Principles of Financial Economics

by Stephen F. LeRoy , Jan Werner , Foreword by Stephen A. Ross

• ISBN13: 9780521584340
• ISBN10: 0521584345
• Format: Hardcover
• Copyright: 2000-11-20
• Publisher: Cambridge University Press

Summary

This book introduces graduate students in economics to the subfield of financial economics. It stresses the link between financial economics and equilibrium theory, devoting less attention to purely financial topics such as valuation of derivatives. Since students often find this link hard to grasp, the treatment aims to make the connection explicit and clear in each stage of the exposition. Emphasis is placed on detailed study of two-date models, because almost all of the key ideas in financial economics can be developed in the two-date setting. The analysis is intended to be comparable in rigor to the best work in microeconomics; at the same time, the authors provide enough discussion and examples to make the ideas readily understandable.

Table of Contents

Foreword	xiii
Preface	xv
Part One Equilibrium and Arbitrage	1	(44)
Equilibrium in Security Markets	3	(12)
Introduction	3	(1)
Security Markets	4	(2)
Agents	6	(1)
Consumption and Portfolio Choice	6	(1)
First-Order Conditions	7	(1)
Left and Right Inverses of a Matrix	8	(1)
General Equilibrium	9	(1)
Existence and Uniqueness of Equilibrium	10	(1)
Representative Agent Models	11	(1)
Notes	11	(4)
Linear Pricing	15	(7)
Introduction	15	(1)
The Law of One Price	15	(1)
The Payoff Pricing Functional	15	(2)
Linear Equilibrium Pricing	17	(1)
State Prices in Complete Markets	18	(1)
Recasting the Optimization Problem	19	(2)
Notes	21	(1)
Arbitrage and Positive Pricing	22	(11)
Introduction	22	(1)
Arbitrage and Strong Arbitrage	22	(1)
Diagrammatic Representation	23	(3)
Positivity of the Payoff Pricing Functional	26	(1)
Positive State Prices	27	(1)
Arbitrage and Optimal Portfolios	27	(3)
Positive Equilibrium Pricing	30	(1)
Notes	30	(3)
Portfolio Restrictions	33	(12)
Introduction	33	(1)
Short Sales Restrictions	33	(2)
Portfolio Choice under Short Sales Restrictions	35	(1)
The Law of One Price	36	(1)
Limited and Unlimited Arbitrage	37	(1)
Diagrammatic Representation	38	(1)
Bid-Ask Spreads	39	(1)
Bid-Ask Spreads in Equilibrium	40	(2)
Notes	42	(3)
Part Two Valuation	45	(30)
Valuation	47	(9)
Introduction	47	(1)
The Fundamental Theorem of Finance	48	(1)
Bounds on the Values of Contingent Claims	49	(3)
The Extension	52	(2)
Uniqueness of the Valuation Functional	54	(1)
Notes	55	(1)
State Prices and Risk-Neutral Probabilities	56	(9)
Introduction	56	(1)
State Prices	56	(3)
Farkas--Stiemke Lemma	59	(1)
Diagrammatic Representation	60	(1)
State Prices and Value Bounds	60	(1)
Risk-Free Payoffs	61	(1)
Risk-Neutral Probabilities	61	(2)
Notes	63	(2)
Valuation under Portfolio Restrictions	65	(10)
Introduction	65	(1)
Payoff Pricing under Short Sales Restrictions	65	(2)
State Prices under Short Sales Restrictions	67	(3)
Diagrammatic Representation	70	(1)
Bid-Ask Spreads	70	(3)
Notes	73	(2)
Part Three Risk	75	(34)
Expected Utility	77	(10)
Introduction	77	(1)
Expected Utility	77	(1)
Von Neumann--Morgenstern	78	(1)
Savage	79	(1)
