accepted model to apply to stock markets. Despite this fact, a lot of studies still rejected the semi strong form of efficiency (Jensen, 978). Throughout the 980 s many of the empirical studies conducted, tried to predict prices using historical data. The EMH was the backbone of theses studies, which attempted to forecast the P/E ratios, the dividend yield term structure variables (Islam et. al., 2005). During this decade there was a lot of variety throughout the empirical studies. Debond and Thaler produced their paper on winners and loser, Lo and MacKinlay found strong evidence that the weekly stock returns are positively correlated, and thus rejecting the random walk hypothesis (Smart et. al., 2004). However many others published good and comprehensive research in this area. Common to them all was that they used Fama s efficient market hypothesis, but the terminology and conception was slightly changing over the years. 9

12 In 99, Fama publishes another article on the efficient market hypothesis, called the efficient market hypothesis II. It surveys the vast amount of studies conducted until 99. Based on the studies Fama clarifies the terminology and structure in this financial research area. He does this by restating the three forms of efficiency into three categories of test (Fama, 99).. Return predictability. 2. Event studies. 3. Private information. These new categories are closely related to the three forms of efficiency stated in his article from 970. The return predictability is thus related to the weak form of efficiency. When Fama surveyed this area he found that most studies trying to prove or disprove the weak form of efficiency used test of return predictability. However the coverage of the return predictability is extended, and also includes forecasting on the basis of dividend yield and interest rates. Using the same methodology, the semistrong form relates to event studies, and the strong form relates to the private information, however the coverage of these two new categories are the same as before (Fama, 99). Some authors continued to use the classic three forms, whereas others use the new categories (Smart et. al., 2004). In 998 Fama agues that, despite the vast amount of market efficiency, the efficient market hypothesis should not be abandoned. He finds that the studies of the market efficiency independently partially can show inefficiency. But when the studies are seen as a whole, there is no clear result of over- or under-reaction due to an event. Instead the results of the bundled studies are randomly, thus underlining the existence of the efficient market hypothesis. Further he argues that the length of period used in the event study is correlated with the fragility of the result. Meaning that event studies with a long period have very vague results, and some times the inefficiency disappears (Fama, 998). 0

13 Fama also find the method of disproving the inefficient market hypothesis wrong. Because the authors simply states that the efficient market hypothesis does not exist, they should instead prove another hypothesis (Fama, 998). The EMH has been one of the key-beliefs among financial investors and especially academics, and this has been underlined by their empirical findings. However since the mid 990 s another group of respected economist, called the financial behaviourists, has gained more and more ground in their effort to reject the EMH. The behaviourist has a different approach to the perception of financial markets. Fundamentally they believe that physiological factors interfere with every kind of people including the investors. Thus the assumption of rational behaving people is incorrect, thus proving that markets are not efficient in the way that Fama et. al. suggests (Smart et. al., 2004). The theories of the behaviourists have also been well documented, thus it must be accepted as a respected challenge to the EMH. One of the bastions of the behaviourists is the financial anomalies, which are found in stock markets all around us. The anomaly areas are elaborated in the next chapter. The battle between the two theories has divided the financial academics in two groups. It is at this state impossible to determine which theory describes the markets best. Both parties share the assumption that the theory of the behaviourist and the EMH theory can not perfectly co-exist.

14 3 Anomalies This chapter will introduce the area of anomalies, in order to develop a common frame of reference throughout the rest of the thesis. A wide perspective will be presented before the focus will be narrowed down to the calendar anomalies. This area will be explained thoroughly and relevant literature will be presented. Moreover some of the critiques of this area will be discussed. Many studies have been conducted to find anomalies, however not many have identified the actual behaviour of the anomalies (Marquering et. al., 2006). Maybe it is because the persistence of many anomalies is short, once they have been found, due to the nature of the anomalies. This is known as the general paradox of anomalies. The paradox starts when individuals use their newly acquired knowledge to exploit the anomaly, which again causes the anomaly to disappear and the market becomes more efficient. In other words when an anomaly has been found it starts to disappear. 3. The definition of anomalies An anomaly is a deviation from the normal. In theory it cannot exist in an efficient market. Deviations do exist, and do concord with the efficient capital market theory, if the deviation is randomly. However the problem is to determine when a deviation is no longer a deviation but an anomaly. A general clear and accepted definition of anomalies does not exist, but some have tried to define it: An asset pricing anomaly is a statistically significant difference between the realized average returns associated with certain characteristics of securities, or on portfolio of securities formed on the basis of those characteristics, and returns that are predicted by a particular asset pricing model (Brennan et. al., 200). With help from Singal (2004) we generalise this to: A persistent statistical difference between the realized average return, and the returns predicted by a particular model. In this thesis we will use the latter definition, whenever referring to an anomaly. 2

