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Model Insight
Barra China Equity Model (CNE5) Empirical Notes
July 2012
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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
