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    Analysing and Interpreting the Yield Curve
    Analysing and Interpreting the Yield Curve
    Analysing and Interpreting the Yield Curve
    Ebook653 pages5 hours

    Analysing and Interpreting the Yield Curve

    By Moorad Choudhry

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    Understand and interpret the global debt capital markets

    Now in a completely updated and expanded edition, this is a technical guide to the yield curve, a key indicator of the global capital markets and the understanding and accurate prediction of which is critical to all market participants. Being able to accurately and timely predict the shape and direction of the curve permits practitioners to consistently outperform the market.

    Analysing and Interpreting the Yield Curve, 2nd Edition describes what the yield curve is, explains what it tells participants, outlines the significance of certain shapes that the curve assumes and, most importantly, demonstrates what factors drive it and how it is modelled and used.

    • Covers the FTP curve, the multi-currency curve, CSA, OIS-Libor and 3-curve models
    • Gets you up to speed on the secured curve
    • Describes application of theoretical versus market curve relative value trading
    • Explains the concept of the risk-free rate
    • Accessible demonstration of curve interpolation best-practice using cubic spline, Nelson-Siegel and Svensson 94 models 

    This advanced text is essential reading for traders, asset managers, bankers and financial analysts, as well as graduate students in banking and finance.

    LanguageEnglish
    PublisherWiley
    Release dateApr 15, 2019
    ISBN9781119141051
    Analysing and Interpreting the Yield Curve
    Author

    Moorad Choudhry

    Moorad Choudhry is Chief Executive Officer, Habib Bank Zurich PLC in London, and Visiting Professor at the Department of Mathematical Sciences, Brunel University. Previously he was Head of Treasury of the Corporate Banking Division, Royal Bank of Scotland. Prior to joining RBS, he was a bond trader and structured finance repo trader at KBC Financial Products, ABN Amro Hoare Govett Limited and Hambros Bank Limited. He has a PhD from Birkbeck, University of London and an MBA from Henley Business School. Moorad lives in Surrey, England.

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      Analysing and Interpreting the Yield Curve - Moorad Choudhry

      Table of Contents

      Cover

      Foreword

      Preface

      Preface to the First Edition

      Acknowledgments

      About the Author

      PART I: Introduction to the Yield Curve

      CHAPTER 1: The Yield Curve

      THE YIELD CURVE FOR BEGINNERS

      YIELD TO MATURITY YIELD CURVE

      THE COUPON YIELD CURVE

      THE PAR YIELD CURVE

      THE ZERO‐COUPON (OR SPOT) YIELD CURVE

      USING SPOT RATES IN BOND ANALYSIS

      THE FORWARD YIELD CURVE

      ANALYSING AND INTERPRETING THE YIELD CURVE

      AN INTRODUCTION TO FITTING THE YIELD CURVE

      SPOT AND FORWARD RATES IN THE MARKET

      THE INTEREST‐RATE SWAP CURVE AND THE SOVEREIGN BOND CURVE

      APPENDIX: CUBIC SPLINE INTERPOLATION

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      CHAPTER 2: A Further Look at Spot and Forward Rates

      ZERO‐COUPON BONDS

      COUPON BONDS

      BOND PRICE IN CONTINUOUS TIME

      INTRODUCTION TO BOND ANALYSIS USING SPOT RATES AND FORWARD RATES IN CONTINUOUS TIME

      APPENDICES

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      PART II: Yield Curve Modelling and Post‐2008 Yield Curve Analytics

      CHAPTER 3: Interest Rate Modelling I: Primer on Basic Concepts

      THE DYNAMICS OF THE YIELD CURVE

      TERM STRUCTURE MODELLING

      BASIC CONCEPTS

      ITÔ'S LEMMA

      APPROACHES TO MODELLING

      ONE‐FACTOR, TWO‐FACTOR AND MULTI‐FACTOR MODELS

      THE SHORT‐TERM RATE AND THE YIELD CURVE

      APPENDICES

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      CHAPTER 4: Interest Rate Modelling II: The Dynamic of Asset Prices

