Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures and Valuation, 2nd Edition

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

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

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

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

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