The Advanced Fixed Income and Derivatives Management Guide

A New Framework for Analyzing and Managing Fixed Income Portfolios

Global traders implementing alpha transfer or complex fixed income strategies need a stable and accurate term structure of interest rates (TSIR) for all fundamental rates. However, theoretical models of TSIR often lack accuracy and practical models such as splines are not mathematically stable.

In The Advanced Fixed Income and Derivatives Management Guide, author Saied Simozar provides a unique and novel solution. In this detailed and practical guide, Simozar lays out a new framework, one that allows analysts and traders to evaluate all global fixed income investments by discount functions, based on a stable TSIR, and perform valuation, risk measurement and performance attribution across all asset classes and currencies in a consistent and accurate way.

Packed with over 700 useful equations and pages of explanation, this book offers investors the most detailed analysis of many fixed income sectors including inflation linked and corporate securities and their respective derivatives as well as American bond options currently available.

You′ll learn to estimate recovery value from market data and assess the impact of recovery value on risks and valuations. The book gives you deeper insight into portfolio construction and optimization, performance attribution, security selection and uncovering arbitrage opportunities. Numerous market based examples of identifying alpha trades are included and many of the analytics are available on the book′s dedicated website (www.wiley.com/go/simozar). You′ll find worksheets, complete with macros, which you can download and use to measure risks and valuations based on the TSIR.

Analysts, portfolio managers and traders, keep this valuable guide at hand and learn to better manage your fixed income investments.

