Asset Pricing and Portfolio Choice Theory

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 ; 17 Term Structure Models ; 17.1 Vasicek Model ; 17.2 Cox-Ingersoll-Ross Model ; 17.3 Multi-Factor CIR Models ; 17.4 Affine Models ; 1 ; 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 ; 19.5 A Model with a Large Number of Investors ; 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