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Quantitative Financial Economics

SERIES IN

FINANCIAL ECONOMICS

AND QUANTITATIVEANALYSIS

Stephen Hall, London Business School, UK

Series Editor:

Editorial Board: Robert F. Engle, University of California, USA

John Flemming, European Bank, UK

Lawrence R. Klein, University of Pennsylvania, USA

Helmut Liitkepohl, Humboidt University, Germany

The Economics of Pensions and Variable Retirement Schemes

Oliver Fabel

Applied General Equilibrium Modelling:

Imperfect Competition and European Integration

Dirk Willenbockel

Housing, Financial Markets and the Wider Economy

David Miles

Maximum Entropy Econometrics: Robust Estimation with Limited Data

Amos Golan, George Judge and Douglas Miller

Estimating and Interpreting the Yield Curve

Nicola Anderson, Francis Breedon, Mark Deacon,

Andrew D e r v and Gareth Murphy

Further titles in preparation

Proposals will be welcomed by the Series Editor

L Quantitative Financial Economi

Stocks, Bonds and Foreign Exchange

Keith Cuthbertson

Newcastle upon Tyne University

and

City University Business School

JOHN WILEY & SONS

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Reprinted December 1996, August 1997, September 1999

All Rights Reserved. No part of this book may be reproduced, stored in a retrieval system, o

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terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by

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Data

Library of Congress Caf˜ging-in-Publicafion

Cuthbertson, Keith.

Quantitative financial economics : stocks, bonds, and foreign

exchange / Keith Cuthbertson.

cm. - (Series in financial economics and quantitative

p:

analysis)

Includes bibliographical references and index.

ISBN 0-471-95359-8 (cloth). - ISBN 0-471-95360-1 (pbk.)

1. Investments - Mathematical models. 2. Capital assets pricing

model. 3. Stocks - Mathematical models. 4. Bonds - Mathematical

models. 5 . Foreign exchange - Mathematical models. I. Title.

11. Series.

HG4515.2.C87 1996

95 - 48355

332.6 - dc20

CIP

British Library Cataloguing in Publicafion Data

A catalogue record for this book is available from the British Library

ISBN 0-471-95359-8 (Cased) 0-471-95360-1 (Paperback)

Typeset in 10/12pt Times Roman by Laser Words, India

Printed and bound in Great Britain by Bookcraft (Bath) Ltd, Avon

This book is printed on acid-free paper responsibly manufactured from sustainable

forestation, for which at least two trees are planted for each one used for paper production.

I

Dedication

To June

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Contents

Series Preface

Introduction

Acknowledgements

Part 1 Returns and Valuation

1 Basic Concepts in Finance

1.1 Returns on Stocks, Bonds and Real Assets

1.2 Utility and Indifference Curves

1.3 Physical Investment Decisions and Optimal Consumption

1.4 Summary

Endnotes

2 The Capital Asset Pricing Model: CAPM

2.1 An Overview

2.2 Portfolio Diversification, Efficient Frontier and

the Transformation Line

2.3 Derivation of the CAPM

2.4 Summary

Appendix 2.1 Derivation of the CAPM

3 Modelling Equilibrium Returns

3.1 Extensions of the CAPM

3.2 A Simple Mean-Variance Model of Asset Demands

3.3 Performance Measures

3.4 The Arbitrage Pricing Theory (APT)

3.5 Testing the Single Index Model, the CAPM and the APT

3.6 Summary

4 Valuation Models

4.1 The Rational Valuation Formula (RVF)

4.2 Summary

Endnotes

Further Reading

5.2 Implications of the EMH

5.3 Expectations, Martingales and Fair Game

5.4 Testing the EMH

5.5 Summary

Endnotes

Empirical Evidence on Efficiency in the Stock Market

6.1 Predictability in Stock Returns

6.2 Volatility Tests

6.3 Summary

Endnotes

Appendix 6.1

Rational Bubbles

7.1 Euler Equation and the Rational Valuation Formula

7.2 Tests of Rational Bubbles

7.3 Intrinsic Bubbles

7.4 Summary

Endnotes

Anomalies, Noise Traders and Chaos

8.1 The EMH and Anomalies

8.2 Noise Traders

8.3 Chaos

8.4 Summary

Appendix 8.1

Appendix 8.2

Endnote

Further Reading

Part 3 The Bond Market

9 Bond Prices and the Term Structure of Interest Rates

9.1 Prices, Yields and the RVF

9.2 Theories of the Term Structure

9.3 Summary

Endnotes

10 Empirical Evidence on the Term Structure

10.1 The Behaviour of Rates of Return

10.2 Pure Discount Bonds

10.3 Coupon Paying Bonds: Bond Prices and the Yield to Maturity

10.4 Summary

Appendix 10.1 Is the Long Rate a Martingale?