Axiomatization of State-Dependent Expected Utility	79	(1)
Axiomatization of Expected Utility	80	(2)
Nonexpected Utility	82	(1)
Expected Utility with Two-Date Consumption	83	(1)
Notes	84	(3)
Risk Aversion	87	(12)
Introduction	87	(1)
Risk Aversion and Risk Neutrality	87	(1)
Risk Aversion and Concavity	88	(2)
Arrow-Pratt Measures of Absolute Risk Aversion	90	(1)
Risk Compensation	90	(2)
Thge Pratt Theorem	92	(2)
Decreasing, Constant, and Increasing Risk Aversion	94	(1)
Relative Risk Aversion	94	(1)
Utility Functions with Linear Risk Tolerance	95	(1)
Risk Aversion with Two-Date Consumption	96	(1)
Notes	97	(2)
Risk	99	(10)
Introduction	99	(1)
Greater Risk	99	(1)
Uncorrelatedness, Mean Independence, and Independence	100	(1)
A Property of Mean Independence	101	(1)
Risk and Risk Aversion	101	(3)
Greater Risk and Variance	104	(2)
A Characterization of Greater Risk	106	(2)
Notes	108	(1)
Part Four Optimal Portfolios	109	(30)
Optimal Portfolios with One Risky Security	111	(7)
Introduction	111	(1)
Portfolio Choice and Wealth	111	(1)
Optimal Portfolios with One Risky Security	112	(2)
Risk Premium and Optimal Portfolios	114	(2)
Optimal Portfolios When the Risk Premium Is Small	116	(1)
Notes	117	(1)
Comparative Statics of Optimal Portfolios	118	(10)
Introduction	118	(1)
Wealth	118	(2)
Expected Return	120	(2)
Risk	122	(1)
Optimal Portfolios with Two-Date Consumption	123	(3)
Notes	126	(2)
Optimal Portfolios with Several Risky Securities	128	(11)
Introduction	128	(1)
Optimal Portfolios	128	(1)
Risk-Return Trade-Off	129	(1)
Optimal Portfolios under Fair Pricing	130	(1)
Risk Premia and Optimal Portfolios	131	(2)
Optimal Portfolios under Linear Risk Tolerance	133	(3)
Optimal Portfolios with Two-Date Consumption	136	(1)
Notes	136	(3)
Part Five Equilibrium Prices and Allocations	139	(30)
Consumption-Based Security Pricing	141	(6)
Introduction	141	(1)
Risk-Free Return in Equilibrium	141	(1)
Expected Returns in Equilibrium	142	(2)
Volatility of Marginal Rates of Substitution	144	(1)
A First Pass at the CAPM	145	(1)
Notes	146	(1)
Complete Markets and Pareto-Optimal Allocations of Risk	147	(10)
Introduction	147	(1)
Pareto-Optimal Allocations	147	(2)
Pareto-Optimal Equilibria in Complete Markets	149	(1)
Complete Markets and Options	150	(1)
Pareto-Optimal Allocations under Expected Utility	151	(2)
Pareto-Optimal Allocations under Linear Risk Tolerance	153	(2)
Notes	155	(2)
Optimality in Incomplete Security Markets	157	(12)
Introduction	157	(1)
Constrained Optimality	157	(1)
Effectively Complete Markets	158	(1)
Equilibria in Effectively Complete Markets	159	(3)
Effectively Complete Markets with No Aggregate Risk	162	(1)
Effectively Complete Markets with Options	163	(1)
Effectively Complete Markets with Linear Risk Tolerance	163	(2)
Multifund Spanning	165	(1)
A Second Pass at the CAPM	166	(1)
Notes	166	(3)
Part Six Mean-Variance Analysis	169	(48)
The Expectations and Pricing Kernels	171	(12)
Introduction	171	(1)
Hilbert Spaces and Inner Products	171	(1)
The Expectations Inner Product	172	(1)
Orthogonal Vectors	172	(1)
Orthogonal Projections	173	(2)
Diagrammatic Methods in Hilbert Spaces	175	(1)
Riesz Representation Theorem	176	(1)
Construction of the Riesz Kernel	177	(1)
