An Effective Analysis of the Size and Value Effect
With
A European Stress Test of the Fama and French Three-Factor Model
July 2007, University of Groningen
Faculty of Economics
Final Draft Master’s Thesis
Program: MSc BA Specialization Finance
Student: Tommie Kroeze s1216481
Email: t.kroeze@student.rug.nl
Table of contents
I. Introduction... 3
II. Theoretical background ... 6
2.1 Small firms, valuations and the cost of capital... 6
2.2 Asset pricing and theories ... 8
2.2.1 Portfolio theory ... 8
2.2.2 CAPM ... 9
2.2.3 Anomalies and other measured effects ... 11
2.3 Explaining the anomalies ... 14
2.4 Fama and French ... 17
2.4.1 Fama and French three-factor model ... 18
2.4.2 Fama and French results ... 19
2.5 Hypotheses ... 24
III. Methodology and Data ... 25
Method ... 25
3.1 The explanatory variables ... 25
3.2 The dependent variable... 27
3.3 The regression and tests... 28
Data... 33
3.4 Data Selection and Collection ... 33
3.5 Descriptive statistics ... 37
3.5.1 Six independent portfolios and explanatory variables ... 39
3.5.2 Fama and French 25 portfolios... 43
IV. Estimation Results ... 46
4.1 Regression with the Market factor... 47
4.2 Regression with the two Fama and French factors SmB and HmL... 49
4.3 Regressions with the Fama and French 3 Factor Model ... 52
4.4 Robustness ... 57
4.5 Results and application of the competing asset pricing models ... 60
V. Conclusion and recommendations for additional research... 62
References ... 65
Appendix ... 69
Appendix A: Data Selection and excess returns ... 69
I. Introduction
The toolbox for making company valuations contains a wide variety of methods. One of these is the widely used Discounted Cash Flow (DCF) methodology. When using the DCF method to valuate a business or a project there are different aspects that have to be taken into consideration. At least two things are imperative to a good valuation; the proper calculation and projection of (free) cash flows and the determination of an appropriate discount rate to discount these cash flows. Making mistakes in these two features of the valuation will largely influence the outcome of the valuation. The CAPM of Sharpe (1964) and Lintner (1965) is a frequent and widely used model for the estimation of the equity cost of capital. The fact that this model is practical and easily applicable in different situations adds to the fact that it is still commonly used. The main premise of the CAPM is the fact that β, the risk factor, is key in explaining the cross-sectional variation of expected stock returns. The risk factor, or β, in the CAPM is the covariance with the market index or a large portfolio. This risk is not diversifiable by investing in a large portfolio of stocks. As will be discussed later in more detail this does not seem to be the complete story. In the early seventies, the CAPM has generally been supported (Black, Jensen and Scholes, 1972 and Fama and Macbeth, 1973), partly because of new statistical methods in place to test the central predictions of the model. From the late seventies onwards, a wide body of research actually found discrepancies in the theory. In the academic financial community there is countless empirical work on the faulty nature of the CAPM. The flaws in theory are generally known as anomalies. An anomaly is described by Schwert (2002) as an empirical result that cannot be verified by an existing asset pricing theory or model. For example, the risk factor in the CAPM is not able to explain the difference in returns between large and small firms. In other words, the existing paradigm is challenged. The discovery of an anomaly asks for a thorough investigation of the theory and the apparent or underlying reasons behind the existence of the anomaly.
Fama and French explicitly and directly incorporates firm size in its model where the CAPM does not is the apparent reason why the Fama and French model is under consideration in this research. In short, the Fama and French three-factor model considers three factors that determine the risk of an asset or a portfolio as compared to a benchmark. These three factors are the Market factor; measured as the return of the market portfolio over the risk-free rate, the Size factor; measured as the difference between the return on a portfolio of small and large company stocks, and the Value factor; measured as the difference between the return on a portfolio of companies with a high book-to-market ratio and low book-to market ratio. While the three factor model is by itself under scrutiny, findings that indicate return-risks related to any of the factors mentioned above will be important here. In practice many reasons for the increased higher risk of smaller companies are brought forward. This research will use the three factor model by Fama and French to provide insights in the possible existence and thereby the direction and dimension of size effects. In addition the value effect will be important as well. The value effect indicates that returns of high B/M ratio firms are higher and these higher returns are not fully explained by the market risk factor, or beta.
In the case of apparent size or book-to-market effects, further investigation of how to incorporate these in valuations is needed. The fundamental research questions in this paper can ultimately be derived from the need for an assessment of an appropriate cost of capital for small companies and the knowledge that the return provided by an asset pricing model is the mirror image of a company’s cost of capital.
The research questions are as follows;
Are there notable differences in the stock returns between small versus large firms and low versus high book-to-market firms in a selection of European stocks for the period 1990-2005?
If the question above can be answered positively, the returns have to be weighed against the level of risk in a formal asset pricing model. This asks for the use of the CAPM or an alternative model, in this thesis the Fama and French three-factor model, which may be better able to explain the variation in stock returns. The second research question is therefore as follows;
Probably the most important thing to establish is an appropriate economic interpretation for the answers of the questions above. You ultimately want to know whether there is a sound economic application for the results for the three factor model;
Is the Fama and French three-factor applicable in real life situations?
It should be noted that the questions stated here do not form a comprehensive list. There are different questions that may arise through answering the questions above.
In this research three OLS regression series will be performed. In each of the regression series the value weighted returns of 25 portfolios sorted by size and book-to-market ratio are the dependent variables. The independent factors are the three factors mentioned above. The regressions results will show whether and to what extent the three factors influence the portfolio stock returns. This research uses a selection of European firms. The sample is gathered from five large European economies. Of each of the firms the return, the market value and book to market value is used.
II. Theoretical background
This section will elaborate on some basic asset pricing theories and the anomalies that seem to exist. Specific attention will be aimed at small (quoted) companies, because an important point is the relation between firm size and the way this may be incorporated in an asset pricing model. The model by Fama and French has indeed explicitly absorbed size as an explanatory factor for returns. Hence, the Fama and French model(s) will be outlined here. Studies that support or reject their theory will be discussed as well. It is also important to take notice of the theories the Fama and French papers actually criticized. Many aspects of early asset pricing literature are of influence in a Fama and French research. This is why an overview of the basic theories and implications of portfolio theory and CAPM theory will be provided in this section. This section will first elaborate on some aspects of small firm valuation and the cost of capital. Then asset pricing theories that have been the major influence of the Fama and French three factor model will be discussed. After that the anomalies and other effects are discussed. Fama and French (1993) describe a model that is able to incorporate some of the size and value effect. This model will be discussed thoroughly, since it is the central directive of this thesis. After all of this literature is discussed, this section will conclude with the research hypotheses.
