Swedroe: Size Premium Persists

Some may have wondered if the size premium had dwindled away, but evidence shows it’s still quite real.

Reviewed by: Larry Swedroe
Edited by: Larry Swedroe

Financial research has uncovered many relationships between investment factors and security returns. As director of research for Buckingham Strategic Wealth and The BAM Alliance, one of the most-asked questions I receive is whether such relationships will continue after that research has been published. Said another way, if everyone knows about a factor premium, should we expect it to continue outside of the sample period?

In 1981, Rolf Banz’s “The Relationship Between Return and Market Value of Common Stocks” concluded that market beta doesn’t fully explain the higher average return of small stocks. Banz found that from July 1926 through 1981, the monthly size premium averaged 30 basis points.

However, post-publication, from January 1982 through December 2017, the monthly premium has averaged just 8 basis points. Skeptics note that when we look at annualized (compound) returns, the data looks even worse. For example, some have pointed out that from 1982 through 2017, while the large-cap Russell 1000 Index returned 11.7%, the small-cap Russell 2000 Index returned just 10.6%. Thus, the size premium has been called into question, and some investors wonder whether it has shrunk or even disappeared.

Today it’s much easier and less costly to diversify the risks of small-cap stocks through mutual funds and ETFs than it was during the period Banz studied. In addition, trading costs, in the form of both commissions and bid/offer spreads, have come way down. Thus, there are logical arguments for why the size premium may have diminished over time.

Small-Growth Anomaly

The size premium issue is complicated by the well-known anomaly that, even though small value stocks have indeed provided higher returns than large value stocks, small growth stocks have provided lower returns than large growth stocks. Using the Fama-French research indexes, from July 1926 through November 2017, the annualized returns for the four asset classes are:

  • Small value: 14.8%
  • Large value: 12.1%
  • Large growth: 9.8%
  • Small growth: 8.7%

While producing lower annualized returns than large growth stocks, small growth stocks also exhibited higher volatility—the annualized standard deviation of returns was 18.3% for large growth and 26.0% for small growth. Note that the standard deviations for large value and small value were 24.7% and 28.2%, respectively.

From the viewpoint of traditional finance, while the returns and volatility of large growth, large value and small value stocks line up as they should (higher returns are positively correlated with higher volatility), the returns and volatility of small growth stocks do not. This is why small growth stocks have been referred to as the “black hole” of investing—and they present an anomaly.

Behavioral Explanation

The field of behavioral finance provides us with an explanation for the anomaly. It exists because investors have a preference for “lottery tickets.” Nicholas Barberis and Ming Huang, authors of the NBER working paper “Stocks as Lotteries: The Implications of Probability Weighting for Security Prices,” found that:

  • Investors have a preference for securities that exhibit positive skewness (values to the right of, or more than, the mean are fewer but farther from it than values to the left of, or less than, the mean). Such investments provide the small chance of a huge payoff (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 because of limits to arbitrage.

First, many institutional investors, such as pension plans, endowments and mutual funds, are prohibited by their charters from taking short positions.

Second, the cost of borrowing a stock in order to short it can be expensive, and there can be a limited supply available to short.

Third, investors tend to be unwilling to accept the risks of shorting because of the potential for unlimited losses—prospect theory at work, with the pain of a loss being much larger than the joy of an equal gain.

Fourth, short-sellers run the risk that borrowed securities will be recalled before the strategy pays off, as well as the risk that the strategy performs poorly in 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 one that impacts the entire asset class—if you screened out the “black hole” stocks, there would be a size premium that could be captured. Said another way, it’s the higher-quality small-cap stocks that explain the size premium.


Comparing Dimensional’s Results

Based on research showing evidence of the small growth anomaly, Dimensional Fund Advisors has long used screens in its funds’ construction rules to eliminate “lottery stocks” (that is, penny stocks, IPOs, stocks in bankruptcy, and small growth stocks with high investment and low profitability). Thus, by reviewing the results of the firm’s small-cap funds, we can determine if there has still been a small-cap premium that investors could have captured, not only in the United States but also in developing and emerging markets.

So that we can use all live funds, the period we will examine covers the almost-20-year period April 1998 through December 2017. We will also examine the last 10 full years of the period (2008 through 2017). (Full disclosure: My firm, Buckingham Strategic Wealth, recommends Dimensional funds in constructing client portfolios.)



Note that in each case, the live small-cap portfolios run by Dimensional Fund Advisors, which include not only expense ratios but all implementation costs, outperformed their large-cap index counterparts (which do not have any expenses) by wide margins. For the longer period, the annualized outperformance was 2.5 percentage points in the U.S., 4.4 percentage points in developed markets and 4.0 percentage points in emerging markets. For the more recent 10-year period, the outperformance was 1.5 percentage points in the U.S., 3.7 percentage points in developed markets and 2.7 percentage points in emerging markets.

Compare these figures with the Fama-French U.S. Small Cap Index’s 1.7 percentage point outperformance of the S&P 500 (11.9% versus 10.2%) since July 1926. In so doing, it certainly doesn’t look like the size premium has disappeared. At the very least, we can say that for almost the last 20 years, intelligently designed, passively managed small-cap funds have been able to capture a size premium.

Before summarizing, we’ll review the findings of an important research paper from AQR Capital Management.

Controlling For Quality

Cliff Asness, Andrea Frazzini, Ronen Israel, Tobias 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.”

On the other hand, high-quality stocks have the following characteristics: low earnings volatility, high margins, high asset turnover, low financial and operating leverage, and low idiosyncratic risk.

Research shows these stocks, the kind of stocks Benjamin Graham and Warren Buffett have long advocated buying, outperform low-quality stocks with the opposite characteristics—those “lottery-ticket” stocks.


In addition, the authors 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.”

Robust Size Premium

Further, Asness, Frazzini, Israel, Moskowitz and Pedersen 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.”

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

The authors found similar results when, instead of controlling for the quality factor, they controlled for the low beta factor—high-beta stocks (those lottery tickets) have very poor historical returns. 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, profitability (referred to as RMW, or robust minus weak) and investment (referred to as CMA, or conservative minus aggressive). High-profitability firms tend to outperform low-profitability ones, and low-investment firms tend to outperform high-investment ones.


In our book, “Your Complete Guide to Factor-Based Investing,” my co-author Andrew Berkin, director of research for Bridgeway Capital Management, and I offer evidence demonstrating the size premium has been persistent across time and economic regimes, pervasive around the globe, has intuitive risk-based explanations, and is implementable. While the publication of research can certainly lead to cash flows that can cause premiums to shrink, if there are risk-based explanations, the premiums should never disappear.

And while, as mentioned, there are some logical explanations for why the size premium may have shrunk (i.e., lower implementation costs), there also remain simple, intuitive, risk-based explanations for why the premium should persist. In addition, Berkin and I showed that the size premium is a unique source of risk and return, having low correlation to other common factors, such as market beta, value, momentum and quality/profitability, providing diversification benefits.

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

Larry Swedroe is a principal and the director of research for Buckingham Strategic Wealth, an independent member of the BAM Alliance. Previously, he was vice chairman of Prudential Home Mortgage.