Why Unpriced Factors Can Explain Returns Without Earning a Risk Premium
Summary
The document distinguishes factors that help describe realized returns from factors that investors should expect to earn compensation for bearing. Common movements among industry returns, driven by influences such as technological change or regulation, can be represented by factors in a return generating model even when those factors are not priced.
The explanation is diversification: if investors can hold multiple industries, exposure to industry specific common variation may be diversified away and need not command a premium. By contrast, variation tied to a risk that matters to investors across their portfolios, such as market exposure, can remain undiversifiable and be priced. The passage uses industry factors to clarify this conceptual distinction, but it does not give an empirical test or resolve whether momentum is priced; its focus is why a factor can matter statistically without implying a theoretical expected return premium.
Key ideas
- A factor can capture shared return variation without representing a priced risk.
- Common industry movements may arise from technological, regulatory, or other shared influences.
- Diversifiable exposure generally need not earn compensation from investors.
- Market related exposure can remain undiversifiable and therefore be priced.
- Evidence that a factor relates to realized returns alone does not establish an expected premium.
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# Why should a factor not priced and yet is relevant to the return generating process
# 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?
## Answer by jd8 (score 2, accepted)
https://quant.stackexchange.com/a/32083
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.