Introduction to Fixed Income Analytics

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 Affiliated 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 finance journals and many books on fixed 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.

• Preface xiiiAbout the Authors xvCHAPTER 1: Time Value of Money 1Future 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 31CHAPTER 2: Yield Curve Analysis: Spot Rates and Forward Rates 33A Bond Is a Package of Zero-Coupon Instruments 33Theoretical Spot Rates 34Forward Rates 44Dynamics of the Yield Curve 57Concepts Presented in this CHAPTER 60Questions 60CHAPTER 3: Day Count Conventions and Accrued Interest 63Day Count Conventions 63Computing the Accrued Interest 74Concepts Presented in this Chapter 76Questions 76CHAPTER 4: Valuation of Option-Free Bonds 77General 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 108CHAPTER 5: Yield Measures 109Sources 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 139CHAPTER 6: Analysis of Floating Rate Securities 141General Features of Floaters 141Valuing a Risky Floater 150Valuation of Floaters with Embedded Options 157Margin Measures 157Concepts Presented in this Chapter 166Questions 167CHAPTER 7: Valuation of Bonds with Embedded Options 169Overview of the Valuation of Bonds with Embedded Options 169Option-Adjusted Spread and Option Cost 170Lattice Model 172Binomial Model 175Illustration 196Concepts Presented in this Chapter 198Questions 198CHAPTER 8: Cash Flow for Mortgage-Backed Securities and Amortizing Asset-Backed Securities 199Cash Flow of Mortgage-Backed Securities 199Amortizing Asset-Backed Securities 238Concepts Presented in this Chapter 242Questions 244CHAPTER 9: Valuation of Mortgage-Backed and Asset-Backed Securities 247Static Cash Flow Yield Analysis 247Monte Carlo Simulation/OAS 249Concepts Presented in this Chapter 270Questions 270CHAPTER 10: Analysis of Convertible Bonds 273General 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 285CHAPTER 11: Total Return 287Computing 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 314CHAPTER 12: Measuring Interest Rate Risk 317The 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 370CHAPTER 13: Value-at-Risk Measure and Extensions 373Value-at-Risk 373Conditional Value-at-Risk 384Concepts Presented in this Chapter 385Questions 386CHAPTER 14: Analysis of Inflation-Protected Bonds 387Breakeven Inflation rate 388Valuation of TIPS 389Measuring Interest Rate Risk 394Concepts Presented in this Chapter 397Questions 397CHAPTER 15: The Tools of Relative Value Analysis 399How Portfolio Managers Add Value 399Yield Spreads over Swap and Treasury Curves 400Asset Swaps 403Credit Default Swaps 410Concepts Presented in this Chapter 413Questions 414CHAPTER 16: Analysis of Interest Rate Swaps 417Description of an Interest Rate Swap 417Interpreting a Swap Position 419Terminology, Conventions, and Market Quotes 421Valuing Interest Rate Swaps 424Primary Determinants of Swap Spreads 440Dollar Duration of a Swap 445Concepts Presented in this Chapter 447Questions 447CHAPTER 17: Estimating Yield Volatility 451Historical Volatility 451Implied Volatility 455Forecasting Yield Volatility 459Concepts Presented in this Chapter 463Questions 463Index 465