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msci.com
Model Insight
The Barra US Equity Model (USE4)
Methodology Notes
Jose Menchero
D.J. Orr
Jun Wang
August 2011
MSCI Research msci.com
© 2011 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document RV May 2011
Model Insight
USE4 Methodology
August 2011
2of 44
Contents
1. Introduction ............................................................................ 3
1.1. Model Highlights .............................................................................................. 3
1.2. Modern Portfolio Theory and Barra Risk Models: A Brief History ..... 3
1.3 Forecasting Portfolio Risk with Factor Models ......................................... 6
2. Factor Exposures ................................................................. 7
2.1 General Considerations .................................................................................. 7
2.2. Data Quality and Outlier Treatment ........................................................... 8
2.3. Style Exposures ............................................................................................... 9
2.4. Industry Factors ............................................................................................... 9
2.5. Multiple-Industry Exposures ...................................................................... 10
3. Factor Returns .................................................................... 13
3.1. Country Factor .............................................................................................. 13
3.2. Relation to Traditional Approach ............................................................. 15
4. Factor Covariance Matrix ................................................. 17
4.1 Established Methods .................................................................................... 17
4.2 Eigenfactor Risk Adjustment ...................................................................... 19
4.3 Volatility Regime Adjustment ..................................................................... 24
5. Specific Risk ........................................................................ 28
5.1 Established Methods .................................................................................... 28
5.2 Bayesian Shrinkage ..................................................................................... 29
5.3 Volatility Regime Adjustment ..................................................................... 31
6. Conclusion ........................................................................... 35
Appendix A: Review of Bias Statistics ............................... 36
A1. Single-Window Bias Statistics ................................................................... 36
A2. Rolling-Window Bias Statistics .................................................................. 37
Appendix B. Eigenfactor Risk Adjustment ....................... 40
REFERENCES ....................................................................... 43
MSCI Research msci.com
© 2011 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document RV May 2011
Model Insight
USE4 Methodology
August 2011
3of 44
1. Introduction
1.1. Model Highlights
This document describes the new methodologies that underpin the USE4 model. Our aim is to produce a
document that is clear and concise, yet comprehensive as well. MSCI prides itself not only on setting the
standard for excellence in factor risk modeling, but also on being the industry leader in model
transparency.
This document is the complement to a companion document: USE4 Empirical Notes. Whereas the
current document focuses on methodology, the Empirical Notes contain detailed information about
USE4 factor structure, extensive analysis on the explanatory power and statistical significance of the
factors, and a systematic investigation into the forecasting accuracy of the model. The Empirical Notes
also provide a thorough comparison with the USE3 model.
The main advances of USE4 are:
An innovative Eigenfactor Risk Adjustment that improves risk forecasts for optimized portfolios by
reducing the effects of sampling error on the factor covariance matrix
A Volatility Regime Adjustment designed to calibrate factor volatilities and specific risk forecasts to
current market levels
The introduction of a country factor to separate the pure industry effect from the overall market and
provide timelier correlation forecasts
A new specific risk model based on daily asset-level specific returns
A Bayesian adjustment technique to reduce specific risk biases due to sampling error
A uniform responsiveness for factor and specific components, providing greater stability in sources of
portfolio risk
A set of multiple industry exposures based on GICS®
An independent validation of production code through a double-blind development process to
assure consistency and fidelity between research code and production code
A daily update for all components of the model
The USE4 model is offered in short-term (USE4S) and long-term (USE4L) versions. Both versions have
identical factor exposures and factor returns, but differ in their factor covariance matrices and specific
risk forecasts. The USE4S model is designed to be more responsive and provide the most accurate
forecasts at a monthly prediction horizon. The USE4L model is designed for longer-term investors who
are willing to trade some degree of accuracy for greater stability in risk forecasts.
1.2. Modern Portfolio Theory and Barra Risk Models: A Brief History
The pioneering work of Markowitz (1952) formally established the intrinsic tradeoff between risk and
return. This paradigm provided the foundation upon which the modern theory of finance was built, and
has proven so resilient that it has survived essentially intact for nearly 60 years. Almost as remarkable is
the vigor with which the theory has been embraced by academics and practitioners alike.
MSCI Research msci.com
© 2011 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document RV May 2011
Model Insight
USE4 Methodology
August 2011
4of 44
The specific problem addressed by Markowitz was how to construct an efficient portfolio from a
collection of risky assets. Markowitz defined an efficient portfolio as one that had the highest expected
return for a given level of risk, which he measured as standard deviation of portfolio returns. Markowitz
showed that the relevant risk of an asset is not its stand-alone volatility, but rather its contribution to
portfolio risk. Thereafter, the concepts of risk and correlation became inseparable.
