Introduction to Fixed Income Analytics Second Edition The Frank J. Fabozzi Series Fixed Income Securities, Second Edition by Frank J. Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L. Grant and James A. Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi Real Options and Option-Embedded Securities by William T. Moore Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi The Exchange-Traded Funds Manual by Gary L. Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited by Frank J. Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J. P. Anson The Global Money Markets by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S. Goodman and Frank J. Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J. Fabozzi Investment Performance Measurement by Bruce J. Feibel The Handbook of Equity Style Management edited by T. Daniel Coggin and Frank J. Fabozzi The Theory and Practice of Investment Management edited by Frank J. Fabozzi and Harry M. Markowitz Foundations of Economic Value Added, Second Edition by James L. Grant Financial Management and Analysis, Second Edition by Frank J. Fabozzi and Pamela P. Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J. Fabozzi, Steven V. Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume 4 edited by Frank J. Fabozzi The Handbook of European Fixed Income Securities edited by Frank J. Fabozzi and Moorad Choudhry The Handbook of European Structured Financial Products edited by Frank J. Fabozzi and Moorad Choudhry The Mathematics of Financial Modeling and Investment Management by Sergio M. Focardi and Frank J. Fabozzi Short Selling: Strategies, Risks, and Rewards edited by Frank J. Fabozzi The Real Estate Investment Handbook by G. Timothy Haight and Daniel Singer Market Neutral Strategies edited by Bruce I. Jacobs and Kenneth N. Levy Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J. Fabozzi and Steven V. Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T. Rachev, Christian Menn, and Frank J. Fabozzi Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J. Fabozzi, Sergio M. Focardi, and Petter N. Kolm Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by Frank J. Fabozzi, Lionel Martellini, and Philippe Priaulet Analysis of Financial Statements, Second Edition by Pamela P. Peterson and Frank J. Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J. Lucas, Laurie S. Goodman, and Frank J. Fabozzi Handbook of Alternative Assets, Second Edition by Mark J. P. Anson Introduction to Structured Finance by Frank J. Fabozzi, Henry A. Davis, and Moorad Choudhry Financial 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. Manning Robust Portfolio Optimization and Management by Frank J. Fabozzi, Peter N. Kolm, Dessislava A. Pachamanova, and Sergio M. Focardi Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T. Rachev, Stogan V. Stoyanov, and Frank J. Fabozzi How to Select Investment Managers and Evaluate Performance by G. Timothy Haight, Stephen O. Morrell, and Glenn E. Ross Bayesian Methods in Finance by Svetlozar T. Rachev, John S. J. Hsu, Biliana S. Bagasheva, and Frank J. Fabozzi Structured Products and Related Credit Derivatives by Brian P. Lancaster, Glenn M. Schultz, and Frank J. Fabozzi Quantitative Equity Investing: Techniques and Strategies by Frank J. Fabozzi, CFA, Sergio M. Focardi, Petter N. Kolm Introduction to Fixed Income Analytics Second Edition Relative Value Analysis, Risk Measures, and Valuation FRANK J. FABOZZI STEVEN V. MANN John Wiley & Sons, Inc. 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. For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993, or fax (317) 572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. For more information about Wiley products, visit our web site at www.wiley.com. 