2.1 Small firms, valuations and the cost of capital
There are different methods to value firms. Among the most used methods are the DCF methods and the methods based on trade or transaction multiples. In the past research using samples of US-based small firms have showed higher average returns on equity than large firms (e.g. Fama and French, 1993). This higher return will often exist because of the relative higher risk of small firms as compared to their larger counterparts. A number of reasons can be mentioned for the existence of this higher risk in small firms. These are summarized below.
The indication ‘small’ still needs some explanation. The size in this research is indicated by the market value of a firm. The listed firms are in general larger than unlisted private firms. When referred to small firms, it means that the market value of the firm is relatively low compared to other listed firms. At what market value a firm is considered small may vary from country to country. One may also think of other criteria to indicate that a firm is small of big. This can be the number of employees or the level of sales. However, in this research the indication for size will be the market value.
equity cost of capital is adjusted through the use of the CAPM, either β or the market risk premium is adjusted. Another possibility is an additional risk factor that will be added to the general model. The other way is to put a premium or discount on the overall estimated value of the firm. The value of a firm may be established through a DCF analysis or a multiples approach. The value is thereafter adjusted by subtracting or adding a fixed or variable amount. One can also think of adjustments in the cash flow projections in a DCF model. However, this last method will often be arbitrary. The question now is: What makes the smaller firm more (or less) problematic or risky than a larger one?
The business of a small firm is often less diversified and therefore the earnings will be more subject to changes in the environment. Furthermore smaller firms suffer from informational disadvantages, which make them less attractive. Several of these informational issues will show up in the valuation of small firms by analysts. For example analysts might be constrained by time or their principals to analyze small firms. Thereby they will be tempted to spend most of their time on larger firms. The lack of available information caused by this negligence makes investing less certain and more risky. Investors want to be compensated for this higher risk and they demand higher returns. Fama and French (1992, 1993) found that the higher level of returns of small firms was not explained by beta.
Another issue, as examined by Gompers and Metrick (1999), is that larger institutional investors often have the lion’s share of their investments invested in relatively large firms. The smallest of stocks are hereby traded infrequently. This makes that the price setting is more effective for the stock of relatively larger firms. Hereby they are also traded more often. Another related issue is the lack of liquidity or marketability of smaller stock, which states that smaller stocks are more difficult to sell (for example see Damodaran, 2002). Thin trading makes that prices are formed with a lag between the actual occurrence of information and the trades that are made. Additionally, smaller firm stocks will have relatively higher transaction costs than larger firm stocks. In short there are different limiting factors that could influence the price setting of small listed stock. In the worst case thin trading or informational issues may cause inefficient price setting for small firm stock. An example of inefficient price setting is a sharp rise or decline in price when a stock is traded, whilst the stock price is otherwise constant over time. Differences in price setting between small firm and large firm stock may cause differences in the average expected return between small and large quoted companies.
persisting effect and the rationale behind this is worth a complete study on its own. The topic for this study is more aimed at the appearance of notable effects in different asset pricing studies or models. Please note that when I refer to an effect I mean that an attribute is found to influence the returns of a company’s stock. This influence cannot be traced back from an asset pricing model. A thorough investigation of all the effects and all asset pricing models is well beyond the scope of this study. Therefore this study will mainly focus on the three factor model by Fama and French (1993) who have explicitly absorbed size and B/M ratio related risk or risk mimicking factors in their model. These will be explained later in more detail.
In short the size effect has been under considerable investigation. To some extent the case can be made that the effect and inherent risks may be diversified away. However, an effect may also persist throughout a wide body of research and it could show fundamental influence over multiple periods. When this is the case, you have to consider making serious adjustment to any of the existing asset pricing models and/or methods.
2.2 Asset pricing and theories
To arrive at the three factor model as an asset pricing model, it is important to have an idea of the theory and models underlying its basics. The following paragraphs will be devoted to a general outline of asset pricing theory and its basic principals.
2.2.1 Portfolio theory
about the volatility of one stock but not about the risk of an entire portfolio. This means that the sum of the variances is not the same as the total variance of a certain portfolio. The measure that can show this is the covariance, which shows how much the return of one stock covaries with the return of a group of stocks. Instead of finding the portfolio with the lowest risk for individual stocks, the main point is now to find a portfolio with the optimal level of covariance. In other words, to decrease risk, one needs to add a stock to a portfolio that has a covariance of less than 1 with the portfolio. In Markowitz’ portfolio theory investors will be mean variance efficient, which basically means that investors will strive for an optimal division between risk and return. This means that an investor will maximize expected return for a given level of variance and will minimize the variance for a given expected return. The efficient set of portfolios consists of the ones that fit within this maximization scheme.
In short, the most significant addition to the field of portfolio theory is the acknowledgment of variance of one stock in the context of a portfolio of stocks. The view here is that the variance of a portfolio investment will only diminish, when there is invested in securities which have a covariance of less than l.
2.2.2 CAPM
Sharpe (1964) picked up the theory by, and partially in conversation with, Markowitz to later make some important additions which would ultimately lead to the CAPM. It was only after the work by Tobin (1958) in this field, that the model was extended with risk-less assets. Adding the risk-free asset to the equation makes that an investor can both invest on risk-free and risky assets. As a result, the risky portfolio is the same for all investors and the variation lies in the choice of how much to invest in the risky portfolio or risk-free assets. The question at his point is which portfolio will be the appropriate one and what quantity of what asset (stock) should be put in it. Sharpe first developed a rather simple, single factor model. Here, the risk of all securities was tied to a general factor. This factor could be the general state of the economy or some economy-wide index. The development and use of an index or state variable would make the calculation of all the individual co-variances unnecessary. The insight that in equilibrium the appropriate proxy for the risky portfolio would be the market portfolio or market index eventually led to the Sharpe-Lintner CAPM and its central predictions.
which the model will work. It is also important because the model by Fama and French that is discussed later relies to a large extent on these same assumptions.