Appendix 10.2 Forward Rates

Endnotes

Further Reading

11.2 Purchasing Power Parity (PPP)

11.3 Interrelationships between CIP, UIP and PPP

11.4 Summary

Appendix 11.1 PPP and the Wage-Price Spiral

12 Testing CIP, UIP and FRU

12.1 Covered Interest Arbitrage

12.2 Uncovered Interest Parity and Forward Rate Unbiasedness

12.3 Forward Rate: Risk Aversion and Rational Expectations

12.4 Exchange Rates and News

12.5 Peso Problems and Noise Traders

12.6 Summary

Appendix 12.1 Derivation of Famaâ€™s Decomposition of the Risk Premium

in the Forward Market

13 The Exchange Rate and Fundamentals

13.1 Flex-Price Monetary Model

13.2 Sticky-Price Monetary Model (SPMM)

13.3 Dornbusch Overshooting Model

13.4 Frankel Real Interest Differential Model (RIDM)

13.5 Testing the Models

13.6 Chaos and Fundamentals

13.7 Summary

Further Reading

Part 5 Tests of the EMH using the VAR Methodology

14 The Term Structure and the Bond Market

14.1 Cross-equation Restrictions and Informational Efficiency

14.2 The VAR Approach

14.3 Empirical Evidence

14.4 Summary

Endnotes

15 The FOREX Market

15.1 Efficiency in the FOREX Market

15.2 Recent Empirical Results

15.3 Summary

Endnotes

16 Stock Price Volatility

16.1 Theoretical Issues

16.2 Stock Price Volatility and the VAR Methodology

16.3 Empirical Results

16.4 Persistence and Volatility

Appendix 16.1 Returns, Variance Decomposition and Persistence

17 Risk Premia: The Stock Market

17.1 What Influences Stock Market Volatility?

17.2 The Impact of Risk on Stock Returns

17.3 Summary

18 The Mean-Variance Model and the CAPM

18.1 The Mean-Variance Model

18.2 Tests of the CAPM Using Asset Shares

18.3 Summary

19 Risk Premia and the Bond Market

19.1 Time Varying Risk: Pure Discount Bonds

19.2 Time Varying Risk: Long-Term Bonds

19.3 Interaction Between Stock and Bond Markets

19.4 Summary

Endnotes

Further Reading

Part 7 Econometric Issues in Testing Asset Pricing Models

20 Economic and Statistical Models

20.1 Univariate Time Series

20.2 Multivariate Time Series Models

20.3 Simple ARCH and GARCH Models

20.4 Rational Expectations: Estimation Issues

Further Reading

References

Index

I

Series Preface I

This series aims to publish books which give authoritative accounts of major ne

financial economics and general quantitative analysis. The coverage of the seri

both macro and micro economics and its aim is to be of interest to practi

policy-makers as well as the wider academic community.

The development of new techniques and ideas in econometrics has been rap

years and these developments are now being applied to a wide range of areas an

Our hope is that this series will provide a rapid and effective means of com

these ideas to a wide international audience and that in turn this will contri

growth of knowledge, the exchange of scientific information and techniqu

development of cooperation in the field of economics.

St

Imperial College, L

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I

Introduction I

This book has its genesis in a final year undergraduate course in Financia

although parts of it have also been used on postgraduate courses in quantitat

of the behaviour of financial markets. Participants in these courses usually h

what heterogeneous backgrounds: some have a strong basis in standard und

economics, some in applied finance while some are professionals working

institutions. The mathematical and statistical knowledge of the participants in th

is also very mixed. My aim in writing the book is to provide a self-containe

introduction to some of the theories and empirical methods used by financial ec

the analysis of speculative assets prices in the stock, bond and foreign exchan

It could be viewed as a selective introduction to some of the recent journa

in this area, with the emphasis on applied work. The content should enable

to grasp that although much of this literature is undoubtedly very innovative

grounded in some fairly basic intuitive ideas. It is my hope that after reading

students and others will feel confident in tackling the original sources.

