Financial Markets Theory: Equilibrium, Efficiency and Information

472 Pages·2003·16.307 MB·English

by  Emilio Barucci (auth.)

Springer Finance
Editorial Board
M. Avellaneda
G. Barone-Adesi
M.Broadie
M.H.A. Davis
c. Klilppelberg
E.Kopp
W. Schachermayer
Springer-Verlag London Ltd.
Springer Finance
Springer Finance is a programme of books aimed at students, academics and
practitioners working on increasingly technical approaches to the analysis of
financial markets. It aims to cover a variety of topics, not only mathematical
finance but foreign exchanges, term structure, risk management, portfolio
theory, equity derivatives, and financial economics.
M. Amman, Credit Risk Valuation: Methods, Models, and Application (2001)
N.H. Bingham and R. Kiesel, Risk-Neutral Valuation: Pricing and Hedging of Financial
Derivatives (1998)
T.R. Bielecki and M. Rutkowski, Credit Risk: Modeling, Valuation and Hedging (2001)
D. Brigo amd F. Mercurio, Interest Rate Models: Theory and Practice (2001)
R. Buff, Uncertain Volatility Models - Theory and Application (2002)
G. Deboeck and T. Kohonen (Editors), Visual Explorations in Finance with Self
Organizing Maps (1998)
R.I. Elliott and P.E. Kopp, Mathematics of Financial Markets (1999)
H. Geman, D. Madan, S.R. Pliska and T. Vorst (Editors), Mathematical Finance
Bachelier Congress 2000 (2001)
Y.-K. Kwok, Mathematical Models of Financial Derivatives (1998)
A. Pelsser, Efficient Methods for Valuing Interest Rate Derivatives (2000)
M. Yor, Exponential Functionals of Brownian Motion and Related Processes (2001)
R. Zagst, Interest-Rate Management (2002)
R.A. Dana and M. /eanblanc, Financial Markets in Continuous Time (2002)
Emilio Barucci
Financial Markets
Theory
Equilibrium, Efficiency and Information
With 14 Figures
, Springer
Emilio Barucci
Dipartimento di Statistica e matematica applicata all'economia
Universita di Pisa
Italy
British Library Cataloguing in Publication Data
Barucci, Emilio
Financial markets theory : equilibrium, efficiency and
information. - (Springer finance)
1. Finance - Mathematical models
I. Title
332'.015118
ISBN 978-1-4471-1093-4 ISBN 978-1-4471-0089-8 (eBook)
DOI 10.1007/978-1-4471-0089-8
Library of Congress Cataloging-in-Publication Data
A catalog record for this book is available from the Library of Congress
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Springer Finance series ISSN 1616-0533
ISBN 978-1-4471-1093-4
http://www.springer.co.uk
© Springer-Verlag London 2003
Originally published by Springer-Verlag London Limited in 2003
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To Teresa and my Parents
Preface
Non domandarci la formula che mondi possa aprirti,
sl qualche stortasillaba esecca come un ramo.
Codesto solo oggi possiamo dirti,
do do
che non siamo, che non vogliamo.
Eugenio Montale Ossi di Seppia (1925)
Thisisjustanotherbook onfinancial markets theory.Why anotherbook?
Most ofthetime an authorwillanswer thattherewasnobook coveringthe
same topics with the same approach.This is also my answer. Organizingmy
lectures for an advanced financial markets theory course, I tried to make my
students understand how financial markets theory was a body in continuous
transformation animated both by a rich theoretical debate and by a strict
interaction with real financial markets. I did not find a book with such an
approach and so I decided to write this one. I hope my students were and
will be fascinated by the picture.
