Outperformance through dividend strategies

Table of content

List of abbreviations

List of figures

List of tables

1 Introduction
1.1 Problem definition
1.2 Scope of work

2 Theoretical basis of portfolio management
2.1 Passive portfolio management
2.1.1 Definition and process
2.1.2 Tracking methods
2.1.3 Market efficiency hypothesis
2.2 Active portfolio management
2.2.1 Visual approach
2.2.2 Quantitative approach
2.2.3 Qualitative approach
2.2.4 Active performance analysis

3 Systematisation of dividend strategies
3.1 Active dividend strategies
3.1.1 Basics of the Dividend Discount Model
3.1.2 Single-stage Dividend Discount Models
3.1.3 Multi-stage Dividend Discount Models
3.2 Semi-active dividend strategies
3.2.1 Dow Dividend Strategy
3.2.2 Top-10 / Low-5 Strategy

4 Empirical study on the DivDAX
4.1 Concept of the DivDAX
4.2 Purpose and examination design
4.2.1 Formulation of hypotheses
4.2.2 Data selection and methodology
4.3 Results of data analysis
4.3.1 Hypothesis 1
4.3.2 Hypothesis 2
4.4 Interpretation of results

5. Conclusion
5.1 Achievement of objectives
5.2 Outlook and perspectives

Appendix

Appendix 1: Composition of the DivDAX from 2005 to 2010

Bibliography

List of abbreviations

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List of figures

Fig. 01: Coherence between number of stocks and Tracking Error

Fig. 02: Coherence between Tracking Error and Beta factor

Fig. 03: Price reactions in different information efficiency stages

Fig. 04: Right-skewed and left-skewed distributions

Fig. 05: Platykurtic and leptokurtic distributions

Fig. 06: Stock value in dependency of g

Fig. 07: Development of the growth rate in the H-Model

Fig. 08: Development of DivDAX and DAX (discrete returns)

Fig. 09: Annual rates of return of DivDAX and DAX

Fig. 10: Monthly out- and underperformance of the DivDAX

Fig. 11: Coherence between DAX DY and DivDAX outperformance

List of tables

Tab. 01 : Differentiation of capital market efficiency types

Tab. 02: Different forms of information efficiency

Tab. 03: Prognosis methods of portfolio management

Tab. 04: Groups of nonlinear time series models

Tab. 05: Different groups of valuating methods

Tab. 06: Different groups of risk figures

Tab. 07: Weightings of the DivDAX as of 01/03/2011

Tab. 08: Volatilities and outperformance of DAX and DivDAX

Tab. 09: LPM of the DAX and DivDAX

Tab. 10: Sharpe Ratio of the Dax and DivDAX

Tab. 11: Tests of normality for the DAX and DivDAX

Tab. 12: Skewness and kurtosis of the DAX and DivDAX

Tab. 13: Maximum profit and loss without countermovement

Tab. 14: Risk adjusted outperformance of the DivDAX

1 Introduction

1.1 Problem definition

During the previous years, investors have shown that they are willing to take on a high level of risk to gain above average profits. Especially since the beginning of the financial crisis in 2007, both institutional and individual investors have tried to extend their investment horizon and develop new strategies to escape from the general decline on nearly all mature markets. Despite all the quantitative oriented and complex methods, dividend strategies have reached new popularity as they can be applied easily and are meant to enable investors to outperform the market. Due to the fact that companies on the German stock market increase their yearly dividend payments and have a high dividend yield on average in comparison to previous periods, the dividend factor becomes more and more important for investors.¹ Further more, the currently low level of interest rates leads to an increasing attractiveness of dividend stocks as they partly offer a dividend yield of more than 7,00% per year.

Empirical studies on several markets all over the world have shown that dividend strategies are able to outperform their particular benchmark on a long term perspective. Thereby, different types of strategies were applied as there are various concepts of dividend orientated investment approaches. Thus, the empirical results are not comparable in each case. Further more, only few studies were published that consider the German market, e. g. Kotkamp and Otte (2001) and Henne et al. (2009). As the former does not consider the market reactions due to the technology bubble and financial crisis and the latter uses a self developed dividend strategy, a current study is necessary that analyzes a possible advantageousness of an objective and traceable dividend strategy approach on the German stock market.

