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Microfoundations of Financial Economics Microfoundations of Financial Economics Microfoundations of Financial Economics Microfoundations of Financial Economics An Introduction to General Equilibrium Asset Pricing Yvan Lengwiler To Brigitte, with love Contents List of boxes xi Preface xiii 1 Introduction 1 1.1 What finance theory is about 1 1.2 Some history of thought 2 1.3 The importance of the puzzles 7 1.4 Outline of the book 9 2 Contingent claim economy 10 2.1 The commodity space 10 2.2 Preferences and ordinal utility 14 2.3 Maximization 16 2.4 General equilibrium 23 2.5 The representative agent 32 Notes on the literature 35 Problems 35 3 Asset economy 37 3.1 Financial assets 37 3.2 Pricing by redundancy 41 3.3 Radner economies 46 3.4 Complete markets (and uniqueness of Arrow prices) 53 3.5 Complications arising from market incompleteness 60 Notes on the literature 65 Problems 65 4 Risky decisions 68 viii Contents 4.1 Bernoulli’s St. Petersburg paradox 69 4.2 Using more structure: probabilities and lotteries 71 4.3 The von Neumann–Morgenstern representation 75 4.4 Measures of risk preference 81 4.5 Assumptions and evidence 86 4.6 Often used specifications 91 Notes on the literature 99 Problems 99 5 Static finance economy 102 5.1 An economy with von Neumann–Morgenstern agents 102 5.2 Efficient risk-sharing 107 5.3 A representative NM agent 112 5.4 Who holds what kind of portfolio? 121 5.5 The stochastic discount factor 126 5.6 The equilibrium price of time 130 5.7 The equilibrium price of risk 132 5.8 Some important special cases 134 Notes on the literature 138 Problems 138 6 Dynamic finance economy 141 6.1 A static dynamic model 141 6.2 Dynamic trading 149 6.3 Models of the real interest rate 162 6.4 Portfolio selection 168 Notes on the literature 170 Problems 170 7 Empirics and the puzzles 172 7.1 Collecting the right data 172 7.2 The equity premium puzzle 176 7.3 Alternative interpretations of the data 184 7.4 Excessive volatility 192 7.5 Anomalies 197 Notes on the literature 198 8 Adapting the theory 199 8.1 Assumptions of the mainstream model 199 8.2 Non-standard preferences 201 8.3 Heterogeneity 214 8.4 Efficiency failure 225 Contents ix Notes on the literature 238 9 Epilog 239 9.1 A mystery 240 9.2 A challenge 241 9.3 The party’s over 242 Appendix A Symbols and notation 245 Appendix B Solutions to the problem sets 247 Bibliography 269 Index 285 List of boxes 2 . 1 Definition of a commodity 14 2 . 2 Equivalent utility functions 15 2 . 3 Maximality condition 19 2 . 4 Classical dichotomy 20 2 . 5 Interest rate as relative price 22 2 . 6 Insurance premium as relative price 22 2 . 7 Contingent claim economy 24 2 . 8 Competitive equilibrium 25 2 . 9 First welfare theorem 29 2 . 10 Loss of distributional information 33 3 . 1 Law of one price 43 3 . 2 Decomposition 43 3 . 3 Risk-neutral probabilities 44 3 . 4 Risk-neutral pricing 45 3 . 5 Risk-neutral returns 45 3 . 6 Asset economy 46 3 . 7 Absence of arbitrage opportunities 49 3 . 8 Radner equilibrium 51 3 . 9 Loss of information on composition 53 3 . 10 Complete markets 54 3 . 11 Reverse decomposition and uniqueness of Arrow prices 54 3 . 12 State-wise dichotomy 58 3 . 13 The one-good one-agent economy 59 3 . 14 Effects of incomplete markets 63 3 . 15 Equilibrium in a quasi-complete market 64 4 . 1 Certainty equivalent and risk premium 73 4 . 2 Expected utility representation 78 4 . 3 Demand for full coverage 82 4 . 4 ARA 84 xii List of boxes 4 . 5 CARA—DARA—IARA 84 4 . 6 Determine your preferences 89 4 . 7 Likely utilities 91 4 . 8 HARA (Merton, 1971) 92 4 . 9 Approximate mean–variance analysis 99 5 . 1 Mutuality principle 107 5 . 2 Efficient allocation of aggregate risk (Wilson, 1968) 112 5 . 3 A distribution-independent representative (Rubinstein, 1974) 116 5 . 4 Sufficient condition for quasi-completeness (Ross, 1976) 118 5 . 5 Quasi-completeness without options 120 5 . 6 SDF 126 5 . 7 Equilibrium SDF as function of aggregate data 127 5 . 8 Risk-neutral probabilities are pessimistic 129 5 . 9 Growth and the risk-free rate 131 5 . 10 Aggregate risk and the risk-free rate 132 5 . 11 CCAPM 133 6 . 1 Fundamental pricing formula 147 6 . 2 Qualitative features of the term structure of interest rates 164 6 . 