Apply, Consider or Omit?

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Apply, Consider or Omit?

An Assessment of the Size Effect in British, French,

German, and Dutch Equity Returns

MICHIEL BROER*

Thesis MSc. BA Corporate Financial Management Rijksuniversiteit Groningen

2012

JEL Codes: G11, G12, G14

Keywords: Size Effect, Capital Asset Pricing Model, Regression Analysis, Anomalies Abstract

This thesis investigates the size effect for listed companies in the United Kingdom, France, Germany, and the Netherlands. To this end, monthly total return data of 2760 firms were analyzed by means of OLS regression of the CAPM model, using the MSCI Europe Total Return Index and the 10 year German Euro Bund as market index and risk-free asset respectively. A size effect is found for the portfolios of the Overall test, the Industry test, and the Market Trend test (especially strong under a market trend of declining returns). After correction for systematic risk, there is a significant difference between the lower return of small firm stocks and the higher returns of large firm stocks in the four countries. The results are robust, however strong January effect is found of which the spread with the rest-of-year returns is negatively correlated with size.

*

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I

Introduction

The value of an asset is important information for many parties in all sectors of the economy. For investors, debt suppliers, and regulation institutions alike this information concerning company equity (as a narrower definition of an asset), is crucial in their respective decision making processes. For investors in pinpointing investment opportunities with a desired risk-return relation, for suppliers of debt in determining whether or not to lend and against a certain rate, and for government agencies the importance is rooted in taxation and intervention reasons. Over the last six decades, the practice of corporate valuation, a form of asset pricing, has become decreasingly arbitrary with a growing body of research serving as a solid theoretical foundation. Many aspects of the models used are increasingly quantifiable for the professionals that use them. There are however, still unexplained factors that need to be clarified to further improve accurate valuation.

To derive the value of a company, there are several methods that can be applied. One of the most broadly used is the discounted cash flow model (DCF) as described by Koller et al. (2005). This model projects future free cash flows to securities holders and discounts these against the appropriate cost of capital. An important element of the cost of capital is the cost of equity. To calculate its magnitude the capital asset pricing model (CAPM) as developed by Sharpe (1964), Lintner (1965), and Black (1972) is widely used. This model will be analyzed in more depth in section II The CAPM model prices market risk, with the assumption that idiosyncratic risk can be diversified away through the formation of portfolios with around 30 stocks. This market risk is the only factor of risk which is assumed to explain the return of the asset under scrutiny. However, this assumption was soon questioned by academics and an increasing number of anomalies of the model were mapped and elaborations on CAPM were constructed, increasing the pressure on the validity of the CAPM model in its purest form.

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counterparts of 15 to 30 percent in the United States.† This is in line with preceding research by Rijken et al. (1999) who found discounts for private companies in the UK ranging from 6 to 16 percent. The study initially found much larger discounts. However, these discounts were significantly reduced after correcting for one important factor: company size.

The size effect, as first discovered by Banz (1981), is one of the most puzzling and thoroughly researched anomalies of the CAPM model to date, and appears to be of significant influence. The size effect is the phenomenon that small listed firms generate a higher, risk-adjusted, return than their larger counterparts. This effect is not accounted for in traditional pricing models and is therefore often separately incorporated in the valuation process by means of a size premium. Therefore the assumption under CAPM model that market risk is the sole measure of risk is challenged.

Due to the frequent absence of thorough and up-to-date research on this effect for non-US regions, this paper will try to identify and quantify the size effect for four European countries: Germany, France, the Netherlands, and the United Kingdom.‡ This is formulated in the research question:

Is there a significant difference between the systematic risk corrected returns of small firm stocks and that of large firm stocks listed in the United Kingdom, France, Germany, and the Netherlands, and what to what environmental characteristics can these differences be attributed ?

A breakdown by industry is made to identify the influence of the different industries on the size effect. Additionally an analysis of the size effect is made to establish the influence of the two major stock market crashes (being the deflating of the dot-com bubble in 2001 and the effect of the financial crisis of 2008/2009 on stock prices). To this end, the size effect under a rising trend is compared to the size effect under generally declining stock prices.

The research methodology of Ibbotson (2008) is applied. Ibbotson (2008) found persistent size premiums for NYSE, AMEX, and NASDAQ listed firms over a period from 1926 to 2007, ranging from -0.33% for large firms to 3.68% for the smallest of firms. The methodology revolves around a model that is in essence a modified version of the CAPM model with a size factor added. The method is used by Ibbotson (2008) and requires the formation of several portfolios of firms ranked by their respective market capitalization. The Betas of each of these portfolios are calculated as well as their monthly returns. Subsequently the risk free rate and the estimated monthly returns are deducted from the arithmetic mean return for each portfolio to arrive at the size premium for that portfolio.

†

Officer (2007) compares acquisition multiples of unlisted firms to those of listed firms with data from the SDC Mergers and Acquisitions database from 1979 – 2003.

‡

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II Literature review

This section will provide an overview of the relevant existing literature on company valuation, the cost of capital, and the size effect. The objective is to clearly outline the prevalent alternatives in valuation methodology, and cost of capital estimation. Furthermore, the aim is to present an insight in the theory and findings concerning the size effect.

First, the different methodologies for the estimation of the value of a company are presented. Once the essential variables of the method of focus, the discounted cash flow method, are clarified, the cost of capital is specifically focused on. The different methodologies of cost of capital estimation are presented to find the modified Capital Asset Pricing model as most suitable technique to use in this study. Subsequently, an assessment of the centre of attention of this paper is presented; the size effect. The section will be concluded by placing its’ content in the light of the remainder of this paper.

II.1 Valuation methodology

Only a limited number of companies worldwide enjoy a listing on a stock exchange. Such a listing offers an indication for the value of a company. However, most companies (especially smaller ones) do not have a listing due to fact that such listing is costly and only useful for companies that have significant trading volumes. Both listed companies and companies without a listing can require valuation with different techniques than stock market valuation alone since it is either absent or a rigid number under influence of unsolicited forces§. For the purpose of arriving at the value of a company, a number of different techniques can be identified. Each method presented below may have its advantages over the other methods in different situations. While some are more thorough than others, their downside is often the labour intensity making them less suitable in situations where speed is of the essence. However, for use in this paper the most thorough and widely used is selected. Ibbotson (2008) identifies three major approaches to business valuation; the Income Approach, the Asset Based Approach, and the Market Based Approach. Additionally, Damodaran (2005b) identifies a fourth category; the Contingent Claim Approach. The Income Approach, as the method of focus, is presented first, followed by the paragraph on the alternative models.