1.2 Scope of work

This study aims to integrate itself into the scientific network of business administration by covering the topic of dividend strategies. Its main objective is to give a theoretical overview on the field of dividend orientated investment strategies under consideration of current scientific literature and research results. Additionally, a practical part is included as the study also applies the theoretical findings empirically by examining a possible outperformance of investment strategies on the German stock market.

Chapter 2 creates the basis as it explains the differences between passive and active portfolio management under consideration of the market efficiency hypothesis. As the active management style contains several different approaches, it is divided in three main categories that are linked to different stages of market efficiency. Due to the fact that dividend strategies aim to outperform the market, they are assigned to semi-active and active portfolio strategies. To get informed about different possibilities of measuring this outperformance, the chapter finishes with a presentation of performance analysis concepts that complement each other. Chapter 3 goes more into details of dividend strategies as it divides them into two basic categories. As the active ones are partly complex and require the estimation of a company’s future growth rate, they are preferably used by institutional investors. In contrast to that, the semi-active dividend strategies can be easily applied also by individual investors as they are linked to objective and clearly defined actual figures. Moreover, a large number of investment opportunities have been developed and issued in the last years that make it easy to follow those dividend strategies. To get an overview on the state of research, several empirical studies concerning the success of dividend strategies on different markets are presented. The last chapter 4 contains an empirical study on the German stock market, which examines the advantageousness of the DivDAX in comparison to the DAX over a time frame of 11 years. After an interpretation of the results, combined with an outlook on possible future research questions, a general conclusion of the theoretical and practical part is made in chapter 5.

2 Theoretical basis of portfolio management

2.1 Passive portfolio management

2.1.1 Definition and process

Passive portfolio management, also called index tracking or indexing, is a strategy that aims to emulate a specific index portfolio in order to equal the return of investment and hold it in line with the index.² It is based on the general assumption of information efficiency and therefore includes that it is not possible to generate outperformance through active asset management due to the fact that all existing information is reflected in a certain asset.³ Especially since the beginning of the financial crisis in 2007, passively managed funds have become more attractive and got enhanced public attention from investors' side due to the fact that funds with an active management style belied their expectations regarding their possibilities to avoid losses in bear markets.⁴ The decision to follow a passive portfolio management style may be based on several reasons, such as the unavailability of information resources, what makes an active strategy impossible, for example for private investors with a focus on emerging markets.⁵ Further more, a passive strategy is advantageous if the process of stock picking creates transaction costs that compensate the possible relative outperformance of an active portfolio management.⁶ The “paradox of investment philosophy” combines the return oriented perspective with risk aspects and concludes that passive portfolio management has mainly three advantages in comparison to an active style that seem to be contradictory.⁷ Passive portfolio management creates lower transaction costs, it has a minimal relative risk and due to empirical studies, the return of passively managed funds is higher than 75% of the active ones. In contrary, actively managed portfolios are more cost intensive and fraught with higher risk within the meaning of the Tracking Error. But there is a theoretical statement that points out the bilateral dependency of active and passive portfolio management, called the “information paradox”.⁸ It describes the fact that even if the passive portfolio management is theoretically and empirically predominant to active asset management, it loses its advantage when all investors act rationally and prefer the passive strategy. In this case, no one processes information from the capital markets and active portfolio management becomes efficient and economically reasonable again.⁹

