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Barra's Multiple-Factor Models for risk (e.g. USE3, USE4, CNE5) are much like those models used in empirical asset pricing studies such as CAPM, Fama-French three-factor model and others.

I'm not very sure about the deep-seated differences between the Barra models and asset pricing models from the theoretical asset pricing lens, though I know what they are doing mathematically.

As we all konw, when we test market efficiency in the framework of Fama and MacBeth (1973), we simply add predetermined explanatory variables to the month-by-month cross-section regressions of returns on market beta (i.e., only market beta is controlled in the regression). If all differences in expected return are explained by beta, the average slopes on the additional variables should not be reliably different from zero. Otherwise, we say we find a "marekt anomaly".

My question is, when we add other variables to the month-by-month regressions, do we need to control those variables used in Barra Models as well as market beta? Does it suffices to only include market beta as control variable for the search of marekt anomalies? Is there any acadimic jouranl artical that uses Barra models' variables as control variables?

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    $\begingroup$ Barra's model is a model of covariance (not of returns). You would use it to predict the volatility of a portfolio. Fama French is a model of returns, it is used to assess if the performance of your portfolio exceeds the prediction of their model, which is one of the most academically accepted models of returns, thus it is considered a difficult model to beat. $\endgroup$
    – nbbo2
    Commented Sep 30, 2019 at 2:56
  • $\begingroup$ @noob2 But the variables in Barra model can also explain the cross sectional difference of average stock returns. Thus, when we use Fama-MacBeth regression to test market anomaly (adding variables other than stock betas to check the significanse of those variables), a significant variable may become insignificant after controlling Barra variables. Then can we determine we find a market anomaly or not? $\endgroup$
    – Gödel
    Commented Sep 30, 2019 at 3:08

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