What are some of the general rules to decide whether a particular factor is a "risk factor" or "anomaly?" Naively speaking, can't you put any anomaly factor on the right-hand-side of the regression and call it a risk factor? For example, momentum has been considered an anomaly in the context of the Fama-French 3-factor model, so Carhart included it in the RHS to create a 4-factor model, yet the latest FF 5-factor model does not include momentum.
A related question is: What distinguishes the 3/4/5-factors in the Fama-French/Carhart models from the rest of the factors in the factor zoo?
Answer
I would say the main difference between "risk factor" and "market anomaly" is that people demand to be compensated for risk and because there are different kinds of risks these can be systematized into risk factors whereas anomalies are results of behavioral biases.
Another big difference would be that risk factors will stay because of the need for compensation whereas anomalies will be arbitraged away in the long run.
I agree that both concepts are not completely orthogonal but that could be because scientists had (and still have) to find systematizations that make sense of the data so that certain ways of organizing the financial world become obsolete in later and more sophisticated models.
A good starting point for this way of thinking is Andrew Ang's new book about factor investing - you can find out more here (and there is even a short video which gives you a nice intuition by comparing factors to nutrients in food):
http://factorinvestingbook.com/
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