2.1.2 Tracking methods

The primary aim of the passive portfolio management is to replicate a certain target portfolio as precisely as possible with the lowest possible cost.¹⁰ The most obvious approach to target an index is the full replication, in which “each in the target portfolio included assets are admitted to the tracking portfolio with the appropriate score”.¹¹ This method may be effective in terms of having the lowest Tracking Error, but it implicates the problems of high transaction costs. Additionally, legal constraints make the implementation of this approach problematically, especially for mutual funds. To name an example, German investment companies cannot allocate more than 5% of their fund assets in securities of the same debtor or 10% maximum if this is contractually agreed.¹² This would make a full replication of the DAX currently impossible, because stocks from the SIEMENS AG are currently weighted with more than 10% in this index.¹³ Further more, due to the fact that stocks are not divisibly, a very high amount of stocks and therefore a large amount of money would be needed to reach the exact weight of each position of the target portfolio.¹⁴ The high number of stocks would also complicate the process of controlling and adjusting the tracking portfolio over a certain period of time. Thus, the full replication of a target portfolio does not seem to be efficient in each case and different approaches may reach the aim of a low tracking error with low cost better.

All methods which implicate to hold a certain part of the assets in an index rather than fully replicate it are classified as sampling methods or approximative methods. The largest holdings approach is the simplest one of them and describes the procedure to select only the largest companies out of an index and weight them after a common feature such as market capitalization or index weighting.¹⁵ As an example, the 164 highest capitalization stocks out of the 1660 different values including MSCI WORLD Index are responsible for 50% of the whole capitalization and the largest 660 companies and about 36% account for 80% of the total capitalization.¹⁶ According to the fact that the return of an index is predominantly determined by the return of its highest weighted assets, this approach may result in a relatively low Tracking Error. As high market capitalization tends to go along with high fungibility, transaction costs are obviously lower than in the case of full replication. Nevertheless, this approach is not sophisticating to investors who seek to create a tracking portfolio that reliably minimizes the Tracking Error, because it does not even build the best portfolio, i. e. the one with the lowest Tracking Error out of the chosen assets if it is only capitalization oriented. Moreover, this approach does not consider the fact that highly capitalized companies have a significantly higher correlation to each other than to companies with strikingly lower capitalization.¹⁷ Therefore, the tracking portfolio based on this selection process is not able to reproduce all trends that are implicated in the target portfolio, specifically the ones that come from the low sized companies.¹⁸

Another theoretically established method of tracking an index is the stratifying sampling. Thereby, assets of a certain target portfolio are categorized in different clusters that concern a special criterion.¹⁹ For example, the MSCI World companies may be categorized by two dimensions such as market capitalization and economic sector. Thereby, it is possible to select a specific number of representatives out of each combination, e. g. low market capitalization / pharmaceuticals and weight it in the tracking portfolio with the identical ratio the combination is represented in the target portfolio. Just like the largest holdings approach, the stratified sampling method does not meet the requirements of a serious attempt to minimize the Tracking Error due to the fact that the categorization is partly subjective, for example concerning the allocation of companies to sectors.²⁰

The most sophisticated and therefore most commonly used approach by institutional investors for tracking a target portfolio is the optimized sampling.²¹ This approach includes different methods, from which the quadratic optimization will be captured more detailed here as being the foundation for similar ways of tracking a portfolio by optimization. As mentioned before, the aim of a tracking portfolio is to replicate the risk and return of a target portfolio with the lowest possible transaction cost. Thus, the tracking portfolio Alpha factor ap, which is the excess return of the tracking portfolio concerning the target portfolio, shall be 0, and the tracking portfolio Beta factor ßP, which is the systematic risk of the tracking portfolio, shall be 1, as the target portfolio Beta factor is also per definition 1.²² Additionally, the residual risk, meaning the unsystematic risk that cannot be attributed to the total market shall be minimized.²³ That implies that the objective function of the quadratic optimization is:

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The side conditions of this objective function are:

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where wPi : relative weight of asset i in the tracking portfolio P

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where ßp : Beta factor of the tracking portfolio P concerning the target portfolio

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where aP : Alpha factor of the tracking portfolio P concerning the target portfolio

In practice, these side conditions are usually complemented by necessary minimum and maximum proportions of single assets, as one has to consider for mutual funds. Important is, that in this approach the assets of the tracking portfolio do not necessarily have to be represented in the target portfolio but can be picked out from the entirety of all investable assets to get a portfolio that fulfills the given requirements.²⁴