The assumptions are as follows:
• Homogenous expectations, which means that all investors share the same beliefs about the returns and variations in returns in the future that investors have complete agreement upon the set of average returns and variations. Furthermore it means that investors handle the same time horizon (holding periods) and share the same time horizon regarding risk, risk measures and market information. Hereby the investor has rational expectations, which means that investors make best guesses about the future given all information. This will maximize their expected utility;
• Risk is measured as the variance of a portfolio. Furthermore there is also risk-free borrowing and lending. This makes that the risk is protected on the downside by the risk-free rate. The upside risk is determined by the amount of diversification and the variance of a portfolio. Investors are able to lend and borrow unlimitedly at the risk-free rate; • Risk and expected return are the only aspects investors care about in valuing stock; • Investors are also risk averse. They are scared of taking risk and prefer low levels of risk; • Other assumptions aim at the market in which the investors trade. In this marketplace there are no taxes, minimum transaction costs and no one investor is capable of influencing the market where there is perfect competition. In addition the market is large and an investor’s wealth (or stock holding) is only small compared to the whole market. • Finally, there are no arbitrage opportunities. An investor is not systematically able to take
advantage of price differences.
The most important relationship in the model is a stock’s covariance with the market. This covariance is non-diversifiable. This is known as the systematic risk. Firm-specific risk on the other hand can be diversified away by forming a portfolio that has a co-variation among the stocks of less than one.
The general (Sharpe-Lintner version) formula of the CAPM can now be described as follows;
Rj = Rf + βi [Rm– Rf],
receives for investing in the relatively risky stocks instead of a risk free asset. βj will be 1 when it has a perfect co-variation with the market. In this linear relation, β is the only measure of risk that explains the cross-sectional variation of stock returns. The relation between risk and return will be of importance throughout this thesis. In the CAPM model, size or B/M ratio effects are dealt with through beta. If small companies show on average higher stock returns, this could be traced back to the level of risk or how the stock relates to the market. We will later see that the Fama and French factors indicate more than one risk return relationship.
The CAPM model is both functional and comprehensible. As mentioned earlier the existing body of literature that provides proof as well as disproof of the model is massive. The first direct challenges to the CAPM were Roll’s critique and the discovery of different anomalies. Through the years there were more and more anomalies that could not be explained by the existing asset pricing models. Below there is a summary of some of the most renowned ones, two of which are the size and value (book-to-market) effect. Bear in mind that these anomalies are not altogether rebuttals of the CAPM as an asset pricing theory. It is much like Newton’s theory of the moon’s orbit that was considered to be erroneous. It was only after centuries and highly sophisticated models that his orbit was officially proven wrong and replaced with supplementary calculations.
Before discussing the anomalies I will shortly discuss one critique by Roll (1977), known as Roll’s critique, comments on one of the central characters of the CAPM. He suggested that it is never really possible to appropriately test an asset pricing model like the CAPM. This is because the market index used cannot be verified. Without knowing whether the market index is a justifiable proxy for the ‘real’ market, the model cannot return the right values. The real world market index should contain all possible priced assets. This may include assets as real estate, land and human resources. Without a proper specification of the market index, the asset pricing model can therefore deliver anomalous returns.
2.2.3 Anomalies and other measured effects
Davis (2001) made a summary of a number of important and recurring anomalies or effects that came into question and these include the following;
showed that the results were not just detected among small firms, as measured by their market capitalization. An example is provided in Bodie, Kane and Marcus (2002), which can also be applied to other effects or anomalies. Of two firms with identical expected earnings, the firm with the higher risk will have a lower price and therefore a higher E/P ratio. This higher E/P value stock with its higher risk will also show higher expected stock returns. When the CAPM is at this point not capable of incorporating the higher risk with beta, the E/P ratio, or another variable for that matter, will function as a supplementary risk factor. This risk factor will surface and the anomalous returns will be noticed. Fama and French (1992, 1993) also examined the E/P ratio in relation to unexplained risk. They found that the influence was in line with the value effect; higher values for the E/P ratios meant higher returns which could not be explained by beta. The size (market value) effect; Banz (1981) was among the first to show that the average returns of small-size firms were higher than the returns of large companies. One would expect this to hold for the CAPM as well, because small firms tend to be riskier (e.g. because of higher earnings volatility). However, the variation in β did not capture this size effect and hence could not explain all the common variation of stock returns. Some authors, such as Keim (1983) and Reinganum (1983), note that the effect is especially noticeable in (the first two weeks of) January. The rational or explanation behind this January effect is manifold and explanations are given from different angles. Below is an explanation of the January in the light of the size effect. More will be explained about the size effect when the work of Fama and French (1992 onwards) is discussed.
January effect for small firms; the stock of small firms will in general experience higher return volatility, provided that the stock is traded enough. Also, small firm stocks generally suffer relatively more short term capital losses throughout the year. For tax purposes these losses are taken before the turn of the year. This is called tax loss selling, which means that investors sell their declining stocks at the end of December. Instead of reinvesting the proceeds, they only wait till January. Small firms will ‘revive’ in January and hence the effect of high returns occurs which cannot be explained by risk. Size is indeed a matter here because small firms are believed to have the greatest proportion of stocks that had declines in price, and the most risky stocks are small during the year (Bodie, Kane and Marcus, 2002).
as value stocks. Furthermore high B/M ratio stocks will often have lower earnings. Following Shleifer (2000) the B/M ratio can be seen as a measure of how cheap a stock is. A low B/M ratio stock is relatively expensive and is called a growth or glamour stock. With this ‘glamour’ comes the advantage of getting a lot of attention. A high B/M ratio stock is relatively cheap. Furthermore, due to their relative unpopularity among investors they are called neglected stocks. A low B/M ratio may say something about the future performance of the stock and is a sign of the unwarranted confidence in the market. This may lead the market to overreact to some news, and people may regard growth stocks’ B/M ratio as informative about the future performance of the company and its stock. This is turn may lead to overreaction and overvaluation of the company and the stock. This works vice versa for the high B/M ratio stocks. Value stocks are not popular, down-and-out and possibly this may even deteriorate. Eventually prices and returns will return to their fundamental1 values. This is because the market realizes it has ‘neglected’ the value stock and valuations will more closely approach the fundamental value of a firm. Now the high B/M ratio stocks will outperform the low B/M ratio stocks. It should be noted that this ‘overreaction’ story is just one of the possible explanations for the effect. Other explanations are aimed at possible distress risks underlying high B/M ratio firms. This distress risk story aims at the underlying problems for low-book to high market ratio firms (Griffin and Lemmon, 2002). Distress firms or high B/M ratio firms are temporarily selling at a low price, because the future looks uncertain. Another risk that is often linked to distress and thus to value firms is the relatively high risk of default. The explanations given behind the fundamental risk reason on the one hand and the irrational investor consideration on the other hand are provided later in more detail.