3 The expectations hypothesis of the term structure 166 Preface Dear reader This book takes you from the level of microeconomics principles through a sequence of carefully elaborated and detailed steps to modern topics in finance. The book is for you if you have been exposed to indifference curves, budget constraints, and maximization but would like to know about the consumption capital asset pricing model, the theory of the term structure of interest rates, the equity premium puzzle, and the social cost of the business cycle. Even if you have not taken a course in basic microeconomics, you can still read this book, because it reviews the part of microeconomics and general equilibrium theory that is relevant for the topics covered in this book. The book was written with three groups of readers in mind: graduate students with a focus on macroeconomics, financial eco- nomics, or monetary economics; MBA students specializing in finance; professionals of the financial community with a sufficient prior know- ledge of mathematics and economics. Essentially, it is suitable for everyone who is seriously interested in financial economics and its relation to the macroeconomy, and has an appetite for the formal analysis of these issues. Dear instructor The book is geared to the needs of MA/MSc or PhD students specializing in financial economics. It can also be used for undergraduate students xiii xiv Preface with a sufficient appetite for formal analysis as an introduction to general equilibrium theory, macroeconomics, or finance—three terms that have begun to overlap increasingly over the last two decades. The material covered fits comfortably into a two semester course. For students with sufficient prior exposure to economics (knowledge of gen- eral equilibrium theory and expected utility theory), chapters 2–4 can be reviewed quickly and the remainder of the book should then fit into one semester. Some knowledge of mathematics is required. This becomes quickly ob- vious simply by looking at the density of the equations in the book: there are fewer than a typical mathematics textbook would have, but considerably more than what someone who is not used to mathematics will feel comfort- able with. We use Euclidean spaces (finite-dimensional real vector spaces), basic statistics (mean, variance, covariance), maximization subject to con- straints, and calculus. More precisely, knowledge of mathematics at the level of Bartle (1976), Simon & Blume (1994), Sundaram (1996), Wein- traub (1982), or any other slightly advanced “Mathematics for Economists” text is more than enough. Use in combination with other books Depending on the class level you may wish to emphasize or de-emphasize different aspects or topics, and it may make sense to combine this text with another one. For a more applied audience and for practitioners, I recommend Cornell (1999) or Siegel (1998) as a starting point. Both books contain detailed discussions of the equity premium puzzle, yet both manage to do away almost completely with mathematics and econometrics. Another good place to start is AIMR’s (2002) published forum on the topic. In this forum, several prominent researchers in the field present their ideas in not too technical a fashion. These ideas are then discussed by a panel. LeRoy & Werner (2001) and Danthine & Donaldson (2002) are compa- rable in style and difficulty to the present book, should you wish to offer an alternative presentation of the material. The main differences are that these two books put less emphasis on aggregation conditions and cover empirical issues to a lesser extent (Danthine & Donaldson) or not at all (LeRoy & Werner). If you want to focus somewhat more on empirical work and your students are technically well-trained, the textbooks by Cochrane (2001) and Camp- bell, Lo & MacKinlay (1997) should provide nice complements, containing Preface xv much more information on econometric issues related to financial market data. The present book can also be used as a supplement to modern macroe- conomics courses. For instance, Ljungqvist & Sargent (2000) contains two chapters on equilibrium asset pricing; if you want to focus more on this topic that would be a valuable addition, especially since, unlike Ljungqvist & Sargent, we develop the topic at sub-sonic speed. For the more theory-minded reader, Gollier (2001a) has created an out- standing research book on the theory of decisions under risk and relations to general equilibrium and asset pricing. An older classic in this domain is Duffie (1988). These titles are clearly more advanced than the present. Finally, Brunnermeier (2001) presents a book that would be very appro- priate as a basis for a follow-on course from this one. He explores the con- sequences of asymmetric information in general equilibrium asset pricing theory, a topic we touch upon here only marginally. Website and supporting material The book’s website1 offers supporting material for instructors. First of all, there is a list of all the references made in the book, with links to online sources where available. This should help instructors collect material for a reader accompanying their course, and should help students collect the relevant literature on their own. The same website offers some Excel files in connection with the problem sets.
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