15 3.2 Anomaly types and literature review There are many types of anomalies, new ones are found and other starts to disappear. Therefore it is impossible to give a complete description of every anomaly at the present time. However we will try to describe and categorize the most of the known and researched anomalies, persistent or distinct Other anomalies In this section a description of some of the non-seasonal anomalies are given. The idea is to broaden the perspective and understanding of what anomalies are The size effect Banz and Ringanum was the first to discover this anomaly in their event study from 98. Using data from the New York stock exchange, they showed that small capitalized firms produce higher returns on average than large capitalized firms. Some argue that the size-effect have disappeared, especially since it has been documented that the effect has been declining since 982. (Constantinides et. al. 2003) The value effect Basu was the first to discover this anomaly, with his papers from 977 and 983. He found that companies with high earnings to price ratio, earned higher returns relative to the CAPM. Other authors have used the same methodology to publish papers where similar anomalies are found to be related with other economic key figures such as the book-to-market ratio or the dividend yields. (Constantinides et. al. 2003) The momentum effect. The basics of this anomaly are that, when looking at the return performance of the last three to five year, the losers will generate a higher return than the winners in the following period. (Constantinides et. al. 2003) The IPO underperformance Event studies show that IPO generally tend to underperform thus not giving the expected return to investors. Ritter concluded in his 99 study that IPO stocks yield 3

16 below normal returns in a period of 36 months following the IPO. (Constantinides et. al. 2003) Calendar anomalies This section will focus on the calendar anomalies, which is categorized as a seasonal anomaly. The seasonality described here is only related to the calendar seasonality, however other seasonal anomalies exist and they are very similar, for example the weather anomaly, which relates the weather with the behaviour of stock dealers The January effect The fundamental pattern of this anomaly is that stock returns in the first few days of January are higher, ranging from four to ten days (Mlambo et. al., 2006). This results in higher returns for January than the rest of the months in the year. The January effect was first showed in 942 by Wachtel in his article Certain observations on Seasonal Movements. However the recognition of a January effect did not happen until Rozeff and Kinney observed and documented it in 976 (Ogden, 990). Since then this anomaly has become one of the most researched anomaly. Thaler (987) discusses a body of possible explanations for the January phenomenon. The most popular one is the well known tax-loss selling motivation (Marquering et. al., 2006). In his studies from 994 including countries all over the globe, with different ending dates for the tax year, Agrawal et. al. (994) finds evidence that the tax selling hypothesis is related to the January effect. However Haug et. al. (2006) finds that a tax legislation change in 986 did not have any consequence on the January effect, even though it should according to the tax hypothesis. Window dressing is another explanation of the January effect. It s argued that larger fund managers increase their portfolios with large well known stocks in December, and then shifts back to small firms in January. This has been linked with Fama s findings from 99, where he finds that the January effect is more persistent in small cap stocks, than in large cap stocks (Pilbeam, 998). 4

