Eugene Fama versus Robert Shiller Is the Belgian market efficient?

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1 Ghent University FACULTY OF ECONOMICS AND BUSINESS ADMINISTRATION ACADEMIC YEAR Eugene Fama versus Robert Shiller Is the Belgian market efficient? Master s thesis submitted to obtain the degree of Master of Science in Business Administration Siemen Six & Randy Van der Auwera under supervision of Prof. Koen Inghelbrecht

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3 PERMISSION Ondergetekenden verklaren dat de inhoud van deze masterproef mag geraadpleegd en/of gereproduceerd worden, mits bronvermelding. Siemen Six Randy Van der Auwera

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5 Table of contents Abstract... II List of abbreviations... III I. Introduction... 1 II. Literature Review The efficient markets hypothesis (EMH) Empirical evidence Behavioural finance The adaptive markets hypothesis (AMH) III. Research Design & Methodology Design Summary statistics Methodology IV. Results Is the Belgian stock market efficient as a whole? And what about the different size-based compartments of the stock market? The Random Walk The Variance ratio... 4 Do we observe a difference in market efficiency between growth and value stocks? The Random Walk The Variance ratio Did the financial crisis marked by the 15 th of September 28 as the starting date have an effect on market efficiency? The Random Walk The Variance ratio... 6 V. Conclusion Conclusions Random Walk autoregression models Conclusions Variance ratios Differences and matches between the RW autoregression models & Variance ratios Fama vs. Shiller, who fits the Belgian stock market?... 7 VI. References VII. Appendix I

6 Abstract This paper analyses the market efficiency of the Belgian stock market. Therefore, we focus on data from 1996 till 214. We evaluate if a random walk is present in the Belgian stock indices by the use of autoregressive models and variance ratios. We also examine whether differences in market efficiency occur when we divide the Belgian market into two indices containing only growth and the other only value stocks. In addition, taken into account the financial crisis of 28, we examine if changes occurred in market efficiency. Our results indicate that the whole Belgian stock market does not follow a convincing random walk over a period. We find the market compartment including only growth stocks to be more efficient than the one including just value stocks, although they are both inefficient. And lastly, our subperiod results show that the financial crisis of 28 mainly increased market inefficiency on the Belgian stock market, whereas in the three-year period before the outbreak of the crisis the market was efficient. Keywords: Market efficiency, random walk, variance ratio We would like to thank Prof. Koen Inghelbrecht for his excellent advice, his assistance with our statistical tests and his positively constructive and deeply valued feedback throughout the semester. II

7 List of abbreviations ACF AMEX AMH AR model BAS index CAPM EMH NASDAQ NYSE OECD RW VAR VR Autocorrelation function American Stock Exchange Adaptive markets hypothesis Autoregressive model BEL All-Share index Capital asset pricing model Efficient market hypothesis National Association of Securities Dealers Automated Quotations New York Stock Exchange Organization for Economic Co-operation and Development Random walk Vector autoregressive regression Variance ratio III

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11 I. Introduction In 213 a Nobel prize was awarded to E. Fama, L.P. Hansen and R. Shiller for their work on security pricing on capital markets 1. This was a remarkable decision as Fama and Shiller have opposing beliefs about efficient capital markets. Fama is a great advocate of efficient capital markets, which simply put, means that all available information about a security is included in the price of that security. He further believes that the markets are still efficient today even after several anomalies occurred, e.g. the IT-bubble in 2 or the recent financial crisis of 28. Fama explains these anomalies by unidentified risk factors and maintains his convictions about the efficient market hypothesis (Cassidy, 213). Shiller, on the other hand, contradicts the efficient market hypothesis and he was one of the first ones to recognize that economic agents are not always rational but are in fact influenced by multiple psychological factors. The irrationality of the agents contribute to market anomalies, as was the case with the IT-bubble and undervaluation or overvaluation of assets in general as well. For Shiller, the anomalies are the best proof that capital markets are not (always) efficient (Cassidy, 213). It is not the purpose of this paper to firmly choose the side of Fama or Shiller, as we will explain that the efficient markets domain is not a strict black and white story but has a grey zone as well. Instead we will explain what efficient markets are, why the efficient market hypothesis is so important and how the work of Shiller and other likeminded behavioural finance-economists fit so well in the debate. With our own research, we want to find out whether the Belgian stock market is efficient or not and therefore we will examine several market indices based on the capitalization of underlying stocks (i.e. stock size). Four market indices are included in our research: the BEL All-Share index (BAS), which represents all stocks noted on the Belgian market, the BEL-2 index comprised out of the 2 most liquid stocks, the BEL Mid containing medium capitalized stocks and the BEL Small index with small capitalized stocks as the underlying securities. We will apply weak-form tests by running autoregression models and calculating variance ratios, which we will compare in order to determine the market efficiency. Depending upon the results we will have an indication of whether the prices on the examined (part of the) market reflect the fundamental value of the underlying security, i.e. in an efficient market or if they do not reflect the true intrinsic value, as in an inefficient market (Fama, 1965). The results have important consequences, especially for investment decisions. In an efficient market one of the best investment choices an investor can make over time is a passive fund mimicking the market index (Bodie et al., 213; Inghelbrecht, 213a). These results can be found in the conclusion section of this paper. In the next section, namely the literature review, we start off with the efficient markets hypothesis in general, followed by important empirical research examining markets in their efficiency. Thereafter, we pay attention to the behavioural finance view on capital markets 1 Article from The New Yorker by J. Cassidy (Inefficient Markets: A Nobel for Shiller (and Fama)) 1

