Asset Pricing with Imperfect Competition and Endogenous ... Asset Pricing with Imperfect Competition

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  • Asset Pricing with Imperfect Competition

    and Endogenous Market Liquidity

    Christoph Heumann

    Inauguraldissertation

    zur Erlangung des akademischen Grades

    eines Doktors der Wirtschaftswissenschaften

    der Universität Mannheim

    vorgelegt im Frühjahrs-/Sommersemester 2007

  • Dekan: Professor Dr. Hans H. Bauer

    Referent: Professor Dr. Wolfgang Bühler

    Korreferent: Professor Dr. Ernst-Ludwig von Thadden

    Tag der mündlichen Prüfung: 20. August 2007

  • To My Parents

  • Contents

    List of Figures vii

    Acknowledgements ix

    1 Introduction 1

    2 Walrasian Asset Prices and Market Microstructure 7

    2.1 The Walrasian Paradigm . . . . . . . . . . . . . . . . . . . . . . . . . 8

    2.2 A CARA-Gaussian CAPM . . . . . . . . . . . . . . . . . . . . . . . . 10

    2.2.1 Description of the Economy . . . . . . . . . . . . . . . . . . . 11

    2.2.2 Walras Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . 12

    2.2.3 Equilibrium Properties . . . . . . . . . . . . . . . . . . . . . . 15

    2.3 The Myth of the Walrasian Auctioneer . . . . . . . . . . . . . . . . . 18

    2.4 Market Liquidity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

    2.4.1 Dimensions of Liquidity . . . . . . . . . . . . . . . . . . . . . 24

    2.4.2 Determinants of Liquidity . . . . . . . . . . . . . . . . . . . . 27

    3 Market Liquidity and Asset Prices: Literature Review 33

    3.1 Exogenous Bid-Ask Spreads . . . . . . . . . . . . . . . . . . . . . . . 35

    3.1.1 Deterministic Liquidity Effects . . . . . . . . . . . . . . . . . . 35

    3.1.2 Liquidity Shocks . . . . . . . . . . . . . . . . . . . . . . . . . 39

    3.1.3 Random Time Variations in Liquidity . . . . . . . . . . . . . . 43

    3.2 Large Investors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

    3.2.1 Static Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

    3.2.2 Dynamic Models with a Single Large Investor . . . . . . . . . 48

    3.2.3 Dynamic Models with Multiple Large Investors . . . . . . . . 51

    v

  • vi

    3.3 Endogenous Market Liquidity . . . . . . . . . . . . . . . . . . . . . . 54

    3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

    4 Asset Prices under Imperfect Competition 61

    4.1 Description of the Economy . . . . . . . . . . . . . . . . . . . . . . . 64

    4.2 Trading with Imperfect Competition . . . . . . . . . . . . . . . . . . 67

    4.3 Equilibrium with Identical Risk Aversion . . . . . . . . . . . . . . . . 73

    4.4 Heterogeneity in Risk Aversion . . . . . . . . . . . . . . . . . . . . . 80

    4.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

    Appendix: Proofs to Chapter 4 . . . . . . . . . . . . . . . . . . . . . . . . 89

    5 Asset Prices with Time-Varying Market Liquidity 97

    5.1 Description of the Economy . . . . . . . . . . . . . . . . . . . . . . . 98

    5.2 Derivation of Equilibrium Orders . . . . . . . . . . . . . . . . . . . . 101

    5.3 Equilibrium Properties in the Basic Scenario . . . . . . . . . . . . . . 104

    5.4 Equilibrium Properties in the Signal Scenario . . . . . . . . . . . . . 108

    5.5 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

    Appendix: Proofs to Chapter 5 . . . . . . . . . . . . . . . . . . . . . . . . 112

    6 Concluding Remarks 117

    References 119

  • List of Figures

    2.1 Price dimensions of market liquidity. . . . . . . . . . . . . . . . . . . 26

    3.1 Standard pricing effect of illiquidity. . . . . . . . . . . . . . . . . . . . 58

    4.1 Trading against a supply curve. . . . . . . . . . . . . . . . . . . . . . 69

    4.2 Market liquidity in the individual trading decision. . . . . . . . . . . 72

    4.3 Pricing effect of illiquidity with endogenous trading. . . . . . . . . . . 77

    4.4 Trading volume with heterogeneity effect. . . . . . . . . . . . . . . . . 86

    5.1 Pricing effect of future illiquidity. . . . . . . . . . . . . . . . . . . . . 107

    vii

  • Acknowledgements

    This thesis grew out of my work as a research and teaching assistant at the Chair

    of Finance at the University of Mannheim; it was accepted as dissertation by the

    Faculty of Business Administration.

