Asset Pricing and Portfolio Choice Theory

In Asset Pricing and Portfolio Choice Theory, Kerry E. Back at last offers what is at once a welcoming introduction to and a comprehensive overview of asset pricing. Useful as a textbook for graduate students in finance, with extensive exercises and a solutions manual available for professors, the book will also serve as an essential reference for scholars and professionals, as it includes detailed proofs and calculations as section appendices.Topics covered include the classical results on single-period, discrete-time, and continuous-time models, as well as various proposed explanations for the equity premium and risk-free rate puzzles and chapters on heterogeneous beliefs, asymmetric information, non-expected utility preferences, and production models. The book includes numerous exercises designed to provide practice with the concepts and to introduce additional results. Each chapter concludes with a notes and references section that supplies pathways to additional developments in the field.

In Asset Pricing and Portfolio Choice Theory, Kerry E. Back at last offers what is at once a welcoming introduction to and a comprehensive overview of asset pricing. Useful as a textbook for graduate students in finance, with extensive exercises and a solutions manual available for professors, the book will also serve as an essential reference for scholars and professionals, as it includes detailed proofs and calculations as section appendices. Topics covered include the classical results on single-period, discrete-time, and continuous-time models, as well as various proposed explanations for the equity premium and risk-free rate puzzles and chapters on heterogeneous beliefs, asymmetric information, non-expected utility preferences, and production models. The book includes numerous exercises designed to provide practice with the concepts and to introduce additional results. Each chapter concludes with a notes and references section that supplies pathways to additional developments in the field.