12 also with attention for empirical research. To end the literature section, we refer shortly to the fairly new adaptive markets hypothesis that combines the two opposing views of market efficiency and behavioural finance. After the literature review we explain our research design and methodology approach and then follows a separate section for the research itself. The next and also last section contains the results of our research in which we will end the paper making our conclusions on market efficiency and compare with the discussed literature in the literature review. 2

13 II. Literature Review 1. The efficient markets hypothesis (EMH) The term efficient market was introduced by Fama, who laid the foundation for efficient markets in his own efficient capital markets -paper in 197 in which he makes a review of the then existing literature and empirical research. This paper is seen as Fama s greatest contribution to this field of research and still gives a good explanation of what the hypothesis essentially includes (Fama, 21). Later on Fama wrote a second review paper on efficient capital markets in Now, first of all, we need to acquaint ourselves with the base work to comprehend efficient markets before we move on to more recent research papers that test efficiency. Fama (197) essentially describes an efficient market as a market in which security prices fully reflect all available information at any time (p. 1). Important elements in this definition are prices, all available information and at any time. First, prices must be obtained by a certain model in order to make everything testable. Second, the information element is crucial in the hypothesis and therefore the criteria for information to consider, are classically divided into three information subsets. Third, at any time signifies that efficient markets are always efficient, i.e. in stable economical and financial times, as well as in times of recession or (excessive/rapid) growth (Fama, 197). It is favourable to discuss some aspects of these elements in greater detail. Prices can be determined by different models in order to make them testable for empirical research. Fama (197) includes base models in his overview paper and two special forms of these base models. As a general rule for these pricing models it is imperative that the assumptions made by the model are valid. Otherwise when testing market efficiency with a model that is based on wrong/non-valid assumptions, the efficiency test will be non-valid as well. Nevertheless, certain assumptions have to be made with each model (Fama, 197). As these assumptions are hardly ever consistent with reality and differ from model to model, according to Fama (1991) this implies that market efficiency cannot be tested in essence. Fama (1991) describes this problem as the joint-hypothesis problem that refers to the need of an asset-pricing model in order to test for market efficiency. Fama (1991) states that evidence or indications of inefficient capital markets could also be caused by a faulty or invalid pricing model used in certain research. Therefore it is unlikely that we will ever be able to measure market efficiency to its full extent and made assumptions will stay rather theoretical. Nevertheless research on efficient markets is all but futile. It has already changed the way investors and academics regard returns on securities etc. (Fama, 1991). The base pricing models are the expected return or fair game models. The most well-known expected return model must be the Capital Asset Pricing Model (CAPM or Sharpe-Lintner model). The type of risk that is taken into account by the CAPM to determine an expected return is the systematic (market) risk. In some research on efficient markets, different models can be used that take other (or additional) risks into account to get to the expected returns. These other models should always be in equilibrium, just as the CAPM. Regardless the risks 3

14 that are included in the model, all expected returns are random and they are a function of the price of the previous period, the random return of one period and an assumed information set (Fama, 197; Bodie et al., 213). Further, the equilibrium expected return given by the model implies that there cannot be made any excess returns over the equilibrium return based on the information set, as the set is already included in the equilibrium expected return. The fair game denomination stems from the fact that the (expected) returns are random and are not influenced by the previous returns, i.e. are a martingale (Fama, 197). This is the base model of which there are two important applications: the submartingale model and the random walk model. The submartingale model has a submartingale in a price series. This means that the price of this period is equal or higher than the price of the previous period. The same goes for expected returns. If the price is just the same as the one from the previous period, the series of prices is just called a martingale which is the same as a fair game model (Fama, 197). The random walk model is used since the beginning of market efficiency research and has two main conditions that need to be fulfilled in order to speak of a random walk model. First, Fama (197) states that successive price changes (i.e. returns) need to be independent, thus not influence each other. Basically this implies that returns should be uncorrelated. The changes of these prices or returns are determined by the information of the particular period regarding the underlying security. Second, these changes in prices or returns need to have an identical distribution. Fama (197) considers this random walk model as an extension of the base expected return or fair game models, which is logical as it is a very similar. Nevertheless there is an important difference namely the second condition: identical distribution of returns. These distributions are assumed to repeat themselves trough time, under influence of changing information and investor preferences that lead to new price/return equilibriums. In these distributions, the order of returns is not important, only that they are identically distributed is of importance (Fama, 197). Practically this means that there need to be as many overvalued returns as there are undervalued returns so the market price will float around the intrinsic value (Fama, 1965). Fama (197) strongly prefers tests using the random walk model (or variation on the model) over tests that ascertain the pure independence between returns in a time series, on account of the fact that the random walk model is based on characteristics of the base ( fair game ) model. Also it is worthwhile to notice the difference between prices and returns. Returns are stationary which lack long memory, whereas prices are non-stationary and have a trending behaviour which makes it easier to estimate values for the following period(s). These characteristics have certain implications for empirical handling that will be considered in our research design (Inghelbrecht, 213b; Koop, 26). There are also implications for the random walk model. When using non-stationary price time series to make forecasts, assumptions have to be made for the order of price changes: they need to follow each other subsequently while being dependent to each other. This obviously means that we cannot longer speak of a random walk model as the independence condition is not met. Instead it 4