      THE BEHAVIOUR OF ASSET PRICES

      STOCHASTIC PROCESSES

      WIENER PROCESS OR BROWNIAN MOTION

      THE MARTINGALE PROPERTY

      GENERALISED WIENER PROCESS

      A MODEL OF THE DYNAMICS OF ASSET PRICES

      STOCHASTIC CALCULUS MODELS: BROWNIAN MOTION AND ITÔ CALCULUS

      BROWNIAN MOTION

      STOCHASTIC CALCULUS

      UNCERTAINTY OF INTEREST RATES

      APPENDICES

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      CHAPTER 5: Interest Rate Models I

      INTEREST RATE MODELS

      INTEREST RATE PROCESSES

      ONE‐FACTOR MODELS

      THE VASICEK MODEL

      THE MERTON MODEL

      THE COX–INGERSOLL–ROSS MODEL

      ARBITRAGE‐FREE MODELS

      THE HO AND LEE MODEL

      THE HULL–WHITE MODEL

      THE BLACK–DERMAN–TOY MODEL

      FITTING THE MODEL

      SUMMARY

      SELECTED BIBLIOGRAPHY AND REFERENCES

      CHAPTER 6: Interest Rate Models II

      MULTI‐FACTOR TERM STRUCTURE MODELS

      THE MULTI‐FACTOR HEATH–JARROW–MORTON MODEL

      JUMP MODELS

      ASSESSING ONE‐FACTOR AND MULTI‐FACTOR MODELS

      CHOOSING A TERM STRUCTURE MODEL

      IMPORTANCE OF PRACTICALITY

      SELECTED BIBLIOGRAPHY AND REFERENCES

      REFERENCES ON ESTIMATION METHOD

      NOTES

      CHAPTER 7: The Index‐Linked Bond Yield Curve

      INDEX‐LINKED BONDS AND REAL YIELDS

      THE REAL TERM STRUCTURE OF INTEREST RATES

      THE TERM STRUCTURE OF IMPLIED FORWARD INFLATION RATES

      ESTIMATING THE REAL TERM STRUCTURE

      FITTING THE DISCOUNT FUNCTION

      DERIVING THE TERM STRUCTURE OF INFLATION EXPECTATIONS

      APPLICATION

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      CHAPTER 8: Yield Curve Analytics in the Post‐2008 Era

      OVERNIGHT INDEX SWAP (OIA) YIELD CURVE

      POST‐CRASH DISCOUNTING PRINCIPLES FOR YIELD‐CURVE CONSTRUCTION

      FOUR CURVES: SOVEREIGN, LIBOR, OIS, AND INTERNAL FUNDING CURVE

      APPENDIX

      REFERENCES

      NOTES

      CHAPTER 9: Negative Interest Rate Analytics

      THE DISCOUNT FACTOR

      EXAMPLE ILLUSTRATIONS

      THE YIELD TO MATURITY

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTE

      PART III: Fitting the Yield Curve

      CHAPTER 10: Estimating and Fitting the Yield Curve I

      YIELD CURVE SMOOTHING

      SMOOTHING TECHNIQUES

      USING A CUBIC POLYNOMIAL

      NON‐PARAMETRIC METHODS

      SPLINE‐BASED METHODS

      NELSON AND SIEGEL CURVES

      COMPARING CURVES

      APPENDICES

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      CHAPTER 11: Estimating and Fitting the Yield Curve II

      RECAP: BOND MARKET INFORMATION

      ESTIMATING YIELD CURVE FUNCTIONS

      CURVE‐FITTING TECHNIQUES: PARAMETRIC

      PARAMETRIC TECHNIQUES

      PARAMETERISED YIELD CURVES

      THE CUBIC SPLINE METHOD FOR ESTIMATING AND FITTING THE YIELD CURVE

      USING A CUBIC SPLINE: THE WAGGONER MODEL

      THE ANDERSON–SLEATH MODEL

      APPLICATIONS

      THE ANDERSON–SLEATH EVALUATION

      REPO AND ESTIMATING THE SHORT END OF THE YIELD CURVE

      APPENDIX 11.1 THE MCCULLOCH CUBIC SPLINE MODEL

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      PART IV: Yield Curves and Relative Value Trading

      CHAPTER 12: Yield Curves and Relative Value

      THE DETERMINANTS OF GOVERNMENT BOND YIELDS

      CHARACTERISING THE COMPLETE TERM STRUCTURE

      IDENTIFYING RELATIVE VALUE IN GOVERNMENT BONDS

      YIELD SPREAD TRADES

      BOND SPREAD WEIGHTING

      TYPES OF BOND SPREADS

      NOTES

      CHAPTER 13: Identifying Relative Value in the US Treasury Market: Acquiring New Benchmark Definitions from an Ancillary Yield Curve