17 Some researchers find that the January return is not statistically different from zero after 987, thus stating that the January anomaly does not exist anymore (Mehdian et. al., 2002). However it s seems that the majority of the articles and books conclude that a January effect exist. Contrary to this, they do not agree on the explanation of it. One of the most recent studies from 2006 seems to agree on that. the January effect is a real and continuing anomaly in stock market returns and one that defies easy explanation (Haug et. al., 2006). Thus the January effect continues to remain an anomaly, and researches continue to try and find the explanation for it Day of the week effect This area also covers what is called the Friday effect and the Monday effect. The fundamental idea of this anomaly is that stock returns on particular days are higher or lower than the rest of the week. Fran cross (973) and Gibbons and Hess (98) have found statistical significant evidence that share prices tend to fall on Mondays and rise on Fridays (Pilbeam, 2006). Some literature tries to exploit this fact, naming it the weekend effect. This is one of the oldest anomalies around, and the literature in this area is overwhelming. Even books with titles as Don t Sell Stocks on Monday have been published (Singal, 2004). Studies in the 990s on this anomaly concluded that the weekend effect is robust and that it is an international phenomenon, (Marquering et. al., 2006). The primary explanation for this is that the weekend effect relies on the behaviour of short sellers, with regard to unhedged short sales as distinct from short sales. In other word this means that short sellers cover their positions on Fridays, and reopen them once the weekend is over. This leads to the weekend effect. Secondary explanations of the weekend effect are daylight saving, specialist related biases, and more. They have been investigated, but they account for a small significance of the anomaly (Singal, 2004) The turn of the month effect Arial was the first to report the findings of the TOM effect. The basic pattern of the anomaly is that a number of days around the turn of the month produce a higher return 5

18 than the rest of the month. The time around the month differs from study to study. A Common used time frame is one day before the TOM and three days after the TOM. In 987 Arial used data from 963 to 98 to discover the seasonal TOM pattern. The data he obtained from the Centre for Research in Security Prices (CRSP), and they were equally in weighted and value weighted stocks. The time interval he used to define the turn of the month was the last day of the month and the following nine days. He compared them with the last eight days of the month excluding the last day of the month. He found that the TOM effect was independent of the January effect. Contrary to this, some authors find the TOM anomaly to disappear. Maberly et. al. (2000) studies the S&P 500 futures over a period of covering 982 until 999, and concludes that the TOM effect disappears in 990. They examine the future market, because this market is particular good to investigate a mechanical trading strategy, due to the absence of short-selling restrictions. Sullivan et. al. agrees on the future market approach in his article from 999, as well as Hensel et. al. (996) and Lakonishok et. al. (988). Many articles still find evidence of the TOM effect, among them Kunkel et. al. (2003). In his survey of stock markets in 9 countries, he finds that a TOM period of 4 days accounts for 87% of the monthly return. Using an OLS regression they determine that the TOM anomaly is a persistent phenomenon on all continents except South America, which was not included in the survey. Further they conclude that from the period of they do not find the TOM effect in the U.S.A. Xu and McConell (2006) is currently working on a paper that researches the U.S.A. market for various effects using CRSP data from Among other things they find that the small cap stocks give a higher return than the large cap stocks in a specified TOM period. Their preliminary conclusion is that the TOM effect is not confined to the small cap stocks, but also found in large cap stocks. 6

19 3.3 The dangers of data mining Anomalies are always proved by using statistical techniques. When evaluating the results prudence and a real life perspective on the findings is a must. Because given the numerous amounts of statistical techniques available, anybody can find some statistical correlation between incidents. But is it real? Or is it artificial? Singal (2004) describes the question you must relate your findings to. Does it make sense? Can the number of birds in San Francisco really mean anything for the stock returns? Intuitiveness and sense has to exist in the results otherwise the results does not reflect an image of the world, but something artificial or made up. When a statistical result crosses the limits of a real reflection of world, and the results no longer make any sense, then the findings is a case of data mining. This expresses a statistical relationship that is not real, but rather a relationship existing only by chance. The incentives to find such artificial anomalies do exist, because cases of data mining often turn our world around. If we for a minute pretended that the case of the birds and stocks was real, then it would be an economic theory breakthrough, or as Fama states Splashy results get more attention and creates an incentive to find them (Singal, 2004). Much scrutiny has been shown to the area of anomalies. In the article The Dangers of Data Mining (Sullivan et. al., 200) the authors study a period of 00 years, and analyses it statistical. They divide the period up into 0 periods, and compare them to each other to see if any of the anomalies are persistent over all periods. They find that calendar anomalies are not persistent over time, and therefore they conclude that calendar anomalies are a product of data mining. Despite this many still perceives the investigation of anomalies, and a large amount of anomaly studies have been conducted since and the results have been positive. One of the responses to the critique is from Kunkel et. al. (2003), he writes: One response to these criticisms is to appeal to unique data sources and robust methodologies. If an anomaly can be shown to exist in many markets and under test conditions that are robust to violations of the OLS assumptions, it provides greater support for the 7