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 2010 332.63’2—dc22 2010026721 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 FJF To my wife Donna and my children Patricia, Karly, and Francesco SVM To my wife, Mary – TDA Contents Preface xiii About the Authors xv CHAPTER 1 Time Value of Money 1 Future Value of a Single Cash Flow 1 Present Value of a Single Cash Flow 4 Compounding/Discounting When Interest Is Paid More Than Annually 8 Future and Present Values of an Ordinary Annuity 10 Yield (Internal Rate of Return) 20 Concepts Presented in this Chapter 26 Appendix: Compounding and Discounting in Continuous Time 27 Questions 31 CHAPTER 2 Yield Curve Analysis: Spot Rates and Forward Rates 33 A Bond Is a Package of Zero-Coupon Instruments 33 Theoretical Spot Rates 34 Forward Rates 44 Dynamics of the Yield Curve 57 Concepts Presented in this Chapter 60 Questions 60 CHAPTER 3 Day Count Conventions and Accrued Interest 63 Day Count Conventions 63 Computing the Accrued Interest 74 Concepts Presented in this Chapter 76 Questions 76 vii viii CONTENTS CHAPTER 4 Valuation of Option-Free Bonds 77 General Principles of Valuation 77 Determining a Bond’s Value 80 The Price/Discount Rate Relationship 84 Time Path of Bond 86 Valuing a Zero-Coupon Bond 90 Valuing a Bond Between Coupon Payments 90 Traditional Approach to Valuation 94 The Arbitrage-Free Valuation Approach 96 Concepts Presented in this Chapter 107 Questions 108 CHAPTER 5 Yield Measures 109 Sources of Return 109 Traditional Yield Measures 113 Yield to Call 121 Yield to Put 123 Yield to Worst 123 Cash Flow Yield 124 Portfolio Yield Measures 125 Yield Measures for U.S. Treasury Bills 128 Yield Spread Measures Relative to a Spot Rate Curve 134 Concepts Presented in this Chapter 137 Appendix: Mathematics of the Internal Rate of Return 138 Questions 139 CHAPTER 6 Analysis of Floating Rate Securities 141 General Features of Floaters 141 Valuing a Risky Floater 150 Valuation of Floaters with Embedded Options 157 Margin Measures 157 Concepts Presented in this Chapter 166 Questions 167 CHAPTER 7 Valuation of Bonds with Embedded Options 169 Overview of the Valuation of Bonds with Embedded Options 169 Option-Adjusted Spread and Option Cost 170 Contents ix Lattice Model 172 Binomial Model 175 Illustration 196 Concepts Presented in this Chapter 198 Questions 198 CHAPTER 8 Cash Flow for Mortgage-Backed Securities and Amortizing Asset-Backed Securities 199 Cash Flow of Mortgage-Backed Securities 199 Amortizing Asset-Backed Securities 238 Concepts Presented in this Chapter 242 Questions 244 CHAPTER 9 Valuation of Mortgage-Backed and Asset-Backed Securities 247 Static Cash Flow Yield Analysis 247 Monte Carlo Simulation/OAS 249 Concepts Presented in this Chapter 270 Questions 270 CHAPTER 10 Analysis of Convertible Bonds 273 General Characteristics of Convertible Bonds 273 Tools for Analyzing Convertibles 276 Call and Put Features 278 Convertible Bond Arbitrage 279 Other Types of Convertibles 283 Concepts Presented in this Chapter 285 Questions 285 CHAPTER 11 Total Return 287 Computing the Total Return 287 OAS-Total Return 290 Total Return to Maturity 291 Total Return for a Mortgage-Backed Security 299 Portfolio Total Return 301 Total Return Analysis for Multiple Scenarios 301 Concepts Presented in this Chapter 314 Questions 314 x CONTENTS CHAPTER 12 Measuring Interest Rate Risk 317 The Full Valuation Approach 317 Price Volatility Characteristics of Bonds 324 Duration 334 Other Duration Measures 350 Convexity 360 Price Value of a Basis Point 365 The Importance of Yield Volatility 367 Concepts Presented in this Chapter 369 Questions 370 CHAPTER 13 Value-at-Risk Measure and Extensions 373 Value-at-Risk 373 Conditional Value-at-Risk 384 Concepts Presented in this Chapter 385 Questions 386 CHAPTER 14 Analysis of Inflation-Protected Bonds 387 Breakeven Inflation rate 388 Valuation of TIPS 389 Measuring Interest Rate Risk 394 Concepts Presented in this Chapter 397 Questions 397 CHAPTER 15 The Tools of Relative Value Analysis 399 How Portfolio Managers Add Value 399 Yield Spreads over Swap and Treasury Curves 400 Asset Swaps 403 Credit Default Swaps 410 Concepts Presented in this Chapter 413 Questions 414 CHAPTER 16 Analysis of Interest Rate Swaps 417 Description of an Interest Rate Swap 417 Interpreting a Swap Position 419 Terminology, Conventions, and Market Quotes 421 Contents xi Valuing Interest Rate Swaps 424 Primary Determinants of Swap Spreads 440 Dollar Duration of a Swap 445 Concepts Presented in this Chapter 447 Questions 447 CHAPTER 17 Estimating Yield Volatility 451 Historical Volatility 451 Implied Volatility 455 Forecasting Yield Volatility 459 Concepts Presented in this Chapter 463 Questions 463 INDEX 465