15 becomes a chartist technique, which is much less used to predict prices and less reliable (Fama, 1965). We will revisit this in the Methodology section when discussing ways to test the random walk. The theory of random walks assumes capital markets to be efficient. This implies that the market price will be more or less the same as the intrinsic ( fundamental ) value of the underlying security. Because of the market efficiency assumption, past and expected future information is reflected in the market price and thus in the intrinsic value. Market prices will float randomly and closely around the intrinsic value (Fama, 1965). This is exactly why we think it is so important to test the efficiency of the Belgian capital market. If the market is proven efficient, investors would be able to use the market price as a good estimate for the intrinsic value of a security in the security selection-decision. This could imply lower information and search costs for investors as they can just invest in a market index fund that is passively managed (Bodie et al., 213; Inghelbrecht, 213a). Nevertheless, Fama (1965) stresses that this does not mean that additional fundamental analysis is redundant, especially not when there is new information that is not yet reflected in the current market price. So active management can surely pay off, provided that the management in control has new (superior) information or that they interpret it in a better way (Bodie et al., 213; Inghelbrecht, 213a). Moving on from the pricing element to the informational element, the three different information subsets into which Fama (197) classifies empirical work are weak form tests, semi-strong form tests and strong form tests. The weak form tests focused originally on information sets that contained only historical prices and later the set also widened to tests that aim to forecast returns using past returns or certain ratios and variables (e.g. dividend yields, earnings to price...). Semi-strong form tests also take into account all publicly made available information (such as announcements of earnings, new product launches, takeovers, changes in management...) and mainly research the time that is needed to reach adjusted market prices. This usually happens by means of event studies. And finally, strong form tests that take public and private information into account (Fama, 197, 1991; Bodie et al., 213). Private information in this context is actually inside information that only a handful of people know about. The information requirements for strong form test are very extensive as the assumption is made that inside information is also reflected in the price (Bodie et al., 213). Having discussed the most important elements of this rudimentary definition of efficient market, there are also some additional softer conditions that can be added. First of all, there are many profit-maximizing investors in direct competition, each making analyses of individual securities and looking for additional information. Secondly, the information is available to all investors, free of charge or almost freely. Thirdly, new information becomes available at random, i.e. unpredictable which means that the prices are random and unpredictable as well. Fourthly, security prices adjust to new information very quickly, almost at once. This fourth condition entails that investors all judge the new information in a very similar way so that market prices change correctly in line with the average opinions of all investors (Fama, 1965, 197; Bodie et al., 213; Inghelbrecht, 213a). Fama (197) also adds 5

16 the assumption of no transaction costs on the market. In real markets this is hardly ever the case, just as some of the four soft conditions mentioned here above. Fama (197) does not reject the efficient market hypothesis if one of these conditions is not met. He sees the absence of some of these conditions as merely potential sources of market inefficiency in a limited extent. The real extent depends on the influence these conditions have on the price formation of a security. 2. Empirical evidence We already noticed the division in three information subsets above and this is important for our own research and the research that we will pay attention to in this section of our paper. As our own research can be classified into the weak form test division we will concentrate on weak form testing. We will first discuss some important aspects of weak form tests that Fama (197, 1991) reviewed in his two overview papers that we did not mention above due to the empirical nature and relevance. As mentioned before, weak form tests also aim to forecast returns using past returns or certain ratios and variables (e.g. dividend yields, earnings to price...). Fama (1991) arranged weak form tests based on time periods from short term to long term. He found that in the short term (daily, weekly and monthly) returns had just a very small part in their variance that could be forecasted. But on the long term (two to ten years), roughly 4% of the variance in returns could be explained. Fama (1991) reports disagreements between academics who contribute this predictable part in the return variance to either irrational bubbles or rational changes in expected returns instead. Once again this questions the existence of efficient capital markets and refers to the opposing views of the behavioural finance-economists and irrationality in capital markets. Fama (1991) reviews research in which random walk tests are carried out by using an autoregressive model of the first order (AR(1)-model). These studies yield different results depending on their time horizon. On the short term, Fama (1991) notices that these models often have very low statistical explanation power, especially when examining individual stocks opposed to portfolios. The autoregressive models to predict returns of an individual stock usually have less than one percent explanation power, which makes these models useless in real life. Then there is also the significance of the lagged variable itself. Fama (1991) acknowledges the statistical but therefore not its economical significance. As the values of autocorrelations usually are around zero, they are not economically significant. Returns with no or very little autocorrelation are evidence in support of a random walk (Fama, 1991). Fama (1991) pays special attention to Lo and MacKinlay (1988), who divided stocks on account of their stock size before testing efficiency using a random walk/autoregressive model. They found significant positive autocorrelations and stronger autocorrelations for smaller stocks. Fama (1991) noticed that this could mean there was spurious positive autocorrelation that is a consequence of the nonsynchronous trading effect of Fisher. The Fisher nonsynchronous trading effect is well explained by Lo and MacKinlay (199) as the 6

