What Happened to the Size Premium?

The size effect, or the negative relation between average stock returns and market capitalization that is not explained by market risk exposure, was first documented by Rolf Banz in his 1981 paper “The Relationship Between Return and Market Value of Common Stocks.” 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 capital asset pricing model’s market beta). However, the size premium has been questioned due to its performance in recent decades.

Over the 97-year period of 1927-2023, the Fama-French U.S. Small Research Index returned 11.7% per year, outperforming the return of 10.1% per year of the Fama-French U.S. Large Research Index by 1.6 percentage points per year. However, over the past 20 calendar years (2004-23), the size effect was negative, with the Small Research Index return of 8.9% underperforming the 10.1% return of the Large Research Index by 1.2 percentage points per year.

Disappearing Size Premium

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 (quality minus junk, or QMJ).

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.”

They added: “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. This is important because, while in the 1990s, 15% of companies in the Russell 2000 had negative 12-month trailing earnings, today that share is about 40%!

Ron Alquist, Ronen Israel, and Tobias Moskowitz also examined the impact of quality on the size effect in their 2018 paper, “Fact, Fiction, and the Size Effect.” They found: “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.”

New Research on the Size Effect

Sara Easterwood, Jeffry Netter, Bradley Paye, and Mike Stegemoller contribute to the asset pricing literature with their study “Taking Over the Size Effect: Asset Pricing Implications of Merger Activity,” published in the March 2024 issue of the Journal of Financial and Quantitative Analysis, in which they established a strong connection between merger and acquisition activity and the size effect.

To establish this connection, they constructed an ex-ante takeover likelihood characteristic and associated “takeover factor”—the estimated likelihood that a firm will be acquired within the next year. Variables included the return on assets of the firm, firm leverage (book debt/asset ratio), cash (the cash and short-term investments/assets ratio), firm size (the natural logarithm of market capitalization), Q (the market/book ratio for the firm), and asset structure (PPE, measured by the property, plant, and equipment/assets ratio).

The model also included two indicator variables. The first, denoted BLOCK, equaled 1 when an external blockholder existed, and zero otherwise. The second dummy variable, denoted INDUSTRY, took the value 1 if at least one acquisition occurred within the industry during the prior year. Consistent with the findings of prior studies, the most important variables, based on odds ratios, were the blockholder indicator (positively related to takeover likelihood), prior industry acquisition activity (positively related to takeover likelihood), and size (negatively related to takeover likelihood).

To test whether M&A news exerts a significant influence on the measured average returns associated with prominent anomaly-based hedge portfolio returns, they decomposed ex-post average returns for the size factor and other anomaly portfolios into a component associated with realized M&A news and a residual. They then measured the M&A component of returns using standard event study methods, with the M&A component of a stock’s daily return equal to the abnormal return on each day the firm was within the defined event window around an acquisition announcement, either as target or acquirer. Outside of this window, the M&A component equaled zero.

Their dataset covered US stocks and all acquisitions from 1990 through 2020, with the acquirer having purchased 50% or more of the target’s shares in the transaction and having owned less than 50% of the target prior to the transaction—a total of 225,243 transactions.

Following is a summary of their key findings:

• The cumulative average return of the average target was over 30% for the full sample of public firms—34% for the smallest quintile and 17% for the largest.
• Target CARs increased over the past 30 years—the average CAR during the most recent decade exceeded that during the 1990s by about 4 percentage points.
• Nearly 50% of takeovers of public firms occurred for firms in the smallest decile portfolio, and nearly two thirds of takeovers involved targets in the smallest quintile portfolio.
• The average annual takeover rate for the small-cap quintile was over 4.3% versus 1.9% for the large-cap quintile—small-cap quintile firms were around 2.3 times more likely to be acquired than large quintile firms.
• The odds ratio of acquiring a firm for the small-cap quintile relative to the large-cap quintile was around one third, and the odds ratio of acquiring a public firm was approximately one tenth.
• The difference in average acquirer CARs between firms in the smallest versus largest capitalization portfolio was around 2.3% (2.9%) for portfolios based on size quintiles (deciles).
• The smallest decile and quintile portfolios both had average M&A return components of approximately 1.8% per year, while the average M&A return components for the largest decile and quintile portfolios were close to zero.
• Positive average returns were associated with size-based hedge portfolios that were driven primarily by M&A news, with acquisition news explaining virtually all of the size premium in US data—the size premium has been largely attributable to narrow-window event returns associated with deal announcements involving public firms.
• The returns on their takeover factor were relatively highly correlated, with returns on the size factor proposed by Fama and French (SMB, or small minus big), and the two factor premia exhibited similar cyclical behavior—returns for both factors were procyclical, tending to be higher during economic expansions and lower just before or during recession periods, including the global financial crisis.
• While the size premium disappeared in recent decades, the premium associated with the takeover factor remained robust.
• The takeover factor dominated the size factor—models including the size factor were unable to price the takeover factor, but models including the takeover factor priced the size factor.
• The annualized average return for a long-short portfolio based on size quintiles was 0.9%, while the realized M&A component of the average return was 1.7%—more than 100% of the total size premium. Thus, the residual size premium was negative, as small firms earned lower average returns relative to large firms after removing the M&A return component.
• Over the most recent 30-year period, 1990-2020, the annualized takeover factor premium was around 6% versus 1.5% for the annualized size factor—the takeover factor was more resilient than the size factor over the past few decades.
• After controlling for takeover exposure, larger firms earned higher average returns relative to smaller firms, in contrast to the conventional negative size relationship.
• Results were substantially similar for the period 1980-89, though data was not as complete.
• The takeover factor was rebalanced annually, resulting in low turnover, and thus turnover costs were unlikely to explain the results.

