Barra Risk Model Handbook - RoyCheng

1 HandbookBarra Risk ModelBarra Risk ModelCopyright 2004 Barra , Inc and/or its subsidiaries and affiliates ( Barra ). All rights reserved. This publication shall be used only in accordance with the terms ofyour license agreement with Barra , but in any event, only for your internal business use. This publication is the confidential and proprietary property of Barra . Nopart of this publication may be reproduced, transmitted, or distributed in any form by any means (electronic, photocopying or otherwise) without the prior writtenconsent of Barra . Barra is a registered trademark, and other Barra product names, service names, slogans or logos referenced in this publication are trademarks,servicemarks, registered trademarks or registered servicemarks of Barra , Inc.

2 And/or its subsidiaries and affiliates. All other company, product or service names ref-erenced in this publication are used for identification purposes only and may be trademarks of their respective AND ITS SUPPLIERS DISCLAIM ALL WARRANTIES, EXPRESS OR IMPLIED, REGARDING THIS PUBLICATION AND THE PRODUCTS AND SERVICES REFERENCEDHEREIN (AND ANY RESULTS TO BE OBTAINED FROM THE USE THEREOF), INCLUDING BUT NOT LIMITED TO ALL WARRANTIES OF MERCHANTABILITY, FITNESSFOR A PARTICULAR PURPOSE OR USE, ORIGINALITY, AND ALL WARRANTIES ARISING FROM COURSE OF PERFORMANCE, COURSE OF DEALING AND USAGE OFTRADE OR THEIR EQUIVALENTS UNDER THE LAWS OF ANY JURISDICTION. THIS PUBLICATION AND THE PRODUCTS AND SERVICES PROVIDED TO YOU ARE PROVIDED AS IS.

3 Accuracy, consistency and completeness of data in this publication and the products and services are not guaranteed. Neither Barra nor any ofits suppliers warrant that the products or services referenced in this publication will be uninterrupted or free from error or from unauthorized hidden programsintroduced into such products without their knowledge. Barra products contain a number of analytical tools that should be used only by sophisticated investmentprofessionals. There is no assurance that the financial instruments identified by the products will perform in a manner that is consistent with their historical charac-teristics or assure the profitability or utility of forecasts or expected values.

4 Barra shall not be deemed to be providing investment management, supervision or advi-sory 03-2004 ContentsContentsiAbout Barra .. vA Pioneer in Risk Management .. vContacting Barra ..viOther Barra Resources ..viIntroduction .. vii1. 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.. 2An 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.

5 11 Summary .. 122. Forecasting Equity Risk ..15A Historical Perspective .. 15 Barra s Equity Multiple-Factor Model .. 19 Common Factors .. 20 Risk Indices .. 20 Industries .. 20 Specific Risk .. 20 Barra Risk ModelHandbookii3. 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 .. 354. Forecasting Fixed-Income Risk.

6 39A Historical Perspective .. 39 Barra s Multiple-Factor Model .. 40 Common Factors .. 41 Interest Rate Risk .. 43 Spread Risk .. 46 Specific Risk .. 49 Summary .. 495. 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 Rotation .. 66 Updating the Model .. 68 Contentsiii6. Spread Risk Modeling ..71 Swap Spread Risk Model .. 72 Data Acquisition and Factor Return Estimation.. 72 Factor Exposure Calculation.

7 72 Detailed Credit Spread Risk Model .. 74 Currency Dependence .. 74 Model Structure .. 76 Data Acquisition .. 79 Factor Return Estimation .. 79 Covariance Matrix Estimation.. 79 Factor Exposure Calculation .. 80 Emerging-Market Risk Modeling .. 80 Model Structure .. 81 Data Acquisition and Factor Return Estimation.. 82 Covariance Matrix Estimation.. 82 Factor Exposure Calculation .. 83 Updating the Model .. 837. Specific Risk Modeling..85 Heuristic Models .. 85 Data Acquisition .. 85 Sovereign, Agency, and MBS Specific Risk Estimation .. 86 Corporate Bond Specific Risk Estimation .. 87 Transition-Matrix-Based Model .. 88 Data Acquisition .. 89 Transition Matrix Generation .. 89 Rating Spread Level Calculation.

8 90 Credit Migration Forecasting .. 93 Updating the Model .. 968. Currency Risk Modeling ..99 Model Structure .. 99 Data Acquisition and Return Calculation .. 100 Estimation of the Covariance Matrix .. 100 Currency Correlation Model .. 101 Currency Volatility Model .. 102 Barra Risk ModelHandbookivVolatility Across Markets .. 104 Time-Scaling Currency Risk Forecasts .. 107 Updating the Model .. 1089. Integrated Risk Modeling .. 111 Model Integration Overview .. 111 Building Global Asset Class Models .. 112 The Structure of Local Models .. 113 Aggregating Local Models .. 113 Implementing Global Factor Models .. 115 Consistency Between Local Models and Global Model .. 116 Global Equities.

9 116 Global Equity Factors .. 117 Exposures of Local Equity Factors to Global Equity Factors . 117 Estimating Returns to Global Equity Factors .. 117 Computing Covariances of Global Equity Factors .. 119 Scaling to Local Markets.. 119 Global Bonds .. 120 Global Bond Factors .. 121 Exposures of Local Bond Factors to Global Bond Factors.. 124 Computing Covariances Of Global Bond Factors .. 124 The Currency Model .. 125 Putting It All Together A Multi-Asset Class Risk Model .. 127 Summary .. 130 Glossary .. 133 Contributors .. 183 Index .. 185 About BarravAbout BarraIn recent years the investment management industry has adjusted to continuing changes theoretical advances, technological devel-opments, and volatility.

10 To address these, investment managers and financial institutions require the most advanced and powerful analytical tools Pioneer in Risk ManagementAs 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 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.