20 conclusion that the anomaly exists. Further he continues that it is well known that when a pattern emerges, the effect fades as the markets incorporate the new knowledge. When conducting an anomaly study, it is important to use a robust statistical method (Kunkel et. al., 2003). Further it is crucial for the support of your result, that you use a time period that extends the time it takes for a market to absorb new knowledge of an anomaly pattern. If not, the results can not be regarded as persistent, and readers will regard the result merely as a chance, instead of an anomaly. 3.4 The best TOM pattern The vast number of TOM anomaly studies, have led to a number of variances in the studies. On the outlook of anomaly studies, they do tend to look the same, but a detailed examination of them reveals differences. One of the great differences in TOM anomaly studies is the different definitions of the TOM period. Ariel study from (987) defines the TOM period from the last day of the month plus the 8 following days of the next month, a TOM period of 9 nine days. Lakonishok et al. (988) are the first to examine in detail which days would accumulate the strongest TOM period. They examine the rate of return for each day in the nine day TOM period as Ariel (987) defined. However they find that the period covering from the last day of the month until the 3 rd day of the following month shows the strongest positive returns, thus a TOM period consisting of these 4 days would be stronger than other TOM periods. In this 4 day period Ariel found a cumulative increase in the rate of return of % compared to an average four day increase of %. Others have also researched the TOM period again. Kunkel et. al. (2003) researches the 8 2 trading days around the TOM to reveal the most significant positive returns. He finds that 87 % of the monthly return occurs in the 4 day period from the last day of the month until the 3 rd day of the following month. Thus Kunkel et. al. (2003) also 2 The 8 days are the nine days before the TOM and the nine days after the TOM. 8

21 ends up using the 4 day period defined by Laksnikok (988), because he finds the TOM period to be strongest there. Further Kunkel et. al. continues that the most used period in anomaly articles is in the recent years are the 4 or 5 day period starting with the last day of the month. Agrawal et. al. (994) are among the many that have used the 4 day period. 9

22 4 Empirical research 4. Data The countries of interest have been selected based on the result of Kunkel et. al. (2003). In each of these countries the object was to find three indices, which on aggregate represents the stock market in the country. Individually however the 3 different indices should represent the overall capitalization of a country stock market in terms of a small cap, a mid cap and a large cap index. 4.. The definition of index capitalization The definition of large, mid and small cap indices is not an international standard. Therefore each index constitutor is entitled to make their own definitions of their indices, sub indices, etc. However when you create an index, it is in the creators interest that, the index can easily be used by all kinds of investors. Standard and Poors is the founder of one of the most known indices in the world, The S&P500. Standard and Poors have a set of specific assumptions and formulas they use to calculate the constituents of the S&P500 ( The S&P500 is updated on a regularly basis, hence some new companies enter the index and others exit the index. The S&P 500 is well known as a large cap index. When entities choose to create a capped index, and baptising it with an international name as Bel small, they deliberately get inspiration from other similar indices in the world. Hence the use of small refers to an index, where the group of constituents relatively to other constituents in that country/market, must be considered as small. Thus there exist some correlation between the names of the indices, but the index definitions are also very influenced by other external factors. Many entities choose to use the same or equivalent set of assumptions and formulas as the S&P500, when they create large cap index similar to that of the S&P500 in another country. However due to country differences and the fact that there can be 20

