Fixed-Income Portfolio Analytics [recurso electrónico] : a Practical Guide to Implementing, Monitoring and Understanding Fixed-Income Portfolios

The book offers a detailed, robust, and consistent framework for the joint consideration of portfolio exposure, risk, and performance across a wide range of underlying fixed-income instruments and risk factors. Through extensive use of practical examples, the author also highlights the necessary technical tools and the common pitfalls that arise when working in this area. Finally, the book discusses tools for testing the reasonableness of the key analytics to help build and maintain confidence for using these techniques in day-to-day decision making. This will be of keen interest to risk managers, analysts and asset managers responsible for fixed-income portfolios. ℗ℓ ℗ℓ Foreword 8 Preface 10 Acknowledgements 12 Contents 14 List of Figures 20 List of Tables 26 1 What Is Portfolio Analytics? 29 1.1 Fixed-Income Portfolio Management 29 1.2 Strategy 30 1.3 Tactics 32 1.3.1 Asset Classes vs. Risk Factors 33 1.4 Strategy and Tactics 35 1.5 Key Characteristics 36 1.5.1 Principles 38 1.6 An Appetizer 39 1.6.1 Exposure 40 1.6.2 Risk 41 1.6.3 Return 43 1.7 The Coming Chapters 44 References 45 Part I From Risk Factors to Returns 47 2 Computing Exposures 48 2.1 A Starting Point 48 2.2 Simple Yield Exposure 49 2.3 Correcting for Our Linear Approximation 56 2.4 Time Exposure 58 2.5 Key-Rate Exposures 60 2.5.1 A Word of Caution 66 2.6 Spread Exposure 67 2.7 Foreign-Exchange Exposure 72 2.8 Concluding Thoughts 73 Reference 73 3 A Useful Approximation 74 3.1 What We Want 75 3.2 The Taylor Series 77 3.3 Applying the Taylor Series 82 3.3.1 Adding Risk Factors 87 3.4 The Foreign-Exchange Dimension 89 3.5 Closing Thoughts 92 References 93 4 Extending Our Framework 94 4.1 Handling Inflation-Linked Bonds 95 4.1.1 Revisiting Exposures 95 4.1.2 Adjusting our Useful Approximation 107 4.2 Handling Floating-Rate Notes 111 4.3 Handling Fixed-Income Derivatives Contracts 117 4.3.1 Interest-Rate Futures 117 4.3.2 Bond Futures 125 4.4 Closing Thoughts 136 References 136 Part II The Yield Curve 137 5 Fitting Yield Curves 138 5.1 Getting Started 139 5.2 Yield Curves 101 142 5.2.1 Pure-Discount Bond Prices 143 5.2.2 Spot Rates 144 5.2.3 Par Yields 145 5.2.4 Implied-Forward Rates 149 5.2.5 Bringing It All Together 151 5.3 Curve-Fitting 153 5.3.1 The Classic Approach 154 5.3.2 Non-Classical Approaches 162 5.4 Concluding Thoughts 173 References 173 6 Modelling Yield Curves 175 6.1 Why a Dynamic Yield-Curve Model? 176 6.2 Building a Model 183 6.2.1 A1 184 6.2.2 A2 186 6.2.3 A3 190 6.2.4 Bringing it All Together 191 6.3 A Statistical Digression 192 6.4 Model Examples 198 6.4.1 A Toy Example 198 6.4.2 A Complex Example 201 6.4.3 A Simpler Example 208 6.5 Concluding Thoughts 213 References 214 Part III Performance 217 7 Basic Performance Attribution 218 7.1 A Single Security 223 7.1.1 Dealing with Cash-Flows 224 7.1.2 Revisiting Our Risk-Factor Decomposition 229 7.2 Attribution of a Single Fixed-Income Security 231 7.2.1 Carry Return 234 7.2.2 Credit-Spread Return 238 7.2.3 Treasury-Curve Return 238 7.2.4 Convexity Return 249 7.2.5 Foreign-Exchange Return 250 7.2.6 Pulling It All Together 251 7.3 Attribution of a Fixed-Income Portfolio 252 7.4 Closing Thoughts 264 References 264 8 Advanced Performance Attribution 265 8.1 Truth in Advertising 266 8.2 Daily Attribution 268 8.3 A Simple Practical Example 273 8.3.1 The Very Fine Print 281 8.4 A Complicated Practical Example 282 8.4.1 An Experiment 282 8.4.2 Regression Analysis 283 8.4.3 An Invented Measure 286 8.4.4 Approximation Errors 287 8.5 Some Frustrating Mathematical Facts 289 8.6 Smoothing Returns 293 8.7 Concluding Thoughts 296 References 296 9 Traditional Performance Attribution 298 9.1 Asset Allocation and Security Selection 299 9.2 The Roll-Down Effect 309 9.3 Concluding Thoughts 315 References 315 Part IV Risk 316 10 Introducing Risk 317 10.1 Defining Risk 317 10.1.1 Determining Outcomes 318 10.1.2 Assigning Probabilities 319 10.1.3 Getting to Risk 320 10.2 A Simple Example 322 10.3 A More Complicated Example 326 10.3.1 