The Expectations Kernel	178	(1)
The Pricing Kernel	179	(2)
Notes	181	(2)
The Mean-Variance Frontier Payoffs	183	(11)
Introduction	183	(1)
Mean-Variance Frontier Payoffs	183	(1)
Frontier Returns	184	(5)
Zero-Covariance Frontier Returns	189	(1)
Beta Pricing	190	(1)
Mean-Variance Efficient Returns	191	(1)
Volatility of Marginal Rates of Substitution	191	(2)
Notes	193	(1)
Capital Asset Pricing Model	194	(10)
Introduction	194	(1)
Security Market Line	194	(3)
Mean-Variance Preferences	197	(2)
Equilibrium Portfolios under Mean-Variance Preferences	199	(1)
Quadratic Utilities	200	(1)
Normally Distributed Payoffs	201	(1)
Notes	201	(3)
Factor Pricing	204	(13)
Introduction	204	(1)
Exact Factor Pricing	204	(2)
Exact Factor Pricing, Beta Pricing, and the CAPM	206	(1)
Factor Pricing Errors	207	(1)
Factor Structure	208	(2)
Mean-Independent Factor Structure	210	(2)
Options as Factors	212	(2)
Notes	214	(3)
Part Seven Multidate Security Markets	217	(28)
Equilibrium in Multidate Security Markets	219	(9)
Introduction	219	(1)
Uncertainty and Information	219	(3)
Multidate Security Markets	222	(1)
The Asset Span	223	(1)
Agents	224	(1)
Portfolio Choice and the First-Order Conditions	224	(1)
General Equilibrium	225	(1)
Notes	226	(2)
Multidate Arbitrage and Positivity	228	(5)
Introduction	228	(1)
Law of One Price and Linearity	228	(1)
Arbitrage and Positive Pricing	229	(1)
One-Period Arbitrage	230	(1)
Positive Equilibrium Pricing	230	(2)
Notes	232	(1)
Dynamically Complete Markets	233	(8)
Introduction	233	(1)
Dynamically Complete Markets	233	(1)
Binomial Security Markets	234	(1)
Event Prices in Dynamically Complete Markets	235	(1)
Event Prices in Binomial Security Markets	236	(1)
Equilibrium in Dynamically Complete Markets	237	(1)
Pareto-Optimal Equilibria	238	(1)
Notes	239	(2)
Valuation	241	(4)
Introduction	241	(1)
The Fundamental Theorem of Finance	241	(3)
Uniqueness of the Valuation Functional	244	(1)
Notes	244	(1)
Part Eight Martingale Property of Security Prices	245	(32)
Event Prices, Risk-Neutral Probabilities, and the Pricing Kernel	247	(11)
Introduction	247	(1)
Event Prices	247	(3)
Risk-Free Return and Discount Factors	250	(1)
Risk-Neutral Probabilities	250	(2)
Expected Returns under Risk-Neutral Probabilities	252	(1)
Risk-Neutral Valuation	253	(1)
Value Bounds	254	(1)
The Pricing Kernel	255	(1)
Notes	256	(2)
Security Gains as Martingales	258	(6)
Introduction	258	(1)
Gain and Discounted Gain	258	(2)
Discounted Gains as Martingales	260	(1)
Gains as Martingales	261	(1)
Notes	262	(2)
Conditional Consumption-Based Security Pricing	264	(7)
Introduction	264	(1)
Expected Utility	264	(1)
Risk Aversion	265	(1)
Conditional Covariance and Variance	266	(1)
Consumption-Based Security Pricing	266	(2)
Security Pricing under Time Separability	268	(1)
Volatility of Intertemporal Marginal Rates of Substitution	269	(1)
Notes	269	(2)
Conditional Beta Pricing and the CAPM	271	(6)
Introduction	271	(1)
Two-Date Security Markets at a Date-t Event	271	(1)
Conditional Beta Pricing	272	(2)
Conditional CAPM with Quadratic Utilities	274	(1)
Multidate Market Return	275	(1)
Conditional CAPM with Incomplete Markets	276	(1)
Notes	276	(1)
Index	277