List of Tables v

List of Figures viii

Abbreviations x

Notation xii

Preface xvii

Acknowledgement xxi

Foreword xxii

Introduction 1

1. Review of Market Analytics 5

1.1. Bond Valuation 5

1.2. Simple Bond Analytics 7

1.3. Portfolio Analytics 9

1.4. Key Rate Durations 13

2. Term Structure of Rates 16

2.1. Linear and Non–linear Space 16

2.2. Basis Functions 18

2.3. Decay Coefficient 22

2.4. Forward Rates 22

2.5. Par Curve 24

2.6. Application to the US Yield Curve 24

2.7. Historical Yield Curve Components 27

2.8. Significance of the Term Structure Components 30

2.9. Estimating the Value of the Decay Coefficient 32

3. Comparison of Basis Functions 36

3.1. Polynomial Basis Functions 36

3.1. Exponential Basis Functions 36

3.1. Orthogonal Basis Functions 37

3.1. Key Basis Functions 38

3.5. Transformation of Basis Functions 40

3.3. Comparison with the Principal Components Analysis 47

3.4. Mean Reversion 53

3.5. Historical Tables of Basis Functions 55

4. Risk Measurement 57

4.1. Interest Rate Risks 57

4.2. Zero Coupon Bonds Examples 59

4.3. Eurodollar Futures Contracts Examples 61

4.4. Conventional Duration of a Portfolio 63

4.5. Risks and Basis Functions 64

4.6. Application to Key Rate Duration 67

4.7 Risk Measurement of a Treasury Index 72

5. Performance Attribution 74

5.1. Curve Performance 74

5.2. Yield Performance 76

5.3. Security Performance 76

5.4. Portfolio Performance 78

5.5. Aggregation of Contribution to Performance 84

6. Libor and Swaps 87

6.1. Term Structure of Libor 89

6.2. Adjustment Table for Rates 90

6.3. Risk Measurement and Performance Attribution of Swaps 92

6.4. Floating Libor Valuation and Risks 94

6.5. Repo and Financing Rate 97

6.6. Structural Problem of Swaps 97

7. Trading 100

7.1. Liquidity Management 100

7.2. Forward Pricing 104

7.3. Curve Trading 106

7.4. Synthetic Securities 111

7.5. Real Time Trading 115

8. Linear Optimization and Portfolio Replication 117

8.1. Portfolio Optimization Example 120

8.2. Conversion to and from Conventional KRD 123

8.3. KRD and Term Structure Hedging 124

9. Yield Volatility 125

9.1. Price Function of Yield Volatility 126

9.2. Term Structure of Yield Volatility 129

9.3. Volatility Adjustment Table 135

9.4. Forward and Instantaneous Volatility 137

10. Convexity and Long Rates 140

10.1. Theorem: Long Rates Can Never Change 140

10.2. Convexity Adjusted TSIR 144

10.3. Application to Convexity 149

10.4. Convexity Bias of Eurodollar Futures 154

11. Real Rates and Inflation Expectations 162

11.1. Term Structure of Real Rates 162

11.2. Theorem: Real Rates Cannot Have Log–normal Distribution 163

11.3. Inflation Linked (IL) Bonds 166

11.4. Seasonal Adjustments to Inflation 173

11.5. Inflation Swaps 179

12. Credit Spreads 184

12.1. Equilibrium Credit Spread 184

12.2. Term Structure of Credit Spreads 186

12.3. Risk Measurement of Credit Securities 187

12.4. Credit Risks Example 188

12.5. Floating Rate Credit Securities 189

12.6. TSCS Examples 191

12.7. Relative Values of Credit Securities 194

12.8. Performance Attribution of Credit Securities 197

12.9. Term Structure of Agencies 199

12.10. Performance Contribution 200

12.11. Partial Yield 203

13. Default and Recovery 206

13.1. Recovery, Guarantee and Default Probability 206

13.2. Risk Measurement with Recovery 211

13.3. Partial Yield of Complex Securities 218

13.4. Forward Coupon 220

13.5. Credit Default Swaps 221

14. Deliverable Bond Futures and Options 226

14.1. Simple Options Model 226

14.2. Conversion Factor 230

14.3. Futures Price on Delivery Date 231

14.4. Futures Price Prior to Delivery Date 231

14.5. Early versus Late Delivery 236

14.6. Strike Prices of the Underlying Options 237

14.7. Risk Measurement of Bond Futures 237

14.8. Analytics for Bond Futures 239

14.9. Australian Bond Futures 240

14.10. Replication of Bond Futures 241

14.11. Backtesting of Bond Futures 244

15. Bond Options 245

15.1. European Bond Options 245

15.2. Exercise Boundary of American Options 249

15.3. Present Value of a Future Bond Option 251

15.4. Feedforward Pricing 257

15.5. Bond Option Greeks 261

15.6. Risk Measurement of Bond Options 263

15.7. Treasury and Real Bonds Options 265

15.8. Bond Options with Credit Risk 266

15.9. Theorem: Credit Prices Are Not Arbitrage–free 269

15.10. Correlation Model 270

15.11. Credit Bond Options Examples 272

15.12. Risk Measurement of Complex Bond Options 274

15.13. Remarks on Bond Options 275

16. Currencies 277

16.1. Currency Forwards 278

16.2. Currency as an Asset Class 279

16.3. Currency Trading and Hedging 280

16.4. Valuation and Risks of Currency Positions 281

16.5. Currency Futures 283

16.6. Currency Options 283

17. Prepayment Model 285

17.1. Home Sale 285

17.2. Refinancing 287

17.3. Accelerated Payments 289

17.4. Prepayment Factor 290

18. Mortgage Bonds 291

18.1. Mortgage Valuation 292

18.2. Current Coupon 295

18.3. Mortgage Analytics 298

18.4. Mortgage Risk Measurement and Valuation 302

19. Product Design and Portfolio Construction 307

19.1. Product Analyzer 309

19.2. Portfolio Analyzer 312

19.3. Competitve Universe 313

19.4. Portfolio Construction 314

20. Calculating Parameters of the TSIR 319

20.1. Optimizing TSIR 321

20.2. Optimizing TSCR 325

20.3. Optimizing TSCR with No Convexity 329

20.4. Estimating Recovery Value 330

20.5. Robustness of the Term Structure Components 330

20.6. Calculating the Components of the TSYV 331

21. Implementation 333

21.1. Term Structure 333

21. 1.1. Primary Curve 333

21. 1.2. Real Curve 334

21. 1.3. Credit Curve and Recovery Value 335

21.2. Discount Function and Risk Measurement 336

21.3. Cash Flow Engine 337

21.4. Invoice Price 340

21.5. Analytics 340

21.6. Trade Date versus Settle Date 342

21.7. American Options 343

21.8. Linear Programming 348

21.9. Mortgage Analysis 349

References 351

Index 352

SAIED SIMOZAR, PhD, has spent almost 30 years in fixed income portfolio management, fixed income analytics, scientific software development and consulting. He is a principal at Fipmar, Inc., an investment management consulting firm in Beverly Hills, CA. Prior to that, Saied was a Managing Director at Nuveen Investments, with responsibilities for all global fixed income investments. He has also been a Managing Director at Bank of America Capital Management responsible for all global and emerging markets portfolios of the fixed income division. Prior to that, he was a senior portfolio manager at Putnam Investments and DuPont Pension Fund Investments.

For any queries about the book, please contact the author at: fixedincomebook@fipmar.com