Swedroe: A Classic Factor Model Improves

November 18, 2015

There has been a great deal of focus by the academic community in recent years on fine-tuning the various factor models used to explain the differences in returns of diversified portfolios.

Marie Lambert, Boris Fays and Georges Hubner contribute to the literature with their 2015 paper, “Size and Value Matter, But Not the Way You Thought.” In their study, the authors examined the construction methodology behind the Fama-French size and value factors.

By way of background, Eugene Fama and Kenneth French created six value-weighted portfolios using two-way sorts on size (splitting the market into the largest half and the smallest half of stocks as ranked by market capitalization) and three-way sorts on book-to-market ratio (with the top 30% of stocks classified as value stocks, the 40% in the middle classified as core stocks, and the bottom 30% classified as growth stocks).

SMB (the small-minus-big, or size, factor) measures the average difference in returns between the average small-cap and average large-cap portfolios, while HML (the high-minus-low, or value, factor) measures the average difference in returns between the average value and average growth portfolios.

Sorting Issues

My colleague and co-author, Kevin Grogan, provided the following insights from the study. To begin, the authors point out that when you use independent sorting, as Fama and French do, the six portfolios will each have approximately the same number of stocks only if size and value aren’t significantly correlated. However, size and value are actually negatively correlated. Small stocks tend to be more value-oriented while larger stocks tend to be more growth-oriented.

The consequences of this are twofold: First, the size effect is not diversified across the book-to-market portfolios, and therefore the size effect cannot be eliminated simply by looking at the portfolio difference. Second, using two size groups instead of three may underestimate the size effect (as was pointed out by Martijn Cremers, Antti Petajisto and Eric Zitzewitz in their 2010 paper, “Should Benchmark Indices Have Alpha? Revisiting Performance Evaluation”).

Lambert, Fays and Hubner hypothesized the existence of a different sorting methodology, one that would produce results providing a better explanation of the differences in returns of a diversified portfolio.

Modifying Fama-French

The authors deviated from the Fama-French portfolio construction methodology in two important ways. First, they used a sequential sorting procedure. This procedure detects whether, when controlling for two out of the three risk dimensions (size, value and momentum), there is still enough return variation related to the risk dimension left uncontrolled.

For example, while a traditional sort on size also leads to a value tilt in the smaller stocks, the authors’ procedure helps mitigate that effect, producing a more independent measure of size.

Second, they use a three-way sort on size (as Fama and French do with value) instead of a two-way sort. This finer classification on size provides a better distinction between small- and large-cap stocks. The two-way sort really compares the returns of large-cap stocks against the combined returns of both midcaps and small-caps.

The authors’ sequential sorting procedure also reverses the correlation between size and value, making them positively correlated. Using such a procedure corrects for the following issues:

  • The Fama-French versions of the SMB and HML premiums both performed very poorly from January 1980 through December 1999. The small-cap premium was actually slightly negative over this period and not statistically significant. The value premium was slightly positive over this period and not statistically significant. Using the altered factors, SMB remains negative and not statistically significant over the period, but HML is highly positive and statistically significant. It appears that the Fama-French HML is contaminated by size effects, while the altered factor helps mitigate this impact.
  • The Fama-French version of SMB is only statistically significant when controlling for profitability or quality. The authors’ version of SMB, however, remains consistently significant without controlling for profitability or quality.
  • Fama and French recently added RMW (the robust-minus-weak, or profitability, factor) and CMA (the conservative-minus-aggressive, or investment, factor) to their three-factor model to create a five-factor asset pricing model. The authors examined whether the additional factors were necessary under a sequential sorting framework. RMW remains significant, but CMA is subsumed by HML and RMW.

Lambert, Fays and Hubner show that they’ve designed a version of the HML factor that absorbs the information driven by the CMA factor. They also show that the Fama-French versions of the HML and SMB factors are being driven by the same source of risk, while the factors they’ve designed are explaining distinct risks.

Redefining the size factor to be consistent with the three-way sorting on value allows for a simpler, more parsimonious model, which is always a good thing, especially in terms of portfolio construction. The more factors you add, the greater the turnover is likely to be, and thus the higher the implementation costs and the lower the tax efficiency.


Larry Swedroe is the director of research for The BAM Alliance, a community of more than 140 independent registered investment advisors throughout the country.

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