The value effect appears in a wide body of research of which the work by DeBondt and Thaler (1985), Fama and French (1992, 1993, 1996) and Lakonishok, Shleifer and Vishny (1994) are some of the most cited. Also the effect is often more apparent and more persistent than the size effect mentioned earlier (Fama and French, 1992 1993). The value effect persists in international settings as well (Fama and French, 1998).
The momentum effect; momentum is the same direction in the rate of return of a stock in a subsequent period. In this context the momentum is seen as companies either having positive streaks or negative streaks for the returns on their stock. A positive streak means that a certain stock had high returns over a number of subsequent periods (i.e. months). The momentum effect
1 When I refer to fundamental values or economic fundamentals, I aim at the present and future information
(Jegadeesh, 1990 and Jegadeesh and Titman, 1993) now describes that companies that had a streak of high positive returns in recent months continue this performance in subsequent months, hereby outperforming the stocks that lost in this period. In other words, the direction of the return of a stock can act as a predictor for further movement of the stock’s return in the same direction. It should be noted that the effect is measured for relatively short period of six to twelve months. The explanations underlying this phenomenon are generally brought forward from behavioral finance. In short this boils down to investors that underreact to news. If initially the news is good (bad) the prices tend to keep trending up (down) and investors hereby underreact to new and more recent information or news. This way, old news goes on as a predictor for stock returns.
Carhart (1997) adds a factor that accounts for momentum to a Fama and French three factor model. One reason for this is to investigate the momentum factor in the light of year-to-year mutual fund performance. The momentum factor applies to a relatively short period of time and this research aims at a cross-section of stock returns for a period of 16 years. This is why the momentum factor is not added to the three factor model. Fama and French are not able to explain the momentum factor with their three factor model, while their model is able to explain some other anomalies. This is another reason to leave momentum out of the analysis.
This is not a complete overview of all the effects, but these anomalies do provide an overview of all the different angles from which the CAPM was assaulted. The B/M ratio and size effects are of special interest throughout this piece. Fama and French have incorporated these as factors in their model. The work by Fama and French (1992 onwards) has further made the CAPM implausible. Before going deeper into Fama and French and their model it is good to be aware of some of the explanations that are brought forward for anomalies or other deviations that exist
2.3 Explaining the anomalies
There are different explanations for the anomalies. Some of these specifically apply to the CAPM and others apply to other asset pricing models and theories as well. Although the Fama and French model is discussed later, some explanations that were given for their findings are also found in this section. Gareiev (www.nes.ru; 26-02-07) has provided a useful division for the anomalies with three basic classes of explanations; (i) a technical explanation, (ii) the explanation of irrational investor behavior, or (iii) an explanation that includes multiple risk factors.
Technical considerations
consideration. Technical is more a collective term that deals with data, the method or model that is used or the people that deal with it. For example it may be that researchers may apply an unjustified interpretation of the results. Also a method to measure an anomaly should be judged with caution. The CAPM is under considerable scrutiny as an asset pricing model (i.e. Fama and French, 1992), so when a ‘new’ model is better than the original CAPM model it is not necessarily good by itself.
An important issue is data dredging, which contains both data snooping and data mining. I have put data mining and snooping under this denominator because I found this in different readings. Data mining is a suggestion that when research is performed with awareness of existing effects, the selection and processing of data is distorted by this prior knowledge. Many efforts are aimed at coming to the ‘appropriate’ or ‘wanted’ result. When this result is eventually presented it is not shown along with the number of failures to come to this result. This way only the fruitful efforts surface and the failures do not. Data mining also aims at the extensive examination of methods or sets of data and eventually finding a pattern (or anomaly). Data mining may work, but it could lead to flawed results as well. Data snooping is more aimed at the successive use of similar (sets of) data in different researches. This makes that results often confirm one another. The basic point is that when confronted with research done in the past, researchers could easily get carried away finding evidence of effects found in the past by using the same data. To solve for the above mentioned issues new research must be aimed at finding out-of-sample evidence. This includes choosing different data(sets), periods, countries, or other distinguishing features for further research. In short, many of the anomalies have been found to be influenced in one way or another by data dredging or data mining. This makes it necessary to keep this in mind in developing this research.
Another technical explanation is the survivorship bias. This problem associated with data or data collection considers that some databases do not take into account the disappearance of data in time throughout the sample. Firms that are de-listed in the time period the analysis takes place are hereby unaccounted for. Mostly firms that have gone bankrupt and are therefore taken out of the sample will be smaller firms and hence the sample will be biased towards smaller companies that perform relatively well. This phenomenon is known as the survivorship bias. Goetzman and Jorion (1999) find that a lot of data used in international research is subject to this bias and more often than not criticism can be conveyed about the use of survivor biased data.
There is also a technical problem concerning the use of historical, or realized returns to eventually come to conclusions about expected returns. Here the statement applies that ‘realized returns are no guarantee for the future’. A problem relating to this latter is more statistically grounded. The errors-in-variables problem is aimed at the fact that the β’s are measured incorrectly in a two step regression. The incorrect β’s are later used in cross-sectional tests and will have an important influence on the results found. When measured better it may indeed cause the anomalies and the true β’s will be more correlated with the anomalous returns.
The CAPM is also criticized for its static character, in which risk is constant through time. Jaganathan and Wang (1996) develop a conditional model where risk is varied in time and find that little of return is now explained by size. They also incorporate human resources in the market factor and find that this is also of significant influence.
Irrational investor behavior
From the part of behavioral finance there comes a wide body of research that tempts to explain any anomaly or other effect. Above are examples of momentum effect (underreaction) and overreaction. In short it boils down to the behavior of investors that influences the prices and returns of stock. When there is no alignment between economic fundamentals and investor beliefs and when irrational decisions are persistent, this will cause returns and prices to deviate from expected values. It is about investors making rational or irrational decisions. This way there are anomalies or other effects noticeable. For example Lakonishok, Shleifer and Vishny (1994) find large spreads of up to 10% a year between growth and value stocks not explained by market risk. They further find that investor base their expectations, which are not only based on economic fundamentals, on the past and extrapolate these findings in the future. The excellent performance, or ‘glamour’, of a company’s stock is taken as a sign of excellent future performance on the stock market.
Multiple risk factors
related to size and B/M ratio that are not explained by (market) beta, this leaves room for a multiple risk factor explanation. However, what these risks exactly are is not discussed thoroughly and Fama and French themselves leave the interpretation for a great deal to others in successive research.
