Return Comovement and the Logic Behind Fama-French Factors

Summary

The document raises a question about how to interpret a passage on stock return comovement and factor models. The cited example imagines a characteristic that predicts higher average returns, such as ticker-letter position, but does not necessarily cause stocks grouped by that characteristic to move together. The central distinction is between explaining differences in average returns and explaining shared variation in returns.

The question connects this distinction to the construction of the size and book-to-market factors used to explain returns across portfolios sorted by those characteristics. It asks why adding characteristic-based portfolios as explanatory factors is not automatically tautological. No answer or empirical analysis is included, so the text does not resolve when such factors improve explanatory power, how the regressions should be specified, or what evidence supports the factor interpretation. Its useful contribution is framing a conceptual issue in asset pricing: a return predictor need not also be a source of covariance or comovement.

Key ideas

• A characteristic can predict average returns without implying that characteristic-sorted stocks move together.
• Return predictability and return comovement are distinct empirical properties.
• The question uses this distinction to examine the logic of size and book-to-market factors.
• The document frames the issue but provides no resolution or empirical test.

Tags

# How to understand stock return comovement


# How to understand stock return comovement












In his book "Asset Pricing" chapter 20, Cochrane said

> For example, suppose that average returns were higher for stocks whose ticker symbols start later in the alphabet. (Maybe investors search for stocks alphabetically, so the later stocks are “over- looked.”) This need not trouble us if Z stocks happened to have higher betas. If not – if letter of the alphabet were a CAPM anomaly like book to market – however, it would not necessar- ily follow that letter based stock portfolios move together. Adding A-L and M-Z portfolios to the right hand side of a regression of the 26 A,B,C, etc. portfolios on the market portfolio need not (and probably does not) increase the R 2 at all.

I am having trouble understanding this example. He is trying to illustrate why forming HML and SMB the way Fama and French did to explain the 25 Size/Book to Market Portfolio is not tautology.

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