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Asset Pricing and Portfolio Choice Theory


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Table of Contents

Preface I Single-Period Models 1 Utility Functions and Risk Aversion Coefficients 1.1 Uniqueness of Utility Functions 1.2 Concavity and Risk Aversion 1.3 Coefficients of Risk Aversion 1.4 Risk Aversion and Risk Premia 1.5 Constant Absolute Risk Aversion 1.6 Constant Relative Risk Aversion 1.7 Linear Risk Tolerance 1.8 Conditioning and Aversion to Noise 1.9 Notes and References Exercises 2 Portfolio Choice and Stochastic Discount Factors 2.1 The First-Order Condition 2.2 Stochastic Discount Factors 2.3 A Single Risky Asset 2.4 Linear Risk Tolerance 2.5 Multiple Asset CARA-Normal Example 2.6 Mean-Variance Preferences 2.7 Complete Markets 2.8 Beginning-of-Period Consumption 2.9 Time-Additive Utility 2.10 Notes and References Exercises 3 Equilibrium and Efficiency 3.1 Pareto Optima 3.2 Social Planner's Problem 3.3 Pareto Optima and Sharing Rules 3.4 Competitive Equilibria 3.5 Complete Markets 3.6 Linear Risk Tolerance 3.7 Beginning-of-Period Consumption 1 3.8 Notes and References Exercises 4 Arbitrage and Stochastic Discount Factors 4.1 Fundamental Theorem on Existence of SDF's 4.2 Law of One Price and Stochastic Discount Factors 4.3 Risk Neutral Probabilities 4.4 Projecting SDF's onto the Asset Span 4.5 Projecting onto a Constant and the Asset Span 4.6 Hansen-Jagannathan Bound with a Risk-Free Asset 4.7 Hansen-Jagannathan Bound with No Risk-Free Asset 4.8 Hilbert Spaces and Gram-Schmidt Orthogonalization 4.9 Notes and References Exercises 5 Mean-Variance Analysis 5.1 The Calculus Approach 5.2 Two-Fund Spanning 5.3 The Mean-Standard Deviation Trade-Off 5.4 GMV Portfolio and Mean-Variance Efficiency 5.5 Calculus Approach with a Risk-Free Asset 5.6 Two-Fund Spanning Again 5.7 Orthogonal Projections and Frontier Returns 5.8 Risk-Free Return Proxies 5.9 Inefficiency of ~Rp 5.10 Hansen-Jagannathan Bound with a Risk-Free Asset 5.11 Frontier Returns and Stochastic Discount Factors 5.12 Separating Distributions 5.13 Notes and References Exercises 6 Beta Pricing Models 6.1 Beta Pricing 6.2 Single-Factor Models with Returns as Factors 6.3 The Capital Asset Pricing Model 6.4 Returns and Excess Returns as Factors 6.5 Projecting Factors on Returns and Excess Returns 6.6 Beta Pricing and Stochastic Discount Factors 6.7 Arbitrage Pricing Theory 6.8 Notes and References Exercises 7 Representative Investors 7.1 Pareto Optimality Implies a Representative Investor 7.2 Linear Risk Tolerance 7.3 Consumption-Based Asset Pricing 7.4 Pricing Options 7.5 Notes and References Exercises II Dynamic Models 8 Dynamic Securities Markets 8.1 The Portfolio Choice Problem 8.2 Stochastic Discount Factor Processes 8.3 Self-Financing Wealth Processes 8.4 The Martingale Property 8.5 Transversality Conditions and Ponzi Schemes 8.6 The Euler Equation 8.7 Arbitrage and the Law of One Price 8.8 Risk Neutral Probabilities 8.9 Complete Markets 8.10 Portfolio Choice in Complete Markets 8.11 Competitive Equilibria 8.12 Notes and References Exercises 9 Portfolio Choice by Dynamic Programming 9.1 Introduction to Dynamic Programming 9.2 Bellman Equation for Portfolio Choice 9.3 The Envelope Condition 9.4 Maximizing CRRA Utility of Terminal Wealth 9.5 CRRA Utility with Intermediate Consumption 9.6 CRRA Utility with an Infinite Horizon 9.7 Notes and References Exercises 10 Conditional Beta Pricing Models 10.1 From Conditional to Unconditional Models 10.2 The Conditional CAPM 10.3 The Consumption-Based CAPM 10.4 The Intertemporal CAPM 10.5 An Approximate CAPM 10.6 Notes and References Exercises 11 Some Dynamic Equilibrium Models 11.1 Representative Investors 11.2 Valuing the Market Portfolio 11.3 The Risk-Free Return 11.4 The Equity Premium Puzzle 11.5 The Risk-Free Rate Puzzle 11.6 Uninsurable Idiosyncratic Income Risk 11.7 External Habits 11.8 Notes and References Exercises 12 Brownian Motion and Stochastic Calculus 12.1 Brownian Motion 12.2 Quadratic Variation 12.3 Ito Integral 12.4 Local Martingales and Doubling Strategies 12.5 Ito Processes 12.6 Asset and Portfolio Returns 12.7 Martingale Representation Theorem 12.8 Ito's Formula: Version I 12.9 Geometric Brownian Motion 12.10 Covariations of Ito Processes 12.11 Ito's Formula: Version II 