§

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i s i s s s k CF k CF k CF PV ) 1 ( ... ) 1 ( ) 1 ( 2 2 1 1       

II.1.1 Income Approach

The first method identified by Ibbotson (2008) is the income approach and is prevalently used in practice. In a general form as depicted in Equation 1, two types of variables have to be quantified to arrive at the Present Value of the asset (

PV

_s).

Equation 1 – Present Value

First, the expected cash flows (

CF

_i) received from holding an asset have to be estimated for all future periods. These cash flows can be dividends received by equity holders in case of company valuation or net cash flows in case of the valuation of a project investment. Second, the appropriate cost of capital (

k

_s) is determined and should reflect this riskiness of the cash flows under scrutiny.

The discounted cash flow (DCF) and the capitalization of earnings methods are the most prominent exponents of the income approach. The distinction between these two methods concerns the stability of future cash flows. In case future cash flows are projected to be relatively stable, the capitalization of earnings method in the form of the Gordon Growth (or Single-Stage) Model is suitable to use. The cash flow of only one period has to be estimated. This amount then has to be divided by the estimated cost of capital from which the expected annual growth rate in perpetuity is already deducted.

In practice, cash flows are rarely that stable and the idea behind the Gordon Growth Model is used only for the cash flows in the far future while using a more agile method; the DCF method. This methods’ focus lies on estimating several periods of future (free) cash flows explicitly and discounting these against a weighted average of the costs of both debt and equity. This discount rate must reflect the risk that accompanies the expected cash flows.

Due to the frequent absence of efficient debt markets for many companies, the book value of debt is often applied. The more complicated part of the approach is a proper estimation of the expected cost of equity. Since the cost of equity is resurfacing in the denominating weighted average cost of capital, an estimated number that is only slightly off the true number will have major impact on the calculated value of the company.

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cash flow to the shareholders and debt holders while the discount rate used is the Weighted Average Cost of Capital (WACC).

II.1.2 Alternative approaches

In addition to the income approach, Ibbotson (2008) identifies the asset-based approach. This technique assesses all business components individually to ultimately generate a value through netting the calculated values of the company’s assets and liabilities. Although having great accuracy and supplying deep insights in the value structure of a company, this method is often considered costly and too time-consuming.

The market approach is the third technique identified by Ibbotson (2008). This method compares financial data of similar listed companies. In addition transaction information of both unlisted and listed comparable companies can be used to arrive at a value of the company’s equity. However, Damodaran (2006) places several question marks with this approach. Although fast, the weakness of this approach is the availability of comparable companies. Instead of using intrinsic information, the valuator relies on data that might not exactly meet requirements. The data finally used has gone through a process of comparatives identification, scaling market prices, and adjusting the data for the encountered differences.

Over the past three decennia, the real option approach to valuation has gained popularity among scholars. The technique is based on the Nobel Prize winning Black-Scholes option pricing methodology of which the fundaments were first published by Black and Scholes (1973).** The real option approach wields the same approach as the Black-Scholes method does: the construction of a replicating portfolio. In his review on the workings of real options Damodaran (2005a) pictures the approach as a more thorough way of valuing assets. Both Koller et al. (2005) and Damodaran (2005a) find the real option approach to be theoretically superior to many other approaches. However, the drawbacks of the model currently outweigh the advantages. Koller et al. (2005) argue that the unavailability of measurable prices on the basis of which a replicating portfolio can be formed makes the technique often unsuitable.

II.1.3 Summary

Taking the above overview of valuation methods into account, the DCF method will be the method of focus in this paper. The predominant factors for this decision are the emphasis on the use of this model by the valuation industry. Moreover, the explicit use of the cost of capital in the model allows for an

**

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evident link to actual practice and will be elaborated on in the next paragraph. Furthermore, the soundness of the technique, unrestricted by neither time nor effort of the author, makes DCF valuation the method of choice.

II.2 Cost of capital

Now that the Discounted Cash Flow model is selected, a deeper analysis of its workings will be performed. Equation 1 in the previous paragraph shows two essential elements that lead to the models ultimate purpose: the calculation of the present value of the company. The first element is the cost of capital that is used as a discounting factor. A review of the academic literature on this factor will be presented in this paragraph, containing an overview of several calculation approaches. The second element, the estimation of Free Cash Flows, is beyond the scope of this paper and will therefore not be analyzed any further.

II.2.1 Weighted Average Cost of Capital

The factor by which the Free Cash Flow is discounted is the Cost of Capital (k in Equation 1). More specifically this discount factor is the Weighted Average Cost of Capital (henceforth: WACC) which Koller et al. (2005) define as an opportunity cost to investors. These investors choose to invest their capital into the company where they could have chosen to invest it in other companies with a comparable risk profile. The authors emphasize the importance of consistency between the free cash flows and the components comprising the WACC. These components are the suppliers of the different types of capital (e.g. equity, debt, and hybrid securities). Equation 2 depicts the market-based WACC in its simplest form where only debt and equity components are accounted for:

e m d k V E T k V D WACC (1 )

Equation 2 – Weighted Average Cost of Capital

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This simplest form of WACC calculation offers a platform for expansion. For each additional type of capital supplied, a term can be added.

The calculation of the cost of debt is somewhat troubling. Little debt is traded publicly, making it difficult to arrive at a correct market value of debt. Moreover, the target level of debt is in most cases either unattainable or unavailable. For these reasons, in the process of company valuation the book value of debt is often applied. To investigate the size premium in stock returns, the cost of equity is the factor that is focused on in this paper.

II.2.2 Capital Asset Pricing Model

The cost of equity can be defined as the required rate of return on equity. The opportunity cost approach to cost of equity views the suppliers of equity capital as wealth maximizing entities that assess all available investment alternatives. For each of these investment opportunities, the level of accompanying risk is evaluated and plotted against the levels of all the other available opportunities. The level of expected return is assessed for all relevant investment opportunities. These two characteristics together form the axioms of the Capital Asset Pricing Model, the evolution of which has been briefly discussed in the introduction section of this paper. The CAPM (and its derivatives) is a widely used cost of equity estimation technique of which the most basic form as presented by Koller et al. (2005) is depicted in Equation 3.