Thebookisdriven bytwoperspectives:onthe oneside the theoreticalde
bate about financial markets and agent's behaviour under risk, on the other
the comparison of theoretical results with the empirical evidence. I intend
to highlight how financial markets theory has developed during the last fifty
years along these two perspectives. The first one has been a driving force
for a long time, my personal reconstruction ofthe development ofthe theory
includes Bachelier (1900), Arrow (1953), Modigliani and Miller (1958), De
breu (1959),Sharpe (1964), Lintner (1965),Black and Scholes (1973), LeRoy
(1973), Merton (1973),Jensen and Meckling (1976), Rubinstein (1976),Ross
(1977), Lucas (1978), Harrison and Kreps (1979), and Grossman (1981). As
a matteroffact, the classical asset pricing theory wasalmost fully developed
bythemid-1980s, thedebatethen turned to the empiricalevidenceand hence
the second perspective came into play. Results are mixed with some puzzles
still alive after 20years.These puzzles generateda debate with developments
inside the classical asset pricing theory as wellas outside with an attempt to
build alternative paradigms (e.g. behavioural finance). Classical asset pric
ing theory tries to explain asset pricing anomalies by changing agent's pref
erences, probability distributions for fundamentals, economic environment
maintaining its traditional pillars, i.e. agents' rationality, equilibrium or no
arbitrage arguments, rational expectations. According to the classical asset
pricing theory, asset prices are explained through risk factors related to as-
viii Preface
set fundamentals. On the other hand, behavioural finance tries to build an
alternative paradigm by relaxingsome hypotheses on agents' rationality and
introducing market frictions. The debate on asset pricing puzzles is one of
the main topics of the book. On this point we followthe Kuhn (1970) per
spective: a paradigm has never been rejected by falsification through direct
comparison with the real world, a new paradigm should be accepted.
The book is organized as follows, Chapters 2-7and Chapter 10cover the
so-called classical asset pricing theory comprehensive of corporate finance
and models with heterogeneous-private information. We present theoretical
results together with their empirical evidence. Chapters 8, 9 and 11 are de
voted to analysing the assumptions made in previous chapters, to discussing
their relevance, how they arecrucial,and to presenting recent developments.
We will show how recent developments address asset pricing puzzles. Our
approach is inspired by the Solow (1956) quotation placed at the beginning
of Chapter l.
Chapter 1 presents some prerequisities useful in the analysis. Results on
decision theory, general equilibrium theory and welfare analysis under cer
tainty are illustrated. The aim of this chapter is to render the book self
contained as far as economic analysis is concerned.
Chapter 2deals with decision theory under risk. Expected utility theory,
risk aversion, portfoliochoicesand insurancedemand are analyed.Thegoal is
to fully understand the behaviour of an agent under risk given some param
eters (prices, returns). Given the (budget) constraint, the agent maximizes
his expected utility (substantial rationality).
Chapter3presents some classical results on stochastic dominance, mean
variance analysis including the construction of the mean-variance frontier,
and mutual funds separation results.
In Chapter 4, we address agents' interaction in a perfectly competitive
financial market. Weare interested in two main topics: Pareto optimality of
equilibrium allocations and asset pricing results (risk premia). We use two
main tools: equilibrium analysis and no arbitrage analysis. The notion of
rational expectations equilibrium is introduced. A key point is the market
completeness assumption. The fundamental asset pricing theorem and risk
neutral evaluation are fully analyed.
In Chapter 5 the Capital Asset Pricing Model and the Arbitrage Pricing
Theory are presented theoretically and are discussed from an empirical point
of view. (Firm specific) anomalies in asset return risk premia are discussed.
Chapter 6extends equilibrium and no arbitrageanalysis to a multiperiod
setting. Efficiency of the equilibrium allocation is investigated as wellas the
fundamental asset pricingtheorem. Asset time series implications are derived
and compared with the empirical evidence. Evidence on return autocorrela
tion, the equity premium puzzle and the risk free puzzle are investigated.
Preface ix
Chapter 7analyses financial markets assuming heterogeneous-privatein
formation. We investigate how prices transmit and aggregate private infor
mation providing a microfoundation to the efficientmarket theory.
Chapter 8 deals with the hypotheses considered in Chapters 1-7 about
probability, agent's preferences representation, agent's rationality, frictions,
marketincompleteness. Wepresentdevelopmentsofthe classicalasset pricing
theory as well as theories relaxing agent's rationality (behavioural finance).
We evaluate the robustness of the results and how each piece of theory ad
dresses asset pricing puzzles and results already explained by the classical
asset pricing theory.
Chapter 9 is devoted to financial markets assuming a non-perfectly com
petitivemarket. Perfect competition is far awayfrom real financial markets.
They are characterized by a precise microstructure and institutional setting
involvingdealers, brokers, specialists and financial intermediaries. Weintend
to analyse how the functioning of the market is affected by its architecture,
the crucial point is the diffusion-aggregation ofinformation and liquidity.
Chapter 10concerns corporatefinance.Wepresent the Modigliani-Miller
theorem as wellas recent developments based oninformationasymmetry and
agency models. Chapter 11deals with financial intermediation and financial
market regulation-design. Most of the theory in previous chapters assumes
atomistic agents, financial intermediation substantially changes the picture.