12.12 Conditional Variances and Covariances 12.13 Transformations of Models 12.14 Notes and References Exercises 13 Continuous-Time Securities Markets and SDF Processes 13.1 Dividend-Reinvested Asset Prices 13.2 Securities Markets 13.3 Self-Financing Wealth Processes 13.4 Conditional Mean-Variance Frontier 13.5 Stochastic Discount Factor Processes 13.6 Properties of SDF Processes 13.7 Sufficient Conditions for MW to be a Martingale 13.8 Valuing Consumption Streams 13.9 Risk Neutral Probabilities 13.10 Complete Markets 13.11 SDF Processes without a Risk-Free Asset 13.12 Inflation and Foreign Exchange 13.13 Notes and References Exercises 14 Continuous-Time Portfolio Choice and Beta Pricing 14.1 The Static Budget Constraint 14.2 Complete Markets 12 CONTENTS 14.3 Constant Capital Market Line 14.4 Dynamic Programming Example 14.5 General Markovian Portfolio Choice 14.6 The CCAPM 14.7 The ICAPM 14.8 The CAPM 14.9 Infinite-Horizon Dynamic Programming 14.10 Dynamic Programming with CRRA Utility 14.11 Verification Theorem 14.12 Notes and References Exercises III Derivative Securities 15 Option Pricing 15.1 Introduction to Options 15.2 Put-Call Parity and Option Bounds 15.3 SDF Processes 15.4 Changes of Measure 15.5 Market Completeness 15.6 The Black-Scholes Formula 15.7 Delta Hedging 15.8 The Fundamental PDE 15.9 American Options 15.10 Smooth Pasting 15.11 European Options on Dividend-Paying Assets 15.12 Notes and References Exercises 16 Forwards, Futures, and More Option Pricing 16.1 Forward Measures 16.2 Forward Contracts 16.3 Futures Contracts 16.4 Exchange Options 16.5 Options on Forwards and Futures 16.6 Dividends and Random Interest Rates 16.7 Implied Volatilities and Local Volatilities 16.8 Stochastic Volatility 16.9 Notes and References Exercises 17 Term Structure Models 17.1 Vasicek Model 17.2 Cox-Ingersoll-Ross Model 17.3 Multi-Factor CIR Models 17.4 Affine Models 17.5 Completely Affine Models 17.6 Quadratic Models 17.7 Forward Rates 17.8 Fitting the Yield Curve 17.9 Heath-Jarrow-Morton Models 17.10 Notes and References Exercises IV Topics 18 Heterogeneous Priors 18.1 State-Dependent Utility Formulation 18.2 Representative Investors in Complete Single-Period Markets 18.3 Representative Investors in Complete Dynamic Markets 18.4 Short Sales Constraints and Biased Prices 18.5 Speculative Trade 18.6 Notes and References Exercises 19 Asymmetric Information 19.1 The No-Trade Theorem 19.2 Normal-Normal Updating 19.3 A Fully Revealing Equilibrium 19.4 Noise Trading and Partially Revealing Equilibria 19.5 A Model with a Large Number of Investors 19.6 The Kyle Model 19.7 The Kyle Model in Continuous Time 19.8 Notes and References Exercises 20 Alternative Preferences in Single-Period Models 20.1 The Ellsberg Paradox 20.2 The Sure Thing Principle 20.3 Multiple Priors and Max-Min Utility 20.4 Non-Additive Set Functions 20.5 The Allais Paradox 20.6 The Independence Axiom 20.7 Betweenness Preferences 20.8 Rank-Dependent Preferences 20.9 First-Order Risk Aversion 20.10 Framing and Loss Aversion 20.11 Prospect Theory 20.12 Notes and References Exercises 21 Alternative Preferences in Dynamic Models 21.1 Recursive Preferences 21.2 Portfolio Choice with Epstein-Zin-Weil Utility 21.3 A Representative Investor with Epstein-Zin-Weil Utility 21.4 Internal Habits 21.5 Linear Internal Habits in Complete Markets 21.6 A Representative Investor with an Internal Habit 21.7 Keeping/Catching Up with the Joneses 21.8 Ambiguity Aversion in Dynamic Models 21.9 Notes and References Exercises 22 Production Models 22.1 Discrete-Time Model 22.2 Marginal q 22.3 Costly Reversibility 22.4 Project Risk and Firm Risk 22.5 Irreversibility and Options 22.6 Irreversibility and Perfect Competition 22.7 Irreversibility and Risk 22.8 Irreversibility and Perfect Competition: An Example 22.9 Notes and References Exercises Appendices A Some Probability and Stochastic Process Theory A.1 Random Variables A.2 Probabilities A.3 Distribution Functions and Densities A.4 Expectations A.5 Convergence of Expectations A.6 Interchange of Differentiation and Expectation A.7 Random Vectors A.8 Conditioning A.9 Independence A.10 Equivalent Probability Measures A.11 Filtrations, Martingales, and Stopping Times A.12 Martingales under Equivalent Measures A.13 Local Martingales A.14 The Usual Conditions Notes References Index