) ) ( ( ) (R_i R_f _i E R_m R_f E  





Equation 3 – Capital Asset Pricing Model

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outperformance relative to their expected performance based on their inherent risk. This causes academics to examine these deviations from the SML by analyzing the characteristics of these stocks and the companies behind them. The aim is to find additional factors that can be included in the standard CAPM to increase the accuracy of the model. The techniques, returns, analysis, and implications concerning this quest form the basis of the remainder of this paper.

II.2.3 Arbitrage Pricing Theory

A further developed technique that is used to estimate the rate of return of an asset is the Arbitrage Pricing Theory model (henceforth: APT model). The model was developed by Ross and Roll (1980). Ibbotson (2008) first identifies two components used by this method that are corresponding with the two factors of the standard CAPM from the previous paragraph; the risk-free rate and the equity risk premium. The addition this method offers is the inclusion of factors of risk other than the single factor the standard CAPM has to offer. This yields a formula which one can extend virtually limitless for each characteristic of assets that has a potential influence on the returns. These building blocks help to better plot the risk-return relationship of asset. The formula of the build-up method is described below in Equation 4. i n i f m i f i R E R R AR A R R E( ) 



( ( ) ) ₁ ...

Equation 4 – APT Model

The first two components of the build-up method equation are identical to the CAPM equation (3). Additionally a component

A

₁

R

_i is added for the first additional factor of risk. This addition can be repeated until the desired number of factors (n) is implemented in the model. Two of these factors are described and used explicitly by Ibbotson (2008). First, a factor related to the relative magnitude of the market value of the firm is used. Second, an industry factor that is determined by the industry in which the company is employing its activities is added. To illustrate the flexibility of the build-up method an array of additional factors have currently been identified; control of the firm, key person presence, and minority shareholder, being only a few. Many of these factors are hard to measure or very heterogeneous, therefore Ibbotson (2008) suggests including the impact of these factors in the estimation of cash flows instead.

II.2.4 Fama and French

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of the tests they performed was that they could not find any proof of average stock returns being positively related to market Beta (which is the main result of the standard CAPM) of NYSE, AMEX, and NASDAQ listed stocks for the period from 1963 to 1990. Additionally for the period from 1941 to 1990 they find the relationship to be weak. The second conclusion the authors draw from their research results is that a size factor and a book-to-market equity factor do help explain the cross-sectional variation in average stock returns for the period from 1963 to 1990.

In essence, the authors took the basic CAPM and added four factors to the market factor as measured by Beta to help explain the variance in stock returns. They found two factors to be of significant influence on average returns. The first additional factor is firm size, measured in terms of market capitalisation of a firm. This factor was included due to the underlying notion of the authors that smaller firms have a higher risk than larger firms. The second additional factor is the book-to-market ratio of a firm. This factor was included by the authors to capture the additional risk that investors encounter when investing in a firm that is in a financially more distressed situation. These two factors are not risks on themselves. They rather serve as proxies for actual risks. The other factors (leverage and Earnings/Price ratio) are absorbed by the inclusion of the factors size, and book-to-market ratio. Fama and French (1993) continued on the subject and drew a three factor model that incorporates the findings of their 1992 paper. Ibbotson (2008) emphasize the importance of the Fama and French three-factor model. In their research on the size effect that primarily focuses on a modified CAPM approach, the authors depict the results of both methodologies for their data graphically and come up with two interesting findings. They qualify the relatively high costs of equity found using the Fama and French three-factor model, compared to the modified CAPM model, as “intuitively appealing” since their dataset of US listed companies from the period 1926 to 2007 has a very high number of small firms and their accompanying size effect. However, the authors expect the Fama and French three-factor model to overcorrect either one or both of the two additional factors (being size, and financial distress). This paper follows the methodology of Ibbotson (2008) and the focus is solely on the size effect.

II.3 The size effect

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the expected return to be incorporated (in relation to the underlying characteristic) in the new, modified CAPM. The inclusion of such a factor helps Beta (formerly the sole measure of systematic risk) to explain the expected returns of a stock.

Schwert (2002) states that the cause of an anomaly can be either market inefficiency or inadequacy in the underlying asset-pricing model (here: CAPM). The author finds that many of the main anomalies studied in the past decades do not show a continuous and consistent presence: “After they are documented and analyzed in the academic literature, anomalies often seem to disappear, reverse, or attenuate”. After performing a closer examination of several anomalies, Schwert (2002) concludes that the possibility exists that some are ostensible while others might be arbitraged away since “the activities of practitioners who implement strategies to take advantage of anomalous behaviour can cause the anomalies to disappear (as research findings cause the market to become more efficient)”. In addition to the size and value anomalies, presented earlier in this chapter, several other anomalies can be found in the literature on the subject. Research on anomalies is broad, often inconsistent and dispersed. Davis (2001) presents an overview of the most pronounced of these anomalies.

First, the Earnings/Price effect is identified by Basu as early as 1977, and backed by several other studies since. This anomaly is the observation that high (low) Earnings/Price stocks have higher (lower) returns. Second, the Long-Term Return Reversals effect is an anomaly first identified by DeBondt and Thaler (1985). The authors define and identify both stocks that have enjoyed low returns in the past three to five years, and stocks that have generated high returns over that same period. After relating these so called losers and winners to their respective stock returns over the subsequent three to five years, the authors find that the losers outperform the winners. This effect is not (entirely) captured by Beta in the standard CAPM (as is the case with all identified anomalies by definition). Third, Rosenberg et al. (1985) prove the existence of the Book-to-Market anomaly. They found that firms with a high ratio of book value of equity to market value of common equity outperform the stock returns of companies with a low ratio. Fourth, the Leverage anomaly concerns the balance between the debt and equity of a company. Bhandari (1988) finds that for his sample highly leveraged companies tend to generate higher returns than companies with lower leverages. Fifth, the Momentum anomaly as identified by Jegadeesh (1990) is claimed to be of influence on stock returns. This anomaly implies that a good (poor) performance in the months prior to a certain point in time is likely to continue in the month thereafter. This effect is stronger for poor performing firms than it is for firms with a good performance. The Momentum effect seems to contradict the Long-term Return Reversals anomaly. However, the former concerns short-run returns while the latter in measured over a longer period of time.