23 huge differences between the value of markets, the assumption and formulas are often altered slightly from country to country. Thus a comparison in absolute numbers is obsolete, due to the difference described prior. However it is feasible to consider the market caps as relative to their own country. Therefore a relative comparison of the large, mid and small cap indices is viable, hence the S&P500 and the BEL20 can be considered as two large cap indices and thus compared relatively to each other. This study uses this relative comparison as the basis for comparing all the indices between each other Data preparation Datastream was used to acquire the daily price indices of all countries except Switzerland. The data of Switzerland was acquired through the Swiss Stock Exchange found on the web ( Of the selected countries we have tried to extract all three index types: Large cap, mid cap and small cap, from st of January 988 until 29 th of December However in countries where this was not obtainable we have used ass many of the three index types as are available, dating as far back as possible. The variance in starting date of the indices used differs a lot, because some markets have constructed indices based on capitalization for a long time and others have just recently made this construction of capitalized indices. Additionally some countries only have large cap indices an example of this is Austria, where only a large cap index was present. After the data was extracted to excel, the daily returns was calculated using the natural logarithm. Then all data was exported to the statistical programme SPSS, where the data work was conducted. Table shows a list of all the indices researched in this study. It shows which country they represent, the starting date of the indices, and their respectable capitalized size. 2

24 Table : list of indices examined 3 Market Name Start Date Cap Australia S&P/ASX 50 0/06/992 Large Australia S&P/ASX MIDCAP 50 3/2/993 Mid Australia S&P/ASX SMALL ORD. DS-CALC. 04/0/988 Small Austria ATX - AUSTRIAN TRADED INDEX 04/0/988 Large Belgium BEL 20 03/0/990 Large Belgium BEL MID 03/05/995 Mid Belgium BEL SMALL 07/03/994 Small Brazil BRAZIL BOVESPA 02/0/992 Large Canada S&P/TSX 60 INDEX 04/0/988 Large Canada S&P/TSX CANADIAN MIDCAP INDEX 28/05/999 Mid Canada S&P/TSX CANADIAN SMALLCAP INDEX 28/05/999 Small Denmark COPENHAGEN KFX DS-CALCULATED 04/0/988 Large Denmark OMX COPENHAGEN MID CAP 02/0/2003 Mid Denmark OMX COPENHAGEN SMALL CAP 02/0/2003 Small France FRANCE CAC 40 04/0/988 Large France FRANCE CAC MID 00 04/0/999 Mid France FRANCE CAC SMALL 90 04/0/999 Small Germany DAX 30 PERFORMANCE 04/0/988 Large Germany MDAX FRANKFURT 04/0/988 Mid Germany SDAX PERFORMANCE 04/0/988 Small Hong Kong HANG SENG HK LARGE CAP 04/0/2000 Large Hong Kong HANG SENG HK MIDCAP 04/0/2000 Mid Hong Kong HANG SENG HK SMALL CAP 04/0/2000 Small Japan TOPIX 00 05/0/993 Large Japan TOPIX MID /0/993 Mid Japan TOPIX SMALL 05/0/993 Small Malaysia FTSE BURSA MALAYSIA LARGE 30 27/06/2006 Large Malaysia FTSE BURSA MALAYSIA MID 70 27/06/2006 Mid Malaysia FTSE BURSA MALAYSIA SMALL CAP 27/06/2006 Small Mexico MEXICO IPC (BOLSA) 05/0/988 Large Netherlands AEX INDEX (AEX) 04/0/988 Large Netherlands AMSTERDAM MIDKAP 04/0/988 Mid 3 The starting date represent the date that the index data was available from. The starting date is not consistent with the date that the index was created. 22