      THE NATURE OF THE UNDERLYING OPTIMISATION: CONVERTING THE PRESENT VALUE APPARATUS INTO A MULTINOMIAL POLYNOMIAL OPTIMISATION

      AN APPROACH TO TREATING UNCERTAINTY QUANTIFICATION

      TWO COALESCING YIELD CURVES PRODUCING POSSIBLE TRADING OPPORTUNITIES ON OCTOBER 18, 2017

      IMPLICATIONS FOR YIELD SPREAD TRADES

      A PROPOSED BUTTERFLY TRADE WITH THE SHORT POSITION STEMMING FROM THE ANCILLARY BOND: 01.868 TABLE 13.4

      WHAT TO EXPECT WHEN BILLS ARE EXCLUDED FROM THE FITTING COMPUTATIONS

      APPENDIX: GEOMETRIC PROGRAMMING

      WEBSITE

      ADDENDUM: EXPERIMENTS FROM 17/12/2018

      SELECTED BIBLIOGRAPHY AND REFERENCES

      NOTES

      APPENDIX: Bond Yield Measurement

      CURRENT YIELD

      SIMPLE YIELD TO MATURITY

      YIELD TO MATURITY

      MODIFYING BOND YIELDS

      CONVERTING BOND YIELDS

      SUMMARY

      NOTES

      Index

      End User License Agreement

      List of Tables

      Chapter 1

      TABLE 1.1 Gilt yields

      TABLE 1.2 Coupon, spot, and forward yields

      TABLE 1.3 Positive yield curve with constant expected future interest rat...

      Chapter 2

      TABLE 2.1 Confirming the forward rate arbitrage

      TABLE 2.2 Hypothetical zero‐coupon yield and forward rates

      Chapter 8

      TABLE 8.1 Constructing the OIS curve.

      Chapter 9

      TABLE 9.1 First example results

      TABLE 9.2 Second example results

      Chapter 11

      TABLE 11.1 Spot rate values using Nelson–Siegel model and user‐ ...

      TABLE 11.2 Gilt redemption yields used to fit curve in Figure 11.1

      Chapter 12

      TABLE 12.1 Duration and yield comparisons for bonds in a hypothetical inv...

      TABLE 12.2 Yields and excess yield spreads for selected gilts, 22 October...

      TABLE 12.3 Bond basis point value, 22 October 1999

      Chapter 13

      TABLE 13.1 Interest Earned from a Treasury Bond 4% Annual Interest

      TABLE 13.2 T‐Bill Pricing Formula: 360 Day Convention

      TABLE 13.3 BEY on Bill Data: DTM = days to maturity; 9/27/02

      TABLE 13.4 29 Bonds and Notes 10/18/17 when Bills used in Curve Fitting

      TABLE 13.5 Excerpts from 258 Notes and Bonds 18/10/2017

      TABLE 13.6 Comparing IRRs: Ancillary and Benchmark

      TABLE 13.7 LP Unique Solution

      TABLE 13.8 31 Bonds and Notes: No Bills 18 October 2017

      Appendix

      TABLE A.1 Discounted margin calculation for an FRN. Calculation carried out on...

      List of Illustrations

      Chapter 1

      FIGURE 1.1 Creating a yield curve in Excel.

      FIGURE 1.2 Yield to maturity yield curves.

      FIGURE 1.3 UK gilt yield curves as at 18 June 2003.

      FIGURE 1.4 UK gilt yield curve and sterling interest rate swap curve as at 18...

      FIGURE 1.5 French and German government yield curves, 18 June 2003.

      FIGURE 1.6 Treasury yield curve as at 18 June 2003.

      FIGURE 1.7 Screen FMC, menu of corporate and government bond yield curves.

      FIGURE 1.8 Screen FMC, AAA‐, A‐, and BBB‐rated corporate...

      FIGURE 1.9 Screen SWCV, selected for sterling swap curve as at 18 June 2003. ...

      FIGURE 1.10 Coupon yield curves.

      FIGURE 1.11 Average yield spreads of UK corporate bonds versus gilts, 2001...

      FIGURE 1.12 Redemption, spot, and forward yield curves: traditional analysis.

      FIGURE 1.13 UK gilt redemption yield curves.