17 problem that arises when multiple time series are sampled at the same time when actually they are not. This problem seems meaningless at first but it can result in biases which is given by the example of Lo and MacKinlay (199) of two stock returns of which one stock is traded less than the other. The return of the most traded stock will most likely be more accurate as it is traded more and new information regarding the stock value is better adopted. In this context, Lo and MacKinlay (1988) remark that small caps are less traded than large caps and thus it takes the small stock longer to soak in new information. On the long term, Fama (1991) cites his earlier work with K. French (1988a, in Fama, 1991) in which they find negative autocorrelations for three to five year returns. Fama (1991) notices the similar findings in research of Shiller but does not agree with Shiller s interpretation of the development of irrational bubbles. Instead of developing irrational bubbles, Fama (1991) contributes the negative autocorrelations to temporary price swings and as one of the conditions of the random walk hypothesis is that random walks must have identical distributions, there should be as many prices undervalued as overvalued to neutralize each other. This is the phenomena of mean-reversion (Fama, 1991). Over the long term this should be the case and thus no reason to reject the efficient market hypothesis is given. Fama (1991) did not find any strongly significant evidence to reject the random walk hypothesis (i.e. absence of autocorrelation or no economical significance) up to then. Finally, variables and ratios used to forecast returns (such as dividend yields and earnings to price) do not prove or disprove efficient markets. Information, that also is reflected in the price is needed to compute these variables or ratios. A lot depends on what kind of information is used (and if the quality is of sufficient quality) which implies that the results of these forecasting indicators are not always rational (Fama, 1991). Furthermore, Fama (1991) warns us about new predictors that may look very promising and trustworthy at first sight but are actually spurious later on. Now we can move on to more recent work. Tóth & Kertész (26) examine market efficiency on the New York Stock Exchange in two different ways, each with an appropriate dataset. They compute time-dependent as well as equal time cross-correlations between the most traded stocks on the NYSE and link these to the Epps effect. Tóth & Kertész (26) describe the Epps effect as the decrease of correlations that occurs when the interval length of returns is decreased. If the Epps effect diminishes over time, which is the main conclusion of the paper, the NYSE should be more efficient according to Tóth & Kertész (26). The two datasets they use are a high frequency set, containing information on all trades for the 19 most traded stocks from 1993 to 23 and a daily return dataset for 116 large stocks from 1982 to 2. Before carrying out cross-correlation tests, Tóth & Kertész (26) had to classify the stocks into two same-sized groups based on market capitalization. The first important conclusion they drew out of the time-dependent tests, was that the average correlation in daily returns between the large caps group and the smaller caps group decreased very strongly to a level at which correlation is negligible (values around zero). Tóth & Kertész (26) deduced out of this result that large stocks do not pull the stock prices of smaller stocks, which implies that price changes of large stocks have no effect on price 7

18 changes of smaller stocks and misguided price changes of smaller stocks based on irrational elements do not occur. Secondly, distributions of time-dependent correlation functions were also studied in the high frequency set, establishing that correlations actually became higher (shown in higher peaks) but nevertheless kept decreasing over time and the time intervals in which correlations decreased became shorter. Tóth & Kertész (26) explain the shorter intervals by improvements in market processes such as better technical infrastructure (faster computers and networks) which in turn speeded up the trades on the market and information flows for traders. Due to the shorter intervals and more uniform adaptations to new information combined with short time correlation peaks of returns in the high frequency set, the first indication of a diminishing Epps effect is presented. Thirdly, the equal time tests in the high frequency set leads to the finding of a rising average correlation over time, except for the year 2 due to the market crash of that year. This similar finding also implies a decrease of the Epps effect. Tóth & Kertész (26) explain the rising correlation by the increase in trading which makes the time scale grow and which in turn results in growing correlations. To conclude, the decrease of the Epps effect is attributed by Tóth & Kertész (26) to strongly decreased lagged autocorrelations and cross-correlations and increased correlations brought by the increased trading. Market efficiency should thus have increased over the examined time span, implying that the extent of the efficiency can change over time. Finally, Tóth & Kertész (26) generalize their findings for the NYSE to other markets as they argue that the causes of the decrease of the Epps effect can be found on those other markets too. Another important research paper is the one of Lee et al. (21) in which market efficiency is examined by using the real stock price indexes in different countries, each within different states of economical development. This paper uses price indexes while other research mostly uses return indexes. In this paper the use of price indexes is explained by the adjustments that were made to the indexes to account for inflation effects, which makes them real price indexes. Lee et al. (21) start with giving an overview of the most important research that is carried out examining price series for the presence of a unit root. The presence of a unit root in a price series implies a random walk which is also stated by Fama (197) and here again by Lee et al. (21). The overview shows that univariate tests in search for a unit root all seem in favour of efficient markets, i.e. a unit root is present in the examined price series. The research by Chaudhuri & Wu (23) is the only exception out of the nine univariate research papers stated in the overview. It examines the price series of 17 emerging stock markets. The result of Chaudhuri & Wu (23) is remarkable but cannot simply be generalized. Evidence is found that 1 out of the 17 emerging markets do not follow a random walk and thus seem to be inefficient. This is a plausible result according to Bodie et al. (213) and Inghelbrecht (213a), as there is less competition in emerging markets due to a fewer number of investors seeking to maximize their profit in comparison to developed markets. And also, the partial unavailability of qualitative information to all of these investors results in slower adjustments of asset prices. Chaudhuri & Wu (23) also take so-called structural breaks into account and the effect they have on price series. In their research, the structural breaks are mostly formed by market characteristics (e.g. liberalization) and thus are specific for each examined market. 8