The book analyses a number of competing models of asset pricing and the me

to test these. The baseline paradigm throughout the book is the efficient market

EMH. If stock prices always fully reflect the expected discounted present valu

dividends (i.e. fundamental value) then the market will allocate funds among

firms, optimally. Of course, even in an efficient market, stock prices may be hig

but such volatility does not (generally) warrant government intervention since

the outcome of informed optimising traders. Volatility may increase risk (of b

for some financial institutions who hold speculative assets, yet this can be m

portfolio diversification and associated capital adequacy requirements.

Part 1begins with some basic definitions and concepts used in the financial

literature and demonstrates the â€˜separation principleâ€™ in the certainty case.

period) Capital Asset Pricing Model (CAPM) and (to a much lesser extent) th

Pricing Theory (APT) provide the baseline models of equilibrium asset retu

two models, presented in Chapters 2 and 3, provide a rich enough menu t

many of the empirical issues that arise in testing the EMH. It is of course

made clear that any test of the EMH is a joint test of an equilibrium returns

rational expectations (RE). Also in Part 1, the theoretical basis of the CAP

variants, including the consumption CAPM), the APT and some early emp

of these models are discussed, and it is concluded with an examination, in

of the relationship between returns and prices. It is demonstrated that any

In Part 2, Chapter 5, the basic assumptions and mathematical formulat

RE-EMH approach are outlined. One view of the EMH is that equilibri

returns are unpredictable, another slightly different interpretation is that one ca

persistent abnormal profits after taking account of transactions costs and adju

risk. In Chapter 6, an examination is made of a variety of statistical tests wh

establish whether stock returns (over different holding periods) are predictabl

whether one can exploit this predictability to earn â€˜abnormalâ€™ profits. This

by a discussion of the behaviour of stock prices and whether these are

solely by fundamentals or are excessively volatile. When discussing â€˜vola

it is possible to highlight some issues associated with inference in small sa

problems encountered in the presence of non-stationary data. The usefulness

Carlo methods in illuminating some of these problems is also examined. Th

evidence in Part 2 provides the reader with an overview of the difficultie

establishing firm conclusions about competing hypotheses. However, at a m

prima facie case is established that when using fairly simple models, the EM

adequately capture the behaviour of stock prices and returns.

It is well known that stock returns may contain a (rational) bubble whic

dictable, yet this can lead to a discrepancy between the stock price and fundam

Such bubbles are a â€˜self-fulfilling prophecyâ€™ which may be generated exogenou

depend on fundamentals such as dividends (i.e. intrinsic bubbles). The intrin

is â€˜anchoredâ€™ to dividends and if dividends are fairly stable then the actual

might not differ too much from its fundamental value. However, the divide

may be subject to â€˜regime changesâ€™ which can act as a catalyst in generatin

in an intrinsic bubble. Periodically collapsing bubbles are also possible: when

is positive, stock prices and fundamentals diverge, but after the â€˜collapseâ€™ the

brought into equality. These issues are addressed in Chapter 7 which also asses

the empirical evidence supports the presence of rational bubbles.

Stock market â€˜anomaliesâ€™ and models of noise trader behaviour are d

Chapter 8, the final chapter in Part 2. The evidence on â€˜anomaliesâ€™ in the stoc

voluminous and students love providing a â€˜listâ€™ of them in examination answ

they are invaluable pieces of evidence, which may be viewed as being comple

the statistical/regression-basedapproaches, I have chosen to â€˜listâ€™ only a few o

ones, since the analytic content of these studies is usually not difficult for

to follow, in the original sources. Such anomalies highlight the potential im

noise traders, who follow â€˜fads and fashionsâ€™ when investing in speculative a

asset prices are seen to be the outcome of the interaction between â€˜smart mon

and â€˜noise tradersâ€™. The relative importance of these two groups in particular m

at particular times may vary and hence prices may sometimes reflect fundam

and at other times may predominantly reflect fads and fashions.