    Acknowledgements are due to many. First, I am obliged to thank my advisor

    Prof. Dr. Wolfgang Bühler for many comments that helped to improve this thesis.

    I would also like to thank my second advisor Prof. Dr. Ernst-Ludwig von Thadden

    for co-refereeing the thesis. Many thanks go to my current and former colleagues at

    the Chair of Finance, namely Martin Birn, Jens Daum, Christoph Engel, Sebastian

    Herzog, Prof. Dr. Olaf Korn, Dr. Christian Koziol, Jens Müller-Merbach, Stephan

    Pabst, Raphael Paschke, Marcel Prokopczuk, Dr. Peter Sauerbier, Dr. Antje Schirm,

    Christian Speck, Volker Sygusch, Dr. Tim Thabe, Monika Trapp, Volker Vonhoff,

    as well as our secretary Marion Baierlein; they provided a friendly and stimulating

    environment to work in.

    Most of all, I thank my family—my parents Herbert and Frieda and my brother

    Dietmar. Their unfailing support throughout the years made this thesis possible.

    Mannheim, September 2007 Christoph Heumann

    ix

  • Chapter 1

    Introduction

    The equilibrium expected return, or the required return, on financial assets is a cen-

    tral variable in financial economics, and understanding the determinants of required

    asset returns is the fundamental goal of asset pricing. The basic insight of traditional

    neoclassical asset pricing models is that the equilibrium expected return of an asset

    is increasing in the systematic risk of the asset, as risk-averse investors require com-

    pensation for bearing non-diversifiable risk. Neoclassical models, however, are based

    on the assumption that markets for financial assets are frictionless. Accordingly,

    trade in these markets is regarded as costless, and the actual process of trading and

    price formation is, in fact, left unmodeled. The starting point of this thesis is that

    real-world financial markets are not frictionless and that trading of financial assets

    can involve considerable costs. This raises the question of how market frictions affect

    required asset returns.

    A market friction of major importance to investors is a lack of market liquidity.

    Roughly stated, market liquidity refers to the ease of trading financial assets, with

    more liquid markets having lower trading costs. Trading costs in illiquid markets

    include execution costs in the form of commissions, bid-ask spreads, and price im-

    pact, and also opportunity costs in the form of delayed and uncompleted trades. The

    effects of such costs on investment performance are often measured by the imple-

    mentation shortfall proposed by Perold (1988), and these effects can be surprisingly

    large. For instance, Perold (1988) shows that a hypothetical “paper” portfolio based

    on the weekly stock recommendations of the Value Line Investment Survey has out-

    1

  • 2 1. Introduction

    performed the market by almost 20% per year over the period from 1965-1986, while

    the corresponding real portfolio of the Value Line Fund has outperformed the market

    by only 2.5% per year—the difference representing the implementation shortfall.

    When trading costs are important to investors, then a lack of market liquidity may

    also affect required asset returns. The standard result here traces back to Amihud and

    Mendelson (1986), who show that trading costs in illiquid markets reduce the price

    of an asset and, equivalently, increase the equilibrium expected return of an asset, as

    investors require compensation for bearing these costs. Hence, required asset returns

    should reflect both a risk premium as compensation for risk and a liquidity premium

    as compensation for illiquidity.

    This pricing effect of illiquidity has become the conventional wisdom on the role

    of market frictions in asset pricing. For instance, Stoll (2000, p. 1483) argues that

    “frictions must be reflected in lower asset prices so that the return on an asset is

    sufficient to offset the real cost of trading the asset, adjusted for the holding period.”

    Following this line of argument, a simple back-of-the-envelope example illustrates the

    effect. For stocks on the New York Stock Exchange, the average effective bid-ask

    spread is approximately 2.2% and the average turnover of the outstanding shares

    is approximately 60% on an annual basis. Ignoring trading costs other than bid-

    ask spreads, these numbers suggest that the average required stock return should be

    increased by a liquidity premium of about 0.6 · 2.2% = 1.3%, which in turn would

    have a large effect on the level of stock prices.1

    Market liquidity is an elusive concept, however, and how exactly illiquidity af-

    fects required asset returns remains a subject of considerable controversy and debate.

    As O’Hara (2003) points out, the principal difficulty for understanding the precise

    relationship between market liquidity and required asset returns is the separation

    of the