Are Size and Book-Value Factors Really Significant ?

A new related paper has been added to:

#25 – Small Capitalization Stocks Premium Anomaly
#26 – Value (Book-to-Market) Anomaly

Authors: Lambert, Hubner

Title: Size Matters, Book Value Does Not! The Fama-French Empirical CAPM Revisited



The Fama and French (F&F) factors do not reliably estimate the size and book-to-market effects. Our paper shows that the former has been underestimated in the US market while the latter overestimated. We do so by replacing F&F's independent rankings by the conditional ones introduced by Lambert and Hubner (2013), over which we improve the sorting procedure. This new specification better reflects the properties of the individual risk premiums. We emphasize a much stronger size effect than conventionally documented. As a major related outcome, the alternative risk factors deliver less specification errors when used to price passive investment indices..

Notable quotations from the academic research paper:

"The paper revisits the size and book-to-market effect in the US market over the 1980-2007 sample period. It demonstrates a strong size but an insignificant book-to-market effect over the sample period. Our result challenges the Fama and French evidence of the presence of a stronger book-to-market than size effect in the US market. Fama and French’s size and book-to-market premiums are indeed shown to be respectively insignificant and positively significant over the analyzed period. Their evidence is partly supported in the standard construction methodology itself as more weight is attributed to the ranking according to the book-to-market dimensions (Fama and French, 1993).

We propose an alternative way to construct the empirical risk factors of Fama and French (1993) that avoids the contamination of the premiums from the correlation structure of the data. Our paper aims indeed at addressing some of the drawbacks identified in this heuristic approach to construct risk factors. Some attention has been drawn to the potential misevaluation of the size and book-to-market effect implied by the way the Fama and French methodology was constructed (Cremers et al., 2010; Huij and Verbeek, 2009; Brooks et al., 2008). The original Fama and French (F&F) method performs a 2×3 sort of US stocks on market capitalization and on book-to-market and forms six two-dimensional portfolios at the intersections of the two independent rankings. The premiums are defined as the spread between the average low- and high-scoring portfolios. Our main argument motivating the modifications brought to the original F&F method is that the independent sorting procedure underlying the formation of the six F&F two-dimensional portfolios distorts the way stocks are ranked into portfolios by placing disproportionate weights between the portfolios.

We follow the methodology of Lambert and Hübner (2013) and apply a generalized Fama and French technique to infer the size, book-to-market and momentum factors from the US stock market over the sample period of 1980-2007. The main innovations of our premiums reside in a monthly rebalancing of the portfolios (underlying the construction of the risk premiums) in order to capture the time-varying dimensions of risk, in a finer size classification and in a conditional sorting of stocks into portfolios. We consider three risk dimensions. The conditional sorting procedure answers the question whether there is still return variation related to the third risk criterion after having controlled for two other risk dimensions. It consists in performing a sequential sort in three stages. The first two sorts are performed on control risks, while we end by the risk dimension to be priced. As in Cremers, Petajusto and Zitzewitz (2010) and in Huij and Verbeek (2009), our paper demonstrates that the book-to-market premium of F&F is overvalued. We perform several asset pricing tests to check the validity and pricing power of our alternative premium specification. Compared to the Fama and French method, our factor construction method better captures the return spread associated with the source of risk to be priced. It maximizes the dispersion in the related source of risk while keeping minimal dispersion in correlated sources of risk. The conditional sorting and the finer size classification contribute to better balance the weights placed on the small/large value/growth portfolios. The great improvement of the new method lies in the reduction of the specification errors when pricing passive benchmark investment portfolios. Besides, without losing in significance, the modified technique is neater and leads to risk premiums that may not necessarily be used jointly in a regression-based model, unlike the original Fama and French factors whose risk exposures are highly sensitive to the inclusion of the other Fama and French risk factors in the regression.

Our paper more generally supports Lambert and Hübner’s (2013) previous evidence that a sequential sorting procedure could be more appropriate to take into consideration the contamination effects between the premiums. We show that the premiums constructed along this way deliver more consistent risk properties while reaching at least the same specification level as the F&F premiums. Given the critical stance of our paper, we have to go quite in depth into the origins of the improvements of the proposed sequential procedure, assorted with various methodological variations, over the original F&F method. The robustness checks deliver clear insights vis-à-vis the key drivers of alternative approach’s pricing performance. It is the replacement of an independent sort by a sequential one that seems to make the largest difference as expected."

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