- II -

Content Overview

List  of abbreviations.  V

List  of symbols  VI

1  Introduction  1

1.1  Introduction to asset pricing  1

1.2  Objective of this paper.  1

2  The Capital Asset Pricing Model  2

2.1  Derivation of the CAPM  2

2.2  The Security Market Line (SML)  4

2.3  Assumptions of the CAPM.  5

3  Problems of the CAPM  6

3.1  Unrealistic assumptions.  6

3.2  Empirical Testing of CAPM.  7

4  New Developments.  9

4.1  Neoclassical Models - Traditional Asset Pricing.  9

4.2  Behavioral Finance  17

4.3  Chaos, synergetic models and neural networks.  24

5  Conclusion  25

Bibliography.   VII

Declaration  of Academic Integrity  XI

- III -

Content

List  of abbreviations  V

List  of symbols  VI

1  Introduction  1

1.1  Introduction to asset pricing.  1

1.2  Objective of this paper  1

2  The Capital Asset Pricing Model.  2

2.1  Derivation of the CAPM  2

2.1.1  Firm-Specific Risk vs. Market Risk  3

2.1.2  The beta coefficient  3

2.1.3  The CAPM Equation  4

2.2  The Security Market Line (SML)  4

2.3  Assumptions of the CAPM  5

3  Problems of the CAPM.  6

3.1  Unrealistic assumptions  6

3.2  Empirical Testing of CAPM  7

3.2.1  General Testing Problems  7

3.2.1.1  The Problem of ex ante Data.  7

3.2.1.2  Roll’s critique  7

3.2.2  Results of empirical Tests.  8

3.2.2.1  Controversy about Beta.  8

3.2.2.2  Empirical support for other risk factors.  8

3.2.3  Conclusion.  9

4  New Developments  9

4.1  Neoclassical Models - Traditional Asset Pricing  9

4.1.1  Smaller’ adjustments of the CAPM  9

4.1.1.1  Zero-Beta CAPM  9

4.1.1.2  Introducing taxes and transaction costs.  10

4.1.1.3  International Capital Asset Pricing Model  10

4.1.1.4  Option pricing in CAPM context  11

4.1.2  Multi-factor Models.  11

4.1.2.1  The Arbitrage Pricing Theory (APT)  11

4.1.2.2  Fama-French Three-Factor Model  12

4.1.3  Multi-period models  13

4.1.3.1  The intertemporal CAPM (ICAPM)  14

4.1.3.2  The Consumption-Based CAPM (CCAPM)  15

4.1.3.3  Production-based Asset Pricing Model.  16

4.1.4  General Puzzles of Traditional Asset Pricing Models.  16

4.1.4.1  Equity premium puzzle  16

4.1.4.2  Risk-Free Rate Puzzle  17

- IV -

4.2  Behavioral Finance  17

4.2.1  Introduction  17

4.2.2  Evidence contradicting the efficient market.  18

4.2.2.1  Royal-Dutch-Shell shares  18

4.2.2.2  IPO Palm  18

4.2.3  Pillars of Behavioral Finance  19

4.2.3.1  Psychology.  19

4.2.3.2  Limits to arbitrage.  21

4.2.3.3  Summary  21

4.2.4  Prospect-Theory Model  22

4.2.4.1  Key Elements  22

4.2.4.2  Assessment  22

4.2.5  Habit Formation Models.  23

4.2.6  Models with heterogeneous Agents.  23

4.2.7  Conclusion.  24

4.3  Chaos, synergetic models and neural networks.  24

5  Conclusion.  25

Bibliography   VII

Declaration  of Academic Integrity  XI

- V - Listof abbreviations APT Arbitrage Pricing Theory BHS Barberis, Huang and Santos B/M Book-to-Market value CAPM Capital Asset Pricing Model CCAPM Consumption-based Capital Asset Pricing Model e.g. for example et al. et alii (= and others) etc. et cetera EU Expected Utility Framework GDP Gross Domestic Product HML High Minus Low ICAPM Intertemporal Capital Asset Pricing Model IPO Initial Public Offering NASDAQ National Association of Securities Dealers Automated Quotations NYSE New York Stock Exchange p. page P/E ratio price-to-earnings ratio RBC Real Business Cycle SMB Small Minus Big SML Security Market Line U.S. United States USA United States of America

- VI - Listof symbols

APT - Beta Coefficient of asset i relative to risk factor j b

ij E beta coefficient

i

E Measure of sensitivity of returns on asset i to change in consumption

C i'

E Measure of sensitivity of returns on asset i to HML

HML i, E Measure of sensitivity of returns on asset i to the hedge portfolio h

R i, h

E Measure of sensitivity of returns on asset i to SMB

SMB i, E beta coefficient of market

M

E ' Expected return on change in consumption ) ( C

Expected premium on companies with a relatively high B/M ratio ) (HML E ) ( h Expected return on hedge portfolio h R E ) ( i Expected Return on asset i R E

Expected return on risk factor j ) ( j R E ) ( M Expected Return on market portfolio R E ) ( ZM Expected return on zero-beta portfolio R E

Expected premium on small companies ) (SMB E Number of hedging assets H number of risk factors N Risk free rate of return R

F

index for time t

- 1 - 1Introduction

1.1 Introduction to asset pricing

Asset pricing theory tries to explain why some assets pay higher average returns than others. Accordingly, the objective is to understand the prices or values of claims to uncertain payments. (Cochrane, 2005, p. XIII)

The central aspect is the risk-return tradeoff. It is rational that investors demand additional return for an asset incorporating more risk. This relationship can also be empirically examined when looking at the return development of different assets. For example, between 1926 and 1999, small U.S. stocks yielded average returns of almost 19%, while at the same time large stocks yielded 13% and US Treasury-Bills only about 4%. When looking at the risk of the assets, as measured by the standard deviation of the returns, the relationship becomes obvious: small stocks had a standard deviation of almost 40%, while large stocks and U.S. treasury-bills had 20 % and 3%, respectively. (Tuck School of Business, 2003, p. 2) Problems arise, however, when one tries to determine the relevant risk factors and their expected compensation. The basis for this theory was already laid in the 1950s and 60s with the portfolio selection theory by Markowitz and the Capital Asset Pricing Model (CAPM) by Sharpe, for which he received a Nobel Prize in 1990. (Wilhelm, 2001, p. 15) The CAPM significantly shaped and changed financial management (Užík, 2004, p. VII). Today it is still widely used in practice and plays the centerpiece in the theoretical discussion of asset pricing, although it continues to be sharply criticized (Fama & French, 2004, p. 25). This leads to a variety of adaptations and further developments of the CAPM, but so far no model has been able to sufficiently persuade financial scientists and practitioners (Užík, 2004, p. VII). As it might seem on first sight, asset pricing is not only solely important for financial investors, because in reverse this also means that companies have to meet the expected returns of their investors. This falls under the ‘Shareholder Value concept’, which has increased in significance over the past years and is being rigorously proclaimed by many investors. According to this concept, companies have to know the return expectations of the investors in order to include them in their capital costs for investment decisions. (Wallmeier, 1997, p. 1)

1.2 Objective of this paper

The objective of this paper is to give an overview of the most important movements of the complex area of asset pricing. This will be tried by logically structuring and building up the