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.