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CAPM model as crafted by Sharpe (1964), Lintner (1965), and Black (1972) and found that a coefficient for the size of a company, in terms of market capitalization, to be an additional explanatory risk factor when explaining stock returns. Thereafter, research on this so-called size effect really took shape.

II.3.1 Early research

Banz (1981) altered the one-risk-factor model through the insertion of a coefficient on the market value of a firm as proxy for size in the standard CAPM model.

] / ) [( ) ) ( ( ) (R_i R_f _i E R_m R_f _i _m _m E  



 









Equation 5 – Banz Asset Pricing Model

Equation 5 used by Banz (1981) is clearly based on the standard CAPM equation. However, the standard CAPM is expanded with the size dependent measure. The market value of the equity of a security (



_i) is related to the average market value of a security in the portfolio (



_m). This fraction serves as a proxy for size and is multiplied in the model by a constant (



) that represents the contribution of the relative size to the expected return of a security. Through the application of this model he uncovered a size effect for NYSE listed firms in the period from 1926 to 1975.†† In other words, while still adjusting for market risk, he found that the inclusion of the size proxy uncovered higher average returns for small companies compared to larger firms. The results further indicated that this size effect was not of a linear form implying that with decreasing market values, increasingly higher risk-adjusted returns are present. These results led the author to classify the standard CAPM as misspecified.

The results of Banz (1981) initiated a wide, and still growing, body of literature on the size effect. Different authors conducted their own research based on either the dataset used by Banz (1981) or a different dataset.

II.3.2 Evidence of the size effect

The different methodologies presented above are applied in a large number of papers. Some of these publications have found significant size premiums for an array of markets and geographic regions. Below a summary of the results of several studies on the subject is presented to give an indication of the presence of the size effect. Therefore this table is not exhaustive and shows important studies for

††

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the US, a broad European study, as well as a study for each of the countries under scrutiny in this paper.

study Area period monthly size premium

Banz (1981) United States 1936 – 1975 0.40%

Fama and French (1992) United States 1962 – 1989 0.63%

Ibbotson (2008) United States 1926 – 2007 0.39%

Annaert et al. (2002) Europe 1974 – 2000 1.45%

Doeswijk (1997) Netherlands 1973 – 1995 0.13%

Louvet and Taramasco (1991) France 1977 – 1988 0.90%

Stehle (1997) Germany 1954 – 1990 0.49%

Strong and Xu (1995) United Kingdom 1973 – 1992 0.61%

Table 1 - Overview of recorded size effects in developed markets

The foregoing table shows that the size effect is not a mere US-phenomenon. Anneart et al. (2002) show for their dataset comprising 15 European countries, a monthly size premium of 1.45% (or 19% annually). Together with the results for France and the UK, the magnitude of the size effect seems to be even larger in Europe, compared to the United States.

II.3.3 Analysis of the size effect

On the one hand, the studies on the size effect provide answers to the questions Banz (1981) concluded his research with. On the other hand, some question marks were put with the results, conclusions, and methodology of his research. This resulted in the current status of the literature we have now-a-days. There is no consensus on some of the most profound questions concerning the size effect.

Immediately after the publication of the paper by Banz (1981), a large number of scholars commenced specific research on the size effect. Other than just establishing its existence, these academics’ ultimate aim was to either gain insight in the workings of the size effect, or to refute the theory on a number of grounds. This resulted in a wide and still growing body of literature. Van Dijk (2007) essentially dissected the academic literature on the subject into two pillars. The first contains the group of scholars that support and explain the size effect. The second pillar consists of academics who question the size effect on a number of grounds. On each important explaining argument within these two pillars a discussion will be presented in the following paragraphs.

Systematic risk

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size effect points at this misspecification of the model. This implies that Beta, being the sole measure of systematic risk in the standard CAPM, should be complemented with one or more factors of risk. This risk, like market risk, is systematic in the sense that it cannot be eliminated trough diversification of investments. Banz (1981) however, does not include a further analysis of the effect in his publication and restricts himself to further research suggestions.

In the subsequent years several authors jumped at his suggestion of uncovering fundamental drivers of the size anomaly. Chan et al. (1985) sought after these drivers on a macroeconomic level. Their research was partly based on an earlier publication by one of the authors; Chen (1983). In addition to the findings of Banz (1981), this study builds on the APT model. The theoretical fundaments of the model are the additional factors (next to the market risk factor) that are each having their respective impact on the cost of capital. Reinganum (1981) and Chen (1983) implement five different macroeconomic factors in their APT model. Additionally, they investigate the effect of firm size in their research.‡‡ Only Reinganum (1981) finds firm size to be of significant influence on stock return. Chan et al. (1985) find a size premium for small companies of around 12 percent per year. To test their basic principle of stock returns reacting to changes in the economic environment, they apply the APT model with six factors (an equally weighted market factor is added). The factor concerning a changing risk premium (return difference between long-term government bonds and ‘bad’ corporate bonds) is included. The authors find a drop of ten percentage points in the size premium for the bottom five percent of the NYSE firms compared to the top five percent. The factor that captures the changing risk premium causes the largest part of this reduction. This supports the view that the size premium for small firms is caused by additional (macroeconomic) risk.

Market liquidity

A second category of academics support the view that the cause of the size effect is market liquidity. Evidence for this position can be found in the results of the study by Dimson and March (1999). The authors examine the long-term performance of small companies in the United Kingdom compared to that of large firms. Interestingly, they advocate a more careful use of both the expressions size effect and size premium arguing that a size premium is a possible result of the size effect since the authors do not find a consistent size premium, observing a reversal of the small firm premium at some point. Therefore, logically, the observance of a size effect can result in a small firm discount as well. The authors find a size premium of 6% for smaller companies from 1955 to the launch of the Hoare Govett Smaller Companies Index (henceforth: HGSC Index) in 1987 of UK listed stocks. After this point in time up to and including the end of the ´90s, the authors found a reversal of the size effect and documented a size discount of the same magnitude. Dimson and March (1999) argue that prior to the launch of the HGSC Index there was less trading in small firm stocks than after the launch. Note that

‡‡

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the launch of the Index came in a period when there was much media attention on the newly found size effect, resulting in numerous investment vehicles that spawned. This increased market liquidity, while simultaneously realizing a self-fulfilling size-premium for investors. In the period thereafter, this size-premium disappeared while maintaining higher market liquidity. The authors find a similar effect for the United States.

