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barra_risk_model_handbook.pdf
About Barra
A Pioneer in Risk Management
Contacting Barra
Other Barra Resources
Introduction
Further references
1. Forecasting Risk with Multiple- Factor Models
What Are Multiple-Factor Models?
How Do Multiple-Factor Models Work?
Advantages of Multiple-Factor Models
An Illustration of Multiple-Factor Models
Model Mathematics
Risk Prediction with MFMs
Summary
2. Forecasting Equity Risk
A Historical Perspective
Barra’s Equity Multiple-Factor Model
Common Factors
Specific Risk
3. Barra Equity Risk Modeling
Model Estimation Overview
Data Acquisition
Descriptor Selection and Testing
Descriptor Standardization
Risk Index Formulation
Industry Allocation
Factor Return Estimation
Covariance Matrix Calculation
Specific Risk Modeling
Updating the Model
4. Forecasting Fixed-Income Risk
A Historical Perspective
Barra’s Multiple-Factor Model
Common Factors
Specific Risk
Summary
5. Interest Rate Risk Modeling
Estimation Process Overview
Term Structure Specification
Factor Shape Determination
Factor Exposure Calculation
Factor Return Estimation
Term Structure Covariance Matrix Construction
Covariance Matrix Correlation
Updating the Model
6. Spread Risk Modeling
Swap Spread Risk Model
Detailed Credit Spread Risk Model
Emerging-Market Risk Modeling
Updating the Model
7. Specific Risk Modeling
Heuristic Models
Transition-Matrix-Based Model
Updating the Model
8. Currency Risk Modeling
Model Structure
Data Acquisition and Return Calculation
Estimation of the Covariance Matrix
Time-Scaling Currency Risk Forecasts
Updating the Model
9. Integrated Risk Modeling
Model Integration Overview
Building Global Asset Class Models
Global Equities
Global Bonds
The Currency Model
Putting It All Together-A Multi-Asset Class Risk Model
Summary
Glossary
A
B
C
D
E
F
G
H
I
K
L
M
N
O
P
Q
R
S
T
U
V
W
Y
Z
Contributors
Index
Barra Risk Model
Barra Risk Model
Handbook
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In particular, historical data and analysis should not be taken as an indication or guarantee
Historical data and analysis should not be taken as an indication or guarantee of any
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(“Barra”), or their affiliates (including without limitation Financial Engineering Associates, Inc.) (alone
or with one or more of them, “MSCI Barra”), or their direct or indirect suppliers or any third party
involved in the making or compiling of the Information (collectively, the “MSCI Barra Parties”), as
applicable, and is provided for informational purposes only. The Information may not be reproduced
or redisseminated in whole or in part without prior written permission from MSCI or Barra, as
applicable.
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The Information may not be used to verify or correct other data, to create indices, risk
models or analytics, or in connection with issuing, offering, sponsoring, managing or marketing any
securities, portfolios, financial products or other investment vehicles based on, linked to, tracking or
otherwise derived from any MSCI or Barra product or data.
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future performance, analysis, forecast or prediction.
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None of the Information constitutes an offer to sell (or a solicitation of an offer to
buy), or a promotion or recommendation of, any security, financial product or other
investment vehicle or any trading strategy, and none of the MSCI Barra Parties endorses,
approves or otherwise expresses any opinion regarding any issuer, securities, financial
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models or other products or services is intended to constitute investment advice or a
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The governing law applicable to these provisions is the substantive law of the State of New
RV 10-2007
Contents
About Barra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v
A Pioneer in Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . v
Contacting Barra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vi
Other Barra Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vi
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
1. Forecasting Risk with Multiple-Factor Models . . . . . . . . . . . .1
What Are Multiple-Factor Models? . . . . . . . . . . . . . . . . . . . . . . . . 1
How Do Multiple-Factor Models Work? . . . . . . . . . . . . . . . . . . . . 2
Advantages of Multiple-Factor Models. . . . . . . . . . . . . . . . . . . . . . 2
An Illustration of Multiple-Factor Models . . . . . . . . . . . . . . . . . . . 3
Model Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Single-Factor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Multiple-Factor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Multiple-Asset Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Risk Prediction with MFMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
The Covariance Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
Deriving the Variance-Covariance Matrix of Asset Returns. . . 10
Final Risk Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2. Forecasting Equity Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
A Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Barra’s Equity Multiple-Factor Model . . . . . . . . . . . . . . . . . . . . . 19
Common Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Risk Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Industries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Specific Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Contents
i
3. Barra Equity Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . 21
Model Estimation Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
Descriptor Selection and Testing . . . . . . . . . . . . . . . . . . . . . . . . . 24
Descriptor Standardization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Risk Index Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Industry Allocation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Factor Return Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Covariance Matrix Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Exponential Weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Covariance Matrix Scaling: Computing Market Volatility . . . 29
Specific Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Updating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4. Forecasting Fixed-Income Risk . . . . . . . . . . . . . . . . . . . . . . 39
A Historical Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Barra’s Multiple-Factor Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Common Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Interest Rate Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Spread Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Specific Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
5.
