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Fixed-Income Securities Valuation, Risk Management and Portfolio Strategies Fixed-Income Securities Valuation, Risk Management and Portfolio Strategies Lionel Martellini Philippe Priaulet and Stephane´ Priaulet Fixed-Income Securities Wiley Finance Series Country Risk Assessment Michael Bouchet, Ephra¨ım Clark and Bertrand Groslambert The Simple Rules of Risk: Revisiting the Art of Risk Management Erik Banks Measuring Market Risk Kevin Dowd An Introduction to Market Risk Management Kevin Dowd Behavioural Finance James Montier Asset Management: Equities Demystified Shanta Acharya An Introduction to Capital Markets: Products, Strategies, Participants Andrew M Chisholm Hedge Funds: Myths and Limits Francois-Serge Lhabitant The Manager’s Concise Guide to Risk Jihad S Nader Securities Operations: A guide to trade and position management Michael Simmons Modeling, Measuring and Hedging Operational Risk Marcelo Cruz Monte Carlo Methods in Finance Peter Jackel¨ Structured Equity Derivatives: The Definitive Guide to Exotic Options and Structured Notes Harry Kat Advanced Modelling in Finance Using Excel and VBA Mary Jackson and Mike Staunton Operational Risk: Measurement and Modelling Jack King Advance Credit Risk Analysis: Financial Approaches and Mathematical Models to Assess, Price and Manage Credit Risk Didier Cossin and Hugues Pirotte Interest Rate Modelling Jessica James and Nick Webber Volatility and Correlation in the Pricing of Equity, FX and Interest-Rate Options Riccardo Rebonato Risk Management and Analysis vol. 1: Measuring and Modelling Financial Risk Carol Alexander (ed) Risk Management and Analysis vol. 2: New Markets and Products Carol Alexander (ed) Interest-Rate Option Models: Understanding, Analysing and Using Models for Exotic Interest-Rate Options (second edition) Riccardo Rebonato Fixed-Income Securities Valuation, Risk Management and Portfolio Strategies Lionel Martellini Philippe Priaulet and Stephane´ Priaulet Copyright c 2003 John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): [email protected] Visit our Home Page on www.wileyeurope.com or www.wiley.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to [email protected], or faxed to (+44) 1243 770620. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. Other Wiley Editorial Offices John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809 John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1 Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should not in any way be attributed to Philippe Priaulet as a representative, officer or employee of HSBC-CCF. The views, thoughts and opinions expressed in this book are those of the authors in their individual capacities and should not in any way be attributed to Stephane´ Priaulet as a representative, officer or employee of AXA. Library of Congress Cataloging-in-Publication Data Martellini, Lionel. Fixed-income securities : valuation, risk management, and portfolio strategies / Lionel Martellini, Philippe Priaulet, and Stephane´ Priaulet p. cm.—(Wiley finance series) Includes bibliographical references and index. ISBN 0-470-85277-1 (pbk. : alk. paper) 1. Fixed-income securities—Mathematical models. 2. Portfolio management—Mathematical models. 3. Bonds—Mathematical models. 4. Hedging (Finance)—Mathematical models. I. Priaulet, Philippe. II. Priaulet, Stephane.´ III. Title. IV. Series. HG4650.M367 2003 332.63 2044—dc21 2003041167 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0-470-85277-1 Typeset in 10/12.5pt Times by Laserwords Private Limited, Chennai, India Printed and bound in Great Britain by Antony Rowe Ltd, Chippenham, Wiltshire This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production. To Adhara, Antonella, Calypso, Daphn´e, Isabelle and Manon To our parents and families To our friends Contents About the Authors xix Preface xxi Acknowledgments xxv Notation xxvii PART I INVESTMENT ENVIRONMENT 1 Bonds and Money-Market Instruments 3 1.1 Bonds 3 1.1.1 General Characteristics