BARRA makes no warranty, express or implied, regarding the Global Equity Risk Model or any results to be obtained from the
use of the Global Equity Risk Model. BARRA EXPRESSLY DISCLAIMS ALL WARRANTIES, EXPRESS OR IMPLIED, REGARDING
THE GLOBAL EQUITY RISK MODEL, INCLUDING BUT NOT LIMITED TO ALL IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE OR USE OR THEIR EQUIVALENTS UNDER THE LAWS
OF ANY JURISDICTION. Although BARRA intends to obtain information and data from sources it considers to be reasonably
reliable, the accuracy and completeness of such information and data are not guaranteed and BARRA will not be subject to
liability for any errors or omissions therein. Accordingly, such information and data, the Global Equity Risk Model, and their
output are not warranted to be free from error. BARRA does not warrant that the Global Equity Risk Model will be free from
unauthorized hidden programs introduced into the Global Equity Risk Model without BARRA's knowledge.
Copyright
BARRA, Inc. 1998. All rights reserved.
0021 O 09/92 RV05/98
i
Contents
About BARRA
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
A pioneer in risk management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
The Global Equity Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
Introduction
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
In this handbook. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
Further references . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Books. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.Risk and Return
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5
Some denitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
Risk measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Return decomposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.The Evolution of Risk Models
. . . . . . . . . . . . . . . . . . . .11
Systematic return and diversication . . . . . . . . . . . . . . . . . . . . . . .11
The Capital Asset Pricing Model. . . . . . . . . . . . . . . . . . . . . . . . . . 12
The Arbitrage Pricing Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
What are multiple-factor models . . . . . . . . . . . . . . . . . . . . . . . . . 13
How do MFMs work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Advantages of MFMs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Model mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Risk prediction with MFMs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
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Global Equity Model
3. The Global Equity Model
. . . . . . . . . . . . . . . . . . . . . . . 21
Model development. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Risk indices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
Local markets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
Industries. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
Currencies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.Model Estimation
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
An overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Risk index selection and standardization . . . . . . . . . . . . . . . . . . . 34
Industry denition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Factor return estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
Covariance matrix calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Exponential weighting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Computing market volatility: GARCH models . . . . . . . . . . 37
Countries in GEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Currency risk estimation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Updating the model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
5.Portfolio Management
. . . . . . . . . . . . . . . . . . . . . . . . . 41
Portfolio construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
Passive management. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Active management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
Model applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6.Global Equity Case Studies
. . . . . . . . . . . . . . . . . . . . . . 47
Case 1: Analyzing an active portfolio . . . . . . . . . . . . . . . . . . . . . . 47
Case 2: Matching the MSEAFE . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Case 3: Creating and optimizing a tilt fund . . . . . . . . . . . . . . . . . 51。