      FIGURE 1.14 Yield curve explained by expectations hypothesis and liquidity pr...

      FIGURE 1.15 Polynomial curve‐fitting.

      FIGURE 1.16 Grid point allocation in regression analysis.

      FIGURE 1.17 US Treasury and US dollar interest rate swap curves, 30 April 201...

      FIGURE 1.18 Cubic spline interpolation matrix.

      Chapter 2

      FIGURE 2.1 US Treasury zero‐coupon yield curve in September 2000.

      FIGURE 2.2 UK gilt zero‐coupon yield curve, September 2000.

      FIGURE 2.3 French OAT zero‐coupon yield curve.

      FIGURE 2.4(a) Hypothetical zero‐coupon and forward yield curves.

      FIGURE 2.4(b) Hypothetical spot and forward yield curves.

      FIGURE 2.5 Hypothetical par, spot, and forward yield curves.

      FIGURE 2.6 Diagrammatic representation of the relationship between the spot a...

      FIGURE 2.7 Diagrammatic representation of calculating area from applying inte...

      Chapter 3

      FIGURE 3.1 Evolution of Brownian or Wiener process.

      Chapter 4

      FIGURE 4.1 An example of a Wiener process.

      FIGURE 4.2 An example of a Poisson process.

      FIGURE 4.3 Standard and generalised Wiener processes.

      Chapter 5

      FIGURE 5.1 Distribution of future interest rates implied by different process...

      FIGURE 5.2 Zero‐coupon bond price curves at and .

      FIGURE 5.3 Forward rate curves with and .

      FIGURE 5.4 Forward rate curves standard deviations of 0.02 and 0.06.

      FIGURE 5.5 Forward rate curves under high standard deviation.

      Chapter 7

      FIGURE 7.1 UK market nominal and real term structure of interest rates, July ...

      Chapter 8

      FIGURE 8.1 GBP SONIA and GBP Swap curves, 13 October 2016.

      FIGURE 8.2 Three‐month Euribor and EONIA spread, 2002–2017.

      FIGURE 8.3 Illustration of example curve construction calculations.

      FIGURE 8.4 Example of a multi‐currency curve.

      FIGURE 8.5 Derivatives book modelled funding profile.

      FIGURE 8.6 Example of forward curve oscillation arising from using flat term ...

      FIGURE 8.7 Bank COF curves.

      Chapter 9

      FIGURE 9.1 Discount factors.

      FIGURE 9.2 Compounding effect.

      FIGURE 9.3 Compounding effect difference.

      FIGURE 9.4 Continuously compounding.

      FIGURE 9.5 YTM of Eidgenossen.

      FIGURE 9.6 Convertible bond negative yields.

      FIGURE 9.7 Convertible bond payoff profile.

      Chapter 10

      FIGURE 10.1 Gilt gross redemption yields, 12 June 2000.

      FIGURE 10.2 Discount factors from gilt prices, 12 June 2000.

      FIGURE 10.3 Zero‐coupon (spot) and forward rates obtained from gilt...

      FIGURE 10.4 Linear interpolation of bond yields, 26 June 1997.

      FIGURE 10.5 Spot and forward rates implied from Figure 10.4.

      FIGURE 10.6 Cubic spline with knot points at 0, 2, 5, 10 and 25 year tenors.

      FIGURE 10.7 Regression line passing through value of and .

      FIGURE 10.8 Piecewise linear regression

      FIGURE 10.9 Illustrating knot points

      Chapter 11

      FIGURE 11.1 A Nelson and Siegel fitted yield curve and gilt redemption yield ...

      FIGURE 11.2 Suggested node points.

      FIGURE 11.3 Yield curves fitted using cubic spline method and Svensson parame...

      FIGURE 11.4 Effect on fitted yield curves of change in long‐dated bond....

      FIGURE 11.5 Comparison of fitted spot yield curve to observed spot yield curv...

      FIGURE 11.6 Fitted yield curves and observed strip yield curve, July 1998.

      FIGURE 11.7 Fitting short‐term yield curves using government repo rates.

      Chapter 12

      FIGURE 12.1 Yield and duration of gilts, 21 October 1999.

      FIGURE 12.2 T‐bill and par yield curve, October 1999.

      FIGURE 12.3 Structure of bond yields, October 1999.

      FIGURE 12.4 2‐year and 10‐year spread, UK gilt market March 1999.