25 Netherlands NETHERLANDS-DS SMALL COMPANIES 02/0/989 Small New Zealand NZX TOP 0 0/07/988 Large New Zealand NZX MID CAP INDEX 08/04/997 Mid New Zealand NZX SMALL COMPANIES 03/0/99 Small Singapore SINGAPORE STRAITS TIMES(NEW) 04/0/988 Large South Africa FTSE/JSE TOP 40 03/07/995 Large South Africa FTSE/JSE MID CAP 03/0/2002 Mid South Africa FTSE/JSE SMALL CAP 03/0/2002 Small Switzerland SLCI 04/0/996 Large Switzerland SMCI 04/0/996 Mid Switzerland SSCI 04/0/996 Small United Kingdom FTSE 00 04/0/988 Large United Kingdom FTSE MID /0/988 Mid United Kingdom FTSE SMALL CAP 04/0/988 Small United States S&P 500 COMPOSITE 04/0/988 Large United States S&P 400 MIDCAP 3/06/99 Mid United States S&P 600 SMALL CAP 04/0/989 Small Due to the differences described in section 4.. the number of constituents varies through time. Additionally the number of constituents in the individual indices is arbitrary, and hence not of primary importance in this study. Additionally many entities do not publicise the number of constituents, due to ongoing change of the indices. However to give the reader some idea of the relative constituent size, the following can be defined for each country: The large cap always has the lowest number of constituents, followed by the mid cap. The small cap has the highest amount of constituents, sometimes outnumbering the amount of constituents in the large cap indices by a factor 2. This is the case is in Japan, where the large cap index has 00 constituents, the mid cap index 400 constituents and the small cap index has 20 constituents. Also the capitalization of each country varies, due to the nature of stock markets which goes up and down. Due to the relative comparison of indices previously discussed in section 4.. the actual capitalization figures of each country is of secondary importance, thus they are not presented in this thesis. In other words a 23

26 snapshot of today s markets capitalization value can easily change overnight. This is because of the daily market changes, which is caused by the nature markets all over the world. Therefore a comparison of the world s capitalized market today can be obsolete tomorrow. However the reader should bear in mind that the largest economies in the world correlate with the largest capitalized stock market. Hence some of the largest capitalized stock market is represented in this study, by the United States, Japan, and the UK. Overall this study includes a large proportion of the world s aggregate capitalized market value Data Bias In order to prevent bias in the data and to prepare the raw data for tests, the raw data from Datastream had to be edited. Some price indices contained observations with the value of zero. These were treated as missing values, and therefore removed from the data sheet. Further analysis showed that when calculating the daily return, some observations had a daily return of zero. The reason for this is most likely holidays in the country where the price indices origins from, thus there is no trade on stock market on the given day. It could also be caused by other events than holiday, but in this study these events are treated as holidays. Additionally the possibility of an index with a daily return of zero on a normal trading day is considered insignificant. To eliminate all holidays and other event days where trading was cancelled, all daily returns of zero was deleted from the data sheet The definition of the TOM and ROM Periods Kunkel et. al. ( 2003) examines and finds the most significant TOM period. This thesis discusses the TOM period in section 3.4, thus we have found no reason to further examine in which period of days the best TOM period is found. Thus in consistency with the study of 2003 and other similar studies we have determined to use the same 4 day TOM period. 24

27 The TOM period is defined as a period of 4 days around the month turn. The last day of the month represents the start of the period, which continues until the 3 rd day of the following month. The rest of the month (ROM) period consists of the period after the TOM period. The ROM period starts on the 4 th day of the month and ends the day before the new TOM period begins, thus being the second last day of the month. Figure shows an overview of the TOM and the ROM periods. Figure : The TOM and the ROM periods TOM: TOM TOM 2 TOM 3 ROM: ROM ROM 2 Day : Month: Jan. Feb. Mar. *The graph gives a visual overview of the periods. The graph does not show holidays, weekends or other days without trading which is not contained by the TOM and ROM periods. As reported in section 4..2 returns on holidays are deleted. Since the specific dates of holidays and the length of them differs widely from country to country, the TOM and the ROM period is not a fixed applicable time period across countries. For example the last day of trading in Belgium in December 990 was the 20 th. Thus the TOM period of December/January is the 20 th plus the st until the 3 rd of January 99. The corresponding TOM period in Australia runs from the 28 th of December until the 3 rd of January 99. The variation is caused by the differences in the Christmas holiday in Belgium and Australia. Therefore the TOM and the ROM period have to be determined from country to country. This means that the binary TOM dummy, described in section 4.2.., used in one country, cannot be used in other countries. Each country has its own specific binary TOM dummy. 25