The book is an adventure in modern financial markets theory with two
plots: theoretical developments and real financial markets. There are two ac
tors: classical asset pricing theory and heretics. Conclusions on the status
of the theory are left to the reader. My personal belief is that classical as
set pricing theory is a strong and flexibleparadigm. Many anomalies can be
reinterpreted inside the paradigm, but some of them are hard to kill. On
the other hand, behavioural finance and alternative approaches provide use
ful insights into understand real financial markets day by day, but they are
not an alternative paradigm. Agent's rationality is a simplification ofhuman
behaviour and therefore some anomalies are expected.
The book can be used inseveral ways.It isan advanced financial markets
theory textbook and it provides a handbook on recent developments of the
literature. The book covers a wide spectrum of topics. We are not going
to deal with mathematical finance topics (option pricing, term structure,
interest rate derivatives) because in our viewthey are mainly an application
of the fundamental asset pricing theorem; there are many interesting and
hard to solve problems in this field, but they are mainly technical problems.
We handle the topics in the simplest setting (finite states-discrete time).
Some parts of the book have been heavily inspired by Barucci (2000). The
book owes a debt to Huang and Litzenberger (1988), which introduced me
to the economic analysis of financial markets. I strongly believe that the
advancement ofthe theory willbe driven in the future by economic analysis,
empirical evidence and the incorporation of the institutional setting in the
x Preface
picture. This book testifies this belief. I hope the reader willfind interesting
hints in reading the book.
It took five years to complete this book. During these years, the book
has been a living companion for me with frustrations, worries, and many
other emotions, now it is only printed paper. I have to thank many for their
encouragement and help. First of all I would liketo thank all my coauthors
for having contributed a lot to this book. lowe enormous intellectual debt
to them. Special thanks to Maria Elvira Mancino for her encouragement.
I would like to thank my colleagues at the University of Pisa, and Bruce
Marshall, and Claudia Neri for carefully reading the final manuscript. The
book is first of all dedicated to my students in the past and in the future,
to their enthusiasm which is a strong motivation for a teacher. The book is
dedicated to all who sympathized, sympathize, or willsympathize with me,
in particular my parents, Teresa and those who are not with me anymore.
Emilio Barucci
Firenze-Pisa
September 2002
Contents
1 Prerequisites ............................................. 1
1.1 Choices under Certainty. ................................ 1
1.2 General Equilibrium Theory. ............................ 4
1.3 Pareto Optimality ...................................... 8
2 Choices under Risk ....................................... 13
2.1 Expected Utility Theory ,....... 16
2.2 Risk Aversion " 19
2.3 Portfolio Problem 25
2.4 Insurance Demand and Prudence ......................... 34
2.5 Notes, References and Exercises .......................... 39
3 Stochastic Dominance, Mutual Funds Separation and
Portfolio Frontier ......................................... 43
3.1 Stochastic Dominance................................... 44
3.2 Mean-Variance Analysis. ................................ 48
3.3 Portfolio Frontier (risky assets) ........................... 50
3.4 Portfolio Frontier (risky assets and a risk free asset) 58
3.5 Mutual Funds Separation. ............................... 65
3.6 Notes, References and Exercises.. ........................ 69
4 General Equilibrium Theory and Risk Exchange. ......... 71
4.1 Risk Sharing and Pareto Optimality 74
4.2 Asset Markets.......................................... 80
4.3 Intertemporal Consumption. ............................. 88
4.4 The Fundamental Asset Pricing Theorem I 96
4.5 Notes, References and Exercises 106
5 Risk Premium: Capital Asset Pricing Model and Asset
Pricing Theory 111
5.1 Capital Asset Pricing Model (CAPM) 112
5.2 Empirical Tests ofthe CAPM 120
5.3 Arbitrage Pricing Theory (APT) 130
5.4 Empirical Tests ofthe APT 137
5.5 Notes, References and Exercises 140
6 Multiperiod Market Models 143
6.1 Portfolio Choice, Consumption and Equilibrium 146
6.2 The Fundamental Asset Pricing Theorem II 160
6.3 Risk Premium and Factor Models 169
6.4 The No Arbitrage Fundamental Equation and Bubbles 174
6.5 Empirical Tests: Price-Dividend Process 179
6.6 Empirical Tests: CCAPM,ICAPM and Risk Premium 206