In the light of the size effect, Ibbotson (2008) find that the size premiums small companies tend to earn are not captured fully by their higher Betas that are logically incurred due to higher levels of risk, compared to their larger counterparts. This is the general case of the size effect. The authors, however, propose a different method of Beta calculation since they expect the traditional methods of Beta calculation to be not sufficiently capable of reducing the magnitude of the size effect by the part of the systematic risk a stock incurs (which is Beta). To illustrate this, Table 1 is taken from Ibbotson (2008).

Company size group (market value) Beta January 2003 – December 2007 Beta 1926-2007

largest companies 0.89 0.90 2 0.97 1.02 3 1.17 1.08 4 1.20 1.11 5 1.23 1.13 6 1.33 1.16 7 1.37 1.21 8 1.53 1.27 9 1.61 1.32 smallest companies 1.42 1.40

Table 2 - OLS Betas for the NYSE Size Portfolio

The table above, shows data to illustrate one of their observations concerning the characteristics of small and large companies. As can be seen, Betas of small US listed companies over a 60-month period compared to the 1926 to 2007 period are much less stable than those of larger US listed companies when comparing those Betas for the same periods of time.

In addition to the 60-month period from Table 2 , Ibbotson (2008) shows that 60-month rolling OLS Betas for the whole period 1926 to 2007 decreases in stability when company size is decreased. To account for this, several alternative Beta estimation techniques will be discussed in section III

Behavioural

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these firms generally are firms that have not been performing well in the past. Therefore part of the size effect may be due to overreaction of stock prices to poor prior performance.

Second, information accessibility is a possible driving force behind the size effect. Hou and Moskowitz (2005) examined the delay in time with which the stock price of a company tends to react to information in order to characterize the level of market frictions. One of their findings is that this delay partly explains the size effect. In other words, smaller companies tend to be more subject to information delay than their larger counterparts. Therefore it takes more time for this information to be absorbed into the stock price.

Questionable

The second pillar that can be identified in the paper of Van Dijk (2007) comprises of those studies that question whether or not size is a factor of risk on itself rather than an expression of some other factor or phenomenon, or a mere statistical observance.

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However, there is no consensus on a single clear explanation of seasonality, and more specifically of the January Effect. A second possible rationalization is ‘window dressing’ which Ibbotson (2008) defines as “(…) the process of dumping money-losing stocks just before year-end so that such stocks are not included in the portfolio managers’ annual reports.” To continue on the U.K. stock market, in their study on seasonal fluctuations in the equity market in the U.K. in the period from 1955 to 1990 Clare et al. (1995) claim that window dressing (or portfolio rebalancing) is, in addition to the argument of tax-loss selling, a possible explanation. The working is the same as for the tax-loss selling argument. However, the rationale is different since the sale-and-buy-back is not prompted by fiscal reasons rather than performance presentation.

Berk (1995) suggests that size might not have to be seen as an anomaly altogether. In his theoretical research on the cause of the size and risk in relation with return, the author argues that the relation between these three variables should always be observed. He supports this view by means of a theoretical example:

“Consider a one-period economy in which all investors trade off risk and return. Assume that all firms in this economy are exactly the same size; that is, assume that the expected value of every firm's end-of-period cash flow is the same. Since the riskiness of each firm's cash flow is different [i.e., the correlation of the cash flows with the underlying risk factor(s) will vary across firms], the market value of each firm must also differ. Given that all firms have the same expected cash flow, riskier firms will have lower market values and so, by definition, will have higher expected returns.”

Berk (1995) concludes that, given this thought experiment, market value as a proxy for size will predict returns. The author combines two observations. First, larger firms in terms of operating characteristics (e.g. earnings) generally have higher market values. Second, market values of firms show a negative correlation with risk. Berk (1995) therefore concludes that without a positive correlation between the size of a company measured on the basis of operating characteristics, and its risk, low market value generally means relatively higher risk. In the eyes of the author, this observed relationship disqualifies the use of the term anomaly. Since market value shows an inverse relationship with unmeasured risk, market value will serve as a proxy for any (not just one specific) factor in different asset pricing models. Therefore the inclusion of market value in asset pricing models can be useful for the assessment of the level of unexplained risk that is left. However, Berk (1995) emphasizes that a relationship between size and risk can not be dismissed completely.

Methodological objections

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incorrect results because of the use of this sorting technique. Much of the published articles on the size effect have been based on the statistical relationship between size and asset prices without the basis of a demonstrated economic theory. The authors emphasize that this mere empirically motivated technique of size-based portfolio formation can induce type I errors.§§

Shumway (1997) argues that the widely used CRSP database for US data fails to include the returns of numerous companies upon delisting. Since delisting is often preceded by negative returns, combined with the fact that delisting is concentrated in the group of firms with small firm sizes, the resulting overly positive returns in this group might explain (part of) the size effect. Correspondingly, Jorion and Goetzmann (1999) take a similar stand in their study on international equities, quantifying this (alternatively labelled) survivorship bias on 25 to 70 basis points annually. Ibbotson (2008) points out that the alleged survivorship bias is concentrated in the category of smallest companies. Since the size effect is also present in several larger market capitalisation categories, the survivorship bias would only marginally account for the size effect.***

Finally, two more insights should be considered when assessing the size effect. First, Knez and Ready (1997) point at the role that statistical outliers possibly play. In their study they find that when the 1% most extreme returns are consistently excluded from the sample, both the size effect, and the value effect disappear. This conclusion should however be treated with caution since that 1% of stock returns do form a normal part of the dataset. The removal of these numbers, without a thorough rationale might also remove the correct reward for an undiscovered source of risk. Second, the observance of the size effect may be coincidental.

Secondly, a general issue might concern data snooping. Lo and MacKinlay (1990) suggest that the focus of scholars on surprising results after such a result is first documented leads to a premature acceptation of the anomaly. Of all data available only the segment used by the scholar who first documented the anomaly is restudied time and time again, while examining other data segments would have led to the dismissal of the anomaly. This might partly hold for some studies. However, the size effect is currently such a widely and international investigated phenomenon that this argument does not hold anymore.

