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The Barra China Equity Model (CNE5)
Empirical Notes
D. J. Orr
Igor Mashtaler
Adam Nagy
July 2012
MSCI Portfolio Management Analytics msci.com
© 2012 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document
Model Insight
Barra China Equity Model (CNE5) Empirical Notes
July 2012
2of 59
1. Introduction ............................................................................ 4
1.1. Model Highlights ........................................................................................... 4
2. Methodology Highlights ...................................................... 5
2.1. Optimization Bias Adjustment .................................................................. 5
2.2. Volatility Regime Adjustment .................................................................... 5
2.3. Country Factor ............................................................................................... 5
2.4. Specific Risk Model with Bayesian Shrinkage ..................................... 6
3. Factor Structure Overview ................................................. 7
3.1. Estimation Universe ..................................................................................... 7
3.2. Industry Factors ............................................................................................ 7
3.3. Style Factors ............................................................................................... 11
3.4. Performance of Factors ........................................................................... 12
4. Model Characteristics and Properties ........................... 20
4.1. Country and Industry Factors ................................................................ 20
4.2. Style Factors ............................................................................................... 24
4.3. Explanatory Power .................................................................................... 25
4.4. Cross-Sectional Dispersion .................................................................... 26
4.5. Specific Risk ................................................................................................ 28
5. Forecasting Accuracy ....................................................... 29
5.1. Overview of Testing Methodology ........................................................ 29
5.2. Backtesting Results .................................................................................. 32
6. Conclusion ........................................................................... 48
MSCI Portfolio Management Analytics msci.com
© 2012 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document
Model Insight
Barra China Equity Model (CNE5) Empirical Notes
July 2012
3of 59
Appendix A: Descriptors by Style Factor .......................... 49
Size ........................................................................................................................... 49
Beta ........................................................................................................................... 49
Momentum ............................................................................................................. 49
Residual Volatility .................................................................................................. 49
Non-linear Size ...................................................................................................... 50
Book-to-Price ......................................................................................................... 50
Liquidity .................................................................................................................... 50
Earnings Yield ........................................................................................................ 51
Growth ..................................................................................................................... 51
Leverage ................................................................................................................. 52
Appendix B: Decomposing RMS Returns........................ 53
Appendix C: Review of Bias Statistics .............................. 54
C1. Single-Window Bias Statistics .................................................................. 54
C2. Rolling-Window Bias Statistics ................................................................. 55
REFERENCES ....................................................................... 58
Client Service Information is Available 24 Hours a Day ............................ 59
Notice and Disclaimer ......................................................................................... 59
About MSCI ............................................................................................................ 59
MSCI Portfolio Management Analytics msci.com
© 2012 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document
Model Insight
Barra China Equity Model (CNE5) Empirical Notes
July 2012
4of 59
1. Introduction
1.1. Model Highlights
This document provides empirical results and analysis for the new Barra China Equity Model (CNE5).
These notes include extensive information on the structure, the performance, and the explanatory
power of the factors. Furthermore, these notes also include a thorough side-by-side comparison of the
forecasting accuracy of the CNE5 Model and the CHE2 Model, its predecessor.
1
The CNE5 Model leverages the same methodologies used for the Barra US Equity Model (USE4). These
details may be found in the companion document: USE4 Methodology Notes by Menchero, Orr, and
Wang (2011).
Briefly, the main advances are:
An innovative Optimization Bias Adjustment designed to improve the factor risk forecasts of
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
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 CNE5 Model is offered in short-term (CNE5S), long-term (CNE5L) and daily (CNE5D) versions. The
three versions have identical factor exposures and factor returns, but differ in their factor covariance
matrices and specific risk forecasts. The CNE5S Model is designed to be more responsive and provide
more accurate forecasts at a monthly prediction horizon. The CNE5L model is designed for longer-term
investors willing to trade some degree of accuracy for greater stability in risk forecasts. The CNE5D
model provides investors of all horizons with a tactical, one-day risk forecast.
1
The China Equity model has been renamed in line with the new generation of Single Country Models that incorporate ISO country codes. Consequently, the
successor to CHE2 has been designated as CNE5 to avoid a naming conflict with previous generations of the Canada Equity Model (also prefixed with “CNE”).
MSCI Portfolio Management Analytics msci.com
© 2012 MSCI Inc. All rights reserved.
Please refer to the disclaimer at the end of this document
Model Insight
Barra China Equity Model (CNE5) Empirical Notes
July 2012
5of 59
2. Methodology Highlights
2.1. Optimization Bias Adjustment
One significant bias of risk models is the tendency to underpredict the risk of optimized portfolios, as
demonstrated empirically by Muller (1993). More recently, Shepard (2009) derived an analytic result for
the magnitude of the bias, showing that the underforecasting becomes increasingly severe as the
number of factors grows relative to the number of time periods used to estimate the factor covariance
matrix. The basic source of this bias is estimation error. Namely, spurious correlations may cause certain
stocks to appear as good hedges in-sample, while these hedges fail to perform as effectively out-of-
sample.
An important innovation is the identification of portfolios that capture these biases and to devise a
procedure for correcting these biases directly within the factor covariance matrix. As shown by
Menchero, Wang, and Orr (2011), the eigenfactors of the sample covariance matrix are systematically
biased. More specifically, the sample covariance matrix tends to underpredict the risk of low-volatility
eigenfactors, while overpredicting the risk of high-volatility eigenfactors. Furthermore, reducing the
biases of the eigenfactors helps improve factor risk forecasts of optimized portfolios.
In the context of the CNE5 Model, eigenfactors represent portfolios of the original pure factors. The
eigenfactor portfolios, however, are special in the sense that they are mutually uncorrelated. Also note
that the number of eigenfactors equals the number of pure factors within the model.
As described in the USE4 Methodology Notes, we estimate the biases of the eigenfactors by Monte Carlo
simulation. We then adjust the predicted volatilities of the eigenfactors to correct for these biases. This
procedure has the benefit of building the corrections directly into the factor covariance matrix, while
fully preserving the meaning and intuition of the pure factors.
2.2. Volatility Regime Adjustment
Another major source of risk model bias is due to the fact that volatilities are not stable over time, a
characteristic known as non-stationarity. Since risk models must look backward to make predictions
about the future, they exhibit a tendency to underpredict risk in times of rising volatility, and to
overpredict risk in times of falling volatility.
Another important innovation in the CNE5 Model is the introduction of a Volatility Regime Adjustment
for estimating factor volatilities. As described in the USE4 Methodology Notes, the Volatility Regime
Adjustment relies on the notion of a cross-sectional bias statistic, which may be interpreted as an
instantaneous measure of risk model bias for that particular day. By taking a weighted average of this
quantity over a suitable interval, the non-stationarity bias can be significantly reduced.
Just as factor volatilities are not stable across time, the same holds for specific risk. In the CNE5 Model,
we apply the same Volatility Regime Adjustment technique for specific risk. We estimate the adjustment
by computing the cross-sectional bias statistic for the specific returns.
2.3. Country Factor
Traditionally, single country models (e.g., CHE2) have included industry and style factors, but no Country
factor. An important improvement with the CNE5 Model is to explicitly include the Country factor, which
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