Barra Risk Models Versus Asset Pricing Models

# Are BARRA's Multiple-Factor Risk models rational asset pricing models?


# Are BARRA's Multiple-Factor Risk models rational asset pricing models?












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 know, 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 "market 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 market anomalies? Is there any academic journal article that uses Barra models' variables as control variables?

## Answer by caio teles (score 3)

https://quant.stackexchange.com/a/80811

As far as I know, Barra's risk factor analysis is not an asset pricing model, but it's a tool to manage risk.

Asset pricing models regard to explain the behavior of average returns of assets/portfolios. Therefore, the factors included in these models must carry premium to explain distortion of mean returns.

## Answer by KaiSqDist (score 2)

https://quant.stackexchange.com/a/82246

This might be better laid out as a comment, but I would like to quote Active Portfolio Management by Grinold & Kahn (2000) (Expected Returns and the APT, Chapter 7) in support of @nbbo2's (and the others) comment on Barra being a model of covariance and not of returns:

> The Barra risk model was constructed to help portfolio managers control risk, not to explained expected returns. However, it does attempt to capture those aspects of the market that cause some groups of stocks to behave differently from others.

In that, the primary purpose of the Barra risk models serve to (1) decompose the risk and explain the variation in returns and (2) predict the risks of these factors themselves.

EDIT - to Mark's Question

My opinion as to why the Barra risk models that require returns decomposition to decompose risk are taken as risk models and not returns models (as compared to common asset pricing models such as the CAPM, APT, FFX etc.), is that risk models take the realized/ex-post returns as the "correct" returns, and their main goal is to explain the systematic variation in the cross-section of returns across assets i.e. risk decomposition through the use of structural factors.

This is different from asset pricing models that do not assume the realized/ex-post returns are "correct" and much rather determine what is the "correct" equilibrium rate of return. This is also why asset pricing models are known as equilibrium pricing models. The assets with returns or prices that deviate from these equilibrium rates of return are subject to a form of price convergence called risk arbitrage (Investments by Bodie, Kane and Marcus). These rates of return may not always exist due to limits to arbitrage in the real world...

To summarize, I think the goal of the model is what classifies the Barra risk models to be called risk rather than return models.

Hopefully I understood your question correctly.