19 Other listed research in the overview of Lee et al. (21), all examining indexes of developed markets and also taking structural breaks into account, finds that the developed markets are efficient. Next to univariate time series analysis, the overview also discusses unit root analysis on panel data. Again, a division is made between research accounting for structural breaks and research that does not. The research, not accounting for structural breaks finds that emerging markets seem to be inefficient whereas developed markets seem efficient. This is basically the same result as with the univariate analyses. A different story applies to research that does take structural breaks into account. Narayan & Smyth (25) find that the 22 developed OECD countries they examined had efficient markets, i.e. presence of a unit root. But then more empirical evidence of the contrary is handed for the G7 countries and a group of Asian countries. And in this category, the own research of Lee et al. (21), covering the data period of 1999 to May 27, also finds market inefficiency for 32 developed (incl. Belgium) and for 26 developing markets. The results of Lee et al. (21) are based on a stationarity test for panel data that accounts for multiple structural breaks opposed to most other tests that take maximum two structural breaks into consideration. Also important is, that Lee et al. (21) find that after a structural breaking point the price level will return to some kind of equilibrium level, which is in accordance with stationarity in prices and thus market inefficiency. Under this assumption it should be possible to predict future price movements based on past prices using technical analysis (e.g. price charting) and in a weak-form efficient market, technical analysis and forecasts based on past prices in general should not be possible (Inghelbrecht, 213a; Lee et al., 21). Lee et al. (21) highlight the importance of structural breaks, as did Chaudhuri & Wu (23). They explain that ignoring such breaks can lead to biases that wrongly accept the presence of a unit root and therefore the random walk hypothesis which implies market efficiency. Furthermore, structural breaks can occur due to many reasons such as crises, regulations and other events that influence stock markets globally as well as domestically. Allowing for structural breaks increases the econometric power of the tests but when comparing end results of several research papers, the answer whether markets are efficient remains inconclusive (Lee et al., 21). Perhaps the most important conclusion that we can draw is that the random walk and thus market efficiency seems stronger in developed markets. Moving on to other research, Kim et al. (211) study predictability of returns using the Dow Jones Industrial Average index with a vast data set covering the period of 19 to 29. They use several tests based on autocorrelations to examine weak-form efficiency. Although they perform weak-form efficiency tests, they do not link their outcomes to the efficient market hypothesis but to the adaptive market hypothesis instead (see section on the adaptive market hypothesis). Nevertheless, the test results apply to both theories. Kim et al. (211) use the automatic variance ratio test, the automatic portmanteau test and a generalized spectral test, all based on autocorrelations. These test results differ over time and evidence is found that return predictability on the market is higher before 198 than after, which implies an increase in market efficiency after 198. These results correspond with Tóth & Kertész (26) who 9