We have now taken knowledge of some possible explanations behind the anomalies. The following paragraph will explain the work by Fama and French and how they incorporated size and value effects (or anomalies) in a three factor asset pricing model.
2.4 Fama and French
With their groundbreaking paper in 1992, Fama and French more or less decapitated the CAPM and its central predictions. The publication showed some interesting findings and the main findings can be summarized as follows; the positive relation between β and return in the CAPM is very weak and therefore β has does not have the required explanatory power. They do find that two easily measured variables, namely size and book-to-market ratio, seem to describe the cross-section variation in stock returns (Fama and French, 1992).
Fama and French (2000), we know size and especially value effects were measured in different country and data settings.
If it is true that size and B/M ratio related risk factors are able to explain the cross-section variation in stock returns, one must have a methodology at hand that is able to demonstrate this. The model Fama and French proposed in their 1993 paper is able to incorporate these factors in a time-series regression model. The method of this paper is now a widely practiced method in this field. A wide body of research replicates the methodology used by Fama and French, sometimes with small alterations to be more robust. Alterations are made for example to account for possible data dredging. Researches on data both in and outside the US have shown that the implications by Fama and French hold (Fama and French, 1998). Of course the theory is also criticized. These critiques are explained in paragraph 2.4.2, after the three-factor model is elaborated more thoroughly.
The starting point for using the Fama and French 1993 methodology and its underlying theory for this paper is the size effect. However, the methodology at hand is simultaneously using the B/M ratio as well. Fama and French found that B/M ratio had an even stronger role than size (1992, 1993). The methodology by Fama and French will be explained in a later section. Next, an indication of the method will be provided. In the following paragraph most attention will be paid to the implications and findings.
2.4.1 Fama and French three-factor model 2
The starting point for the paper in 1993 was of course their influential paper a year earlier. The asset pricing tests in this paper were different from their earlier work. The main finding of the paper was the identification of five common risk factors that influence the returns of stocks and bonds. Since this research is only interested in equity returns, all attention will be aimed at the common risk factors in stocks. These factors are; market risk premium (like in the CAPM) and factors associated with size and B/M ratio. Where size is the market value of equity and B/M ratio is the book value of common equity divided by the market value of equity. Previous work by Fama and Macbeth (1973) and Fama and French (1992) had used a cross-section regression analysis, where the 1993 paper used a time-series regression analyses. This method regresses the monthly returns on stocks (or portfolios of stocks) on the three market factors. The following equation is the basic equation of the Fama and French three-factor model;
2 This section shows the method and results by Fama and French in their 1993 paper and will therefore
E(Ri) – Rf = βi (E(Rm)- Rf) + siSmB + hiHmL ,
Where E(Ri) is the expected return on a stock or a portfolio of stocks, Rf is the risk-free rate, E(Rm) is the return on a market portfolio, E(Rm)- Rf is the market risk premium similar to the CAPM, SmB, small minus big, is the portfolio that mimics the risk factor in returns related to size, HmL, high minus low, is the portfolio that mimics the risk factors related to the B/M ratio and βi, si, hi are sensitivities or factor loadings.
The SmB and HmL may need some further explanation. In order to find factors that proxy for the size or value related risks in returns it is required to construct factors that mimic these possible risks. Therefore SmB (HmL) is constructed as the mimicking risk factor associated with size (B/M ratio). The construction of these factors will be by means of dividing the stocks in portfolios. The SmB is the realization of the return on a factor portfolio that buys small stocks and sells large stocks and HmL is the realization of the return on a factor portfolio that acquires high B/M ratio stocks and sells low B/M ratio stocks (Davis, 2001). It should be seen more or less in the same way as the market risk premium, which is the return of a large portfolio minus the return on a risk-free asset. In fact, this is the risk of holding or investing in the relatively risky market portfolio instead of investing in the risk-free asset. The mimicking risks are now the risks associated with such a portfolio allocation. Although Fama and French (1993) have admitted that the factors are arbitrarily chosen, the factors do seem to work in the model. This means that the risk factors are indeed able to explain some of the variation in stock returns that is left unexplained by the market risk factor.
2.4.2 Fama and French results
The portfolios based on size and B/M ratio show some distinct differences in the returns of portfolios for small versus big and high versus low B/M ratio stocks. This indicates that there is a difference in the returns of the portfolios as expected. In table 1 are the average value weighted monthly returns for the 25 size B/M ratio portfolios. In bold are the differences between the smallest and largest size portfolios (below) and the high and low B/M ratio portfolios. Without taking into account any risk premium of small size over large or high B/M ratio over low, a size and value premium are observable. If the values in table 1 indeed point towards the mentioned premiums and there are factors that are able to explain these premiums, a time-series regression analysis is required. This time series analysis will show what factors are of importance and in what combination. In the three different models, 25 regressions are performed by Fama and French. The bold differences are significant at a 5% significance level in the for the B/M ratio in size quintile 1 to 4 and for the size effect in B/M quintile 2 to 5. The t-tests used are explained in the methodology section.
Book-to-Market Ratio Quintiles Size
Quintiles Low 2 3 4 High
Excess Return : Rpf - Rf Small 0.39% 0.70% 0.79% 0.88% 1.10% 0.71% 2 0.44% 0.71% 0.85% 0.84% 1.02% 0.58% 3 0.43% 0.66% 0.68% 0.81% 0.97% 0.54% 4 0.48% 0.35% 0.57% 0.77% 1.05% 0.57% Big 0.40% 0.36% 0.32% 0.56% 0.59% 0.19% -0.01% 0.34% 0.47% 0.32% 0.51%
This table shows the value weighted excess returns for the 25 size and book-to-market sorted portoflios of Fama and French. The research is performed for a selection of US stocks in a 29 year period
Table 1: Excess returns from Fama and French 1993, table 2.
The results of the Fama and French regressions show clearly that the three factor model is an improvement of the market model. This meant that the three factors were better able to explain the common variation in stock returns. The results and improvements of the Fama and French model are shown in table 2. The bold values show an improvement of the three factor model over the market model. These improvements are described below.
the three-factor model. On average this is 0,055 for the three-factor model and for the market model it is 0,136, with a maximum of 0,18 and 0,42 respectively. Perhaps the most important improvements of the three-factor model over the market model are the improved values for the intercepts. The intercepts for the three-factor model are low and closer to zero than the intercepts of the regressions of the market model. The intercepts can be seen as abnormal returns that are left unexplained by the model, which will be explained in the methodology section in more detail. The t-values show only three cases where the intercept is significantly different from zero for the three factor model. In the market model 9 out of 25 values are significantly different from zero and they are on average further away from zero.
