Has the Size Premium Disappeared?

Using Morningstar’s data, we see that while small-growth stocks make up only about 2% of the total market capitalization, they are about one-third of the capitalization of small stocks. This creates a challenge (a hurdle to overcome) for the size premium, as the small-growth stocks “pollute” the size factor – if not for the performance of small-growth stocks, the size premium would be larger and more persistent.

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 (QMJ, or quality minus junk).

They noted: “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.”

The authors found: “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.” This led them to conclude that 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 nonprice-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.”

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 noted: “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 also tend to be low-quality stocks. In addition, they found that small stocks have negative exposure to the newer factors of 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.

Building on the findings of the above paper, Ron Alquist, Ronen Israel and Tobias Moskowitz, members of the research team at AQR Capital Management, also examined the impact of quality on the size effect in their May 2018 paper, “Fact, Fiction, and the Size Effect.” To summarize, they noted:

1. The size effect diminished shortly after its discovery and publication.

2. Because small-cap stocks typically have higher 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. The size effect 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 (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 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).

5. It has not been statistically significant outside the United States.

6. It is found mostly in microcaps (the bottom 5% of all stocks); thus, it is more difficult to implement (making the control/minimization of trading costs critical).

However, they “save” the size effect by demonstrating that 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. Alquist, Israel and Moskowitz noted: “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 nonmarket-based size measures, making the size premium a much stronger and more reliable effect after controlling for quality.”

A nail in the size factor premium?

Building on their prior work, the research team at AQR dug deeper into the performance of small stocks in their September 18, 2020, article, “There Is No Size Effect: Daily Edition,” published in Cliff’s Perspectives. Following is a summary of their findings.

1. While small stocks have outperformed, the outperformance is cut roughly in half once one accounts for the higher betas of small stocks. In other words, small stocks have earned higher returns than large stocks. However, about half of the premium was due to more exposure to the market beta premium, not a size premium.

2. The original research misestimated betas due to liquidity differences, with the smallest stocks being highly illiquid. The authors noted: “If any stocks, but most likely applying to the small and very small, are illiquid enough that they trade infrequently, then when they finally do trade their price changes may reflect not just the contemporaneous market moves but also past market moves (as they never recorded a price change to account for those at the time).” To address this issue, they used lagged returns. Once liquidity is taken into account by using lagged returns, the size premium disappears.

AQR demonstrated that the size premium doesn’t work alone, but does work when combined with other factors (such as momentum, value and high quality) – those factors all have larger premiums in small stocks than in large stocks. In other words, the size effect can be resuscitated by building portfolios that combine it with other factors.

Implementation: Does the size effect survive transaction costs?

Based on research showing evidence of the small-growth anomaly, Dimensional has long used screens in its fund 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 I can use all live funds, and using the analysis tools at Portfolio Visualizer, I will examine the more than 22-year period from April 1998 through September 2020. (Full disclosure: My firm, Buckingham Strategic Wealth, recommends Dimensional funds in constructing client portfolios.)

For the more than 22-year period from April 1998 through September 2020, in each case there was a realized size (small) premium, ranging from 0.4% to as much as 3.7%. These results are net of not only expense ratios but all implementation costs, while index returns do not include any costs that would be incurred by live funds.

We now turn to examining what the future might hold for small stocks.

Future expected returns

With their study, “Small-Cap Allocations: Timing the Entry,” published in the September 2020 issue of The Journal of Portfolio Management, authors Eric Sorensen and Sebastian Lancetti provide some insights as to what the future might hold. They began by examining historical relative valuations. They formed a composite value metric for each stock in the Russell 1000 and 2000 indices based on book-to-price, earnings-to-price and sales-to-price to create a median score. The following chart shows the relative valuations of small and large stocks over the period 1996-April 2020.

It shows that because of the relatively poor performance of small stocks over the past few years, small stocks are historically relatively cheap. That raises the question of performance after periods of relative cheapness. The chart below breaks the relative cheapness scores into deciles and shows the performance over the following three-year period.

As illustrated, the historical annualized size premium following periods of extreme cheapness (such as the current one) has been in excess of 7% a year.

The following chart also shows that small stocks look relatively cheap based on trailing five-year earnings.

While valuations of small stocks look relatively attractive, investors must recognize that cheap stocks can continue to get cheaper, especially if the greater economic cycle risk of small stocks is realized. Thus, diversifying across multiple unique sources of risk and return, and having the discipline to adhere to a well-thought-out plan, is always the strategy that will most likely allow you to achieve your financial goals.

Larry Swedroe is the chief research officer for Buckingham Wealth Partners.

Important Disclosure: Indices are not available for direct investment. Their performance does not reflect the expenses associated with the management of actual portfolios nor do indices represent results of actual trading. Information from sources deemed reliable, but its accuracy cannot be guaranteed. Performance is historical and does not guarantee future results. Total return includes reinvestment of dividends and capital gains. The analysis in this article is for information and educational purposes only and should not be construed as specific investment, accounting, tax, or legal advice. The analysis in this article is based upon third party data and information available at the time and may become outdated or otherwise superseded at any time without notice. Certain information contained herein is based upon third party data which is deemed to be reliable but its accuracy and completeness cannot be guaranteed. By clicking on any of the third-party links above you acknowledge it solely at your convenience, and do not necessarily imply any affiliation, sponsorship, endorsement or representations whatsoever by us regarding third-party websites. We are not responsible for the content, availability, or privacy policies of these sites, and shall not be responsible or liable for any information, opinions, advice, products or services available on or through them. The opinions expressed by featured authors are their own and may not accurately reflect those of Buckingham Strategic Wealth®., Buckingham Strategic Partners® (collectively Buckingham Wealth Partners). R-20-1232

[1] Looking at average annual returns (the way factor premia are calculated), instead of compound returns, the stocks in deciles 6-10 did outperform those in deciles 1-5, 12.8% versus 12.4%.

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