BAM Intelligence

Rediscovering the Size Effect

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 U.S. after the publication of Banz’s work. Using data from Dimensional Fund Advisors, from 1984 through 2017, the annual size premium in U.S. stocks was just 0.3% on an annual average basis and a negative 0.1% on an annualized basis.

However, it’s interesting to note that, despite the negative annualized return premium to small stocks, over the same period, Dimensional’s U.S. micro-cap fund (DFCSX) returned 11.8%, providing a 0.8 percentage point higher return than the Vanguard S&P 500 ETF (VOO), which returned 11.0%. 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.

Controlling For Quality

Cliff Asness, Andrea Frazzini, Israel, Moskowitz and Lasse Pedersen—authors of the January 2015 paper “Size Matters, If You Control Your Junk”—examined the problem of the disappearing size premium by controlling for the quality factor.

They note: “Stocks with very poor quality (i.e., ‘junk’) are typically very small, have low average returns, and are typically distressed and illiquid securities. These characteristics drive the strong negative relation between size and quality and the returns of these junk stocks chiefly explain the sporadic performance of the size premium and the challenges that have been hurled at it.”

High-quality stocks have the following characteristics: low earnings volatility, high margins, high asset turnover, low financial and operating leverage, and low idiosyncratic risk. The research shows these types of stocks, the kind that Benjamin Graham and Warren Buffett have long advocated buying, outperform low-quality stocks with opposite characteristics (those “lottery-ticket” equities).

The authors additionally found that “small quality stocks outperform large quality stocks and small junk stocks outperform large junk stocks, but the standard size effect suffers from a size-quality composition effect.” In other words, controlling for quality restores the size premium.

The authors thus concluded the challenges to the size premium “are dismantled when controlling for the quality, or the inverse ‘junk,’ of a firm. A significant size premium emerges, which is stable through time, robust to the specification, more consistent across seasons and markets, not concentrated in microcaps, robust to non-price based measures of size, and not captured by an illiquidity premium. Controlling for quality/junk (the QMJ factor) also explains interactions between size and other return characteristics such as value and momentum.”

They further found that “controlling for junk produces a robust size premium that is present in all time periods, with no reliably detectable differences across time from July 1957 to December 2012, in all months of the year, across all industries, across nearly two dozen international equity markets, and across five different measures of size not based on market prices.”

They also note: “When adding QMJ as a factor, not only is a very large difference in average returns between the smallest and largest size deciles observed, but, perhaps more interestingly, there is an almost perfect monotonic relationship between the size deciles and the alphas. As we move from small to big stocks, the alphas steadily decline and eventually become negative for the largest stocks.”

Additional Findings

Another important finding was that higher-quality stocks were more liquid, which has important implications for portfolio construction and implementation.

Asness, Frazzini, Israel, Moskowitz and Pedersen found similar results when, instead of controlling for the quality factor, they controlled for the low-beta factor. High-beta stocks (again, those lottery tickets) have very poor historical returns. And those high-beta stocks tend to be the same low-quality stocks. In addition, they found that small stocks have negative exposure to two relatively new factors, the profitability factor (referred to as RMW, or robust minus weak) and the investment factor (referred to as CMA, or conservative minus aggressive). High-profitability firms outperform low-profitability ones, and low-investment firms outperform high-investment ones.

Of interest is that the Q-factor model (which includes the market beta, size, profitability and investment factors) proposed in the 2012 paper “Digesting Anomalies: An Investment Approach” is able to explain almost all the anomalies that plague the Fama-French four-factor model (market beta, size, value and momentum). The sole, big exception is the poor performance of small growth stocks with low profitability.

Asness, Frazzini, Israel, Moskowitz and Pedersen concluded that “size matters—and in a much bigger way than previously thought—but only when controlling for junk. Controlling for junk, a much stronger and more stable size premium emerges that is robust across time, including those periods where the size effect seems to fail; monotonic in size and not concentrated in the extremes; robust across months of the year; robust across non-market price based measures of size; not subsumed by illiquidity premia; and robust internationally. These results are robust across a variety of quality measures as well.”

Black Hole Of Investing

The bottom line is that the size premium is “diluted” by the universe of “junk” small stocks, which is perhaps the greatest anomaly in finance—these stocks have high-risk characteristics but well-below-market returns, a persistent market inefficiency. The field of behavioral finance provides an explanation for this phenomenon—it exists because investors have a preference for “lottery tickets.”

