I get this question from interviewer about what is alpha model, what is risk model and why is Fama-French a risk model.
As my understanding, alpha model forecast expected return, so the factor could be stock specific. And risk model forecast stock correlation, and the factors in risk model need to be a risk index and can't be stock specific.
But why Fama-French a risk model? It is a model for expected return, you could argue that it could model correlation. But it gives information that small out perform big and high value out perform low. In general, what makes a factor risk and what makes a factor alpha?
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2 Answers
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I feel in need for adding a differnt answer than the previous one.
Cochrane states in the preface of his book Asset Pricing:
In absolute pricing, we price each asset by reference to its exposure to fundamental sources of macroeconomic risk. [...]. The absolute approach is most common in academic settings, in which we use asset pricing theory positively to give an economic explanation for why prices are what they are, or in order to predict how prices might change if policy or economic structure changed.
Factor models like Fama-French can be expressed in terms of
$$E[R^e] = \beta' \lambda$$
where $\beta$ are the multiple regression coefficients of excess returns $R^e$ on the factors and $\lambda$ represents the factor risk premia.
The intuition underlying the Fama-French model is to capture risks, which were empirically found in academic research (while testing the CAPM) to influence asset returns. See this answer adressing the Fama-French factors:
The reason pointed out by FF that firms with high ratios of book-to-market value are more likely to be in financial distress and small stocks may be more sensitive to changes in business conditions and thus provide higher historical-average return than predicted by CAPM
In fact, it is less a statistical model and rather a risk model based on economic observations and relations.
To be very precise, one has to say that the Fama-French risk-factors serve as a proxy for the exposure towards latent risk factors, which are not captured by the CAPM. Empirical findings give strong evidence, that the latent risk factors are cross-sectionally highly correlated with firm size (and respectively book-to-market ratio).
Relating to Cochrane's quote, the Fama-French model is an absolute pricing model, which corrects asset returns for risk. Therefore, it is a valid risk-model.
References:
Cochrane (2005), Asset Pricing, rev. ed., Princeton University Press.
answered Sep 13, 2018 at 8:46
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$\begingroup$ I feel Fama-French is very different from the other risk model for example BARRA, but I wasn't clear what is a difference, can you talk a little about it? Also is the term 'risk model' used differently by academia and practitioner? $\endgroup$– JOHNCommented Sep 13, 2018 at 14:33
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$\begingroup$ You mention macroeconomic risk, Cochrane makes very clear that we need to connect variation in returns (the factors) to variation in marginal utility (a measure of risk that must contain something observable like consumption) before we can call it a risk model, nobody has done this well, as far as we know they could be picking up correlated mistakes in investors probability assesments. See "Interpreting Factor Models by, Kozak, Nagel, Santosh" for example. papers.ssrn.com/sol3/papers.cfm?abstract_id=2945654. $\endgroup$– jd8Commented Sep 14, 2018 at 13:21
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$\begingroup$ I have read the paper and find no argument for Fama-French being not a risk-factor model. The authors just provide a interpretation, that there is no clear distinction between factor pricing and behavioral asset pricing. They develop a factor model of the SDF based purely on information from the covariance of returns and show, that a small number of PC factors performs as well as popular risk-models. While it is a great paper, their model is purely based on "statistical reasons" and do not provide an "economic" story behind the cross-section as established factor-models do. $\endgroup$ Commented Sep 19, 2018 at 8:11
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It's not a risk model. It's a statistical model. The Fama-French 3 factor model describes correlation in the 25 size and book-to-market portfolios by using "factors" which are constructed using long-short portfolios on size and book to market. If you take a principal components of the size book-to-market portfolios you will get something that looks similar. They call it a risk model, but there is no theory.
The alpha, then, is an intercept of a regression model which picks up average returns not explained by the variation in size and book to market factors.