§§

A type I error, or error of the first kind, occurs when one rejects a null-hypothesis when in reality this hypothesis is true. In the light of the size effect this means that an effect of this kind is observed when in reality there is none.

***

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II.4 Hypotheses

The literature review that is presented above provides a clear overview of the evidence, explanations, and critiques concerning the size effect. The following null-hypothesis and alternative-hypothesis for firms in the sample countries, can now be drawn:

Ho : The returns of firms with a small market capitalization do not differ significantly from firms with a large market capitalization after the correction for systematic risk.

H1 : The returns of firms with a small market capitalization differ significantly from firms with a large market capitalization after the correction for systematic risk.

These hypotheses are tested in order to answer the research question. The selected countries are mature, developed economies. The United Kingdom, France, and Germany are the dominant economies of Europe. The Netherlands (as the home country of the author) is a smaller and less dominant market, but shares those characteristics with the former three countries and is therefore a useful addition to the dataset. Much of the research on the size effect has focussed on the US market. This research offers an insight in the presence and magnitude of the size effect in bulk of European economic activity. It provides further deepening on the subject by investigating the existence and magnitude of the size effect in different market trends and in the ten industries that the economy consists of. A separate test for the UK-market and the non-UK firms in the dataset is executed since the characteristics of the UK market are somewhat different due to a higher focus on equity in the UK (e.g. the early founding of the HGSC Index). Additionally, France, Germany, and the Netherlands for more of an economic union due to a single currency and intense trading.

Based on the literature on the size effect, the expectation is that firms with relatively small market capitalizations do have significantly different returns from firms with large market capitalizations. Beforehand, the sign of the size effect is unclear since positive size effects are recorded as well as reversal of the size effect (e.g. by Dimson and March (1999)).

II.5 Summary

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Currently, in practice the size effect is widely applied. Dimson and March (1999) best summarize this need for the application of the size effect and thus for its quantification in the following quote: “The size effect thus continues to be a crucial consideration in area’s such as asset allocation, benchmarking, performance measurement and attribution, and the design of event studies (…). Investors and researchers who fail to take account of the size effect thus still run the risk of reaching seriously flawed conclusions. Even Murphy’s Law is unlikely to afflict the size effect, as opposed to the size premium”.

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III Data and methodology

In this chapter, the requirements for the data that will be used are presented. Additionally, the methodological framework will be explained. This methodology is based on the methodology applied by Ibbotson (2008) in their research on the size effect, which is used to address and quantify the size premium for US listed stocks. They have been publishing an annual research on several topics concerning stocks and bonds for over twenty-five years.††† The methodology paragraph is followed by the descriptive statistics of the dataset that will be under scrutiny in this paper.

III.1 Data characteristics

The data that will be taken into the dataset is selected on the basis of several criteria that are all presented in their respective subparagraphs. The database that is used is Datastream which is powered by Thomson Reuters and provides financial statistical data. In order to test the hypotheses presented earlier in this paper, the methodology that will be used follows that of Ibbotson (2008) to a certain extend. However, due to data restrictions, focus, and restricted means this study deviates on certain points from the afore mentioned publication. The description of the applied methodology can be found in the Methodology section of this chapter. The model used to test for the presence of a size effect is based on the standard CAPM model. This modified CAPM is used to arrive at ten different size premiums, each for a different category of market capitalisation. This model is depicted in Equation 6 – Modified CAPM i f m i f i R E R R SP R E( ) 



( ( ) )

Equation 6 – Modified CAPM

In the above equation,

SP

_i represents the size premium factor for a firm based on its market capitalization. This size premium element in the Modified CAPM Equation, is the factor to be determined in this research. To this end, ten portfolios are constructed as will be laid out in the methodology paragraph below. However, first the characteristics of the risk-free asset, the chosen benchmark, and the securities will be discussed.

†††

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Risk-free asset

The risk-free rate ideally is the rate of return of an alternative investment in a risk-free asset. Koller et al. (2005) regard the risk-free asset in this form as practically theoretical since the only way to generate such an asset is by means of constructing a portfolio that has a Beta of zero (no covariance with the market). Such construction is deemed complex. Therefore the authors suggest using long-term government bonds. These bonds should only be issued by government of countries that have virtually zero chance of defaulting and should be local in order to be a true risk-free alternative. For European stocks both Ibbotson (2008) and Koller et al. (2005) suggest using German Eurobonds since these bonds are relatively liquid and have lower credit risk. Government bonds of both the US and Western European countries have very low Betas making them a suited alternative to the zero-Beta constructed portfolios.

In this paper, the 10-year German Eurobond will be used as risk-free alternative. The return on this bond that is used is solely the income return. Ibbotson (2008) claims that of the three return components that make up the total return on a government bond (income return, capital return, and reinvestment return) only income return is truly risk-free since the other two components react to changes in the economic environment. Income return only depends on default risk which is deemed to be absent.

Securities

The majority of the data in the dataset concerns the securities. These securities are all listed in one of the four selected countries being the United Kingdom, Germany, France, and the Netherlands. These securities must meet several requirements to be taken into the dataset. First, only ordinary shares qualify for inclusion so that for example preferred stock, and certificates are omitted. Second, the security has to be a major and primary listing to prevent double-counting of cross-listed shares. Third, data on total returns, and market value of a security has to be available for a minimal period of 30 months. Ibbotson (2008) applies a 60 months minimum, yet they note that this is a rather arbitrary decision. The choice for the use of 30 monthly data points means that the data is still statistically significant, while maintaining a higher number of firms in the sample. This increases the quality of the analysis. Fourth, firms with market values below €1 million are omitted to forestall market liquidity problems that can influence returns.

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Industries

Different industries will be examined to quantify possible size effect differences. To that end, all companies that are taken into the dataset will be assigned their industry code as defined by the Thomson Reuters Business Classification system. This way all companies can be assigned to one of ten possible industries (Basic Materials, Cyclical Consumer Goods & Services, Energy, Financials, Healthcare, Industrials, Non-Cyclical Consumer Goods & Services, Technology, Telecommunications Services, and Utilities). This distinction is made in order to test for industrial differences concerning the size effect as well as to quantify this industry related size effect.