PrefaceI Single-Period Models1 Utility Functions and Risk Aversion Coefficients1.1 Uniqueness of Utility Functions1.2 Concavity and Risk Aversion1.3 Coefficients of Risk Aversion1.4 Risk Aversion and Risk Premia1.5 Constant Absolute Risk Aversion1.6 Constant Relative Risk Aversion1.7 Linear Risk Tolerance1.8 Conditioning and Aversion to Noise1.9 Notes and ReferencesExercises2 Portfolio Choice and Stochastic Discount Factors2.1 The First-Order Condition2.2 Stochastic Discount Factors2.3 A Single Risky Asset2.4 Linear Risk Tolerance2.5 Multiple Asset CARA-Normal Example2.6 Mean-Variance Preferences2.7 Complete Markets2.8 Beginning-of-Period Consumption2.9 Time-Additive Utility2.10 Notes and ReferencesExercises3 Equilibrium and Efficiency3.1 Pareto Optima3.2 Social Planner's Problem3.3 Pareto Optima and Sharing Rules3.4 Competitive Equilibria3.5 Complete Markets3.6 Linear Risk Tolerance3.7 Beginning-of-Period Consumption 13.8 Notes and ReferencesExercises4 Arbitrage and Stochastic Discount Factors4.1 Fundamental Theorem on Existence of SDF's4.2 Law of One Price and Stochastic Discount Factors4.3 Risk Neutral Probabilities4.4 Projecting SDF's onto the Asset Span4.5 Projecting onto a Constant and the Asset Span4.6 Hansen-Jagannathan Bound with a Risk-Free Asset4.7 Hansen-Jagannathan Bound with No Risk-Free Asset4.8 Hilbert Spaces and Gram-Schmidt Orthogonalization4.9 Notes and References Exercises5 Mean-Variance Analysis5.1 The Calculus Approach5.2 Two-Fund Spanning5.3 The Mean-Standard Deviation Trade-Off5.4 GMV Portfolio and Mean-Variance Efficiency5.5 Calculus Approach with a Risk-Free Asset5.6 Two-Fund Spanning Again5.7 Orthogonal Projections and Frontier Returns5.8 Risk-Free Return Proxies5.9 Inefficiency of ~Rp5.10 Hansen-Jagannathan Bound with a Risk-Free Asset5.11 Frontier Returns and Stochastic Discount Factors5.12 Separating Distributions5.13 Notes and ReferencesExercises6 Beta Pricing Models6.1 Beta Pricing6.2 Single-Factor Models with Returns as Factors6.3 The Capital Asset Pricing Model6.4 Returns and Excess Returns as Factors6.5 Projecting Factors on Returns and Excess Returns6.6 Beta Pricing and Stochastic Discount Factors6.7 Arbitrage Pricing Theory6.8 Notes and ReferencesExercises7 Representative Investors7.1 Pareto Optimality Implies a Representative Investor7.2 Linear Risk Tolerance7.3 Consumption-Based Asset Pricing7.4 Pricing Options7.5 Notes and ReferencesExercisesII Dynamic Models8 Dynamic Securities Markets8.1 The Portfolio Choice Problem8.2 Stochastic Discount Factor Processes8.3 Self-Financing Wealth Processes8.4 The Martingale Property8.5 Transversality Conditions and Ponzi Schemes8.6 The Euler Equation8.7 Arbitrage and the Law of One Price8.8 Risk Neutral Probabilities8.9 Complete Markets8.10 Portfolio Choice in Complete Markets8.11 Competitive Equilibria8.12 Notes and ReferencesExercises9 Portfolio Choice by Dynamic Programming9.1 Introduction to Dynamic Programming9.2 Bellman Equation for Portfolio Choice9.3 The Envelope Condition9.4 Maximizing CRRA Utility of Terminal Wealth9.5 CRRA Utility with Intermediate Consumption9.6 CRRA Utility with an Infinite Horizon9.7 Notes and ReferencesExercises10 Conditional Beta Pricing Models10.1 From Conditional to Unconditional Models10.2 The Conditional CAPM10.3 The Consumption-Based CAPM10.4 The Intertemporal CAPM10.5 An Approximate CAPM10.6 Notes and ReferencesExercises11 Some Dynamic Equilibrium Models11.1 Representative Investors11.2 Valuing the Market Portfolio11.3 The Risk-Free Return11.4 The Equity Premium Puzzle11.5 The Risk-Free Rate Puzzle11.6 Uninsurable Idiosyncratic Income Risk11.7 External Habits11.8 Notes and ReferencesExercises12 Brownian Motion and Stochastic Calculus12.1 Brownian Motion12.2 Quadratic Variation12.3 It? Integral12.4 Local Martingales and Doubling Strategies12.5 It? Processes12.6 Asset and Portfolio Returns12.7 Martingale Representation Theorem12.8 It?'s Formula: Version I12.9 Geometric Brownian Motion12.10 Covariations of It? Processes12.11 It?'s Formula: Version II12.12 Conditional Variances and Covariances12.13 Transformations of Models12.14 Notes and ReferencesExercises13 Continuous-Time Securities Markets and SDF Processes13.1 Dividend-Reinvested Asset Prices13.2 Securities Markets13.3 Self-Financing Wealth Processes13.4 Conditional Mean-Variance Frontier13.5 Stochastic Discount Factor Processes13.6 Properties of SDF Processes13.7 Sufficient Conditions for MW to be a Martingale13.8 Valuing Consumption Streams13.9 Risk Neutral Probabilities13.10 Complete Markets13.11 SDF Processes without a Risk-Free Asset13.12 Inflation and Foreign Exchange13.13 Notes and ReferencesExercises14 Continuous-Time Portfolio Choice and Beta Pricing14.1 The Static Budget Constraint14.2 Complete Markets12 CONTENTS14.3 Constant Capital Market Line14.4 Dynamic Programming Example14.5 General Markovian Portfolio Choice14.6 The CCAPM14.7 The ICAPM14.8 The CAPM14.9 Infinite-Horizon Dynamic Programming14.10 Dynamic Programming with CRRA Utility14.11 Verification Theorem14.12 Notes and ReferencesExercisesIII Derivative Securities15 Option Pricing15.1 Introduction to Options15.2 Put-Call Parity and Option Bounds15.3 SDF Processes15.4 Changes of Measure15.5 Market Completeness15.6 The Black-Scholes Formula15.7 Delta Hedging15.8 The Fundamental PDE15.9 American Options15.10 Smooth Pasting15.11 European Options on Dividend-Paying Assets15.12 Notes and ReferencesExercises16 Forwards, Futures, and More Option Pricing16.1 Forward Measures16.2 Forward Contracts16.3 Futures Contracts16.4 Exchange Options16.5 Options on Forwards and Futures16.6 Dividends and Random Interest Rates16.7 Implied Volatilities and Local Volatilities16.8 Stochastic Volatility16.9 Notes and ReferencesExercises17 Term Structure Models17.1 Vasicek Model17.2 Cox-Ingersoll-Ross Model17.3 Multi-Factor CIR Models17.4 Affine Models17.5 Completely Affine Models17.6 Quadratic Models17.7 Forward Rates17.8 Fitting the Yield Curve17.9 Heath-Jarrow-Morton Models17.10 Notes and ReferencesExercisesIV Topics18 Heterogeneous Priors18.1 State-Dependent Utility Formulation18.2 Representative Investors in Complete Single-Period Markets18.3 Representative Investors in Complete Dynamic Markets18.4 Short Sales Constraints and Biased Prices18.5 Speculative Trade18.6 Notes and ReferencesExercises19 Asymmetric Information19.1 The No-Trade Theorem19.2 Normal-Normal Updating19.3 A Fully Revealing Equilibrium19.4 Noise Trading and Partially Revealing Equilibria19.5 A Model with a Large Number of Investors19.6 The Kyle Model19.7 The Kyle Model in Continuous Time19.8 Notes and ReferencesExercises20 Alternative Preferences in Single-Period Models20.1 The Ellsberg Paradox20.2 The Sure Thing Principle20.3 Multiple Priors and Max-Min Utility20.4 Non-Additive Set Functions20.5 The Allais Paradox20.6 The Independence Axiom20.7 Betweenness Preferences20.8 Rank-Dependent Preferences20.9 First-Order Risk Aversion20.10 Framing and Loss Aversion20.11 Prospect Theory20.12 Notes and ReferencesExercises21 Alternative Preferences in Dynamic Models21.1 Recursive Preferences21.2 Portfolio Choice with Epstein-Zin-Weil Utility21.3 A Representative Investor with Epstein-Zin-Weil Utility21.4 Internal Habits21.5 Linear Internal Habits in Complete Markets21.6 A Representative Investor with an Internal Habit21.7 Keeping/Catching Up with the Joneses21.8 Ambiguity Aversion in Dynamic Models21.9 Notes and ReferencesExercises22 Production Models22.1 Discrete-Time Model22.2 Marginal q22.3 Costly Reversibility22.4 Project Risk and Firm Risk22.5 Irreversibility and Options22.6 Irreversibility and Perfect Competition22.7 Irreversibility and Risk22.8 Irreversibility and Perfect Competition: An Example22.9 Notes and ReferencesExercisesAppendicesA Some Probability and Stochastic Process TheoryA.1 Random VariablesA.2 ProbabilitiesA.3 Distribution Functions and DensitiesA.4 ExpectationsA.5 Convergence of ExpectationsA.6 Interchange of Differentiation and ExpectationA.7 Random VectorsA.8 ConditioningA.9 IndependenceA.10 Equivalent Probability MeasuresA.11 Filtrations, Martingales, and Stopping TimesA.12 Martingales under Equivalent MeasuresA.13 Local MartingalesA.14 The Usual ConditionsNotesReferencesIndex