There are several approaches to modelling noise trader behaviour. For exa

are based on maximising an explicit objective function, while others involve

responses to market signals. As soon as one enters the domain of non-linear

possibility of chaotic behaviour arises. It is possible for a purely (non-linear) de

in the near future, relative to those in the more distant future, when pricing sto

are therefore mispriced and physical investment projects with returns over a sh

are erroneously preferred to those with long horizon returns, even though the

a higher expected net present value. Illustrative models which embody the a

are presented in Chapter 8, along with some empirical tests.

Overall, the impression imparted by the theoretical models and empiri

presented in Part 2 is that for the stock market, the EMH under the assumptio

invariant risk premium may not hold, particularly for the post-1950s period.

the reader is made aware that such a conclusion is by no means clear cut and

sophisticated tests are to be presented in Parts 5 and 6 of the book. Through

it is deliberately shown how an initial hypothesis and tests of the theory of

the unearthing of further puzzles, which in turn stimulates the search for e

theoretical models or improved data and test procedures. Hence, by the end of

reader should be well versed in the basic theoretical constructs used in anal

prices and in testing hypotheses using a variety of statistical techniques.

Part 3 examines the EMH in the context of the bond market. Chapter 9 o

various hypotheses of the term structure of interest rates applied to spot yield

period yields and the yield to maturity and demonstrates how these are interr

dominant paradigms here are the expectations hypothesis and the liquidity

hypothesis, both of which assume a time invariant term premium. Chapter 10

empirical tests of the competing hypotheses, for the short and long ends of th

spectrum. In addition, cointegration techniques are used to examine the comp

rity spectrum. On balance, the results for the bond market (under a time inv

premium) are found to be in greater conformity with the EMH than are the

the stock market (as reported in Part 2). These differing results for these two

asset markets are re-examined later in the book.

Part 4 examines the FOREX market and in particular the behaviour of spot a

exchange rates. Chapter 11 begins with a brief overview of the relationshi

covered and uncovered interest parity, purchasing power parity and real interest

Chapter 12 is mainly devoted to testing covered and uncovered interest parity a

rate unbiasedness. The degree to which the apparent failure of forward rate un

may be due to a failure either of rational expectations or of risk neutrality is

The difficulty in assessing â€˜efficiencyâ€™ in the presence of the so-called Peso pr

the potential importance of noise traders (or chartists) are both discussed, in the

illustrative empirical results presented. In the final section of Part 4, in Chapter

theories of the behaviour of the spot exchange rate based on â€˜fundamentalsâ€™

flex-price and sticky-price monetary models, are outlined. These monetary mod

pursued at great length since it soon becomes clear from empirical work that

for periods of hyperinflation) these models, based on economic fundamentals, ar

deficient. The final chapter of Part 4 therefore also examines whether the â€˜sty

of the behaviour of the spot rate may be explained by the interaction of no

and smart money and, in one such model, chaotic behaviour is possible. T

conclusion is that the behaviour of spot and forward exchange rates is little u

of market participants (although space constraints prevent a discussion of

models).

In Part 5 the EMH using the VAR methodology is tested. Chapter 14 begi

term structure of interest rates and demonstrates how the VAR equations can

provide a time series for the forecast of (a weighted average of) future chang

term rates of interest, which can then be compared with movements in the

spread, using a variety of metrics. Under the null of the expectations hypothes

yields a set of cross-equation parameter restrictions. These restrictions are sho

an intuitive interpretation, namely, that forecast errors are independent of inform

in generating the forecast and that no abnormal profits can be made. Having

the basic principles behind the VAR methodology it is then possible succinc

with its application to the FOREX (Chapter 15) and stock market (Chapter

are two further interesting aspects to the VAR methodology applied to the sto

First, the VAR methodology is useful in establishing links between early emp

that looked at the predictably of one-period returns and multi-period return

that examined volatility tests on stock prices. Second, the link between the per

one-period returns and the volatility of stock prices is easily examined withi

framework. Broadly speaking the empirical results based on the VAR approa

that the stock and FOREX markets (under a time invariant risk premium) do n

to the EMH, while for the bond market the results are more in conformity

some puzzles still remain.

Part 6 examines the potential impact of time varying risk premia in the

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