# Why should a factor not priced and yet is relevant to the return generating process

I am reading Elton's AFA presidential adress article here. http://people.stern.nyu.edu/eelton/working_papers/Expected_Return_Realized_Return.pdf

In the paper, he is warning against using the average of realized return as an estimate of expected return. I have a question regarding his last comment just above the Summary section. iced.

Now consider momentum. Accept for a moment the empirical evidence that momentum is related to realized returns. If there is any connection between momentum and changes in the opportunity set, I am not aware of it. Thus, momentum is the kind of factor that is likely to appear in the return- generating process and likely to appear priced in sample but for which there is no theory that would suggest that it should be priced and for which current testing procedures are unlikely to be helpful.

I can understand why from the model he kept in mind: $$R_{it} -R_{ft}= \alpha_i+\sum\beta_{ij}^uI_{jt}^u + \sum\beta_{ij}^PI_{jt}^P +e_{it}$$ wehre $I_{jt}^u$ and $I_{jt}^P$ are unpriced and priced factor mimicking index portfolios. My question is why in the first place that the unpriced factors should enter into the return generating process?

## 1 Answer

Consider industry returns, industry returns tend to move together due to many factors - technological innovation, regulation, etc - and this common variation can be captured by a factor.

However, industry factors are not priced. Why? What matters is risk (which I will define as covariation of returns with something that matters to the investor), as an investor I can invest in multiple industries and not have to worry about any one in particular. Competition among speculative investors will mean that I won't be compensated for this diversifiable risk.

So, even if I buy stocks in multiple industries they will have some undiversifable common variation - like the market factor - which is the priced part.

• p.s. In my opinion this is one of the most important papers in academic finance. Most researchers these days implicitly assume that ex-post average returns are a good proxy for ex-ante expected returns without thinking. This is rarely true, formation of portfolios helps but it's not perfect. – jd8 Jan 25 '17 at 1:35
• Welcome to QuantStackExchange, jd8. – Alex C Jan 25 '17 at 2:52