FABOZZI

MANN

To remain a competitive fi xed income investor, both seasoned professionals and newcomers must stay up to date and

knowledgeable about this continually evolving fi eld.

Nobody understands this better than fi xed income experts Frank Fabozzi and Steven Mann. And now, with the revised and updated Introduction to Fixed Income Analytics, Second Edition, they provide complete coverage of the most important issues in this area. Following in the footsteps of the popular fi rst edition, this reliable resource skillfully details the key analytical concepts used in the fi xed income market and illustrates how they are computed.

This book addresses everything from the valuation of fi xed income securities with embedded options to the features of structured products—such as mortgage-backed securities and asset-backed securities—while also offering insights on basic principles like the time value of money. Updated to refl ect current market trends, Introduction to Fixed Income Analytics, Second Edition will help practicing investment professionals invest wisely in this new era, as well as assist those aspiring to enter the fi eld. Along the way, this practical guide:

• Outlines approaches to bond valuation based on the discounted cash fl ow framework as well as relative value analysis

• Ties in analytical concepts with what is available on the Bloomberg Terminal and walks you through relevant Bloomberg functions

• Explains a superior metric for quantifying a portfolio’s risk exposure: conditional value-at-risk (VaR)

• Describes the various issues associated with interest rate swaps—from counterparties and risk-return profi le to economic interpretation—and illustrates how to value them

Each chapter includes end-of-chapter questions so readers can test their knowledge of the concepts discussed as well as refi ne any computational skills needed to succeed.

Understanding fi xed income analytics is essential in today’s dynamic fi nancial environment. The Second Edition of Introduction to Fixed Income Analytics will help you build a solid foundation in this fi eld.

FRANK J. FABOZZI, PHD, CFA, CPA, is Professor in the Practice of Finance and Becton Fellow at the Yale School of Management and Editor of the Journal of Portfolio Management. He is an Affi liated Professor at the University of Karlsruhe’s Institute of Statistics, Econometrics, and Mathematical Finance and on the Advisory Council for the Department of Operations Research and Financial Engineering at Princeton University.

STEVEN V. MANN, PHD, is Professor of Finance at the Moore School of Business, University of South Carolina. He has published over seventy articles in fi nance journals and many books on fi xed income and derivatives topics, including The Global Money Markets, Measuring and Controlling Interest Rate and Credit Risk, Securities Finance (as a coeditor), and The Handbook of Fixed Income Securities (as an assistant editor). Mann is an active consultant to clients that include some of the largest investment/commercial banks in the world as well as a number of Fortune 500 companies.

Jacket Image: iStockphoto

With the Second Edition of Introduction to Fixed Income Analytics, Frank Fabozzi

and Steven Mann return with a fully updated guide to the discipline of fi xed

income analysis. Written for both fi nancial professionals and fi xed income

newcomers, this essential resource carefully covers the crucial elements of today’s

complex bond marketplace—from the various issues associated with investing

in fi xed income securities to the fundamentals of valuation and interest rate risk.

Fabozzi and Mann offer invaluable fi xed income insights, with discussions of

relative value analysis and value-at-risk measures; analysis of mortgage-backed

and asset-backed securities, convertible fi xed income securities, and volatility

estimation; and information on instruments like Treasury infl ation-protected

securities (TIPS). They also highlight one of the most popular systems relied

upon by fi xed income professionals—the Bloomberg Terminal—and tie in

important analytics and functionality.

The fi xed income market is one of the largest in the world. It spans many

sectors, from Treasuries to mortgages to high yield bonds. If you want to gain a

fi rm understanding of the tools and techniques needed to succeed in this fi eld,

look no further than Introduction to Fixed Income Analytics, Second Edition.

$100.00 USA / $120.00 CAN

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FRANK J. FABOZZI • STEVEN V. MANN

Relative Value Analysis,Risk Measures, and Valuation

SE C ON D E DI T ION

S E C O N D E D I T I O N

S E C O N DE D I T I O N

Introduction to Fixed Income

Analytics Second Edition

The Frank J. Fabozzi SeriesFixed Income Securities, Second Edition by Frank J. FabozziFocus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. AbateHandbook of Global Fixed Income Calculations by Dragomir KrginManaging a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. FabozziReal Options and Option-Embedded Securities by William T. MooreCapital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. FabozziThe Exchange-Traded Funds Manual by Gary L. GastineauProfessional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. FabozziInvesting in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia PilarinuHandbook of Alternative Assets by Mark J. P. AnsonThe Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad ChoudhryThe Handbook of Financial Instruments edited by Frank J. FabozziCollateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. FabozziInterest Rate, Term Structure, and Valuation Modeling edited by Frank J. FabozziInvestment Performance Measurement by Bruce J. FeibelThe Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. FabozziThe Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. MarkowitzFoundations of Economic Value Added, Second Edition by James L. GrantFinancial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. PetersonMeasuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi,

Steven V. Mann, and Moorad ChoudhryProfessional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. FabozziThe Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and Moorad ChoudhryThe Handbook of European Structured Financial Products edited by Frank J. Fabozzi and

Moorad ChoudhryThe Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi and

Frank J. FabozziShort Selling: Strategies, Risks, and Rewards edited by Frank J. FabozziThe Real Estate Investment Handbook by G. Timothy Haight and Daniel SingerMarket Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. LevySecurities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi and

Steven V. MannFat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and

Frank J. FabozziFinancial Modeling of the Equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M.