Nicholas Barberis and Ming Huang—authors of the paper “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices,” which appeared in the December 2008 issue of American Economic Review—found that:

  • Investors have a preference for securities that exhibit positive skewness, which occurs in cases where values to the right of (more than) the mean are fewer but farther from it than values to the left of (less than) the mean. Such investments provide the small chance of a huge payoff (that is, winning the lottery). Investors find this small possibility attractive. The result is that positively skewed securities tend to be “overpriced”—they earn negative average excess returns.
  • The preference for positively skewed assets explains the existence of several anomalies (deviations from the norm) to the efficient market hypothesis, including the low average return on IPOs, private equity and distressed stocks, despite their high risks.

In theory, we would expect anomalies to be arbitraged away by investors who don’t have a preference for positive skewness. They should be willing to accept the risks of a large loss for the higher expected return that shorting overvalued assets can provide. However, in the real world, anomalies can persist due to limits to arbitrage.

First, the charters of many institutional investors, such as pension plans, endowments and mutual funds, prohibit them from taking short positions. Second, the cost of borrowing a stock to short it can be expensive, and there can be a limited supply of such stocks available to short.

Third, most investors are unwilling to accept the risks associated with shorting because of the potential for unlimited losses. This is prospect theory at work; the pain of a loss is felt more deeply than the joy of an equal gain. Fourth, short-sellers run the risk that borrowed securities are recalled before the strategy pays off, as well as the risk that the strategy performs poorly over the short run, triggering an early liquidation.

Taken together, these factors suggest that investors may be unwilling to trade against the overpricing of skewed securities. This allows the anomaly to persist.

The conclusion we can draw is that the issue of the size premium’s “disappearance” may be a function of this “black hole” rather than something that affects the entire asset class. If you screened out the “black hole” stocks, a size premium could be captured. Said another way, it’s the higher-quality small stocks that explain the size premium.


These findings have important implications for investors when implementing passive strategies that include exposure to small stocks. How a fund defines its universe of small stocks eligible for purchase can make a significant difference in performance.

For example, the aforementioned Dimensional micro-cap fund, DFCSX, which outperformed VFINX, an S&P 500 index fund, by 0.8 percentage points per year over a period in which there was no annualized size premium, has long included negative screens for lottery stocks (such as small-cap growth stocks with high investment and low profitability, penny stocks, IPOs and stocks in bankruptcy). In addition, Dimensional also engages in patient trading to reduce transaction costs, accepting what should be random tracking error.

We see something similar when we look at Dimensional’s results outside the U.S. From inception in October 1996 through May 2018, and again using Dimensional data, the firm’s international small-cap fund (DFISX) returned 7.5% versus the 5.4% return of the MSCI EAFE Index. From inception in June 1998 through May 2018, Dimensional’s emerging markets small-cap fund (DEMSX) returned 11.9% versus a return of 8.5% for the MSCI Emerging Markets Index.

Clearly, all three Dimensional funds were able to realize economically significant premiums after implementation costs. Does your small-cap fund incorporate such strategies, or does it simply replicate an index that might ignore these issues?

This commentary originally appeared June 15 on

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Larry Swedroe, Director of Research

Director of Research

Larry Swedroe is director of research for the BAM ALLIANCE.

Previously, Larry was vice chairman of Prudential Home Mortgage. Larry holds an MBA in finance and investment from NYU, and a bachelor’s degree in finance from Baruch College.

To help inform investors about the evidence-based investing approach, he was among the first authors to publish a book that explained evidence-based investing in layman’s terms — The Only Guide to a Winning Investment Strategy You’ll Ever Need. He has authored six more books:

What Wall Street Doesn’t Want You to Know (2001)
Rational Investing in Irrational Times (2002)
The Successful Investor Today (2003)
Wise Investing Made Simple (2007)
Wise Investing Made Simpler (2010)
The Quest for Alpha (2011)

He also co-authored four books: The Only Guide to a Winning Bond Strategy You’ll Ever Need (2006), The Only Guide to Alternative Investments You’ll Ever Need (2008), The Only Guide You’ll Ever Need for the Right Financial Plan (2010) and Investment Mistakes Even Smart Investors Make and How to Avoid Them (2012). Larry also writes blogs for and Index Investor Corner on

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