Fixed Income Attribution

ANDREW COLIN is Fixed Income Research Director for the StatPro Group plc. He has previously worked or consulted for Citibank London, Zurich Investment Management, the Commonwealth Bank, Suncorp Metway, Chubb Security, Arthur Andersen, EDS, Alcatel and the Royal Australian Navy. Andrew is Adjunct Professor in the Faculty of Business at Queensland University of Technology, Brisbane, and holds a PhD in Mathematics from the University of St Andrews. His research interests include risk management and machine intelligence.

• Preface xiiiAcknowledgements xvA Note on Notation xviiPart I: Concepts of Attribution 11 Attribution in the Investment Process 31.1 Introduction 31.2 The problem 31.3 Adding value to portfolios 41.4 Skill in investment 51.4.1 Luck 51.4.2 Skill 51.5 Picking the good from the bad 51.6 Insight from attribution 61.7 Example 71.8 Living without attribution 81.9 Why is attribution difficult? 91.10 What does this book not cover? 91.11 What are we aiming for? 92 Calculation of Returns 112.1 Introduction 112.2 Getting it right 112.3 Rate of return 122.4 Linking performance over multiple intervals 122.5 Performance of single securities in the presence of cash flows 122.6 Performance of portfolios without cash flows 132.7 Performance of portfolios with cash flows 132.8 Portfolio cash flow assumptions 142.9 Example 1 152.10 Performance contribution 162.11 Bringing it all together 162.12 The effects of futures on performance 172.13 Short position 172.14 Example 2: Some unusual asset allocations 172.15 Example 3: A pathological case 182.16 Example 4: A portfolio with zero market value 192.17 Geometric compounding 192.17.1 Stock return 192.17.2 Portfolio return 202.17.3 Sector return 202.18 Performance from several sources of return 203 Simple Attribution 233.1 Introduction 233.2 Equity attribution 233.3 Additive attribution 243.4 Basic attribution: top-down or bottom-up? 253.5 Which assumptions to use? 263.6 Example 273.6.1 Measuring overall investment performance 273.7 Attribution at the sector level 283.8 Attribution for single stocks 293.9 Combining attribution returns over time 313.10 Self-consistency across time 323.11 Summary 334 Yield Curves in Attribution 354.1 Introduction 354.2 Yield curves 354.3 What is a yield curve? 364.4 Why yield curves matter in attribution 364.5 Different types of yield 374.5.1 Coupon rate 374.5.2 Current yield (or running yield) 374.5.3 Yield to maturity 374.6 Zero-coupon yield 384.7 Sovereign and credit curves 384.8 What should a curve look like? 384.9 Different types of curve – advantages and disadvantages 394.9.1 Par curves 394.9.2 Duration curves 394.9.3 Zero-coupon curves 394.10 Comparing different curve types 404.11 How do yield curves behave? 404.12 Credit curves 434.13 Finding yield curve data 435 Interest Rate Risk and Portfolio Management 455.1 Introduction 455.2 Return in fixed income portfolios 455.3 Risk numbers and interest rate sensitivity 455.4 Aggregating risk numbers 465.5 Hedging risk 475.6 Portfolio structure 475.7 Risk immunization 486 Measuring Changes in Yield Curves 516.1 Introduction 516.2 Curve shapes 516.3 Curves – the raw data 516.4 A typical curve movement 516.5 Describing curve changes 536.5.1 Should one go any further? 556.5.2 Can one use other movement descriptions? 556.6 Worked examples 556.7 Model-free representations of curves 566.8 Fitted model representations 576.9 Shift and curve positioning analysis 576.10 Polynomial term structure models 586.10.1 Example 1: Worked example for polynomial model 596.11 Nelson–Siegel term structure models 606.11.1 Example 2: Worked example for Nelson–Siegel model 626.12 Principal component analysis 636.13 Fitting data to models 646.14 Constraints in curve fitting 647 Converting Yield Movements into Performance 657.1 Pricing from first principles 657.2 Measuring the effects of yield curve shifts 667.3 Perturbational pricing 67Part II: Sources of Attribution Return 718 The Hierarchy of Fixed Income Returns 738.1 Subjectivity in attribution 738.2 Excess precision 739 Yield Return and Coupon Return 759.1 Yield return 759.2 Decomposition into coupon and convergence return 759.3 Coupon return 759.4 Convergence return 769.5 Decomposition into systematic and specific return 769.6 Calculating yield return 7710 Treasury Curve Return 7910.1 Movements in the Treasury curve 7910.2 No curve analysis 7910.3 Shift/twist/butterfly 7910.4 Duration attribution 8011 Roll Return 8311.1 Introduction 8311.2 Maximizing roll return 8311.3 Measuring roll return 8411.4 Measuring the effect of roll 8511.5 Separating roll return from yield curve return 8512 Credit Return 8712.1 Introduction 8712.2 Credit spread and security-specific return 8712.3 Curves and securities 8812.4 Fine structure credit curve movement 8812.5 Different types of credit attribution 8912.6 Swap curve attribution 8912.7 Credit curve attribution 8912.8 Sector curve attribution 9212.9 Country attribution 9313 Optionality Return 9514 Asset Allocation Return 9714.1 Case 1 9714.2 Case 2 9814.3 Case 3 9815 Other Sources of Return 10115.1 Convexity return 10115.2 Liquidity (security-specific) return 10115.3 Trading and price return 10215.4 Residual return 10316 Worked Examples 10516.1 Example 1: Yield return and term structure return 10516.1.1 Decomposing returns 10616.2 Example 2: Yield return and detailed term structure return 106Part III: Fixed Income Attribution in Practice 10917 Implementing an Attribution System 11117.1 Build or buy? 11117.2 Match to existing investment process 11117.3 Can the attribution approach be extended? 11117.4 Performance calculation engine 11117.5 Integration with other systems 11217.6 Benchmark and data issues 11217.7 Reporting 11217.8 IT requirements 11317.9 Cost 11317.10 Time 11317.11 Management support 11317.12 Intellectual capital 11317.13 Interface to legacy systems 11417.14 User expectations 11417.15 In general 11418 Fixed Income Benchmarks 11518.1 Introduction 11518.2 Benchmark replication 11618.3 Availability of data 11718.4 Replicating benchmark returns from data 11818.5 Treatment of cash 11919 Presenting Attribution Results 12119.1 Introduction 12119.2 Reporting formats 12119.3 Presenting numerical data 12219.3.1 Paper reports 12219.3.2 On-line reporting 12219.3.3 OLAP technology 12219.4 Presenting graphical data 12619.5 Report design 13120 Beyond Fixed Income Attribution 13320.1 Fixed income attribution in the investment process 13320.1.1 Improved term structure modelling 13320.1.2 Risk and reward 13420.1.3 What-if risk modelling 13520.1.4 Portfolio optimizers 13520.1.5 Systems integration 13620.2 Conclusion 136Appendix A Derivation of the Normal Equations for a Least Squares Fit 137A.1 Polynomial functions 137A.2 Nelson–Siegel functions 137References 139Index 141