Focardi, and Petter N. KolmAdvanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by

Frank J. Fabozzi, Lionel Martellini, and Philippe PriauletAnalysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. FabozziCollateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S.

Goodman, and Frank J. FabozziHandbook of Alternative Assets, Second Edition by Mark J. P. AnsonIntroduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad ChoudhryFinancial Econometrics by Svetlozar T. Rachev, Stefan Mittnik, Frank J. Fabozzi, Sergio M. Focardi, and

Teo Jasic Developments in Collateralized Debt Obligations: New Products and Insights by Douglas J. Lucas,

Laurie S. Goodman, Frank J. Fabozzi, and Rebecca J. ManningRobust Portfolio Optimization and Management by Frank J. Fabozzi, Peter N. Kolm,

Dessislava A. Pachamanova, and Sergio M. FocardiAdvanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T. Rachev,

Stogan V. Stoyanov, and Frank J. FabozziHow to Select Investment Managers and Evaluate Performance by G. Timothy Haight,

Stephen O. Morrell, and Glenn E. RossBayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and

Frank J. FabozziStructured Products and Related Credit Derivatives by Brian P. Lancaster, Glenn M. Schultz, and Frank J. FabozziQuantitative Equity Investing: Techniques and Strategies by Frank J. Fabozzi, CFA, Sergio M. Focardi,

Petter N. Kolm

John Wiley & Sons, Inc.

Introduction to Fixed Income

Analytics Second Edition

Relative Value Analysis, Risk Measures, and Valuation

FRANK J. FABOzzI STEVEN V. MANN

Copyright © 2010 by John Wiley & Sons, Inc. All rights reserved.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey.Published simultaneously in Canada.

No part of this publication may be reproduced, stored in a retrieval system, or transmit-ted in any form or by any means, electronic, mechanical, photocopying, recording, scan-ning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions.

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. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages.

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Library of Congress Cataloging-in-Publication Data:

Fabozzi, Frank J.Introduction to fixed income analytics : relative value analysis, risk measures, and valua-tion / Frank J. Fabozzi, Steven V. Mann.—2nd ed.

p. cm.—(Frank J. Fabozzi series ; 191)Includes index.ISBN 978-0-470-57213-9 (cloth); 978-0-470-92209-5 (ebk); 978-0-470-92210-1 (ebk)

1. Fixed-income securities. 2. Fixed income securities—Mathematics. 3. Rate of return. 4. Risk management. I. Mann, Steven V. II. Title. HG4650.F335 2010332.63’2—dc22

2010026721

Printed in the United States of America.

10 9 8 7 6 5 4 3 2 1

FJFTo my wife Donna

and my children Patricia, Karly, and Francesco

SVMTo my wife, Mary – TDA

Contents

vii

Preface xiiiAbouttheAuthors xv

ChAPter1timeValueofMoney 1

Future Value of a Single Cash Flow 1Present Value of a Single Cash Flow 4Compounding/Discounting When Interest Is Paid

More Than Annually 8Future and Present Values of an Ordinary Annuity 10Yield (Internal Rate of Return) 20Concepts Presented in this Chapter 26Appendix: Compounding and Discounting in Continuous Time 27Questions 31

ChAPter2YieldCurveAnalysis:SpotratesandForwardrates 33

A Bond Is a Package of Zero-Coupon Instruments 33Theoretical Spot Rates 34Forward Rates 44Dynamics of the Yield Curve 57Concepts Presented in this Chapter 60Questions 60

ChAPter3DayCountConventionsandAccruedInterest 63

Day Count Conventions 63Computing the Accrued Interest 74Concepts Presented in this Chapter 76Questions 76

viii Contents

ChAPter4ValuationofOption-FreeBonds 77

General Principles of Valuation 77Determining a Bond’s Value 80The Price/Discount Rate Relationship 84Time Path of Bond 86Valuing a Zero-Coupon Bond 90Valuing a Bond Between Coupon Payments 90Traditional Approach to Valuation 94The Arbitrage-Free Valuation Approach 96Concepts Presented in this Chapter 107Questions 108

ChAPter5YieldMeasures 109

Sources of Return 109Traditional Yield Measures 113Yield to Call 121Yield to Put 123Yield to Worst 123Cash Flow Yield 124Portfolio Yield Measures 125Yield Measures for U.S. Treasury Bills 128Yield Spread Measures Relative to a Spot Rate Curve 134Concepts Presented in this Chapter 137Appendix: Mathematics of the Internal Rate of Return 138Questions 139