Three-factor model Market model
Low 2 3 4 High Low 2 3 4 High
R² R² Small 94% 96% 97% 97% 96% 67% 70% 68% 65% 61% 2 95% 96% 95% 95% 96% 79% 79% 76% 76% 71% 3 95% 94% 93% 93% 93% 84% 84% 80% 79% 74% 4 94% 93% 91% 89% 89% 89% 90% 87% 80% 76% Big 94% 92% 88% 90% 83% 89% 92% 84% 79% 69% 1- [β] 1-[β] Small 0.04 0.02 0.05 0.09 0.04 0.4 0.26 0.11 0.06 0.08 2 0.11 0.06 0 0.03 0.09 0.42 0.15 0.12 0.02 0.13 3 0.12 0.02 0.02 0.03 0.09 0.36 0.15 0.04 0.04 0.08 4 0.07 0.08 0.04 0.05 0.18 0.24 0.14 0.03 0.05 0.1 Big 0.04 0.02 0.02 0.01 0.06 0.03 0.01 0.11 0.16 0.11 α; intercept α; intercept Small -0.34 -0.12 -0.05 0.01 0.00 -0.22 0.15 0.30 0.42 0.54 2 -0.11 -0.01 0.08 0.03 0.02 -0.18 0.17 0.36 0.39 0.53 3 -0.11 0.04 -0.04 0.05 0.05 -0.16 0.15 0.23 0.39 0.50 4 0.09 -0.22 -0.08 0.03 0.13 -0.05 -0.14 0.12 0.35 0.57 Big 0.21 -0.05 -0.13 -0.05 -0.16 -0.04 -0.07 -0.07 0.20 0.21
This table shows the main results for the market factor model and the three factor model for the Fama and French (1993) regressions. The bold numbers show improvements of the three factor model over the market factor model. These results are taken from table 4, 6 and 9 of Fama and French 1993. The adjusted R² is shown first. 1-[β] is the absolute difference between 1 and beta, where beta is expected to be close to one. Beta in this model is the coefficient for the market factor taken from the regression. Finally α is the
intercept, which can be seen as the abnormal return that is left unexplained by the model. A larger α means that less of the variation in excess (portfolio) stock returns is explained by any of the models.
Table 2: Important findings for the Fama and French three-factor model regressions.
two main reasons. First of all, it shows the motive for using the model because it has proved to have obvious improvements over the market model or CAPM model. Secondly, to a large extent the same method will be used here. The noticeable differences in returns of portfolios of small versus large and high versus low B/M ratio stocks and the results above form the basis for investigating and interpreting research like this. Furthermore, understanding the results from Fama and French helps to interpret the work that has been done after the 1993 paper was published.
companies with big market power increase the last decade, thereby beating small firms. However, this has been different in the past. It could also be that size is related to industry and with it to industry performance. Thereby the differences in presence and direction of the size effect are merely industry related.
Berk (1995, 1996) raises the question of the use of the market value (or book-to-market value) in factor models. He challenges the characterization of a size effect as an anomaly, with the use of market value as its measure. He examines the seemingly mechanical relation between returns and prices. His arguments focus on the tautological relation between market value and expected returns. This tautology means that there will always be an inverse relation between size and expected returns. This means that with the market value (price x number of shares), there will always be an effect measurable in an existing asset pricing model. If the existing model is flawed, then size will in general pick up any risk or risk factor that is left unrewarded by the model. A short example from Berk (1995) may clarify this. Suppose a number of firms with the same dividends and thereby same expected cash flows in a single period model. The same dividends imply that the firms have in principle the same size (at least of operations). The market value of the company may be given by the following equation:
t R DIV P ) 1 ( + = ,
He states that although the size factor will not proxy for any risk variable, it will be useful in determining the risk that is left over by the risk factor in the existing model (CAPM for example). Berk (2000) further finds that the size effect fails to appear when physical measures for size are used that are unrelated to stock price, such as earnings and number of employees.
2.5 Hypotheses
The Fama and French model is attacked from different angles. However, the model has been proved to function in different countries and throughout different datasets. Without going further into the wide body of research supporting or disproving the three factor model, the following hypotheses can be stated for this research:
HO: There are significant differences in the returns of small versus big firms and high versus low B/M ratio firms.
H1: There are no significant differences in the returns of small versus big firms and high versus low B/M ratio firms.
H2: The Fama French Three-Factor model is a better model to explain the variation in stock returns and a potential size and value effect than the CAPM or market model.
H3: The Fama French Three-Factor model is not better model in explaining the variation in stock returns and a potential size and value effect than the CAPM or market model.
III. Methodology and Data
This section will elaborate on the method and the data used in this paper. First the model will be discussed. Here, the variables in the model and how these will be explored will be explained. Thereafter will be a description of the data and some important descriptive statistics will be discussed.
The three models will be tested by using a standard OLS regression method. The main research objects are the listed firms of five European countries. Different aspects of these firms will be examined and these aspects determine whether the firms are included in the final sample. The time period for this research is the 192 month period from January 1990 to December 2005. Nowadays more data can be collected and more data is available for individual months. This makes that time periods of over 20 years are no longer necessary. In the data section more will be explained about the chosen countries in the data section.
For clarity the three models that are to be tested are in table 3.
Fama French three factor model
Ri – Rf = α + βi (Rm- Rf) + sSmB + hHmL + ε
▪Ri is the portoflio return ▪Rf is the risk free rate
▪Ri-Rf is the excess portfolio return that is regressed ▪ α is the intercepts, or the 'abnormal' return ▪ βi, beta, is the coefficient for the market risk premium or the market risk coefficient
▪Rm is the return on a market index or large portoflio ▪Rm - Rf is the market risk factor or market risk premium
▪ s is the coefficient or factor loading for SmB; the risk factor associated with size
▪ h is the coefficient or factor loading for HmL; the risk factor associated with B/M ratio
▪ ε is an error term for the regression Market model
Ri –Rf = α + βi (Rm- Rf ) + ε
Two factor model
Ri – Rf = α + sSmB + hHmL + ε
Table 3: A description of the three models in this paper and the variables
Method
3.1 The explanatory variables
To fit the factors as explanatory variables in the model, Fama and French construct six portfolios based on size and B/M ratio. One sort is made based on size and two sorts are made based on the B/M ratio. The difference in number of sorts is because the B/M ratio seemed to be a more distinctive factor and of more influence than size in Fama and French (1992). In June each year the firms that fall below (above) the median value for size of the NYSE are put in the group for small (big) firms. The other sort is based on NYSE value for B/M ratio and the dividing lines here are the 30th and 70th percentile of the NYSE B/M ratio value. In this way 63 size-B/M ratio portfolios are formed, which is shown in figure 1. Subsequently, the value weighted returns are calculated for each portfolio. I construct six portfolios in a similar way, although there are some differences. In contrast to Fama and French who devise stocks to the portfolios once a year, I do this each month. Thus the sorts (median value) for the market value are determined each month. Nowadays it is possible to acquire short term information and so monthly information on market values is readily available. The B/M ratio is often only established once a year. This yearly availability of data limits me to use yearly observations for the B/M ratio.
