GLENN M. SCHULTZ is the Director of mortgage analytics for Performance Trust Capital Partners. He co-edited (with Frank Fabozzi) Structured Products and Related Credit Derivatives (Wiley), as well as authored several chapters in the Handbook of MBS Securities and The Handbook of Fixed Income Securities.

Foreword iii

Acknowledgments v

Introduction ix

Preface xix

Part I Valuation of Fixed Income Securities 1

Chapter 1 The Time Value of Money 3

1.1 Present Value 4

1.2 Future Value 5

1.3 Present Value of an Annuity 6

1.4 Future Value of an Annuity 7

1.5 Solving Financial Questions with Present and Future Value 8

1.6 Application to Fixed Income Securities 9

Chapter 2 Theories of the Term Structure of Interest Rates 11

2.1 The Rational or Pure Expectations Hypothesis 13

2.2 The Market Segmentation Theory 17

2.3 The Liquidity Preference Theory 17

2.4 Modeling the Term Structure of Interest Rates 19

2.5 Application of Spot and Forward Rates 21

Chapter 3 Fixed Income Metrics 27

3.1 Maturity 28

3.2 Yield to Maturity 28

3.3 Weighted Average Life 34

3.4 Duration 36

3.4.1 Macaulay Duration 37

3.4.2 Modified Duration 39

3.5 Convexity 42

3.6 Fisher-Weil Duration and Convexity 45

3.7 Effective Duration 51

3.8 Effective Convexity 53

3.9 Summing the Aforementioned Measures of Duration and Convexity 54

3.10 Key Rate Duration 55

Chapter 4 The Valuation of Fixed Income Securities 59

4.1 A Valuation Framework for Fixed Income Securities 60

4.2 Application of the Framework to Structured Securities 61

4.3 Twist and Shift: Characterizing Changes in the Level, Steepness, and Curvature of the Term Structure 63

4.4 Case Study: 4.00% 30-year MBS 65

4.5 Scenario Comparative Analysis 74

Chapter 5 Fixed Income Return Analysis 77

5.1 Return Strategies 78

5.2 The Components of Return 80

5.3 The Buy and Hold Strategy 80

5.4 Total and Absolute Returns 83

5.5 Deconstructing the Fixed Income Return Profile 84

5.6 Estimating Bond Returns with Price and Risk Measures 86

Part II Residential Mortgage Backed Securities 89

Chapter 6 Understanding Mortgage Lending and Loans 91

6.1 Classification of Real Estate 92

6.2 Residential Mortgage Loan Amortization 100

6.3 Deconstructing the Amortization Table 103

6.4 Mortgage Servicing 104

Chapter 7 Modeling Cash Flows 107

7.1 Prepayment Conventions 108

7.2 Modeling MBS Cash Flows 111

7.2.1 0% PPC Assumption - No Prepayment 112

Chapter 8 Mortgage Prepayment Analysis 117

8.1 Big Data - What is it? 118

8.2 The Statistical Learner 118

8.3 Survival Analysis 120

8.4 The Cox Proportional Hazards Model 125

8.5 Data Types 127

8.6 Case Study: FHLMC 30-yr Loan Level Prepayment Analysis 128

8.7 Survival Analysis - Modeling Loan Cohorts 139

Chapter 9 The Predictive Prepayment Model 145

9.1 Turnover 147

9.2 Loan Seasoning 147

9.3 Seasonality 149

9.4 Borrower Incentive to Refinance 150

9.5 Borrower Burnout 153

9.6 Application of the Prepayment Model 162

Part III Valuation of Mortgage Backed Securities 167

Chapter 10 Mortgage Dollar Roll 169

10.1 Evaluating the Dollar Roll 171

10.2 Risk Associated with the Dollar Roll 179

Chapter 11 Relative Value Analysis 183

11.1 Liquidity 184

11.2 Static Cash Flow Analysis 185

11.3 Return Analysis 189

Chapter 12 Option Adjusted Spread Analysis 197

12.1 Numerical Methods of Modern Financial Theory 199

12.2 Cox, Ingersoll, Ross Theory of the Term Structure 201

12.3 Calibrating the Model 206

12.4 Building the Option Adjusted Spread (OAS) Model 208

12.5 OAS Analysis as a Decision Making Tool 216

12.6 OAS Distribution Analysis 219

12.7 OAS Analysis Strengths and Limitations 225

Part IV Structuring Mortgage Backed Securities 227

Chapter 13 Introduction to REMICs 229

13.1 Background and Legal Structure 230

13.2 Two Tiered REMICs 234

13.3 REMIC Arbitrage 235

13.4 Bond Lab MBS Structuring Model 237

Chapter 14 Stripped Mortgage Backed Securities 239

14.1 Key Rate Duration Analysis 243

14.2 Option Adjusted Spread Analysis 245

14.3 The Information Content of the IO-PO Market 249

Chapter 15 Sequentially Structured REMIC 255

15.1 Key Rate Duration Analysis 259

15.2 Option Adjusted Spread Analysis 261

15.3 Weighted Average Life and Spot Spread Analysis 261

15.4 Static Cash Flow Analysis 266

Chapter 16 Planned Amortization Class (PAC) and Companion REMICs 269

16.1 The PAC Bond Sinking Fund Schedule 270

16.2 Key Rate Duration Analysis 277

16.3 Option Adjusted Spread Analysis 279

16.4 OAS Distribution Analysis 280

16.5 A Final Word Regarding PAC Bands 284

16.6 Static Cash Flow Analysis 285

Chapter 17 Sequential IO REMIC 287

17.1 Key Rate Duration Analysis 290

17.2 OAS Distribution Analysis 292

Chapter 18 PAC-Floater-Inverse Floater REMIC 295

18.1 Structuring the Floater and Inverse Floater 296

18.2 A Framework for Floating Rate Securities 301

18.3 Option Adjusted Spread Analysis 304

18.4 Key Rate Duration Analysis 304

Chapter 19 Accrual REMIC Z-bond 311

19.1 Key Rate Duration Analysis 317

19.2 Option Adjusted Spread Analysis 318

Part V Mortgage Credit Analysis 323

Chapter 20 Mortgage Default Modeling 325

20.1 Case Study FHLMC 30-year Default Analysis 327

20.2 Other Variables Influencing Borrower Default 335

20.3 Spread at Origination (SATO) and Default 340

20.4 Default Model Selection 340

Chapter 21 The Predictive Default Model 345

21.1 Constant Default Rate 347

21.2 Borrower Original Loan to Value Default Multiplier 348

21.3 Updated Loan to Value Default Multiplier 349

21.4 Spread at Origination (SATO) Default Multipliers 351

21.5 Completing the Prepayment Model 353

Chapter 22 The Basics of Private Label MBS 357

22.3 Y Structure 359

22.4 Shifting Interest 362

22.5 Deep Mortgage Insurance MI 363

22.6 Excess Interest 365

22.7 Overcollateralization 366

22.8 Structural Credit Protection 366

22.9 Hedging Asset/Liability Mismatches 369

Chapter 23 Sizing Mortgage Credit Enhancement 373

23.1 Simulating Borrower Default Rates 375

23.2 Estimation of Cumulative Default Rates 375

23.3 Translating Credit Enhancement to a Third Party Guarantee Fee 378

23.4 Role of the Credit Rating Agencies (NRSROs) 379

Chapter 24 Index 383

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