Risk management : approaches for fixed income markets

"Golub-Tilman will, I believe, become an absolutely essential reference text for fixed income portfolio managers, traders, issuers, and scholars. It is comprehensive and clearly written. While rigorous, it is easy to understand because of its many practical examples."
-- Richard Roll , The Allstate Chair in Finance and Insurance, The Anderson School at UCLA, Past President, American Finance Association

"Outstanding and unique! A thorough discussion of the theoretical underpinning of risk management combined with keen insights from a practitioner's perspective. This text will rank among the most essential readings for both market professionals and academics."
-- Gregory J. Parseghian , Senior Vice President and Chief Investment Officer, Freddie Mac

"The most systematic and comprehensive overview of fixed income risk management."
-- Philippe Jorion , Professor of Finance, University of California-Irvine, Author, Value at Risk: The New Benchmark for Controlling Derivatives Risk

"An inside look at approaches to fixed income risk management developed at a leading investment firm. The rigorous presentation covers both theoretical and practical considerations as well as their applications to portfolio management. Very interesting and highly recommended."
-- Charles W. Grant , Managing Director of Fixed Income, Virginia Retirement System

"Few, if any, financial studies have managed to reconcile practical market experience and scientific discipline within such an original approach and with such elegance! An absolute must for anyone in the world of fixed income."
-- Michele Donegani , Head of Asset Allocation and Manager Selection, European Investment Managers (EIM)

Author Notes

BENNETT W. GOLUB is a founding partner and Managing Director of BlackRock, Inc., a global money management and risk advisory firm. Currently, he is co-head of its Risk Management and Analytics Group and is a member of its Investment Strategy Group and Management Committee. In addition to developing BlackRock's risk advisory business, Dr. Golub is actively involved in the creation of analytical tools used in measuring and managing market and credit risks of fixed income and equity portfolios. He has authored many articles on risk management and financial modeling and is a frequent lecturer at industry conferences and meetings. Dr. Golub earned an S.B. and an S.M. in Management and a Ph.D. in Applied Economics and Finance, all from the Massachusetts Institute of Technology.

LEO M. TILMAN is Director in the Risk Management and Analytics Group at BlackRock, Inc. He specializes in the creation of new risk management methodologies, marketing of risk management services, financial modeling, and risk advisory work. His primary focus is solving a wide range of portfolio management, trading, asset allocation, and enterprise-wide risk management problems through the use of financial modeling techniques. Mr. Tilman has published extensively on risk management, financial modeling, applied statistics, decision-making, and expert systems. He is a frequent guest lecturer on the topics of risk management and financial modeling. Mr. Tilman received a B.A. in Mathematics and an M.A. in Statistics with a concentration in Finance, both from Columbia University.