Low Neutral High
Small S/L S/N S/H
< Median
Big B/L B/N B/H
> Median
30%low 30%high
Figure 1: Six Size B/M ratio portfolios and the sorts
Another issue is the look-ahead bias and how it is avoided. The look-ahead bias deals with the availability of data from the past how this is accounted for. It is often the case that book data of a firm is only official after a few months in the new year. When using past data one would be ‘cheating’ by acting as if the book data was already known beforehand. If you do not account for this, the research may suffer from a look-ahead bias. To make sure the data is known, we establish the B/M ratio sorts at the start of July of year t for the December value of year t-1. We use this value till the end of June of year t +1. This way the sorts (30th and 70th percentile) for the
3 Please note that when I refer to a portfolio number, I count from left to right. In figure 1 this means that
B/M ratio are established in July of year t and re-established a year later at the end of June year t+1. This is also done in Fama and French for the B/M ratio by determining the sorting values in June.
The SmB factor is formed by taking the difference between simple averages of the returns in the three small portfolios and the three big portfolios. The HmL is formed by the difference in returns between the two high portfolios and the two low portfolios. The division of portfolios can be shown as follows: 3 ) ( ) (SL SN SH BL BN BH SMB= + + − + + , 2 ) ( ) (SH BH SL BL HML= + − +
The division is repeated each month and a new market value sorting point (the median) is established each month. Size is the stock price of ordinary common stock times the amount of common stock. The book value is calculated as the book value of shareholders’ equity. Negative market value and B/M ratio firms are discarded and other types than ordinary stocks are neglected. The market factor or market premium factor is the return on a large market portfolio minus the riskfree rate. This could be a large international index or the return of the portfolio of selected firms in the sample. The chosen market index is the MSCI European index from DataStream, since this index had most correlation (over 93%) with the value-weighted return of all the firms in the sample. A large correlation shows that the chosen index looks very much like the index or portfolio that can be constructed from the firms in the sample. The risk-free rate is the monthly return on the German three month T-bill rate. Germany was chosen because its central bank plays an important role in European exchanges. Many European countries followed the German Mark as its lead currency and therefore the interest rates (like the riskfree rate) of the countries will follow the German rate closely. The three month rate was chosen, following Annaert et al. (2002) and Crombez (2001), because it is truly a risk-free rate over such a short period.
3.2 The dependent variable
Book-to-Market Ratio Quintiles Size
Quintiles Low 2 3 4 High
Small S/L S/2 S/3 S/4 S/H <20% 2 2/L 2/2 2/3 2/4 2/H >20<40% 3 3/L 3/2 3/3 3/4 3/H >40<60% 4 4/L 4/2 4/3 4/4 4/H >60<80% Big B/L B/2 B/3 B/4 B/H >80% <20% >20<40% >40<60% >60<80% >80% percentiles / quintiles
Figure 2: 25 Size B/M ratio portfolios and the sorting points.
The excess returns, as measured by the return over the risk-free rate, for each month are the value weighted returns of each portfolio. In this value weighing of the portfolios there is some size (market value) measure for the returns. This will be discussed in the results later. The dependent portfolio sorts are made at the same time as the independent sorts, so the same things hold about the time the sorts are made.
When sorts are made yearly as in Fama and French (1993) this will add to the possibility that a certain fast-growing company will be in a low portfolio throughout the year, or the other way around. This is why monthly sorts are used in this research along with the fact that information is more readily available.
3.3 The regression and tests
slope of the coefficient is examined. Also the absolute difference of the coefficient to 1 is examined.
One other important and determining test for an asset pricing model is the intercept test. The values for the intercepts provide information about the amount of excess returns that is left unexplained or the abnormal return left over by the regression. In short this method of testing stems from the time-series analysis of Jensen (1968) for mutual funds. From what is known as Jensen’s α, one can see whether a fund has performed better or worse than a benchmark. This benchmark is often the market or a risk-free rate. Jensen used the CAPM to perform a time-series test. The null hypothesis for the intercepts is: H0:αj = 0. When α is significantly indistinguishable from zero, there is no variation in abnormal returns left unexplained by the model. When it is significantly different from zero you can conclude one of two things. The first is that the asset pricing model is incorrect (i.e. there is a pricing error) and apparently there are other explanatory variables that cause variation in returns. The second possibility is that a portfolio has outperformed the benchmark and this is a probably a one time event. In fact, this is also a sign of incorrectness of the asset pricing model, although from a different angle. The alphas are tested for significance using standard t-tests. The t-test for all the coefficients is a two sided t-test with a null hypothesis of a mean value of zero. Fama and French find much smaller, intercepts for the three-factor model. Furthermore the intercepts are indistinguishable from zero.
The t-tests that are performed in this research are performed with a corresponding significance level. Throughout this paper there will be referred to a certain x% level of significance. If a value is found to be significant at this level, it means the following: There is less than x% chance (for example; less than 5% chance) that the value (or difference) that is observed can be found.
Tests Test statistic Critical value / meaning
1. T-test for zero means of intercepts and coefficients
μ / Standard error (μ),
where μ is the mean or coefficient value
● Two sided: critical value (α) 5%; T-statistic value (192 observations ≈ 200 = normality assumption)
2. T-test for similar means of two dependent paired series
mean difference / standard error
● Two sided paired t-test, critical value (α) 5%, T-statistic value
3. T-test for difference in intercpets or slopes
Difference ( α or slope)/ standard error
● Two sided paired t-test, critical value (α) 5%, T-statistic value
4. R² and adjusted R² R² = 1 - [regression sum of squares / total sum of squares] adjusted R² = 1-[T-1 / T-k(1-R²)]
● Measure of how much of the variation in a dependent variable is explained by the explanatory variables. The adjusted R² corrects for the loss of degrees of freedom
5. GRS F-statistic See text ● F-statistic; Reject hypotheses of
jointly zero intercepts if value exceeds 1,57 (df ≈ 165)
When I refer to differences in the values for intercept between different regressions, I will test these differences using a t-test. The difference between two values is then divided by the standard error. The standard error is the squared root of the variances of the pair of intercepts or slope coefficients. The tests that are described above and later on in this paragraph are in table 4.