      Chapter 13

      FIGURE 13.1 Ancillary & Benchmark Curves including Bills, 18 October 2017.

      FIGURE 13.2 Ancillary Curve: No Bills, 18 October 2017.

      FIGURE 13.3 Results from December 2018 (i)

      FIGURE 13.4 Results from December 2018 (ii)

      Appendix

      FIGURE A.1 Comparing yield measures for a 6% bond with five years to maturity.

      FIGURE A.2 The bond price/yield relationship.

      Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States. With offices in North America, Europe, Australia, and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding.

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      For a list of available titles, visit our website at www.WileyFinance.com.

      Analysing and Interpreting the Yield Curve

      Second Edition

      MOORAD CHOUDHRY

      With contributions from Polina Bardaeva, Ken Kortanek, Kevin Liddy, Wolfgang Marty and Vladimir Medvedev

      Wiley Logo

      First published 2004

      Second Edition published 2019

      © 2004, 2019 Moorad Choudhry

      John Wiley & Sons Ltd

      Registered office

      John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

      For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book, please see our website at 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 or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

      Wiley publishes in a variety of print and electronic formats and by print‐on‐demand. Some material included with standard print versions of this book may not be included in e‐books or in print‐on‐demand. If this book refers to media such as a CD or DVD that is not included in the version you purchased, you may download this material at http://booksupport.wiley.com. For more information about Wiley products, visit www.wiley.com.

      Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.

      Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

      The views, thoughts and opinions expressed in this book are those of the author in his individual private capacity and should not in any way be attributed to any employing firm, or to Moorad Choudhry as a representative, officer, or employee of any employing institution or affiliated firm.

      Whilst every effort has been made to ensure accuracy, no responsibility for loss occasioned to any person acting or refraining from action as a result of reading any material in this book can be accepted by the author, publisher or any named person or corporate entity. The author may or may not hold, or have held, any security identified in this book.

      Library of Congress Cataloging‐in‐Publication Data

      Names: Choudhry, Moorad.

      Title: Analysing and interpreting the yield curve / Moorad Choudhry.

      Other titles: Analysing & interpreting the yield curve | Analyzing and interpreting the yield curve

      Description: Second edition. | Chichester, UK : Wiley, 2019. | Series: Wiley finance | Revised edition of the author's Analysing and interpreting the yield curve, c2004. | Includes bibliographical references and index. |

      Identifiers: LCCN 2018056454 (print) | LCCN 2018057854 (ebook) | ISBN 9781119141068 (AdobePDF) | ISBN 9781119141051 (ePub) | ISBN 9781119141044 (hardback)

      Subjects: LCSH: Bonds—Valuation—Econometric models. | BISAC: BUSINESS & ECONOMICS / Banks & Banking.

      Classification: LCC HG4651 (ebook) | LCC HG4651 .C6793 2019 (print) | DDC 332.63/23—dc23

      LC record available at https://lccn.loc.gov/2018056454

      Cover Design: Wiley

      Cover Images: top: © Gen Epic Solutions/Shutterstock, bottom: © hywards/shutterstock

      ffirs03uf001

      For Lindsay

      Ultimate Yummy Mummy

      Foreword

      It is an honour to be asked to contribute a few words at the beginning of this publication.

      Moorad and I first met back in 2010. We were both attending the Group Balance Sheet Management Committee at The Royal Bank of Scotland, our employer at the time. Although I forget the specific theme of the discussion, I remember our desire, incidentally which was not necessarily shared by the other committee members, to investigate and better understand a trend in the balance sheet of our organisation and in the wider economy.

      Respecting each other's viewpoint, we quickly became good friends. However, we are like chalk and cheese. In Belbin's terminology, Moorad possesses many of the qualities of the Plant and Resource Investigator, being creative, imaginative and free‐thinking as well as outgoing and enthusiastic, whereas I am most comfortable in the role of the Completer Finisher.

      Although our shared passion for the financial markets became evident at our first meeting, it was only later I realised Moorad also possesses a burning desire to pass on his knowledge, understanding and perceptive insights to others, by either delivering lectures and presentations or through the written word.

      I first became aware of Moorad's teaching skills in 2014 when he invited me to speak to students studying for the Certificate of Bank Treasury Risk Management. This is a practitioner‐oriented professional qualification in bank asset‐liability management, which is delivered to a global audience and was developed by Moorad and the team from WBS Training Ltd. There are also his numerous short course and conference performances I could highlight, all with financial risk management as the enduring theme.

