Swedroe: Rediscovering Size Effect

June 15, 2018

The first major anomaly to the first formal asset-pricing model, the capital asset pricing model (CAPM), was the size effect. The size effect is the phenomenon that small-cap stocks on average outperform large-cap stocks over time. The size premium is the average annual return achieved by being long small-cap stocks and short large-cap ones.

The size effect was first documented by Rolf Banz in his 1981 paper, “The Relationship Between Return and Market Value of Common Stocks,” which was published in the Journal of Financial Economics. After the 1992 publication of Eugene Fama and Kenneth French’s paper, “The Cross-Section of Expected Stock Returns,” the size effect was incorporated into what became finance’s new workhorse asset-pricing model, the Fama-French three-factor model (adding value and size to the CAPM’s market beta).

Unfortunately, the size premium basically disappeared in the United States after the publication of Banz’s work. Using data from Dimensional Fund Advisors, from 1982 through 2017, the annual size premium in U.S. stocks was just 0.9% on an annual average basis and 0.0% on an annualized basis.

However, it’s interesting to note that, despite the absence of a return premium to small stocks, over the same period, Dimensional’s U.S. micro-cap fund (DFCSX) returned 12.2%, providing a 0.6 percentage point higher return than the Vanguard S&P 500 Index Fund (VFINX), which returned 11.6%. I’ll come back to that point in my summary. (Also, in the interest of full disclosure, my firm, Buckingham Strategic Wealth, recommends Dimensional funds in constructing client portfolios.)

Size Needs Other Factors

The lack of a size premium over the past 34 years has led to much debate on the subject. Ron Alquist, Ronen Israel and Tobias Moskowitz, members of the research team at AQR Capital Management, contribute to the literature on the size effect with their May 2018 paper, “Fact, Fiction, and the Size Effect.”

They presented data demonstrating that:

  1. The size effect diminished shortly after its discovery and publication
  2. Because small-cap stocks typically have larger market betas than large-cap stocks, part of the size premium may simply be the equity market risk premium in disguise (CAPM alphas account for these beta differences)
  3. It is dominated by a January seasonal effect; there is a large (more than 2% over the full period, though just 1% since 1976) and statistically significant (with a CAPM t-stat greater than 5 in the full period and greater than 2 since 1976) premium in January but nowhere else
  4. It does not work for other asset classes outside of individual equities
  5. It is not robust to other measures of size that do not include market capitalization (such as number of employees, sales and book value of equity)
  6. It has not been statistically significant outside the U.S.
  7. It is found mostly in micro-caps (the bottom 5% of all stocks); thus, it is more difficult to implement (making the control/minimization of trading costs critical)


However, they do “save” the size effect by demonstrating it is made much stronger (and implementation costs are reduced) when size is combined with the newer common factors of profitability, quality and defensive (low beta)—the return premium is greater for other factors in small stocks.

These findings enabled the authors to conclude: “On its own [emphasis mine], a size factor is not a particularly strong source of expected returns in practice.” Importantly, they add that controlling for quality not only resurrects the size premium, it “also reconciles many of the empirical irregularities associated with the size effect that we (and the literature) have documented.”

Alquist, Israel and Moskowitz continue: “For instance, controlling for quality resurrects the size effect after the 1980s and explains its time variation, restores a linear relationship between size and average returns that is no longer concentrated among the tiniest firms, revives the returns to size outside of January and simultaneously diminishes the returns to size in January—making it more uniform across months of the year, and uncovers a larger size effect in almost two dozen international equity markets, 30 where size has been notably weak. These results are robust to using non-market based size measures, making the size premium a much stronger and more reliable effect after controlling for quality.”

With that more recent finding in mind, I’ll review the results of an earlier AQR paper on the subject.

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