Enter the Distribution 330 10.3.2 Relaxing Normality 332 10.3.3 The Role of Dependence 334 10.4 A Specific Risk Measure 337 10.4.1 Looking Backwards 339 10.4.2 Looking Forward 341 10.4.3 Comparing Forward- and Backward-Looking Perspectives 344 10.5 Using Tracking Error 346 10.6 Concluding Thoughts 348 References 349 11 Portfolio Risk 350 11.1 The Punchline 353 11.2 Getting Started 355 11.2.1 Portfolio Weights 356 11.2.2 Incorporating Risk-Factor Exposures 359 11.2.3 Handling Market Movements 362 11.2.4 Computing Return Distributions 365 11.3 Understanding and Exploring ΩR 367 11.3.1 Variance 101 367 11.3.2 Linking Covariance and Correlation 370 11.3.3 Classic and Alternative Estimators of ΩR 372 11.3.4 Simulating Random Realizations 379 11.4 The Final Results 385 11.5 Attributing Risk 388 11.6 Concluding Thoughts 399 References 400 12 Exploring Uncertainty in Risk Measurement 401 12.1 Sensitivity Analysis 402 12.1.1 Setting the Stage 403 12.1.2 The Data Frequency 406 12.1.3 Weighting Scheme 409 12.1.4 Role of Dependence 415 12.1.5 Summing Up 418 12.2 Backtesting 419 12.2.1 A Heuristic Perspective 420 12.2.2 A More Formal Perspective 423 12.2.3 Thinking Optimally 427 12.3 Concluding Thoughts 434 References 434 Part V Risk and Performance 435 13 Combining Risk and Return 436 13.1 The Data 439 13.1.1 Understanding Our data 440 13.2 Dampening Return Noise 446 13.2.1 The Moving Average 446 13.2.2 The Hodrick–Prescott Filter 447 13.2.3 The Kernel Regression 448 13.2.4 An Engineering Approach 449 13.2.5 Model Comparison 451 13.2.6 Implications of Filtering 452 13.3 Combining Risk and Return 454 13.3.1 Moving to the Risk-Factor Level 458 13.4 So What? 459 13.5 Concluding Thoughts 461 References 462 14 The Ex-Post World 463 14.1 Basic Statistical Analysis 464 14.2 Some Theory 475 14.2.1 Introducing β 476 14.2.2 Introducing α 479 14.2.3 α and β 481 14.3 Relative Risk 483 14.4 Risk-Adjusted Ratios 488 14.5 Beyond CAPM 495 14.6 Bringing It All Together 498 14.7 Concluding Thoughts 499 References 500 A Some Mathematical Background 501 A.1 Set Theory 502 A.2 Probability 503 A.2.1 Conditional Probability 505 A.2.2 Independence 507 A.3 Statistics 507 A.3.1 Distributions and Densities 508 A.3.2 Working with Distribution and Density Functions 512 A.3.3 Some Sample Statistical Distributions 513 A.3.4 Multivariate Statistics 520 A.4 Matrix Theory 524 A.4.1 Solving Linear Systems 527 A.4.2 Cholesky Decomposition 532 A.4.3 Eigenvalues and Eigenvectors 534 References 539 B A Few Thoughts on Optimization 540 B.1 A Linear Program 542 B.1.1 A Simple Case 543 B.1.2 Extending the Simple Case 547 B.2 Concluding Thoughts 548 References 549 Index 550 Author Index 556 Front Matter....Pages i-xxvii What Is Portfolio Analytics?....Pages 1-18 Front Matter....Pages 19-19 Computing Exposures....Pages 21-46 A Useful Approximation....Pages 47-66 Extending Our Framework....Pages 67-109 Front Matter....Pages 111-111 Fitting Yield Curves....Pages 113-149 Modelling Yield Curves....Pages 151-192 Front Matter....Pages 193-193 Basic Performance Attribution....Pages 195-241 Advanced Performance Attribution....Pages 243-275 Traditional Performance Attribution....Pages 277-294 Front Matter....Pages 295-295 Introducing Risk....Pages 297-329 Portfolio Risk....Pages 331-381 Exploring Uncertainty in Risk Measurement....Pages 383-416 Front Matter....Pages 417-417 Combining Risk and Return....Pages 419-445 The Ex-Post World....Pages 447-484 Back Matter....Pages 485-544 The book offers a detailed, robust, and consistent framework for the joint consideration of portfolio exposure, risk, and performance across a wide range of underlying fixed-income instruments and risk factors. Through extensive use of practical examples, the author also highlights the necessary technical tools and the common pitfalls that arise when working in this area. Finally, the book discusses tools for testing the reasonableness of the key analytics to help build and maintain confidence for using these techniques in day-to-day decision making. This will be of keen interest to risk managers, analysts and asset managers responsible for fixed-income portfolios. ℗l ℗l