A plot of expected return versus volatility for the set of all efficient portfolios maps out a curve known as
the efficient frontier. In order to construct the efficient frontier using the Markowitz prescription, an
investor must provide expected returns and covariances for the universe of all investable assets. The
Markowitz procedure identifies the optimal portfolio corresponding to the risk tolerance of any given
investor.
Tobin (1958) took the Markowitz methodology and extended it in a very simple way that nonetheless
had profound implications for portfolio management. By including cash in the universe of investable
assets, Tobin showed that there existed a single portfolio on the efficient frontier that, when combined
with cash, dominated all other portfolios. For any investor, therefore, the optimal portfolio would
always consist of a combination of cash and the “super-efficient” portfolio. For instance, risk-averse
investors may combine the super-efficient portfolio with a large cash position, whereas risk seekers
would borrow cash to purchase more of the super-efficient portfolio. As a result, according to Tobin, the
optimal investment strategy consists of two separate steps. The first is to determine the super-efficient
portfolio. The second step is to determine the appropriate level of cash that matches the overall risk
tolerance of the investor. This two-step investment process came to be known as the Tobin separation
theorem.
The next major step in the development of Capital Market Theory was due to Sharpe (1964). By making
certain assumptions (e.g., that all investors followed mean-variance preferences and agreed on the
expected returns and covariances of all assets) Sharpe was able to show that the super-efficient
portfolio was the market portfolio itself. Sharpe’s theory, known as the Capital Asset Pricing Model,
predicts that the expected return of an asset depends only on the expected return of the market and
the beta of the asset relative to the market. In other words, within CAPM, the only “priced” factor is the
market factor.
Using the CAPM framework, the return of any asset can be decomposed into a systematic component
that is perfectly correlated with the market, and a residual component that is uncorrelated with the
market. The CAPM predicts that the expected value of the residual return is zero. This does not preclude
the possibility, however, of correlations among the residual returns. That is, even under the CAPM, there
may be multiple sources of equity return co-movement, even if there is only one source of expected
return.
Rosenberg (1974) was the first to develop multi-factor risk models to estimate the asset covariance
matrix. This work was later extended by Rosenberg and Marathe (1975), who conducted a sweeping
econometric analysis of multi-factor models. The intuition behind these models is that there exists a
relatively parsimonious set of pervasive factors that drive asset returns. Returns that cannot be
explained by the factors are deemed “stock specific” and are assumed to be uncorrelated.
Rosenberg founded Barra, which made widespread use of multi-factor risk models and dedicated itself
to helping practitioners implement the theoretical insights of Markowitz, Tobin, Sharpe, and others. The
first multi-factor risk model for the US market, dubbed the Barra USE1 Model, was released in 1975.
That model was followed by the USE2 Model in 1985, and USE3 in 1997. Rapidly changing volatility
levels during and after the Internet Bubble highlighted the need for more responsive risk models, and in
2002 the USE3 Model was upgraded to incorporate daily factor returns.
MSCI Research msci.com
© 2011 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document RV May 2011
Model Insight
USE4 Methodology
August 2011
5of 44
Another key step in developing the theoretical edifice of quantitative investing came with the publishing
in 1995 of an influential book entitled Active Portfolio Management, written by Grinold and Kahn while
at Barra. The widespread success of this book prompted a second edition by Grinold and Kahn (2000),
and it serves today as an essential guidebook for many quantitative investment firms.
For modeling global portfolios, an important milestone came in 1989 with the development of the first
Barra Global Equity Risk Model (GEM). This model was estimated via monthly cross-sectional regressions
using countries, industries, and styles as explanatory factors, as described by Grinold, Rudd, and Stefek
(1989).
GEM was followed by a second-generation Global Equity Risk Model, GEM2, as described by Menchero,
Morozov, and Shepard (2008). GEM2 incorporated several advances over the previous model, such as
improved estimation techniques, higher-frequency observations, and the introduction of the World
factor to place countries and industries on an equal footing.
Barra also pioneered the use of integrated models, which combine the breadth of a global model with
the detail of local single-country models. An innovative feature of this approach is that it assures
consistency between the risk forecasts used by portfolio managers in the front office and risk managers
in the middle office. The first-generation Barra Integrated Model (BIM) was introduced in 2002. The
second-generation Barra Integrated Model, described by Shepard (2011), incorporated important
advances in methodology, such as using the GEM2 model to estimate covariances among local factors
and employing higher-frequency observations.
Barra risk models have long played an important role in applying the concepts of modern portfolio
theory to solve practical investment problems. At MSCI, we are dedicated to continuing this proud
tradition of developing industry-leading risk models. The release of the new Barra US Equity Model,
USE4, marks only the latest step in this ongoing journey.
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