      When it comes to writing, Moorad is both versatile and prolific. By my counting, this updated edition of Analysing and Interpreting the Yield Curve is his third book of the year so far. However, there's still a way to go to catch Corin Tellado, a renowned Spanish author who published over 4,000 novels in her lifetime. The comparison is probably unfair as it is doubtless a more difficult challenge to combine risk management theory, practice and current market developments in a captivating read, whilst also pursuing a full‐time career in banking!

      Moorad is a past master at simplifying complex ideas and communicating them in an easy going and engaging manner. In these respects, this book is no different to all his other publications. Compared to the first edition, sections have been added for the latest developments in the financial markets, including: the multi‐currency yield curve, the SONIA curve, the interpretation of negative yield curves, a post‐crash discounting technique for the swap curve and how to use the theoretical and observed US Treasury curve as a means of identifying relative value in bond spread trades. These concepts will be of interest to anyone working in the bond markets, be they a trader, sales‐person, fund manager, research analyst, investor or issuer, or, like me, simply a student of the financial markets.

      I commend this book to you, hope you enjoy the read and leave you with the words of Benjamin Franklin:

      An investment in knowledge pays the best interest.

      Chris Westcott

      Former Treasurer, Retail and Wealth Division

      The Royal Bank of Scotland

      1 May 2018

      Preface

      The yield curve, and everything about it, was my first and most intense love in finance. It probably still is. I could talk about it for hours, at any time, day or night. I think it is the most significant topic in banking, the very foundation of finance. But it's interesting to me to observe how the perception, and indeed the requirement, for technical excellence in banking changes subtly the more senior the level of practitioner. The higher one rises in the profession, the less it would appear that one needs to know about subjects such as the curve, how to interpret it, how best to interpolate it, and how to understand and make sense of what it's trying to tell us. What I thought was the most important and vital issue in finance, something that absolutely everyone had to know about, turns out to be just one more arcane specialism that is not discussed that often at the bank's asset‐liability committee (ALCO), hardly at all at the executive management committee (EXCO), and fewer times still at the Board.

      No matter, I still think that it's a very important topic and it's a pity that it isn't viewed in this way by everyone in banking. But that's their look out. The fact that you are reading this book shows that you agree that it's a worthwhile topic to get to grips with!

      So, fully 15 years after the first edition, is there anything new to write about on the curve? As it happens, yes, a fair bit. The global financial markets are a very different beast today compared to what they were in 2003. Of course, the fundamentals of yield curve analysis, interpolation, and interpretation remain unchanged. But the behaviours of curves are different in various nuanced ways (and some not so nuanced, and in fact very much in your face – for example, the negative interest rate curves that are a commonplace in some countries in the eurozone). That’s why I think this book was worth updating, so that we might cover issues such as multi‐currency curves, the overnight index swap (OIS) curve, and key factors in post‐crash discounting of the swap curve. And speaking of interest‐rate swaps, it is routine to see (for example, in US dollar markets) the swap curve trading through the sovereign bond curve. That would have been inexplicable when I was working as a government bond primary dealer in the 1990s … but then again, negative interest rates as routine would also have been inexplicable. Plenty for us to be getting on with then. And in an era of ever more intensive regulator and compliance burden, having to deal with a purely technical subject may even come across as a breath of fresh air to some practitioners!

      I always try to emphasise the practical and the user‐friendly in all my writing. There is such a disconnect between academia and practice in finance that there would be little value in me expounding purely on the theoretical. Unfortunately (or fortunately, depending on your point of view), the yield curve is one of those topics that it is difficult to leave the technical out of. That said, I hope the contents of the book are of relevance and practical value to the practitioner in banking and finance. This is not intended to be a textbook describing nothing that actually takes place in a bank, unlike some finance textbooks I have encountered over the years. Rather, it is meant for those who need to update the curve for use in internal funds transfer pricing, or to estimate the value to be derived from purchasing one bond in preference to another bond, or to price a new issue private placement structured product, or to have an idea of what the market thinks the state of the economy is. In other words, this book is for anyone that is using the yield curve for one or more of its myriad different practical applications in the financial markets.