Interest Rate Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . 51
Estimation Process Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Term Structure Specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
Estimation Algorithm Implementation . . . . . . . . . . . . . . . . . 58
Factor Shape Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Factor Exposure Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
Factor Return Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Term Structure Covariance Matrix Construction . . . . . . . . . . . . . 66
Covariance Matrix Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Updating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
ii
Barra Risk Model
Handbook
6. Spread Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . .69
Swap Spread Risk Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Data Acquisition and Factor Return Estimation. . . . . . . . . . . 70
Factor Exposure Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 70
Detailed Credit Spread Risk Model . . . . . . . . . . . . . . . . . . . . . . . 71
Currency Dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Factor Return Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Covariance Matrix Estimation. . . . . . . . . . . . . . . . . . . . . . . . 77
Factor Exposure Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 78
Emerging-Market Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . 78
Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Data Acquisition and Factor Return Estimation. . . . . . . . . . . 80
Covariance Matrix Estimation. . . . . . . . . . . . . . . . . . . . . . . . 80
Factor Exposure Calculation . . . . . . . . . . . . . . . . . . . . . . . . . 81
Updating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
7. Specific Risk Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . .83
Heuristic Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Sovereign, U.S. Agency, and MBS Specific Risk Estimation . . 84
Corporate Bond Specific Risk Estimation . . . . . . . . . . . . . . . 85
Transition-Matrix-Based Model. . . . . . . . . . . . . . . . . . . . . . . . . . 86
Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Transition Matrix Generation . . . . . . . . . . . . . . . . . . . . . . . . 87
Rating Spread Level Calculation . . . . . . . . . . . . . . . . . . . . . . 88
Credit Migration Forecasting . . . . . . . . . . . . . . . . . . . . . . . . 91
Updating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
8. Currency Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . .97
Model Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Data Acquisition and Return Calculation . . . . . . . . . . . . . . . . . . 98
Estimation of the Covariance Matrix . . . . . . . . . . . . . . . . . . . . . . 98
Currency Correlation Model . . . . . . . . . . . . . . . . . . . . . . . . . 99
Currency Volatility Model. . . . . . . . . . . . . . . . . . . . . . . . . . 100
Contents
iii
Volatility Across Markets . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Time-Scaling Currency Risk Forecasts . . . . . . . . . . . . . . . . . . . . 105
Updating the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
9.
Integrated Risk Modeling . . . . . . . . . . . . . . . . . . . . . . . . . 109
Model Integration Overview . . . . . . . . . . . . . . . . . . . . . . . . . . 109
Building Global Asset Class Models . . . . . . . . . . . . . . . . . . . . . 110
The Structure of Local Models . . . . . . . . . . . . . . . . . . . . . . 111
Aggregating Local Models . . . . . . . . . . . . . . . . . . . . . . . . . . 111
Implementing Global Factor Models . . . . . . . . . . . . . . . . . . 113
Consistency Between Local Models and Global Model . . . . 114
Global Equities. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
Global Equity Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Exposures of Local Equity Factors to Global Equity Factors . 115
Estimating Returns to Global Equity Factors . . . . . . . . . . . . 115
Computing Covariances of Global Equity Factors . . . . . . . . 117
Scaling to Local Markets. . . . . . . . . . . . . . . . . . . . . . . . . . . 117
Global Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Global Bond Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Exposures of Local Bond Factors to Global Bond Factors. . . 122
Computing Covariances Of Global Bond Factors . . . . . . . . 122
The Currency Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Putting It All Together—A Multi-Asset Class Risk Model . . . . . 125
Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Glossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
iv
Barra Risk Model
Handbook
About Barra
In recent years the investment management industry has adjusted
to continuing changes—theoretical advances, technological devel-
opments, and volatility. To address these, investment managers
and financial institutions require the most advanced and powerful
analytical tools available.
A Pioneer in Risk Management
As the leading provider of global investment decision support
tools and innovative risk management technology, Barra has
responded to these industry changes by providing quantitative
products and services that are both flexible and efficient.
Barra products are a combination of advanced technology and
superior analytics, research, models, and data that provide clients
around the world with comprehensive risk management solutions.
Barra uses the best data available to develop econometric financial
models. In turn, these models are the basis of software products
designed to enhance portfolio performance through returns fore-
casting, risk analysis, portfolio construction, transaction cost anal-
ysis, and historical performance attribution.
With more than 80 researchers in offices around the world and
products that cover most of the world’s traded securities, Barra
maintains one of the strongest risk management research practices
in the world today.
About Barra
v
Contacting Barra
Client Services is available 24 hours a day, Monday through Fri-
day. You can reach the Client Services as follows:
Web:
http://www.barra.com/support/service_request/
new_request.asp
Phone: North America:
888.588.4567
Europe:
Asia:
+44 (0)20.7618.2222
+813 5424 5470 (Japanese)
For local access numbers, visit the Client Support web site,
http://support.barra.com.
Client Services is your first point of contact concerning your
Barra product or service. Support desk analysts are available to
assist you with general, technical, data, product usage, and model
questions.
Other Barra Resources
You can visit the Library at http://support.barra.com for more
information on the topics discussed in this handbook.
In addition to handbooks and reference guides, Barra offers
numerous workshops and seminars throughout the year. For more
information, visit the Events Calendar at http://www.barra.com.
vi
Barra Risk Model
Handbook
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