INTRODUCTION ................................................................................................................................................................................ 5
1. MOTIVATION FOR USING THE LEHMAN BROTHERS RISK MODEL ................................................................................. 13
A. Lehman.s Approach to Risk Modeling: The Historical-Parametric Approach .................................................................... 14
B. Weighting Historical Observations ..................................................................................................................................... 16
C. Why a Multi-Factor Model and Not an Asset Volatility Model? .......................................................................................... 17
D. The Lehman Brothers Advantage ...................................................................................................................................... 18
2. THE ANNOTATED RISK REPORT .......................................................................................................................................... 20
A. The Risk Report for a U.S. Aggregate Portfolio ................................................................................................................. 20
B. Risk Reports for a Euro Aggregate (and Sterling) Portfolio ............................................................................................... 36
C. The Risk Report for a Global Aggregate Portfolio .............................................................................................................. 46
3. RISK MODEL APPLICATIONS ................................................................................................................................................ 56
A. Structuring an Efficient Active Portfolio .............................................................................................................................. 56
B. Evaluating Proposed Trades .............................................................................................................................................. 58
C. Optimizing a Portfolio ......................................................................................................................................................... 59
D. Constructing Proxy Portfolios ............................................................................................................................................ 68
E. Scenario Analysis ............................................................................................................................................................... 72
F. Risk Budgeting ................................................................................................................................................................... 73
4. MODEL OVERVIEW BY ASSET CLASS ................................................................................................................................ 75
A. Yield Curve Return Models ................................................................................................................................................ 76
B. Swap Spread Return Models ............................................................................................................................................. 78
C. Volatility Return Models ..................................................................................................................................................... 79
D. Spread Return Models ....................................................................................................................................................... 79
i. Spread Return Models for Agency and Credit ............................................................................................................. 81
ii. Spread Sector Return Models for MBS, CMBS, and ABS .......................................................................................... 82
iii. Default Risk Model for U.S. and Euro Baa and High-Yield Assets ............................................................................. 85
iv. Spread Return Model for Inflation-Linked Securities .................................................................................................. 87
v. Spread Return Model for Emerging Market Securities ............................................................................................... 89
E. Idiosyncratic Return Model ................................................................................................................................................ 91
F. Putting Asset Class Models Together................................................................................................................................ 91
5. PREDICTIVE POWER OF THE MODEL.................................................................................................................................. 93
A. Testing Model Performance ............................................................................................................................................... 93
B. Relevance of Changes in Swap Spreads as a Risk Factor? .............................................................................................. 94
6. RELATIONSHIP WITH OTHER MODELS ............................................................................................................................... 96
A. Scenario Analysis ............................................................................................................................................................... 96
B. Value-at-Risk and Monte Carlo Simulation ......................................................................................................................... 97
C. Performance Attribution ..................................................................................................................................................... 98
D. Asset Allocation .................................................................................................................................................................. 98
E. Optimal Risk Budgeting ..................................................................................................................................................... 99
CONCLUSION................................................................................................................................................................................ 102
APPENDICIES
APPENDIX A: A MULTI-FACTOR RISK MODEL TUTORIAL ....................................................................................................... 104
a. Risk and Return of a Fixed Income Security .................................................................................................................... 104
b. Risk and Return of a Fixed Income Portfolio .................................................................................................................... 108
c. Risk and Return of One Portfolio versus Another ............................................................................................................ 112
APPENDIX B: BASIC RISK MODEL MATHEMATICS ................................................................................................................... 115
APPENDIX C: RISK MODEL TERMINOLOGY.............................................................................................................................. 118
APPENDIX D: RISK MODEL FACTOR DESCRIPTIONS .............................................................................................................. 124