      Hence this second edition, which I hope you find of interest and of some use. As Ian MacDonald said in the preface to his final update of the majestic Revolution In The Head, no further editions will be forthcoming. Or as the last Oi! album proclaimed, That's yer lot!.

      Comments on the text are welcome and should be sent to me via John Wiley & Sons Limited.

      All the best.

      Moorad Choudhry

      Surrey, England

      19 December 2018

      A Solid Bond In Your Heart

      Preface to the First Edition

      As Sir Arthur Conan Doyle would have put it, so elementary a form of literature as the textbook on financial economics hardly deserves the dignity of a preface. It is possible though, to bring some instant clarity to the purpose of such a book if we open with a few words here.

      In my book The Bond and Money Markets, I try to explain, from first principles, just how important the global debt market is, and describe the various participants that interact with each other in this market. Given the importance of the global bond market, one can never learn too much about it. But this is not a book about the bond market; rather it is about a very specific, and important part of the bond markets. In developed markets, as well as a fair number of developing ones, there is usually a large number of bonds trading at one time, at different yields and with varying terms to maturity. Investors and traders incessantly examine the relationship between the yields on bonds that are in the same class; plotting yields of bonds that differ only in their term to maturity produces what is known as the yield curve. The yield curve represents the bond market. It is sometimes referred to as the term structure of interest rates, but as we shall see later in this book, this expression refers to only one specific type of yield curve. There are lots of different yield curves. We shall examine them all in detail later.

      Much of the analysis and pricing activity that takes place in the bond markets revolves around the yield curve. The primary yield curve in any domestic capital market is the government bond yield curve, so for example, in the US market it is the US Treasury yield curve. So in this book we will talk mainly, but not exclusively, about the government yield curve. And because the author spent over five years as a United Kingdom government bond trader (or gilt‐edged market maker), most of the examples will be from the gilt market. But the principles remain the same. It is the importance of the yield curve to just about every aspect of finance that has been the motivation behind writing this book. Our objective is to:

      describe what the yield curve is;

      explain what it tells us;

      try to explain why it assumes certain shapes;

      show how we can use it;

      introduce how it is modelled;

      show how it is fitted from market rates.

      We begin with some basic description of bonds and bond mathematics, just to set the scene. We assume a basic knowledge and familiarity with bonds and market institutions, and concentrate on the yield curve. It is an arcane, specialist topic but well worth getting familiar with. We explain term structure theory, describe the most popular mathematical approaches used to model the yield curve, and show how to fit the yield curve using econometric techniques. This knowledge is of great use to just about anyone involved in the bond markets: traders, bond salespersons, fund managers, research analysts, issuers of bonds … in fact issuers, investors, and all the middlemen in between. Investors in the equity markets can also benefit from an understanding of the yield curve, as it enables one to gain a better insight into market sentiment.

      We must necessarily be quite focused and specialist in our discussion of the yield curve. Hopefully the more technical material is presented in good order so that it remains accessible. There are any number of textbooks available for the complete beginner, which are recommended in end‐chapter reading lists, along with further reading.

      Moorad Choudhry

      Surrey, England

      30 June 2003

      Acknowledgments

      Special thanks to The Raynes Park Footy Boys and The Pink Tie Brigade.

      Thanks to everyone at Wiley, including Stephen Mullaly, Syd Ganaden, Jean‐Karl Martin, Debbie Scott, Sandra Glue, Banurekha Venkatesan, Elisha Benjamin, Katy Smith and Aida Ferguson.

      Big thanks to my co‐authors, Polina Bardaeva, Ken Kortanek, Kevin Liddy, Wolfgang Marty, and Vladimir Medvedev. It's a privilege to work with you.

      Thanks to Marc Dodd and everyone at King & Shaxson Ltd, and Martin Ward at One Savings Bank for helping to make my latest return to the markets so enjoyable.

      Thanks to everyone at Crown Law and NZIRD, fab people to work with, including Jane Norris, Meghan Nicholson, Lina Worthing, Paul Hale, and Mike Cook.

      Thanks to everyone at Alderwick James, including Mr Alderwick and Ms James themselves as well as Liliana Lolata, Jolene Rodrigues, Sally Thurwood, and Sally Baldeh.

      Thanks to everyone at The BTRM. What a genuinely great bunch of people I am privileged to work with.

      Thanks to Philip Curtis‐Evans at Bloomberg for his assistance and instant responses whenever I requested screen print permissions.