Time period

Koller et al. (2005) make a clear division between the use of data from a long period and a short period of time. Data from a longer period of time should be collected in case the market risk premium stays more or less equal over time. This reduces estimation error that may be caused by a low number of observations. In case the market risk premium varies significantly over time and the estimation error is small, the authors suggest the application of a shorter time span. The authors therefore propose the examination of the existence of trends versus the error level of short term estimations. For the US stock market, they find no significant trend, as well as significant high short term error levels. This suggests the use of data from the longest period possible.

For the four selected countries in this paper, the period of time covered by the dataset is restricted by the country for which data from the shortest period of time is available. This is given in by the wish to create a dataset that continuously comprises all four selected countries. Total returns on securities are only available from 1988 onwards, due to the absence of detailed dividend data in Datastream for dates before that point in time.

To minimize the influence of the state of the economy, the dataset is further restricted by the Juglar-cycle. Small and large companies may react differently to changes in the macro-economic environment. From all economic cycles, the Kondratieff-cycle has the longest span of time. This cycle is named after its discoverer, Nikolai Kondratieff, and further developed by Schumpeter (1939). Each Kondratieff-cycle has a duration of approximately 50 years and is made up of four stages (prosperity, recession, depression, and recovery). In turn, the Kondratieff-cycle covers five Juglar-cycles. Van der Meer et al. (2008) describe the Juglar-cycle as a business-cycle related to the investment behaviour of companies and typically have a duration of seven to eleven years.

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half of 2009.‡‡‡ The graph further shows that the two previous Juglar-troughs occurred ultimo 2001, and ultimo 1993. Appendix C shows that the Dutch economy closely follows the US economy which is the case for all developed European economies. Therefore the Juglar-cycle data for the Dutch economy is applied to establish the period for the data for all four countries under scrutiny. This leads to a selected period from January 1st 1991 to October 31st 2010.

Benchmark

The stock market index against which all stock returns are benchmarked should be broad, in order to reflect market behaviour properly. The index that best meets this requirement is the MSCI Europe index.§§§ MSCI Barra defines the index as: “a free float-adjusted market capitalization weighted index that is designed to measure the equity market performance of the developed markets in Europe”. The MSCI Europe index comprises over 600 stocks listed in 16 European countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom). The four selected countries dominate the index. In order to properly account for dividends and distributions, the index data will be extracted based on total returns. Failing to do so would measure performance less accurately. The index covers approximately 85% of the market capitalization of listed stocks in four countries. It should be noted that this implies a slight bias towards the larger firms. In the results section of this paper, the correlation of the MSCI Europe index with the data of stock returns will indicate the suitability of the index for use as a benchmark. The data concerning this index will be based on total return values which simulate dividend reinvestment, as is the case with the security returns in the dataset.

Overview

With the definition of the risk-free asset and appropriate benchmark, the demarcation of both the time period and the geographical area, and the lay-out of the basic requirements for the securities a summarizing overview is presented in Appendix E.

‡‡‡

The Dutch governmental statistical institution CBS (Centraal Bureau voor de Statistiek) publishes the lowest recorded percentages of Dutch industrial production on their website for the first and second quarter of 2009 (-13.0%, and -12.9% respectively).

§§§

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III.2 Methodology

The methodology applied in this paper follows that of Ibbotson (2008) to a certain extend. First, the size effect will be examined for the entire dataset by means of portfolio creation and OLS regression techniques. Second, to gain further insight into the presence of the size premium, an industry based analysis follows. The dataset, comprising companies of all four countries, is divided into ten categories representing the ten industries mentioned earlier. For each of these categories a small, and a large portfolio are constructed, based on the market capitalization of the securities. The aim here is to quantify industry specific size premiums. Third, the dataset is split into two separate datasets; one with data of periods of rising stock prices, the other with data from periods of declining share prices. This way, the effect of the market trend in stock prices on the presence and magnitude of the size effect is investigated.

Additionally, three robustness checks are executed. The effect of country selection is analyzed by separating the UK firms from the firms from the other three countries. The period selection is investigated by testing two Juglar periods separately. Finally the January-effect is tested for.

Portfolio creation

Based on the market capitalizations of the firms in the dataset, ten equally populated portfolios are constructed each month. This differs from the Ibbotson (2008) methodology in two ways.

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The monthly portfolio arithmetic log-returns are calculated on a value weighted basis. To this end, the natural logarithmic returns of each of the securities in the portfolio are represented in the portfolio average based on the fraction of a securities market value in the portfolio’s total market value. This way a dollar-to-dollar representation is guaranteed.

Finally, the monthly creation of portfolios with a significant amount of firms should reduce the impact of idiosyncratic risk of each firm. In their study on 3290 securities listed on the New York and American Stock Exchange Elton and Gruber (1977), found that a portfolio reaches well-diversification status at the incorporation of 20 securities.**** This number will be applied in this paper as a minimum per portfolio in order to qualify for further analysis.

Beta calculation

When calculating expected returns with the standard CAPM, Beta represents the coefficient with which the market premium (market return minus the return on the risk-free asset over the same period) is multiplied to arrive at the expected excess return of a security. In essence it represents the sensitivity of the returns of a share to the market as a whole. Beta only represents unavoidable or systematic risk. This is the risk that cannot be cancelled out by means of diversification with investments in others assets in the market, which can be done to annul unsystematic risk. Beta is calculated by means of OLS regression in Eviews 6.0.

Overall size effect test

With all the relevant variables discussed and the portfolio formation, and Beta calculation laid out, the tests to uncover a possible size effect will be presented. The excess returns per portfolio over the risk free rate are calculated on a month-by-month basis, as well as the monthly excess returns of the market over the risk free return. In conjunction with the calculated portfolio Beta’s, these returns are tested using OLS in the statistical analysis software Eviews 6.0.

Additionally, as discussed in the literature review section of this paper, seasonality as found by Keim (1983) and more recently by Ibbotson (2008) might be present. To uncover possible seasonality in the size effect, the size effect of each calendar month are examined independently.

Industry size effect test

Moreover, industry specific tests are performed to gain insight in the contribution to a possible size effect of different industries. To realize this, the same methodology is used for the initial test. However, on the part of the formation of portfolios, the set up is slightly adjusted. In the initial test, ten portfolios are constructed. For an industry specific analysis, the adoption of the original

****

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methodology would lead to one hundred different portfolios to be tested since each of the ten industries would have a ten size-portfolio subdivision. The dataset is not large enough to execute this way of portfolio formation. This can for example be seen in the Industrials sector that only has 236 securities for the entire period. Therefore, in each industry two portfolios are constructed; one with firms with a small market capitalization and one with large market capitalization firms. The differences between these two portfolios for every industry should uncover possible industry specific size effects.