To complete this chapter, it is necessary to amplify the idea of the Tracking Error which was already mentioned before. The Tracking Error is a concept to “understand the potential performance of a common stock portfolio relative to a benchmark index”.²⁵ It expresses the level a portfolio was actively managed over a certain period of time, irrespective of if that was intended or not. The Tracking Error has become an important and established key figure for both passive and active portfolio managers and is defined as being the standard deviation of the active return ??, i. e. the excess return of a tracking portfolio concerning its target portfolio over a certain period of time.²⁶ Therefore, the key figure can be mathematically expressed with the following term:²⁷

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where TE : Tracking Error

?? : active return

rA again can be defined as being the difference between the return of the

tracking portfolio and the one of the benchmark, i. e. the target portfolio:²⁸

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where rP : return of the tracking portfolio P

rB : return of the benchmark B

Inferring, the residual risk of the tracking portfolio ^, which minimization is defined in as being the objective function of the quadratic optimization according to formula (1), is equal to the active risk SD(rA) of the portfolio.²⁹ Therefore, the aim of the quadratic optimization is to minimize the Tracking Error of the tracking portfolio:

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Although being commonly used, the Tracking Error is partially also defined as being not the standard deviation, but the variance of the active return of a tracking portfolio.³⁰ Passively managed index funds with benchmarks of high liquidity have nowadays typically an average Tracking Error of 1% to 3% on annual basis, which means that the standard deviation of the yearly differences

between the return of tracking portfolio and target portfolio are 3% at most.³¹ Until 2004, this has strongly decreased, mainly because of higher liquidity and less transaction costs due to modern forms of trading. Theoretically, index related products should have a long term Tracking Error of 0, which is practically not possible due to the existence of transaction costs and the indivisibility of shares.³² Especially for tracking portfolios of mid cap and small cap benchmarks, that usually have a higher volatility than blue chip indices, a Tracking Error in the area of 0% to 1% is extremely difficult to realize due to the fact that there is an impact of the benchmark risk, i. e. its volatility on the tracking error of an appropriate target portfolio.³³ The mathematical derivation is based on the CAPM, which expresses that:³⁴

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where ep : residual return of the tracking portfolio P

To get the active return rA of the tracking portfolio P according to formula (6), rB has to be subtracted on both sides:³⁵

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Now it is necessary to determine the variances o2 on both sides and then getting the common term of the Tracking Error on the left side by dividing through o. As there is no correlation between the benchmark return and the residual variance, ep can be neglected here in the last step:³⁶

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where ?2 (x) : variance of x

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where o(x) : standard deviation of x

As a(p - rB ) is the standard deviation of the active return rA and therefore the Tracking Error of th portfolio P, it can clearly be seen that it increases ceteris paribus in proportion to the risk of the benchmark B, defined as its volatility aPrB ). Thus, it is reasoned that Tracking Portfolios of benchmarks with a relatively high volatility, typically mid cap and small cap indices or secondary stock benchmarks in general, usually have higher Tracking Errors. To put it in another way, a large-cap tracking portfolio needs less different stocks out of its benchmark to reach a certain Tracking Error level than a mid cap or small cap tracking portfolio, which is illustrated in the following:

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Fig. 01: Coherence between number of stocks and Tracking Error³⁷

There is obviously also a coherence between the Tracking Error of P and its Beta factor ßp in formula (11). Focardi and Fabozzi (2004) derive this coherence mathematically and define it as being:³⁸

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According to this, the Tracking Error of P increases both when ßP falls below or rises above the value of 1, i. e. in each case it distances itself from the Beta factor of the benchmark, regardless in which direction. The coherence between ßp and the Tracking Error of P can be illustrated in fig. 02:

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Fig. 02: Coherence between Tracking Error and Beta factor ³⁹

Under the assumption that a portfolio manager can only choose between investing in a full replication of the target portfolio or in cash, the Tracking Error of his portfolio increases with the rate he holds cash, whereas its volatility decreases.⁴⁰

