Acknowledgements

Preface

1 An introduction to attribution

1.1 Securities, portfolios and risk

1.2 Types of risk

1.3 Return and attribution

1.4 Strategy tagging

1.5 Types of attribution

1.6 Book structure

PART I Equity attribution

2 The basics of performance measurement

2.1 Introduction

2.2 Defining return

2.3 Compounded returns

2.4 Time-weighted and money-weighted returns

2.5 Portfolio returns

2.6 Transactions and cash flow

2.7 Sector returns

2.8 Calculating portfolio returns over successive intervals

2.9 Futures cash offsets

2.10 Edge cases

2.11 External returns

2.12 Benchmarks

2.13 Active return

2.14 Stochastic attribution

2.15 Liability-driven investment (LDI)

3 Equity attribution

3.1 Introduction

3.2 Brinson attribution

3.3 Single level Brinson attribution

3.4 Multiple-level asset allocation

3.5 Off-benchmark securities

3.6 Successive portfolio attribution

3.7 Security-level attribution

4 Currency attribution

4.1 Introduction

4.2 Currency attribution returns

4.3 Performance and attribution on unhedged portfolios

4.4 Attribution on an unhedged portfolio

4.5 Portfolio hedging

4.6 Currency forwards

4.7 Hedging and risk

4.8 Naïve attribution on a hedged portfolio

4.9 Measuring hedge returns

4.10 Brinson attribution on a hedged portfolio

4.11 Problems with the Brinson approach when hedging is active

4.12 Calculating base and return premiums

4.13 The Karnosky-Singer attribution model

4.14 Running Karnosky-Singer attribution on an unhedged portfolio

5 Smoothing algorithms

5.1 Why returns do not combine neatly over time

5.2 The importance of internally consistent return contributions

5.3 Path-independence

5.4 Carino smoothing

5.5 Geometric smoothing

5.6 Foreign exchange return and smoothing

5.7 Summary

PART II Fixed income attribution

6 An overview of fixed income risks

6.1 Introduction

6.2 What is a bond?

6.3 Pricing conventions

6.4 Maturity

6.5 Coupons

6.6 Discounted cash flows and net present value

6.7 Pricing a bond from its discounted cash flows

6.8 Bond yield and carry return

6.9 Prices and yields

6.10 Return of a bond

6.11 Credit effects

6.12 The three Cs

7 Yield curves in attribution

7.1 Introduction

7.2 Why interest rates vary by term

7.3 Interpolation

7.4 Par curves and zero curves

7.5 Credit spreads

8 Pricing, risk and the attribution equation

8.1 Introduction

8.2 Pricing securities from first principles

8.3 Calculating return using the perturbational equation

8.4 Residuals

8.5 Stand-alone portfolios

PART III Sources of fixed income return

9 Carry return

9.1 Introduction

9.2 Carry-based investment strategies

9.3 Types of yield

9.4 Calculating carry return

9.5 Pros and cons of YTM

9.6 Decomposing carry

9.7 Which yield to use?

9.8 Decomposing carry return

9.9 Yield for non-bond securities

9.10 Using yield to maturity in attribution reports

10 Sovereign curve attribution

10.1 Introduction

10.2 Yield curve models

10.3 Parallel shift and modified duration, and why they matter

10.4 Measuring twist

10.5 Taxonomy of curve shifts

10.6 Sources of yield curve data

11 Sector and credit return

11.1 Credit spreads

11.2 Sectors and credit ratings

11.3 Building sector curves

11.4 Attribution using sector curves

11.5 Attribution on Euro bond portfolios

11.6 Attribution on credit portfolios

11.7 Credit attribution without a credit curve

12 Other security-specific sources of return

12.1 Paydown

12.2 Convexity

12.3 Rolldown

12.4 Liquidity return

13 Balanced attribution

13.1 Introduction

13.2 Calculating balanced attribution

14 Duration allocation attribution

14.1 Introduction

14.2 Return of a single fixed income security

14.3 Calculating duration returns

14.4 Discussion

PART IV Attribution on fixed income securities

15 Bonds

15.1 Introduction

15.2 Bond pricing formulae

15.3 Types of bond

15.4 Repos

16 Money market securities

16.1 Introduction

16.2 Money market yield curves

16.3 Money market curve decomposition

16.4 Cash

16.5 Bank bills and discount securities

16.6 Accrual securities

16.7 Floating rate notes

16.8 Interest rate and credit risk

16.9 FRN types

16.10 Yields and discount margins

16.11 FRN durations

16.12 Decomposing the return of an FRN

16.13 Yield curve attribution

16.14 Attribution with complete data

16.15 Attribution with incomplete data

16.16 Treatment of FRNs in commercial systems

16.17 FRNs and securitisation

16.18 Currency forwards

16.19 Repurchase agreements (Repos)

16.20 Money market benchmarks

17 Inflation-linked securities

17.1 Introduction

17.2 Overview of the inflation-linked bond market

17.3 What is an inflation-linked security?

17.4 The Canadian model for inflation-linked deb

17.5 Inflation ratios

17.6 Real yields and nominal yields

17.7 Pricing an inflation-linked bond

17.8 Real yield term structure

17.9 Pricing an inflation-linked bond .

17.10 Modified duration and return of inflation-linked gilts

17.11 Breakeven yields in attribution

17.12 Inflation swaps

17.13 Practical considerations

18 Futures

18.1 Introduction

18.2 How futures work

18.3 Attribution on bond futures

18.4 Futures contracts on other fixed income securities

18.5 Heuristics for dealing with futures

19 Annuities and amortising securities

19.1 Introduction

19.2 Prepayments

19.3 Mortgage-backed securities

20 Swaps

20.1 Introduction

20.2 Two-leg swaps

20.3 Single-leg swaps

20.4 Modelling swaps

20.5 Types of swap

20.6 Credit default swaps

21 Options and callable bonds

21.1 Introduction

21.2 Measuring yield on bonds with embedded options

21.3 Optionality in practice

22 Collateralised and securitised debt

22.1 Introduction

22.2 Securitisation

22.3 Collateralised debt

22.4 Attribution on securitised debt

PART V Attribution in practice

23 Popular attribution models

23.1 The Campisi model

23.2 Duration attribution

23.3 The Tim Lord model

23.4 Key rate attribution

23.5 Top-down attribution

24 Reporting

24.1 Treatment of residuals

24.2 Unattributed return

Afterword

Appendix A: A summary of the Karnosky-Singer attribution model

Appendix B: Explicit pricing of an FRN

Appendix C: Attribution on Australian and New Zealand bond futures

Appendix D: Parametric and non-parametric yield curve models

Appendix E: Replicating the return of a hedged benchmark

Appendix F: Duration-weighted yields

Appendix G: Combining duration allocation returns

Appendix H: Sources of yield curve data

Bibliography

Index

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