lehman brothers
Global Risk Model: A Portfolio Manager's Guide
129 Pages
INTRODUCTION ................................................................................................................................................................................. 5
1. MOTIVATION FOR USING THE LEHMAN BROTHERS RISK MODEL ................................................................................. 13
A. Lehmanís 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