20 also found rising efficiency in their datasets starting from the eighties and nineties. And just as Tóth & Kertész (26), Kim et al. (211) also explain the rise in efficiency by infrastructural innovations on the stock markets in the sixties and seventies of which the effects manifested from the eighties onward. But does this mean that markets were inefficient before 198? Kim et al. (211) do not necessarily think so because there still is a difference between theoretical and economical gains. Although return predictability seemed possible at times (from an ex post view), the possibility of attaining financial benefits is questionable as there are still transaction costs and uncertainties associated with the used forecast models that need to be considered. However, evidence is presented that market efficiency is not proven for the whole period and it is shown that the efficiency changes over time. In addition to examining return predictability (i.e. weak-form efficiency), Kim et al. (211) also run a regression model to find out if and if so, what market conditions contribute to return predictability. On the one hand, dummy variables are used to allow for the effects of market turmoil (crashes, crises, bubbles...) and on the other hand economic variables (interest rates, inflation, market price-earnings ratio...) are included. The findings of the regression are that return predictability is influenced by market conditions and the degree of predictability differs over time. For example, return predictability lacks when the market crashes but predictability is fairly high in times of economical or political crises. Furthermore, Kim et al. (211) find that risk-free rates, inflation and market volatility are significant economic variables in the regression results. Although the part of the research of Kim et al. (211) involving the effect of market conditions is mainly to test a part of the adaptive markets hypothesis, it also has important implications for all research on weak-form efficiency and may help explain the differences and contradictions in weak-form results found by the many researchers. Kim et al. (211) point out that the results of previous empirical research are influenced by the market conditions that are present at the time of the studied dataset, which is referred to by the authors as the data-snooping bias. The need to put an examined dataset in a larger timeframe is hereby put forward but is not always achievable by restrictions in data collection. The datasnooping bias is a plausible explanation for the many conflicting results that are found in the literature and also is of importance for Kim et al. (211) as their results are also deviating from most general conclusions of previous work that may be (out)dated and in need of revision. 3. Behavioural finance Behavioural finance, that challenges the rationality of stock markets, is the counterpart of the Efficient Market Hypothesis (EMH). One of its important founders is Robert J. Shiller, one of the three Nobel Prize winners of 213, who contradicts the EMH with his empirical research. Instead assuming that investors are fully rational and that share prices do reflect all available information, proponents of the behavioural finance believe that investors are not completely rational like the EMH assumes. In contrast to the EMH, irrational investor characteristics have to be incorporated in asset pricing models (Barberis and Thaler, 23). Therefore, behavioural 1

21 finance is based on the psychology and the sociology of investors to explain changes in stock prices. Stock return predictability Since the EMH does not cope with irrational behaviour which can be found in stock market prices, behavioural finance tries to find the answer to the question why market inefficiencies exist. Behavioural finance first started to challenge the EMH with research on dividends, real interest rates and changes in the intertemporal rate of substitution. It first started with Shiller (23) who mentioned that changes in the stock prices are partly due to psychological elements and not completely due to the fundamental value that changes when new information is made publicly. Furthermore, Shiller (1987) examined if the dividend changes, changes in the real interest rates and changes in the intertemporal marginal rate of substitution could explain the volatility in share prices. He concluded that the volatility could only be partly explained by these indicators while the extra volatility remained unexplained. Concerning these indicators, dividend changes contribute little to the variability of share prices and the other two indicators are also a small part of the observed variability (Shiller, 1987). Like in Shiller (1987), we present a formula of how the price of a stock is obtained: Pt= Dt/(1+r) + Dt/(1+r)² + Dt/(1+r)³+ The price of a stock, which is shown in the formula above, presents all dividends (i.e. future and present ones) discounted by r, which is the real rate of return. Regarding to this formula, the EMH assumes that all future dividends are known by investors. Yet, Shiller criticizes this assumption with evidence from Marsch and Merton (1986; in Shiller, 1987) who say that dividends may follow a random walk and that future dividends are more uncertain than presumed by the efficient markets model. Grossman and Shiller (1981) researched price swings of stock market indices in order to find evidence of market inefficiency. The goal of their paper was to find determinants other than new information. They found that price changes were not only represented by new information but also by changes in the real interest rates. Their paper shows a positive relation between real interest rates and share prices which have a stable dividend in real terms. They stress that very high real interest rates cause serious increases in stock prices, even dramatically. In their paper, it is also assumed that when present consumption is abnormally low in comparison with the future consumption, real interest rates will be large. People will try to hold their current consumption level and for that reason, stock prices have to be lower than future stock prices in order to prevent dissavings (i.e. people will tend to sell their stocks). Because dividends, real interest rates and the intertemporal rate of substitution could not fully explain excess volatility, research started to investigate serial correlation. In the opinion of Fama, extra volatility that consists of overreactions and underreactions on new events in the stock markets is equally distributed. However, Shiller (23) contradicts this criticism because there is no psychological principle that explains why people always react too strongly on new circumstances. The fact that market anomalies disappear after a certain time, which would provide evidence of market efficiency, can be contradicted by Shiller. He argues that 11