Despite of the undoubtedly high expressiveness of the Tracking Error as a key indicator for the performance of a passive portfolio manager, its interpretation requires some specific considerations. While being based on a two-sided risk measurement, the Tracking Error does not differentiate between positive and negative deviations from the benchmark and considers both as risk. Further more, comparisons between various sources of Tracking Error results have to be handled with care, because different databases lead to different results, for example depending on if the data was taken on daily, monthly or yearly base. Moreover, in every passive fund segment that has to cope with high transaction costs, as it is in the field of commodity funds due to the necessary process of rolling the futures, the Tracking Error does not clearly reflect the performance of the manager, because relatively high costs inevitably lead to deviations between tracking portfolio and benchmark.⁴¹

2.1.3 Market efficiency hypothesis

The market efficiency hypothesis is one of the most constitutive and crucial theory of the economic sciences and plays a special role regarding to the portfolio theory. It was reasoned basically in the early seventies by Eugene F. Fama, Professor of Finance at the University of Chicago Booth School of Business and has been developed further until today.⁴² The hypothesis expresses in principal that capital markets, i. e. the market participants process information efficiently at all time and includes in a broader sense three elements due to different perspectives:^{43 44}

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Tab. 01: Differentiation of capital market efficiency types⁴⁵

Technical efficiency includes the validity of the actuarial expectation-variance efficiency, which is based on the portfolio selection theory of Harry M.

Markowitz and expresses that portfolio turnovers cannot lead to an improvement of the risk-return profile of a portfolio.⁴⁶ Additionally, technical efficiency means that capital is allocated in its best way, i. e. that it generates the highest possible output in a certain period.⁴⁷ The third requirement for the existence of technical efficiency is that the market is always approaching a Pareto-efficiency, expressing that there is an optimal distribution of scarce resources and no benefit of one individual without an appropriate loss of another market participant.⁴⁸

Institutional efficiency as a second element of market efficiency contains the smooth possibility for institutional market participants such as credit institutes to handle transactions without or with very low transaction cost.⁴⁹ Moreover, institutional efficiency stands for barriers to entry a market.⁵⁰

The central element of market efficiency in a strict sense is information efficiency.⁵¹ After the original definition of Fama (1970), a market is efficient, if “security prices at any time fully reflect all available information”.⁵² In the case of a market fulfilling this requirement, it can be called a “fair market” as “there is no way to use currently available information to earn a return above normal”.⁵³ A “normal return” in this case means a return that is on the level of the appropriate benchmark of a certain market. Fama (1970) developed a so called “Fair Game Process” which constitutes that the market functions as a filter for relevant information and implicates them immediately and in the right way in a certain asset price what leads to a maximum of entropy, meaning that there is the highest possible information content in an asset.⁵⁴ Spremann (2006) differentiates between relevant and irrelevant information concerning the asset pricing in an efficient market by categorizing them in five types of information:⁵⁵

1. New information that is unexpected, but irrelevant for asset prices.
2. New information that is important and relevant for asset prices, but that have been foreseeable.
3. Information that is new and relevant for asset prices.
4. Information that enunciate the current sentiment or future prospects of financial specialists.
5. Information about what is the right valuation model for certain companies or assets in general.

According to Spremann (2006), investors react only on information of category 3, 4 and 5, thus new and relevant one. Additionally to the price-efficiency, the Random-Walk assumes a second requirement for information efficiency especially of security markets, saying that asset prices follow a random walk in the sense that “any new information arriving between this and next period create only a random deviation from this period’s best forecast”.⁵⁶ As all investors do have the same information at the same time concerning the information efficiency hypothesis, it would also be impossible for individuals to gain profit by arbitrage. Moreover, arbitrage efficiency means that there is no relevant information regarding assets that can be interpreted without any risk (information arbitrage).⁵⁷

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¹ Cp. Sommer, U. (2010), p. 23.

² Cp. Leser, H., Rudolf, M. (2003), p. 35.

³ Cp. Fama, E. (1991), p. 1575.