      For very kind and very much appreciated comments on Linked In, all the more touching as I have never actually met them, a very special thanks to Brian Twomey, Donald Van Deventer and David Harper. It meant a lot to me, thank you gentlemen.

      And a very big, big thanks to Mike Kirsopp and everyone at Cambridge & Counties Bank. And I mean everyone! The bank has at least one thing in common with the New Zealand All Blacks…

      flast02uf001

      About the Author

      Moorad Choudhry is Head of ALM at Cambridge & Counties Bank in Leicester.

      He was previously a gilt‐edged market‐maker and money markets trader at Hoare Govett Securities Limited (later ABN Amro Hoare Govett Limited) and a sterling bond proprietary trader at Hambros Bank Limited. He subsequently traded money markets, asset‐backed commercial paper, and structured finance repo at KBC Financial Products (a subsidiary of KBC Bank N.V.), and was latterly Treasurer, Corporate Banking Division at The Royal Bank of Scotland.

      But don't forget the songs

      That made you cry,

      And the songs that saved your life,

      Yes, you're older now

      And you're a clever swine,

      But they were the only ones who ever stood by you.

      ______ The Smiths, Rubber Ring (Rough Trade Records, 1985)

      PART I

      Introduction to the Yield Curve

      In Part I we describe the yield curve itself. The bulk of the discussion is in Chapter 1, which looks at the different types of yield curve and, more importantly, introduces the main theories of the yield curve. We also look at interpreting the curve. The language is non‐specialist and should be accessible to anyone with an involvement in the financial markets. This is followed by a look at spot and forward rates, and the derivation of such rates from market yields.

      For this second edition we have relegated the introductory chapter on bond yield measurement to the main Appendix.

      After a couple of months, his patriotic zeal got on my nerves so much I began to question whether I agreed with him about communism being evil. I agreed it was a bad idea but no longer felt so sure it would ruin the planet. I began to consider the danger of blind faith in, or blind hatred of, a single idea, any idea.

      ______ Robert Wideman, Unexpected Prisoner: Memoir of a Vietnam POW, 2016

      CHAPTER 1

      The Yield Curve

      The main measure of return associated with holding bonds is the yield to maturity (YTM) or gross redemption yield (GRY). In developed markets there is usually a large number of bonds trading at one time, at different yields and with varying terms to maturity. Investors and traders frequently examine the relationship between the yields on bonds that are in the same class. Plotting yields of bonds that differ only in their term to maturity produces the yield curve. The yield curve is an important indicator and knowledge source of the state of a debt capital market.¹ It is sometimes referred to as the term structure of interest rates, but strictly speaking this is not correct, as this expression should be reserved for the zero‐coupon yield curve only. We shall examine this in detail later.

      Much of the analysis and pricing activity that takes place in the bond markets revolves around the yield curve. The yield curve describes the relationship between a particular redemption yield and a bond's maturity. We should be aware that the GRY of a bond is only ever the actual yield one receives during the period one holds the bond if certain specific, and generally unrealistic, conditions are met. However, we will leave the discussion of this for later.

      Plotting the yields of bonds along the maturity term structure will give us our yield curve. It is very important that only bonds from the same class of issuer or with the same degree of liquidity are used when plotting the yield curve. For example, a curve may be constructed for UK gilts or for AA‐rated sterling Eurobonds, but not a mixture of both, because gilts and Eurobonds are bonds from different class issuers. The primary yield curve in any domestic capital market is the government bond yield curve, so for example, in the US market it is the US Treasury yield curve. With the advent of the euro currency in 11 (ultimately 19) countries of the European Union, in theory any euro‐currency government bond can be used to plot a default‐free euro yield curve. In practice, only bonds from the same government are used, as for various reasons different bonds within euro‐currency countries trade at different yields. Outside the government, bond markets yield curves are plotted for Eurobonds, money market instruments, off‐balance sheet instruments, in fact virtually all debt market instruments. Therefore it is always important to remember to compare like‐for‐like when analysing yield curves across markets.

      In this chapter, we look at the yield to maturity yield curve as well as other types of yield curves that may be constructed. We also consider how to derive spot and forward yields from a current redemption yield curve. The main emphasis though, is on interpreting the shape of the yield curve, and explaining why it assumes the shapes it does. Later in the book we examine more advanced techniques for

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