About the Author

Kerry E. Back is J. Howard Creekmore Professor of Finance at the Jones School of Business at Rice University, and is the author of A Course in Derivative Securities: Introduction to Theory and Computation, as well as numerous journal articles in finance, economics, and mathematics.


"Kerry Back has created a masterful introduction to asset pricing and portfolio choice. It is easy to foresee this text becoming a new standard in finance PhD courses as well as a valued reference for seasoned finance scholars everywhere. The coverage of topics is comprehensive, starting in a single-period setting and then moving naturally to dynamic models in both discrete and continuous time. The numerous challenging exercises are yet another big strength. In short, an impressive achievement."--Robert F. Stambaugh, Miller Anderson & Sherrerd Professor of Finance, The Wharton School, University of Pennsylvania "Kerry Back offers us a rigorous, but accessible treatment of the asset pricing theory concepts that every doctoral student in finance should learn. A distinguished scholar in the field provides a presentation that is clear yet concise, and at the end of each chapter exercises that are an invaluable pedagogical tool for both students and instructors."--Eduardo Schwartz, California Chair in Real Estate and Land Economics, UCLA Anderson School of Management "In Asset Pricing and Portfolio Choice Theory Kerry Back has given us a comprehensive, rigorous and at the same time elegant and self-contained treatment of the important developments in this vast literature. It will be useful to graduate students and advanced undergraduate students in economics, finance, financial engineering, and management science as well as interested practitioners."--Ravi Jagannathan, Chicago Mercantile Exchange/John F. Sandner Professor of Finance and a Co-Director of the Financial Institutions and Markets Research Center, Kellogg School of Management, Northwestern University

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