fixed income - DavidJamiesonBolder Fixed-Income Portfolio Analytics A Practical Guide to Implementing Monitoring and Understanding Fixed-Income

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Unformatted text preview: David Jamieson Bolder Fixed-Income Portfolio Analytics A Practical Guide to Implementing, Monitoring and Understanding Fixed-Income Portfolios Fixed-Income Portfolio Analytics David Jamieson Bolder Fixed-Income Portfolio Analytics A Practical Guide to Implementing, Monitoring and Understanding Fixed-Income Portfolios 123 David Jamieson Bolder Bank for International Settlements Basel Switzerland ISBN 978-3-319-12666-1 ISBN 978-3-319-12667-8 (eBook) DOI 10.1007/978-3-319-12667-8 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2015930328 © Springer International Publishing Switzerland 2015 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer International Publishing Switzerland is part of Springer Science+Business Media ( ) À Nancy, la plus belle saison de ma vie Foreword Global fixed-income markets are enormous and growing. Trillions of dollars in numerous currencies are invested in these markets by a broad range of investors including pension funds, insurance companies, commercial banks, corporate treasuries, endowments, sovereign-wealth funds, and central-bank reserve managers. Each of these investors allocates significant resources towards evaluating, monitoring, and understanding the day-to-day exposures, performance, and risks associated with the underlying market risk factors found in their portfolios. It is precisely this type of careful attention by individual investors that leads to liquid, wellfunctioning, and efficient markets. Quantitative tools are an important aspect of this ongoing oversight and implementation of fixed-income portfolio strategies. Use of quantitative models, however, requires both expertise and caution. Models can be powerful tools for dealing with the uncertainty in fixed-income markets, but since they are only mathematical simplifications of a complex reality, they can also go wrong. This book, written by David Bolder, a member of the staff in the Banking Department at the Bank for International Settlements (BIS), is written with this point firmly in mind. It does not provide a prescriptive solution to fixed-income analytics, but rather takes a suggestive approach. In other words, instead of telling you what you should do, it indicates techniques that you might want to consider, examine further, or possibly implement. Moreover, it consistently tries to offer alternatives—which may perform better or worse under different sets of circumstances—for any given element of analysis. True quantitative expertise is based on the mastery of a wide range of techniques, where the underlying approaches are developed from alternative perspectives. This is an important element of the BIS philosophy and one of the central tenets of this book. This book simultaneously places a high value on the ongoing validation of these quantitative models. Chapters 8 and 12 are particularly useful in this respect, because they investigate a range of techniques for gauging the accuracy and robustness of one’s fixed-income performance and risk measures, respectively. Considering alternative models is always essential, but outlining, in advance, a framework for evaluating the robustness of these models is also critical. vii viii Foreword Why does this matter? Quantitative-based approaches, such as those presented in this book, necessarily involve assumptions and approximations. These assumptions will not always hold, nor will the approximations always be good. Realizing this fact about quantitative modelling is important. Prudent fixed-income management, therefore, also requires regular evaluation of one’s model results with realized market outcomes—often this is termed back-testing or model validation. This book wisely builds this concept into its overall quantitative framework. Putting these ideas into the public domain, an approach that is also consistent with the mandate of the BIS, is another way to assess the usefulness and validity of the quantitative approaches suggested in this book. Books are written to share knowledge, suggest ideas, and create discussion. Such a discussion can only propel the fixed-income investment community forward to better, more complete, and more robust quantitative methods. In summary, no quantitative model is perfect. Faced with the complexity of investing sizeable amounts of money in fixed-income markets, quantitative techniques are nonetheless necessary and useful for a broad spectrum of institutions. Focusing on a range of alternative techniques, making model validation a central part of one’s framework, and actively seeking feedback from the academic and practitioner community foster both a better understanding of one’s models and the underlying markets. It also ensures that these models continue to be useful to fixed-income investors. This book’s commitment to these principles makes me confident that it will be a valuable contribution to the literature. Basel, Switzerland September 2014 Jaime Caruana Preface A journey of a thousand miles must begin with a single step. Lao Tsu The first step in the creation of this book was the in-house development of a software application. The objective of this application was to provide decision-support analytics to a group of portfolio managers. Decision support means, in this context, the comparison of portfolios along a wide range of dimensions, the simulation of portfolio trades, the computation and attribution of risk and performance, and the provision of some optimization tools. We came, over the course of the project, to describe this collection of methods and techniques as portfolio analytics. The portfolios in question were, and still are, comprised of a relatively wide range of high-credit fixed-income instruments including principally sovereign, supranational, agency, and highly rated corporate bonds. The portfolios also included a range of ancillary instruments such as foreign-exchange swaps, bond and rate futures, inflation-linked bonds, and interest-rate swaps. In other words, these portfolios hold the typical fixed-income instruments found in the tool-kit of a reserve-portfolio manager in a central bank, a sovereign-wealth fund, a pension fund, an insurance company, an endowment, or an international institution. When one sets out to build such a system, the first step involves the establishment of a consistent framework for the classification, comparison, and analysis of different portfolios relative to their benchmark. Such a framework necessarily involves taking explicit decisions and making assumptions about the treatment of a wide range of instruments. I found this task to be particularly challenging given the relative dearth of detailed reference books describing methods for fixed-income portfolio analytics—there were references on fixed-income risk, performance, and exposure, but relatively little combining them in a single setting. The learning curve was steep, but the reward was an in-depth and practical understanding of a number of related ideas that are reasonably well described by the term, fixedincome portfolio analytics. Given the nature and mandate of my employer—the Bank of International Settlements (BIS), which is an international institution serving global central banks—it was naturally decided to share this knowledge with our ix x Preface customers. I consequently began to design presentations for various knowledgesharing seminars, with central-bank reserve managers, hosted by the BIS. Presentations can, however, be dangerous. With presentations, participants tend to forget exactly what the speaker said and later, in the comfort of their office, tend to re-interpret the meaning of a slide or a comment in a manner that the speaker did not actually intend. Moreover, an oral presentation rarely has the time—nor do listeners