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