22 anomalies also disappear in inefficient markets and therefore is not an evidence of market efficiency. Clearly, the random walk model has to be innovated. As mentioned in the EMH section, the random walk hypothesis implies that price changes are independent (Fama, 197). Put differently, the changes of the stock prices are uncorrelated with each other which indicates that the probability of a negative return is the same as for a positive return. This implies that returns are not predictable as well. In contrast to the efficient market hypothesis and its literature, autocorrelations are found by several researchers who contradict the EMH. One of these contradicting papers is from Barberis et al (1998), who observed autocorrelations. Barberis et al. (1998) found positive and negative autocorrelations which caused overreactions and underreactions of share prices. After good news, they analyzed positive autocorrelations during three to five years. They had two remarks about autocorrelations. First, their study shows an underreaction to sole announcements from the company which results in negative autocorrelation in stock returns. Second, an overreaction happens when these sole announcements are followed by the same information. Actually, investors underreact because there is some uncertainty about the effect on the long term; therefore, investors will wait for more confirming news. Investors will believe, when the announcement is confirmed by extra news, that the effects will be persistent on the long term. Lo and McKinley (1988) also find, positive autocorrelations on the long term but do not find negative autocorrelations. Their findings are derived from weekly and monthly returns. They tested if the random walk model could be rejected when weekly trading data was observed. Results confirmed that share prices do not follow the random walk hypothesis, and that weekly returns do not follow the stochastic behaviour as assumed in the random walk hypothesis. Furthermore, the rejection is even stronger when the model is tested on small capitalization stocks. But as seen before when discussing the EMH, Fama (1991) disregards these results due to a possible nonsynchronous trading effect. Some papers argue that small stocks are different due to infrequent trading (i.e. less trading implies that new information is being observed slower). In fact, the intermittently trading of shares is a possible source of bias (Dimson, 1979). As a result, he finds each estimated beta of his asset-pricing model, for instance a CAPM model, to be underestimated. However, the use of weekly trading data minimizes the different biases that come from infrequent trading (Lo and McKinley, 1988). After all, their study concludes that infrequent trading is not the whole reason why they are able to reject the random walk hypothesis. The literature provides sufficient arguments against the criticism of biases due to the infrequent trading of shares. Serial correlation Because serial correlation is a valid explanation for excess volatility, several researchers tried to clarify why serial correlation exists and why arbitrage is not a realistic solution. If under and overreactions occur, this implies that returns are not independent, which is not in line with the first assumption of the random walk. We will further discuss the second assumption that goes about the rationality of investors and the effectiveness of arbitrage. Depending on the level of rationality by investors, we can distinct two kinds of stock market traders. One type of stock market traders are irrational investors, which are also called noise traders. The 12

23 other type of investors, are rational stock market traders. Barberis and Thaler (23) disprove the assumption of the EMH, stating that any mispricing will quickly disappear because of riskless arbitrage opportunities. Irrational investors who drive prices away of its fundamental value will attract rational investors. Therefore, rational investors will bring the price back to its fundamental value, eventually leading to an equilibrium. However, Barberis and Thales (23) argue that arbitrage opportunities can be risky and costly. Consequently, this investment strategy becomes unattractive which leads to prices that are not in accordance with all publicly available information. They sum up several reasons why arbitrage can be unattractive. First, investing in stock market produces costs such as bid-ask spreads, commissions and fees for shorting stocks and options. Second, irrational markets are not always able to move the price to its fundamental value which makes it risky for an arbitrageur. The infamous risk is noise trader risk which is the risk that irrational traders pose, on the short term, as the capability of pushing the price away from the fundamental value. Hischleifer (21) also argues that arbitrage by irrational investors can arbitrage efficient prices away. An arbitrageur bears not only noise trader risk, but also fundamental risk. For instance, an arbitrageur accepts fundamental risk when he shorts an overpriced stock, of which the dividend news caused an overreaction. What if the news about the future dividend suddenly seems better than expected? Consequently, the fundamental value increases and the arbitrageur s short position will become a losing position. Third, investors who apply the wrong models to determine the fundamental value (i.e. model risk), bear the risk of arbitraging a stock which price equals the fundamental value. Last, research like Shiller (23), Long et al. (199) and Barberis & Thaler (23) indicate the existence of positive feedback. This phenomenon happens when investors buy when prices rise and sell when prices go down. As a result, when irrational traders purchase shares and prices go up, rational traders follow suit. Eventually, prices quickly increase and an overreaction happens. Admittedly, stop loss orders can influence stocks which are sold after price declines (Long et al., 199). The fact that rational traders act irrational in order to benefit from the momentum and that irrational traders do not leave the market after a price correction is explained by Long et al. (199). Long et al. (199) provide three reasons why noise traders do not leave the market after participating in it. First, the capital market s circumstances change over time, and so learning from past mistakes is rather limited. Second, when positive feedback traders leave the market, they can reconsider to turn back later. Last, if noise traders hold riskier positions than rational investors, higher returns can be earned. Shiller (23) found that these anomalies, like panics and crashes, disappear over time but that overreactions and underreactions are common phenomena that lead to excess volatility. Cutler, Poterba and Summer (1991) plead for a model where rational and irrational investors interact, thus, forming market equilibria. Equilibria which are formed by the demand of rational investors, who base their decisions on expected returns, and irrational investors (i.e. feedback traders), who base their decisions on realized returns. Eventually, excess volatility can take place when behavioural effects arise. In the next paragraph, excess volatility will be further discussed and linked with empirical results. 13