typically have the patience—to go sufficiently deep into the mathematical details. The appreciation of these facts was the genesis of this book. What the reader might find appealing about this work is that it is not an academic work. Instead, it is written for practitioners by a practitioner. The techniques in the following pages are not theoretical—they are used daily in a living, working fixedincome portfolio analytic system. The ideas in this text are inputs to internal and external reports used to take decisions on large fixed-income portfolios. This does not mean that this book has no academic value. On the contrary, many academic concepts and references are employed. What it does mean, however, is that is a practical document intended to help solve practical problems. Having made this point, the development in the following chapters does not represent the only, nor even the best, approach for the analysis of fixed-income portfolios. Our philosophy in the construction of the application—and the preparation of this book—was the development of a relatively simple, robust, and transparent framework. The advantage of such an approach is that one’s computations and analysis are subsequently easier to explain to managers, senior management, and one’s analyst colleagues. A clear disadvantage is that the system is always open to criticism that the techniques used are not sufficiently complex and that some of the approximations lack accuracy—we accept this critique and, moreover, encourage others to both challenge and improve upon the methods presented in this text. Basel, Switzerland September 2014 David Jamieson Bolder Acknowledgements Writing a book is no small undertaking and it is rarely the work of a single person. This work is no exception. Many people were involved, directly or indirectly, in the preparation of this book. I would first of all like to sincerely thank Jean-Pierre Matt for making this project possible and for consistently supporting the necessary effort involved in the production of this text. Understanding the needs of fixed-income investors—people who trade in, follow, and basically live in actual markets on a daily basis—is critical to building a practical approach. I would thus like to particularly thank my colleagues Danilo Maino, Alex Joia, Mark Vincent, Peter Van Der Meulen, Jacob Nelson, Mattias Will, and Miklos Endreffy for their constructive criticism and ideas for improvement in the internal software program underlying this analytical framework. This book took form over the course of a number of years and, during this time, has formed the base material in a series of week-long workshops for centralbank reserve managers. The participants in these seminars deserve my sincere gratitude. Their constant attentiveness, ongoing interest, and active questioning of the ideas and techniques—both during and often long after the workshops—were an invaluable source of motivation and improvement. I would like to thank Christophe Laforge for many valuable conversations during the initial stages of this project. His calm, open, and logical approach to discussing problems helped me to build a better basic framework. Finally, and perhaps most importantly, I would like to thank my wife and son for their support, understanding, and patience with the long hours involved in preparing this work. It should, of course, go without saying that all of my thanks and acknowledgement are entirely without implication. All errors, inconsistencies, shortcomings, or faults in logic remain entirely my responsibility. xi Contents 1 What Is Portfolio Analytics? . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.1 Fixed-Income Portfolio Management . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.2 Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.3 Tactics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.3.1 Asset Classes vs. Risk Factors . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.4 Strategy and Tactics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.5 Key Characteristics .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.5.1 Principles.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.6 An Appetizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.6.1 Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.6.2 Risk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.6.3 Return . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 1.7 The Coming Chapters .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Part I 1 1 2 4 5 7 8 10 11 12 13 15 16 17 From Risk Factors to Returns 2 Computing Exposures .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.1 A Starting Point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.2 Simple Yield Exposure .. . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.3 Correcting for Our Linear Approximation . . . . . .. . . . . . . . . . . . . . . . . . . . 2.4 Time Exposure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.5 Key-Rate Exposures.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.5.1 A Word of Caution . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.6 Spread Exposure.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.7 Foreign-Exchange Exposure .. . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 2.8 Concluding Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . Reference .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 21 21 22 29 31 33 39 40 45 46 46 3 A Useful Approximation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.1 What We Want. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.2 The Taylor Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 47 48 50 xiii xiv Contents 3.3 Applying the Taylor Series . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.3.1 Adding Risk Factors .. . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.4 The Foreign-Exchange Dimension . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 3.5 Closing Thoughts.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 4 55 60 62 65 66 Extending Our Framework.. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 67 4.1 Handling Inflation-Linked Bonds . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 68 4.1.1 Revisiting Exposures . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 68 4.1.2 Adjusting our Useful Approximation ... . . . . . . . . . . . . . . . . . . . 80 4.2 Handling Floating-Rate Notes . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 84 4.3 Handling Fixed-Income Derivatives Contracts .. . . . . . . . . . . . . . . . . . . . 90 4.3.1 Interest-Rate Futures . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 90 4.3.2 Bond Futures .. . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 98 4.4 Closing Thoughts.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 109 References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 109 Part II The Yield Curve 5 Fitting Yield Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.1 Getting Started.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2 Yield Curves 101 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.1 Pure-Discount Bond Prices. . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.2 Spot Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.3 Par Yields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.4 Implied-Forward Rates . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.2.5 Bringing It All Together .. . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3 Curve-Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3.1 The Classic Approach . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.3.2 Non-Classical Approaches . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 5.4 Concluding Thoughts . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . References .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . 113 114 117 118 119 120 124 126 128 129 137 148 148 6 Modell...
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