28 4.2 Methodology We measure the daily rate of return in each index. Directly this makes the currency type obsolete in each country. However if you compared two stocks with the same nominal value a difference could be tracked. Thus a 5% increase in stocks noted in US dollars, may not be as much as the same 5% increase in an equivalent stock noted in Euros, due to the exchange risk exposure. Kunkel et. al. ( 2003) finds this difference insignificant. Thus it is obsolete to incorporate the exchange rate risk exposure in this study hence we do not adjust for exchange rates. Many studies have used parametric test to research anomalies. This has proven to be sufficient, when the assumptions are only mildly violated. Despite the acceptance of these studies, some have still argued that the mild violation of the statistical assumptions makes the results useless. In order to meet the demands of these people we have decided to eradicate this dilemma in the best possible way. Therefore we use both parametric and non-parametric tests in this study. This will increase the robustness of the study and eliminate the discussion regarding the mild violations. Further it will decrease the chances of data mining as discussed in section 3.3. First we examined the data fundamentally. This included testing for skewness, kurtosis, and normal distribution. The summary of the findings are reported in Table 2. Then we conducted 2 parametric tests, and a non-parametric test, on each of the three chosen indices from each country. The parametric test is a simple linear regression and a one-way ANOVA test. The non-parametric test is a Wilcoxon signed rank (WSR) test. The conclusion of these 3 tests will determine if a TOM effect exist in each index in each country. It will also reveal if all three indices in a country has a TOM effect, and how large the effect is. After finding which indices and countries contain the TOM-effect, we now want to examine the relationship between the TOM-effect and the capitalization of the indices. Thus we divided all indices up in three groups: The small, the mid and the large capitalized indices. Then we tested if the TOM effect in the three groups was considered to be equal or not. We used a one-way ANOVA, and Tukey s test of multiple comparison as our parametric test. The non-parametric test consisted of the 26

29 Kruskal-Wallis test and Dunn s confidence interval test. Apart from examining the relationship between the capitalization and the TOM-effect, it was in our interest to see if we could separate any of the capitalized groups from each other, in terms of TOM-effect. To conduct this we used latter statistical approach described above. As the result in shows, only the small cap indices had the consistency of an independent group of TOM-effects. Hence we examined this group of small cap indices a little further to see if any attributes could be identified in this group the results are shown in section Again we used a one-way ANOVA test and Tukey s test as the parametric test. Kruskal-Wallis and Dunn s confidence intervals were used as our non-parametric test. Thus the object of these tests was to examine the perspective of capitalization, It was found obsolete to examine the mid and the large cap group in the same depth as the small cap group, since the results did not indicate that these two groups could be separated. Finally we wanted to examine the TOM effect in the perspective of countries. In order achieve this we compared the TOM effect of the small, mid and large cap indices in all countries. The statistical methods did not change from the approach described above. The result of this can be found in section Simple linear regression model of the TOM-effect. We will use the same linear regression model as Lakonishok et. al. (988) and Kunkel et. al. (2003) used in their studies to test for the TOM anomalies. The simple linear regression model is one of the most used statistical models in event studies. The model predicts two variables, based on the other variables. The expression tested is: 27

30 Equation : simple linear regression of the TOM-effect. R = α + β D + ε t TOM t Where: R t is the return on Day t. α is the intercept representing the mean return for the ROM period. D TOM is a binary dummy variable for the TOM period. β is a coefficient, representing the difference between the mean TOM return and the mean ROM return. ε is the error term. Equation is used on all 3 different capitalized indices in all countries included in the data. Each of the three different capitalization indices in all countries is examined independently. The result for small, mid and large cap indices are shown in Table 6, Table 7 and Table 8 respectfully. The fundamental idea of the regression is: When the beta coefficient is larger than the alpha coefficient and the significance levels are acceptable, then the regression indicates that the mean return for the TOM period is larger than the mean return of the ROM period. In order to conduct a regression analysis, a set of assumptions must be fulfilled. These are (Aczel 999): The relationship between X and Y is a straight line relationship. The value of the independent variable X is assumed fixed (not random); the only randomness in the values comes from the error termε. The errors ε are normally distributed with a mean 0 and a constant varianceσ 2. The errors are uncorrelated (not related) with one another in successive observations One-way ANOVA test To test if there is a difference between samples, we use a parametric one-way ANOVA test. We use this test the first time, when testing if there is a difference 28