24 Empirical studies Before we discuss the behavioural characteristics of stock market traders and their effects, which cause serial correlation and excess volatility, we investigate the literature thoroughly on excess volatility in stock markets globally. First, we begin with the paper of Cuthbertson and Hyde (22). They investigated the efficiency of German and French stock markets. The Campbell-Shiller VAR methodology is used and applied on monthly data from January 1973 till June 1996 (Cuthbertson and Hyde, 22). Results conclude that excess volatility exists in both stock markets, but only when they assume that excess volatility remains constant. Nevertheless, if the model assumes that the risk premium changes over time then no evidence of excess volatility can be found. Cutler, Poterba and Summer (1991) explain that the existing models in the field of finance are not capable to justify changes in risk premia. They also assert that autocorrelations of the stock returns cannot be produced by changes in the risk factors. Since 1926, excess returns are found in the US stock market by the study of Mehra and Prescott (1985; in Cutler, Poterba and Summer (1991)) and they state that the found deviations are not consistent with the empirical risk of the stock returns. DeLong and Becht (1992) analyzed the German market from 1876 till 199 and come to different conclusions. Before the First World War, the market has no excessive volatility which supports the EMH. In contrast to the previous period, later periods are marked with excess volatility. DeLong and Becht (1992) owe this to the structure of the capital markets. Before the First World War, the capital market was monopolized by six major banks. This institutional structure made it able for these banks to have almost perfect information since they were stockholders, investment banks and receivers of deposits at the same time. Furthermore, these banks had a long-term investment horizon which made the capital market very stable. On the contrary, the capital markets became well-developed after As a result, more investors could trade on the stock market which became less informed and in which these investors were not sufficiently able to price the stock to its correct fundamental value. Now, we will discuss the effects caused by behavioural characteristics. Positive-feedback effects Lakonishok et al. (1992) researched institutional traders in order to evaluate positive-feedback effects and herding. Their study made use of data coming from the SEI, which is an investments company with more than five hundred funds. Results showed that, for small stocks, positive-feedback effects could be found but herding did almost not occur. While for large stocks, there was weak evidence of herding and positive-feedback effects. As a result, larger stocks seem to be less inefficiently priced than smaller stocks. Like Barberis and Thaler (23) argue, some groups of shares have better average returns than others, in the literature also known as the cross-section of average returns. These differences are not justified by the CAPM, therefore, seen as anomalies in capital markets. They find a higher average return for the small stock decile than for the big stock decile. Despite the use of the same data like Fama and French (1992; in Barberis and Thaler, 23), they conclude that the higher return is more than a compensation for the additional risk. 14

25 Excessive volatility cannot be explained by the efficient markets hypothesis. In other words, if markets are efficient, how can bubbles arise? Kindleberger and Aliber (211) studied different bubbles throughout the history and found that during times of manias (i.e. when prices deviate significantly from their fundamental value) a general irrationality is present. Waves of excessive optimism lead to bubbles which eventually implode by excessive pessimism. Long et al. (199) justify this process of up- and downswings, which may lead to speculation, with evidence of positive return correlations at short time periods till the price is restored to the fundamental value. Kindleberger and Aliber (211) conclude that stock prices are influenced by insiders who follow the trend and by outsiders who act irrationally. The investment strategy where high-priced securities are sold and low-priced securities are bought is normally executed by the insiders. However, the outsiders adopt a reversed investment strategy, which leads to destabilizing speculation. If all future dividends are known, markets would be rational. This will also imply, in theory, that all investors have sufficient knowledge of the discount rate (Shiller, 1987). In reality, future dividends are uncertain and are the cause for market irrationality among rational and irrational investors. The part of excessive volatility was an unexplained mystery in the beginning of behavioural finance. Nowadays, many researchers succeeded in finding explanations for this excess volatility but it still remains a complex process. Many studies appear to find different effects, which are very divergent, forming a base to explain anomalies. After a brief description of behavioural critiques on conventional financial theory, we will take a closer look at one of the most important biases in the literature that explain excess volatility and other anomalies in the stock markets. When individuals participate in stock markets, they must make difficult and complex choices that cause irrationalities (Bodie et al., 213, p. 266); these irrationalities can be distinct and divided into two major categories. The first category contains anomalies caused by investors which are not always able to interpret information correctly, thus, estimate faulty probability distributions of future returns. The second category contains investors which are aware of the probability distributions, but still make suboptimal decisions. Another point of criticism, besides the complex choices made by investors, is the limitation of the realization of arbitrage opportunities (Bodie et al., 213, p. 266). We start with the discussion of biases due to incorrect information processing and we will end with biases due to investors behavioural characteristics. To sum up, we start with the representativeness bias, overconfidence, stock splits, conservatism and end with regret avoidance, mental accounting and prospect theory. Representativeness bias Investors who make prognoses do not know the true probabilities of their forecasted events, which is why they base their forecasts on experience and recent events. These past events are largely representative but do not completely represent the properties of the population (Tversky and Kahneman, 1973). Consequently, investors are subject to the representativeness bias. Tversky and Kahneman (1972, 1973; in Bodie et al., 213, p. 267) indicate that forecasts can be too extreme, thus, earning expectations will be too high which would eventually cause a stronger surge in share prices than normally (i.e. overreaction). De Bondt and Thaler (199; in Bodie et al., 213, p. 267) researched the link between P/E effects and the 15