Frequently Used Abbreviations and Notations	p. xi
Foreword	p. xiii
Preface	p. xvii
Acknowledgments	p. xxi
Chapter 1 The Art and Science of Risk Management	p. 1
1.1 The "Brave New World" of Risk Management	p. 1
1.2 Market Risk Management Process	p. 8
1.3 Theory, Practice, and Computation: Challenges Specific to Fixed Income Markets	p. 12
1.3.1 Price Discovery	p. 13
1.3.2 Dynamic Portfolio Characteristics	p. 14
1.3.3 New Securities, New Structures, and the Absence of Historical Information	p. 15
1.4 Statistical Challenges: Risk Management versus Valuation	p. 17
1.5 Evolution of Risk Management Ideas	p. 18
Chapter 2 Parametric Approaches to Risk Management	p. 24
2.1 Introduction	p. 24
2.2 Measuring Interest Rate Exposure: Analytical Approaches	p. 26
2.2.1 Macaulay and Modified Duration, and Convexity	p. 26
2.2.2 Option-Adjusted Framework: OAV, OAS, OAD, OAC	p. 34
2.2.3 Dynamic Nature of Local Risk Measures: Duration and Convexity Drift	p. 42
2.2.4 Scenario Analysis	p. 46
2.3 Measuring Interest Rate Exposure: Empirical Approaches	p. 48
2.3.1 Coupon Curve Duration	p. 48
2.3.2 OAS Curve Duration	p. 51
2.3.3 Empirical (Implied) Duration	p. 52
2.4 Measuring Yield Curve Risk	p. 56
2.4.1 Key Rate Durations	p. 56
2.4.2 Key Treasury Rate Durations	p. 62
2.4.3 Yield Curve Reshaping Durations	p. 66
2.5 Measuring Basis Risks	p. 72
2.5.1 Volatility Duration	p. 72
2.5.2 Spread Duration	p. 74
2.6 Measuring Mortgage-Related Risks	p. 76
2.6.1 Prepayment Duration	p. 76
2.6.2 Mortgage/Treasury Basis Duration	p. 77
2.7 Measuring Impact of Time	p. 79
Chapter 3 Modeling Yield Curve Dynamics	p. 87
3.1 Probability Distributions of Systematic Risk Factors	p. 87
3.2 Principal Components Analysis: Theory and Applications	p. 93
3.2.1 Introduction	p. 93
3.2.2 Principal Components Analysis	p. 95
3.2.3 The First Principal Component and the Term Structure of Volatility	p. 103
3.2.4 Example: Historical Steepeners and Flatteners of the U.S. Treasury Curve	p. 105
3.3 Probability Distributions of Interest Rate Shocks	p. 107
3.4 Historical Plausibility of Interest Rate Shocks	p. 114
3.4.1 Explanatory Power	p. 115
3.4.2 Magnitude Plausibility	p. 116
3.4.3 Shape Plausibility	p. 117
3.4.4 Example: An Extreme Market Move During the 1998 Crisis	p. 120
Chapter 4 Measuring Interest Rate, Basis, and Currency Risks	p. 124
4.1 Deterministic versus Probabilistic Risk Methodologies	p. 124
4.1.1 Introduction	p. 124
4.1.2 Value-at-Risk	p. 132
4.2 Measuring U.S. Interest Rate Risk	p. 136
4.2.1 Variance/Covariance Value-at-Risk and Ex Ante Tracking Error	p. 142
4.2.2 Principal Components Durations, Key Rate Durations, and Value-at-Risk	p. 142
4.2.3 Effective Risk Profile and Other Practical Applications	p. 148
4.2.4 Application: Managing a Large Number of Portfolios Against Different Benchmarks	p. 151
4.3 Measuring Nondollar Interest Rate, Basis, and Currency Risks	p. 156
4.3.1 Global Variance/Covariance Value-at-Risk	p. 156
4.3.2 Non-Dollar Interest Rate Risks	p. 158
4.3.3 Foreign Currency Risks	p. 160
4.3.4 Overview of Systematic Basis Risks	p. 163
4.3.5 Implied Volatility Risks	p. 163
4.3.6 Mortgage Basis Risks	p. 166
4.3.7 Credit Spread Risks	p. 170
4.3.8 Applications of VaR to Portfolio and Risk Management	p. 177
4.4 Risk Decomposition	p. 178
4.5 Generic Basis Risks and Their Interest Rate Directionality	p. 183
4.5.1 Swap Spread Duration	p. 184
4.5.2 Generalized Duration	p. 190
Chapter 5 Value-at-Risk Methodological Trade-Offs	p. 200
5.1 General Formulation of Value-at-Risk	p. 200
5.2 Traditional VaR Trade-off: Nonlinearity versus Computational Time	p. 201
5.3 Additional Trade-off Dimension: Nonlinearity versus Distribution of Risk Factors	p. 205
5.3.1 Traditional and Principal Components Scenario Analysis	p. 208
5.3.2 Grid Monte-Carlo Simulation VaR	p. 213
5.3.3 Example: Measuring Risk of Duration-Neutral Yield Curve Bets	p. 217
5.3.4 Incorporating Evolution of Securities through Time into VaR	p. 226
5.3.5 Dimensionality Reduction Tool: Principal Components in Return Space	p. 229
5.4 Incorporating Nonlinearity Into Global Value-at-Risk	p. 234
5.5 Historical Simulation Value-at-Risk	p. 240
5.6 Value-at-Risk Horizon	p. 243
5.7 Value-at-Risk, Catastrophic Events, and Stress Testing	p. 247
Chapter 6 Using Portfolio Optimization Techniques to Manage Risk	p. 255
6.1 Risk Measurement versus Risk Management	p. 255
6.2 Typical Fixed Income Hedges	p. 258
6.3 Parametric Hedging Techniques	p. 261
6.4 Generalized Approach to Hedging (with William De Leon)	p. 264
6.5 Variance/Covariance VaR and Partial Duration Hedge Optimizations	p. 268
6.5.1 Basic Optimization Variables	p. 268
6.5.2 Example: Hedging Interest Rate Risk of a Mortgage-Backed Security	p. 272
6.5.3 Example: Managing Fixed Income Portfolios Against Their Benchmarks	p. 277
6.5.4 Example: Incorporating Yield Curve Bets Into Hedge Optimizations	p. 280
6.6 General Portfolio Optimizations: Return versus Risk and Cost	p. 284
6.6.1 Additional Optimization Variables	p. 284
6.6.2 Example: Hedging Interest Rate Risk With Swaps, Caps, and Floors	p. 287
6.6.3 Example: Asset/Liability Management via Monte-Carlo Simulation VaR	p. 287
Appendix Description of the Sample Portfolio	p. 295
Bibliography	p. 298
Index	p. 305
About the Authors	p. 311

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