⁴ Cp. Krink, T., Mittnik, S., Paterlini, S. (2009), p. 172.

⁵ Cp. Bruns, C., Meyer-Bullerdiek, F. (2008), p. 108.

⁶ Cp. Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 245.

⁷ Bruns, C., Meyer-Bullerdiek, F. (2008), p. 108.

⁸ Cp. Lahusen, R., Müllers, J. (2003), p. 42.

⁹ Cp. Fama, E. (1970), p. 387.

¹⁰ Cp. Bruns, C., Meyer-Bullerdiek, F. (2008), p. 110.

¹¹ Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 248.

¹² Cp. InvG (2010), §60 I.

¹³ Cp. Deutsche Börse AG (2011a).

¹⁴ Cp. Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 246.

¹⁵ Cp. Neubert, A. (1998), p. 86.

¹⁶ Cp. Deutsche Bank (2011).

¹⁷ Cp. Kanas, A. (2004), p. 588.

¹⁸ Cp. Neubert, A. (1998), p. 87.

¹⁹ Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 249.

²⁰ Cp. Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 252.

²¹ Fabozzi, F., Jones, F., Vardharaj, R. (2002), p. 163.

²² Cp. Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 256.

²³ Cp. Poddig, T., Brinkmann, U., Seiler, K. (2005), p. 257.

²⁴ Cp. Specht, K., Gohout, W. (2009), p. 82.

²⁵ Cp. Grinold, R., Kahn, R. (1995), pp.47.

²⁶ Cp. Faber, P. (2007), p. 138.

²⁷ Cp. Klein, C., Kundisch, D. (2009), p. 1144.

²⁸ Cp. Faber, P. (2007), p. 139.

²⁹ Cp. Jegadeesh, N. (1992), p. 337.

³⁰ Cp. Grinold, R., Kahn, R. (1995), p. 15.

³¹ Cp. Focardi, S., Fabozzi, F. (2004), p. 559.

³² Cp. Focardi, S., Fabozzi, F. (2004), p. 559.

³³ According to: Fabozzi, F., Jones, F., Vardharaj, R. (2002), p. 171.

³⁴ Cp. Focardi, S., Fabozzi, F. (2004), p. 561.

³⁵ According to: Fabozzi, F., Jones, F., Vardharaj, R. (2002), p. 176.

³⁶ Cp. Focardi, S., Fabozzi, F. (2004), p. 560.

³⁷ Cp. Schmitz, A. (2010), p. 19.

³⁸ Cp. Chordia, T., Roll, R., Subrahmanyam, A. (2008), p. 250.

³⁹ Cp. Islam, S., Watanapalachaiku, S. (2005), p. 53.

⁴⁰ According to: Loistl, O. (1990), p. 64.

⁴¹ Cp. Markowitz, H. (1952), pp. 77.

⁴² Cp. Hauser, S. (2003), p. 21.

⁴³ Cp. Brown, D. (1975), p. 464.

⁴⁴ Cp. Mama, H. (2010), p. 16.

⁴⁵ Cp. Loistl, O. (1990), pp. 64.

⁴⁶ Cp. Bruns, C., Meyer-Bullerdiek, F. (2008), p. 73.

⁴⁷ Fama, E. (1970), p. 383.

⁴⁸ Ritchken, P. (1988), p. 114; Schmeisser, W. (2010), p. 275.

⁴⁹ Cp. Schlenger, C. (1998), p. 58; Fogler, H. (1995), pp. 40.

⁵⁰ Cp. Spremann, K. (2006), p. 156.

⁵¹ Su, D. (2003), p. 86.

⁵² Cp. Menkhoff, L., Tolksdorf, N. (2001), p. 5.

⁵³ Cp. Summers, L. (1986), p. 593.

⁵⁴ Cp. Spremann, K. (2006), p. 157.

⁵⁵ Cp. Spremann, K. (2006), p. 157.

⁵⁶ Cp. Fama, E. (1970), p. 383.

⁵⁷ Cp. LeRoy, S. (1989), p. 1592.