Market Trend size effect test

Furthermore, the both positive and negative trends in terms of investment returns may influence the spread and sign of the size effect. Bergmann et al. (2009) identify four phases related to the two directions of the swings based on the MSCI World Index, the NASDAQ Composite, and the LPX50 Index. The first phase from the early nineties up to and including February 2000 the authors typify as a period with positive returns prior to the dot-com bubble. Consequently phase two is labelled “Burst of the dot-com bubble” and spans the period from March 2000 to March 2003 and is characterised by negative stock returns. The general sign of the returns switches again at the start of phase three that runs from April 2004 to June 2007 and is branded “Buyout boom” due to the increased number of buyouts on which the authors partly focus in their paper. This third phase is abruptly halted in July 2007 when the recent global financial crisis claims its first victims. This preludes the sub sequential fourth phase called “Credit crunch – financial crisis”.

The phases as drafted by Bergmann et al. (2009) largely correspond with the dataset under scrutiny in this paper. As can be seen in Appendix D, the time spanning the data consists of two major periods of a rise in stock prices (ultimo 1990 – September 2000, and January 2003 – May 2007), and two periods of declining prices (September 2000 – January 2003, and May 2007 – February 2009). To examine the behaviour through time of the size effect, the dataset is subdivided into two segments, each comprising either the two periods of rising or declining stock prices. The methodology that is originally applied for examination of the entire dataset is employed here as well.

Robustness checks

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than France, Germany, and the Netherlands are. These differences might influence results, therefore an analysis without the UK is called for. Finally, a robustness check for the January Effect is performed. Keim (1983) found that for NYSE and AMEX listed stock over the period 1963 – 1979, 50% of the size effect can be attributed to the abnormal returns in January.

Analysis Summary Test/ Check

Overall complete unsegmented dataset test

Industry per industry size effect testing test

Market trend size effect under increasing vs declining stock prices test

Split sample integral testing of two separate Juglar business cycles robustness

Ex-UK test comprising French, German, and Dutch companies robustness

January effect testing of the presence of a January effect in the size effect robustness

Table 3 – Summary Tests and Robustness Checks

In all, six tests and robustness checks will be performed. Above, Table 3 presents a concise outline of these tests and checks.

III.3 Descriptive statistics

In this paragraph an overview of characteristics of the relevant data, rendered on the basis of the previously described quantitative limitations, and qualitative requirements is presented. First, the general characteristics of this dataset are drawn out followed by the presentation of the specifics of the formed portfolios.

Dataset

In order for this thesis to remain concise and readable, only the main characteristics of the total dataset are presented as well as those of the division by industry. The descriptive statistics concerning segmentation by Juglar-period, market trend, and UK/non-UK are presented in Appendix F additionally. All numbers are averages of monthly data unless stated otherwise.

market value (€ * 1M)

country # firms frequency (%) average median maximum minimum standard error

United Kingdom 1324 48.0% 797.73 45.88 82529.50 1.06 4413.06

France 657 23.8% 1443.47 81.12 86792.09 1.20 6031.88

Germany 645 23.4% 1075.03 89.29 64060.85 1.24 4831.20

Netherlands 135 4.9% 2585.11 240.29 80451.97 2.96 8879.29

Total 2760 100.0% 1090.70 62.48 86792.09 1.06 5262.06

Table 4 – Market value per country

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average contribute little under one quarter of the observations, whereas about five percent of the dataset consists of Dutch firms. The number of firms seems to be negatively correlated with both the average and the median market value of a country. This implies an even larger share for UK-listed companies in the smaller market value portfolio’s; a claim that is supported by the country’s lower average minimum value.

monthly log return

country # firms frequency (%) average median maximum minimum standard error

United Kingdom 1324 48.0% -0.18% -0.16% 102.70% -119.90% 15.00%

France 657 23.8% 0.24% 0.11% 101.36% -93.13% 13.75%

Germany 645 23.4% -0.45% -0.48% 91.63% -92.91% 13.92%

Netherlands 135 4.9% 0.40% 0.35% 37.78% -38.51% 9.91%

Total 2760 100.0% -0.11% -0.15% 102.70% -119,90% 14.54%

Table 5 – Monthly log return per country

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# firms

TRBC UK FR DE NL Total

50 Energy 47 11 11 4 72

51 Basic Materials 128 51 67 17 262

52 Industrials 304 117 121 36 577

53 Cyclical Consumer Goods & Services 319 142 108 19 587

54 Non-Cyclical Consumer Goods & Services 90 83 63 17 254

55 Financials 201 124 130 20 476 56 Healthcare 69 27 32 3 131 57 Technology 129 87 84 17 317 58 Telecommunications Services 15 5 7 2 28 59 Utilities 23 11 22 0 55 Total 1324 657 645 135 2760 frequency (%) TRBC code UK FR DE NL Total 50 Energy 65.3% 14.7% 15.5% 4.9% 2.6% 51 Basic Materials 48.7% 19.4% 25.5% 6.3% 9.5% 52 Industrials 52.6% 20.3% 20.9% 6.3% 20.9%

53 Cyclical Consumer Goods & Services 54.3% 24.1% 18.4% 3.3% 21.3%

54 Non-Cyclical Consumer Goods & Services 35.5% 32.8% 25.0% 6.9% 9.2%

55 Financials 42.3% 26.0% 27.3% 4.3% 17.2% 56 Healthcare 52.9% 20.6% 24.6% 2.2% 4.8% 57 Technology 40.6% 27.4% 26.6% 5.4% 11.5% 58 Telecommunications Services 52.0% 17.9% 23.4% 5.5% 1.0% 59 Utilities 43.5% 20.7% 41.5% 0.0% 2.0% Total 48.0% 23.8% 23.4% 4.9% 100.0%

Table 6 – Frequency per industry

The distribution of firms among industries per country is shown in Table 6. In total, most industries comprise sufficient firms to subdivide into the size portfolios needed for testing. Only 58 Telecommunications Services and 59 Utilities do not contain the minimum average number of firms required for adequate research and will be omitted in the results section of this paper.

Apply, Consider or Omit?