Testing the CAPM on the German Stock Market

Table of contents

List of figures

List of abbreviations

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1 Introduction
1.1 Motivation and Objective
1.2 Course of Exploration

2 The Capital Asset Pricing Model
2.1 The Model
2.2 Criticism and Shortcomings

3 Previous Research

4 Empirical Study
4.1 Data
4.2 Methodology
4.3 Results, Interpretations and Findings

5 Summary and Conclusion

Appendix

References

List of figures

Figure I: The Securities Markt Line (SML)

Figure II: Average excess monthly returns versus systematic risk for the 10-year period 8.1995-7.2005

List of abbreviations

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List of symbols

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1 Introduction

1.1 Motivation and Objective

The capital asset pricing model (CAPM) is one of the most important models in financial economics and has a long history of theoretical and empirical investigations.^[1] It was developed by William Sharpe (1964) and John Lintner (1965) and offered first insights in how the risk of an investment affects the expected returns, resulting in a Nobel Prize for Sharpe in 1990.^[2] The CAPM states that the risk of an asset is measured by the beta of its cash flows with respect to the return of the market portfolio of all assets in the economy.^[3] The fact that is so easy to understand underlines the importance of the model and contributes to its success in today’s business world. Over 40 years after it was developed, the CAPM is still used in many different fields e.g. to evaluate the performance of a managed portfolio or a mutual fund,^[4] assess the risk of a cash flow or estimate the cost of capital of a firm.^[5] A recent study states that nearly three fourth of U.S. companies almost always use the CAPM when determining their cost of capital.^[6] On top of that it is the preferred asset pricing model in finance and investment courses.^[7] Furthermore, one can determine the required rate of return of any risky asset when using the CAPM.^[8]

Although the model is widely accepted and practically used as explained above, it is nevertheless far from being perfect as outlined in its record of empirical studies.^[9] Generally criticized is on the one hand that the underlying assumptions of the model are very theoretical and thus not able to illustrate reality and on the other one that there are problems in implementing well-founded tests of the model relating to the choice of the right market portfolio.^[10] But, the success of the CAPM will remain as long as there is no other model which offers as “[…] powerful and intuitively pleasing predictions about how to measure risk and the relation between risk and return.”^[11]

The objective of this study is to empirically test the CAPM on the German stock market. Since most of the empirical studies that have been made in the past focus on the U.S. stock market, this paper will try to find out if the results of these U.S. empirical studies can also be shown on the German stock market. Therefore, the goal of this paper is to analyze the relationship between risk and return on the German stock market to find out whether the CAPM holds.

1.2 Course of Exploration

Before the empirical investigation is commenced, a theoretical background is presented that will supply the reader with the required knowledge to understand the CAPM and its implications. Firstly, the model is pointed out in chapter 2 by explaining the underlying concepts and the area of practical applications of the CAPM. Within these explanations the Sharpe-Lintner version, which is also the model to be tested in this paper, and its assumptions are presented. The next section of the paper sums up the critique and the shortcomings of the model.

Chapter 3 will then provide the reader with a brief overview about the literature debate which is connected to the topic of this paper. In order to do so, the main and often cited studies about testing the CAPM and their conclusions are presented firstly, before some previous studies on the German market and their implications are summarized.

The fourth chapter includes the main part of this paper, where the empirical study about testing the CAPM on the German stock market is developed. Section 4.1 describes the data which is being used, before the methodology of the empirical part is explained in detail in the following in order to provide the reader with an overview about how the empirical study has been structured. Section 4.3 describes the results that have been found and analyzes the findings.

Finally, the conclusion is drawn and the results of the paper are summed up in the last chapter.

2 The Capital Asset Pricing Model

2.1 The Model

This study will focus on the Sharpe-Lintner version of the CAPM, which is based on the one period mean-variance portfolio theory of Markowitz.^[12] The Markowitz Model assumes that investors are risk averse and only care about risk (variance) and return (mean) of their one-period investment return.^[13] Therefore investors choose “[…] mean-variance-efficient […]”^[14] portfolios meaning that they either maximize the expected return, given a certain variance of portfolio return or minimize the variance, given a certain expected return.

To obtain the CAPM in its basic form some assumptions need be fulfilled and are explained in the following. Firstly, investors are risk averse as in the Markowitz Model and evaluate their investment only in terms of expected return and variance of return measured over the same single holding period. The second assumption is that capital markets are perfect meaning that all assets are infinitely divisible, that no transaction costs, short selling restrictions or taxes occur, that all investors can lend and borrow at the risk free rate and that all information is costless and available for everyone. Thirdly, all investors have the same investment opportunity. Finally, all investors estimate the same individual asset return, correlation among assets and standard deviations of return.^[15] Based on these assumptions, Sharpe and Lintner developed the following formula, which states that the expected return on any asset i, E(Ri), is the risk-free rate, Rf, plus a premium per unit of beta risk, which is calculated by subtracting the risk free rate from the expected return of the market, E(RM) and multiplying the result with the risk premium in terms of the asset’s market beta,Abbildung in dieser Leseprobe nicht enthalten iM. The latter one is calculated by the covariance of the individual asset returns, Ri, with the market return, RM, divided by the variance of the market return.

E(Ri) = Rf + [E(RM)-Rf]Abbildung in dieser Leseprobe nicht enthalteniM, i=1,…N.

Given:

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The main underlying concept is that assets with a high risk (high beta) should earn a higher return than assets with a low risk (low beta) and vice versa. This seems to be a very intuitive concept since no investor would be willing to take on more risk if it is not rewarded by a higher expected return. The implication which can be drawn out of this is that all assets with a beta above zero bear some risk and therefore their expected return is above the return of the risk-free rate. As there is only systematic risk in the CAPM world, assets which are completely uncorrelated to the market and thus have a beta of zero should earn a return which is equal to the risk-free rate. This is a fact because only the systematic risk resulting out of economic activity counts in the CAPM, whereas unsystematic risk can be eliminated by using a high degree of diversification.^[16] Consequential, there is only one risk-return efficient portfolio, which is also called market portfolio and will be hold by every single investor. Therefore, the investors in the CAPM just have to decide how much to invest in the market portfolio, which has a beta of one and the remainder will be invested in the risk-free rate. Resulting out of that is the securities market line on which all investors will plot their securities in equilibrium. The above mentioned choice of the investor, to put part of their investment into the market portfolio and the other one into the risk free rate, determines the location of the portfolio on the securities market line.^[17]

[...]

^[1] See JAVED (2000), pp. 2f.

^[2] See PEROLD (2004), p. 3.

^[3] See JAGANNATHAN/ WANG (1996), pp. 3f.

^[4] See FAMA/ FRENCH (2004), p. 44.

^[5] See FAMA/ FRENCH (2004), p. 25.

^[6] See GRAHAM/ HARVEY (2001), pp. 187-244.

^[7] See JAGANNATHAN/ WANG (1996), p. 4.

^[8] See REILLY/ BROWN (2003), p. 238.

^[9] See ROLL (1977), pp.129-177; BANZ (1981), pp. 3-18; FAMA/ FRENCH (1992), pp. 427-465.

^[10] See FAMA/ FRENCH (2004), p. 25.

^[11] FAMA/ FRENCH (2004), p. 25.

^[12] See FAMA/ FRENCH (2004), p. 26.

^[13] See MARKOWITZ (1952), pp. 77-91.

^[14] FAMA (1996), p. 441.

^[15] See PEROLD (2004), pp. 15f.

^[16] See SHARPE (1964), p. 441.

^[17] See PEROLD (2004), pp. 15-17.