of Bonds 3 1.1.2 Bonds by Issuers 17 1.2 Money-Market Instruments 25 1.2.1 Definition 25 1.2.2 The Role of the Central Bank 25 1.2.3 T-Bills 26 1.2.4 Certificates of Deposit 28 1.2.5 Bankers’ Acceptances 29 1.2.6 Commercial Papers 29 1.2.7 Interbank Deposits 30 1.2.8 Repo and Reverse Repo Market Instruments 30 1.3 End of Chapter Summary 32 1.4 References and Further Reading 33 1.4.1 Books and Papers 33 1.4.2 Websites and Others 33 1.5 Problems 34 1.5.1 Problems on Bonds 34 1.5.2 Problems on Money-Market Instruments 36 1.6 Appendix: Sector Breakdown of the Euro, the UK and the Japan Corporate Bond Markets 37 2 Bond Prices and Yields 41 2.1 Introduction to Bond Pricing 41 2.2 Present Value Formula 43 viii Contents 2.2.1 Time-Value of Money 43 2.2.2 The Mathematics of Discounting 43 2.2.3 Nominal versus Real Interest Rates 45 2.2.4 Time Basis and Compounding Frequency Conventions 46 2.2.5 Continuous Compounding 47 2.3 Taxonomy of Rates 49 2.3.1 Coupon Rate and Current Yield 49 2.3.2 Yield to Maturity 49 2.3.3 Spot Zero-Coupon (or Discount) Rate 51 2.3.4 Forward Rates 52 2.3.5 Bond Par Yield 54 2.4 End of Chapter Summary 54 2.5 References and Further Reading 54 2.6 Problems 55 PART II TERM STRUCTURE OF INTEREST RATES 3 Empirical Properties and Classical Theories of the Term Structure 63 3.1 Definition and Properties of the Term Structure 63 3.1.1 What Kind of Shape Can It Take? 65 3.1.2 How Does It Evolve over Time? 68 3.2 Classical Theories of the Term Structure 81 3.2.1 The Pure Expectations Theory 82 3.2.2 The Pure Risk Premium Theory 83 3.2.3 The Market Segmentation Theory 85 3.2.4 The Biased Expectations Theory: An Integrated Approach 86 3.2.5 Illustration and Empirical Validation 86 3.2.6 Summary and Extensions 87 3.3 End of Chapter Summary 88 3.4 References and Further Reading 89 3.4.1 On the Empirical Behavior of the Yield Curve 89 3.4.2 On the Principal Component Analysis of the Yield Curve 90 3.4.3 On the Classical Theories of the Term Structure of Interest Rates 90 3.5 Problems 91 4 Deriving the Zero-Coupon Yield Curve 96 4.1 Deriving the Nondefault Treasury Zero-Coupon Yield Curve 96 4.1.1 How to Select a Basket of Bonds? 96 4.1.2 Direct Methods 97 4.1.3 Indirect Methods 103 ix Contents 4.2 Deriving the Interbank Zero-Coupon Rate Curve 130 4.2.1 How to Select the Basket of Instruments? 130 4.2.2 Interpolation Methods 132 4.2.3 Least Squares Methods Based on Rates 132 4.2.4 Least Squares Methods Based on Prices 133 4.3 Deriving Credit Spread Term Structures 136 4.3.1 Disjoint Methods 136 4.3.2 Joint Methods 137 4.4 End of Chapter Summary 142 4.5 References and Further Reading 144 4.6 Problems 146 4.7 Appendix: A Useful Modified Newton’s Algorithm 155 PART III HEDGING INTEREST-RATE RISK 5 Hedging Interest-Rate Risk with Duration 163 5.1 Basics of Interest-Rate Risk: Qualitative Insights 163 5.1.1 The Five Theorems of Bond Pricing 163 5.1.2 Reinvestment Risk 164 5.1.3 Capital Gain Risk 165 5.1.4 Qualifying Interest-Rate Risk 166 5.2 Hedging with Duration 167 5.2.1 Using a One-Order Taylor Expansion 167 5.2.2 Duration, $Duration and Modified Duration 170 5.2.3 How to Hedge in Practice? 173 5.3 End of Chapter Summary 175 5.4 References and Further Reading 176 5.4.1 Books 176 5.4.2 Papers 176 5.5 Problems 177 6 Beyond Duration 182 6.1 Relaxing the Assumption of a Small Shift 182 6.1.1 Using a Second-Order Taylor Expansion 182 6.1.2 Properties of Convexity 185 6.1.3 Hedging Method 187 6.2 Relaxing the Assumption of a Parallel Shift 188 6.2.1 A Common Principle 188 6.2.2 Regrouping Risk Factors through a Principal Component Analysis 192 6.2.3 Hedging Using a Three-Factor Model of the Yield Curve 195 6.3 End of Chapter Summary 199 x Contents 6.4 References and Further Reading 200 6.5 Problems 201 PART IV INVESTMENT STRATEGIES 7 Passive Fixed-Income Portfolio Management 213 7.1 Straightforward Replication 213 7.2 Replication by Stratified Sampling 214 7.3 Tracking-Error Minimization 216 7.3.1 Optimization Procedure
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