The tests for the intercepts described above have the disadvantage that they are hard to interpret and compare with one another. The problem is that when the intercepts are tested by themselves the results are inconclusive for mutual comparison. This is why the joint test for intercepts was established by Gibbons, Ross and Shanken (GRS, 1989) to test whether the intercepts of all regressions are jointly different from zero. If this is the case, the asset pricing model is able to explain the variation in stock returns and no variance in stock returns is left unexplained by the variables or risk factors in the model; i.e. the asset pricing model does a good job. The GRS test provides an F-statistic and it accounts for correlation in the estimates of the errors of the alpha’s. The GRS test uses the error terms (residuals) and intercepts from the regressions. It assumes a normal distribution for the residuals. The null hypothesis is that all intercepts of all regressions together are jointly similar to zero at a significance level of 5%. The GRS-statistic for the market (CAPM) model and the factor models are different in some aspects. The test statistics are found as follows; Market model:
α
α
Market) (StDev Market) (Mean 1 N 1 -N -T ' 1 1 2 2 − − Σ × + × With (N, T-N-1) degrees of freedom.
In this statistic T is the number of observations for each factor (months) and N is the number of regressions (25). α is the (Nx1) vector of the regression intercepts. Σ-1 is the inverse covariance matrix for the residuals of the regression. Market is the market risk premium.
The multi-factor statistic is as follows: 1 N L -N -T L 1 L ' 1 ' Ω + Σ × − −
µ
µ
α
α
With (N, T-N-L) degrees of freedom.
for the factors. The number of degrees of freedom is 25 and 165. The accompanying critical F-value is about 1,57 4 at a significance level of 5%. This means that the null hypotheses of jointly zero intercepts will be rejected if the GRS F-statistic is above this value: The asset pricing model is not working well enough.
Fama and French (1993) also perform some robustness tests. These will be explained in short here. First the residuals are investigated. When the residuals show predictability, then the slopes of the variables should vary through the different time periods and this will reduce the validity of the regression slopes. The residuals, belonging to the regressions with the selected portfolios, do not seem to be predictable and therefore the slopes of the regression are considered fairly stable through time. Secondly, it is checked whether the results are merely a result of the existence of January or seasonal effects. This does not seem to be the case. Some January effects are observed. However these effects can be largely attributed to the seasonal effects in the chosen mimicking risk-factors. Third, Fama and French have performed some split-sample tests. This is done primarily to withstand the possible criticism that the size and B/M ratio factors lead to the results because they are used in both the explanatory as well as the explained variables. The explanatory and dependent variables are now split in different samples. The results of the regression on this different sample do not take off a lot from the original sample. Finally, to see whether there are other factors that could produce the same results as the size-B/M ratio portfolios, other factors are taken into consideration. This is done by forming portfolios based on other ratios, such as the price/earnings ratio and the dividend/price ratio. In short, the results seem to be robust for this measure as well, although some evidence is provided against the three factor model by including the earnings/price ratio in portfolio division.
The results from the three regression models in this thesis will also be exposed to a sensitivity analysis. Five robustness tests will be performed. First, the 16 year time period will be split in two periods of 8 years. The time period of 16 years will in general include two 8-year business cycles. The first 8-year period will not have the boom and the bubble for the dot.com industry in it, which could make the results different. Another thing is that in the US, it has been shown that big firms underperformed small firms in the period from 2002 until 2006. A problem could be that the 8 year period under consideration is too short for analysis. However, since sorts and measurements are made monthly there will be sufficient data for the analysis. A second factor of importance could be the countries under consideration. A large part of the sample, or about half,
4 This value is found with the FINV function in MS Excel: FINV(probability, deg_freedom1,
is made out of firms from the UK. We will see if subtracting these firms from the sample will influence the dependent portfolio returns or the explanatory variables. Third, to see if the dead firms make a difference, the listed firms are investigated separately. Remember that the dead firms were added to get a sample of firms that truly existed within the chosen period and to evade the survivorship bias. Fourth, to find out whether extremely large or small firms are of influence, the sorts are made again and the extremes for the market values are set at a minimum of 10 mln €’s (or the 10th percentile) and at a maximum of the 95th percentile in value. The fifth and final sensitivity test will be performed to see whether a size or value effect is due to extraordinary run-ups of (small firm) returns in January. To investigate this, the returns for the 25 portfolios are split in averages for January and February till December. It should be clear that some robustness tests apply to other data or other sorting methods and some apply to other methods. Some changes are made in this research to answer to data snooping issues, or other methodological matters. Other changes are made to make this research specific and original. These changes will be tested for robustness. Some results will appear from changing the portfolios and observing the returns, whilst for other robustness tests regression estimates will have to be compared.
Taking into consideration the work by Fama and French and the corresponding view by others this thesis makes some adjustments to the original Fama and French (1993) methodology. In part this is because of the different sample that will be used and a different period. Also this is done to simplify some aspects of the method by Fama and French. Some of the main differences between this research and research of the same kind by others will be in the data selection and collection and database used. These differences will be explained in the data section below.
Fama French Research This Research Reason
1. Use of US CRSP database Database Out-of-sample test
2. Only listed stock Inclusion of the delisted / dead stocks Overcome survivorship bias 3. Use of Database breakpoints Use of self-made breakpoints Suited for this research 4. Fama and French Sorts Excel sorts and PF distribution Suited for this research 5. Yearly redirection Monthly redirection Faster fit to up-to-date values
Table 5: Important alterations to original Fama and French research method and data.
Data
By the description of the methodology of Fama and French in the previous section a general framework for the research design for this thesis is provided. For a large part the method used by Fama and French will be replicated, although alterations to the methodology and data gathering methods will be made to suit the research to another sample. These alterations or changes will also make this research distinctive from others. In the past a lot of research has been performed on a sample of US firms and not as much on European firms. Examples of European research in this field are Fama and French (1998) and Annaert et al. (2002). This paper will be looking at firms in some large European markets and the data and data selection methods will be fitted accordingly.
3.4 Data Selection and Collection
