Arbitrage: Elements of Financial Economics

175 Pages·1991·9.03 MB·English

by  Michael Allingham (auth.)

ARBITRAGE
Also by Michael Allingham and published by
Palgrave Macmillan
GENERAL EQUILIBRIUM
THEORY OF MARKETS
VALUE
Arbitrage
Elements of Financial Economics
Michael Allingham
Professor of Economic Theory
University of Kent
M
MACMILLAN
© Michael Allingham 1991
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First published 1991
Published by
MACMILLAN ACADEMIC AND PROFESSIONAL LT D
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and London
Companies and representatives
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Edited and typeset by PoveyfEdmondson
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Printed in Great Britain by
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British Library Cataloguing in Publication Data
Allingham, Michael
Arbitrage: Elements of Financial Economics.
1. Investments: Securities
I. Title
332.632
ISBN 978-0-333-55781-5 ISBN 978-1-349-21385-6 (eBook)
DOI 10.1007/978-1-349-21385-6
Contents
Preface Vlll
PART I FOUNDATIONS
1 Securities and Arbitrage 3
Financial economics 3
Dates and states 4
Securities 6
The securities market 8
Prices and arbitrage 10
Appendix l3
Bibliography 15
2 The Basic Arbitrage Theorem 17
Arbitrage portfolios 17
State prices 22
The martingale property 25
Many periods 28
Corporate securities 34
Evidence 37
Appendix 39
Bibliography 44
PART 11 A SINGLE PERIOD
3 Exact Arbitrage: A Capital Asset Pricing Model 47
A pricing relation 47
Units of value 50
The security market line 52
The capital market li ne 55
v
vi Contents
Evidence 60
Fund evaluation 64
Appendix 66
Bibliography 67
4 Approximate Arbitrage: The Arbitrage Pricing
Technique 69
An exact factor model 69
Mean-variance efficiency 73
An approximate factor model 75
Units of value 78
Infinite markets 81
Evidence 85
Portfolio selection 89
Appendix 92
Bibliography 96
PART 111 MANY PERIODS
5 Static Arbitrage: Futures 101
Forward contracts 101
Futures contracts 106
Forward-futures equivalence 110
Evidence 115
Synthetic indexation 117
Bibliography 118
6 Dynamic Arbitrage: Options 119
Calls and puts 119-
A pricing formula 129
American options 139
Futures options 148
Corporate securities revisited 154
Evidence 157
Portfolio insurance 159
Bibliography 161
Contents vii
7 Information Arbitrage: Market Efficiency 163
The efficient market hypothesis 163
Evidence 165
Weak and strong efficiency 165
Bibliography 167
Index 169
Preface
This book uses the concept of arbitrage to value securities,
that is, to construct the elements of financial economics.
The importance of arbitrage in the context of certainty has
long been recognised: it is, for example discussed in detail in
Walras's Elements 0/ Pure Economics of 1874. But its use in
the absence of certainty, and thus in financial economics, is a
more recent development, originating (at least explicitly) in
the work of Black and Scholes on options in 1973. In this
context it provides an alternative to the concept of equi
librium which has provided the central paradigm of financial
economics since the development of the capital asset pricing
model by Sharpe and Lintner in 1964 and 1965.
The book is divided into three parts. Part I develops the
foundations for the study: it introduces the concepts of
securities and arbitrage (Chapter 1) and establishes the basic
arbitrage theorem, that security prices may be expressed as
expected discounted values (Chapter 2). Part II applies the
basic theorem in a single-period setting: it develops aversion
of the capital asset pricing model under exact arbitrage
(Chapter 3) and the arbitrage pricing technique under
approximate arbitrage (Chapter 4). Part III extends the
discussion to a many-period setting: it uses static arbitrage
to value futures and related securities (Chapter 5), dynamic
arbitrage to value options and other derivatives (Chapter 6),
and, as a coda, information arbitrage to investigate market
efficiency (Chapter 7).
Within each chapter the basic theory is developed quite
comprehensively, while empirical evidence and applications
are discussed more selectively. The presentation assumes an
understanding of only the most basic concepts of mathe
matics and statistics, detailed references being provided in the
few instances where more advanced concepts are introduced.
An appendix to the chapter discusses any connection with the
viii
Preface IX
equilibrium approach to the subject, while works drawn on,
and related works, are listed in the chapter's bibliography.
MICHAEL ALLINGHAM