ChAPter6AnalysisofFloatingrateSecurities 141

General Features of Floaters 141Valuing a Risky Floater 150Valuation of Floaters with Embedded Options 157Margin Measures 157Concepts Presented in this Chapter 166Questions 167

ChAPter7ValuationofBondswithembeddedOptions 169

Overview of the Valuation of Bonds with Embedded Options 169Option-Adjusted Spread and Option Cost 170

Contents ix

Lattice Model 172Binomial Model 175Illustration 196Concepts Presented in this Chapter 198Questions 198

ChAPter8CashFlowforMortgage-BackedSecuritiesandAmortizingAsset-BackedSecurities 199

Cash Flow of Mortgage-Backed Securities 199Amortizing Asset-Backed Securities 238Concepts Presented in this Chapter 242Questions 244

ChAPter9ValuationofMortgage-BackedandAsset-BackedSecurities 247

Static Cash Flow Yield Analysis 247Monte Carlo Simulation/OAS 249Concepts Presented in this Chapter 270Questions 270

ChAPter10AnalysisofConvertibleBonds 273

General Characteristics of Convertible Bonds 273Tools for Analyzing Convertibles 276Call and Put Features 278Convertible Bond Arbitrage 279Other Types of Convertibles 283Concepts Presented in this Chapter 285Questions 285

ChAPter11totalreturn 287

Computing the Total Return 287OAS-Total Return 290Total Return to Maturity 291Total Return for a Mortgage-Backed Security 299Portfolio Total Return 301Total Return Analysis for Multiple Scenarios 301Concepts Presented in this Chapter 314Questions 314

x Contents

ChAPter12MeasuringInterestraterisk 317

The Full Valuation Approach 317Price Volatility Characteristics of Bonds 324Duration 334Other Duration Measures 350Convexity 360Price Value of a Basis Point 365The Importance of Yield Volatility 367Concepts Presented in this Chapter 369Questions 370

ChAPter13Value-at-riskMeasureandextensions 373

Value-at-Risk 373Conditional Value-at-Risk 384Concepts Presented in this Chapter 385Questions 386

ChAPter14AnalysisofInflation-ProtectedBonds 387

Breakeven Inflation rate 388Valuation of TIPS 389Measuring Interest Rate Risk 394Concepts Presented in this Chapter 397Questions 397

ChAPter15thetoolsofrelativeValueAnalysis 399

How Portfolio Managers Add Value 399Yield Spreads over Swap and Treasury Curves 400Asset Swaps 403Credit Default Swaps 410Concepts Presented in this Chapter 413Questions 414

ChAPter16AnalysisofInterestrateSwaps 417

Description of an Interest Rate Swap 417Interpreting a Swap Position 419Terminology, Conventions, and Market Quotes 421

Contents xi

Valuing Interest Rate Swaps 424Primary Determinants of Swap Spreads 440Dollar Duration of a Swap 445Concepts Presented in this Chapter 447Questions 447

ChAPter17estimatingYieldVolatility 451

Historical Volatility 451Implied Volatility 455Forecasting Yield Volatility 459Concepts Presented in this Chapter 463Questions 463

InDex 465

Preface

xiii

Participants in the fixed income market are inundated with terms and con-cepts in both the popular press and, more typically, in research reports

and professional journal articles. Making life more difficult for profession-als in this market sector is the fact that for some important analytical con-cepts, the same concept is referred to in different ways by different dealer firms and asset management firms. The purpose of this book is to describe the key analytical concepts used in the fixed income market and illustrate how they are computed. The book is not only intended for professionals but also newcomers to the field. It is for this reason that we provide end of chapter questions.

Although market professionals often want a walk through demonstra-tion of how a metric is computed, once they are comfortable with the con-cept and its computation, professionals then rely on vendors of analytical systems. Probably the most popular system relied upon by fixed income professionals is the Bloomberg System. For this reason, every chapter ties in the analytical concepts that are available on Bloomberg and walks the reader through the relevant Bloomberg screens. We want to thank Bloom-berg Financial for granting us permission to reproduce the screens that we used in our exhibits.

We begin the book with an explanation of the most basic concept in finance: the time value of money. In Chapter 2, we describe yield curve analysis, discussing the importance of spot rates and forward rates. The fixed income market has adopted various conventions for determining the number of days when computing accrued interest when trades are settled. These market conventions are the subject of Chapter 3.

The basics of bond valuation are covered in Chapter 4. Our focus in this chapter is on option-free bonds (i.e., bonds that are not callable, putable or convertible) and that have a fixed coupon rate. Yield measures for bonds are covered in Chapter 5.

The analysis of floating rate securities and bonds whose coupon interest is linked to some inflation measure are the subjects of Chapters 6 and 14, respectively. Bonds with embedded options are the subjects of Chapters 7, 9, and 10. Chapter 7 explains how to analyze callable and putable agency and corporate bonds. All residential mortgage-backed securities and certain