Given these findings, it seems likely that takeover activity also accounted for a significant proportion of the measured size premium during the 1960s and 1970s. From 1960 to 1979, the Fama-French U.S. Small Research Index returned 11.6% per year, outperforming the return of 6.8% per year of the Large Research Index by 4.8 percentage points per year.

Easterwood, Netter, Paye, and Stegemoller also examined the impact of the M&A component on other factors:

• The M&A component of average returns was small for the value factor.
• In contrast to size, the average M&A component for long-short portfolios based on gross profitability was negative because less profitable firms in the short leg of the gross profitability hedge portfolios tended to be smaller and more likely to become targets.
• Other anomalies that exhibited a significant M&A expected return component included idiosyncratic volatility, net issuance, price, and several multicharacteristic strategies that involved profitability (for example, value-profitability).
• Dividend payers were less likely to be takeover targets. In addition, a measure of momentum in the form of the cumulative return over the preceding year and a measure of the idiosyncratic volatility of returns, defined as the realized volatility of daily returns over the previous year, were both highly significant and negatively related to takeover.

Their findings led the authors to conclude “that the traditional size factor can be interpreted as a proxy for a takeover factor, in the sense that the size factor implicitly embeds exposure to underlying state variables that drive time-varying takeover activity. The takeover factor earns a much higher premium than the size factor, especially over recent decades. Asset pricing tests consistently favor the takeover factor relative to the size factor.” They added: “Researchers and practitioners should replace the conventional size factor with a takeover factor in benchmark asset pricing models.”

Investor Takeaways

The first takeaway is that the empirical evidence demonstrates that if investors are going to tilt their portfolios to small stocks, they should focus on small, quality stocks. While there are not yet any mutual funds or exchange-traded funds that target the M&A factor, there are investment firms that use systematic, transparent, and replicable factor-based strategies that access the factors that Easterwood, Netter, Paye, and Stegemoller found to exhibit a significant M&A expected return component (such as small, value companies that are profitability and show positive momentum). These include AQR, Avantis, Bridgeway, and DFA.

Another is that Easterwood, Netter, Paye, and Stegemoller showed that most takeovers are of smaller companies and that their takeover factor has subsumed the explanatory power of the size factor in the cross-section of expected returns. Because the passage in 2002 of the Sarbanes-Oxley Act greatly increased the cost of being a public company, today companies are waiting to become much larger before going public. The result is that by 2020 the number of US publicly listed stocks had fallen 50% over the prior 20 years, to about 3,500.

In Europe today, 96% of firms with revenue greater than $100 million are private.

Another outcome from the passage of Sarbanes-Oxley has been that the smallest quintile is made up of much larger stocks today than has been the case historically. For example, Vanguard Small-Cap ETF VB, with $54 billion in assets under management, had an average market cap of $6.8 billion (not so small cap) at the end of March 2024. The takeaway is that to capture the takeover premium in small companies, private markets (in the form of private equity) provide a greater opportunity than in public markets. For investors in public markets, they can still focus on quality/profitability, but it is now harder to access smaller companies as they are remaining private for much longer periods. This is important since all factor premiums have been found to be greater in the smallest stocks. Investors seeking greater exposure to the M&A factor (as well as to the size, value, profitability, and momentum factors) might consider funds such as Dimensional US Small Cap Value ETF DFSV, which had an average market cap of about $2.8 billion, Avantis Small Cap Value ETF AVUV, which had an average market cap of $2.5 billion, and EA Bridgeway Omni Small-Cap Value ETF BSVO, which had an average market cap of around $1 billion.

Another related takeaway is that because the factor premiums in current asset pricing models have been larger in small caps than in large caps, the opportunity to capture them should also be greater now in private equity than in public markets while also earning the illiquidity premium.

Good News

The good news is that not only has private equity become more accessible, but competition is driving down fees. They are significantly lower than the historically traditional 2% annual fee/20% carry fee. In addition, private equity firms such as Blackstone BX, Pantheon, and JPMorgan have introduced “evergreen” funds that avoid the problems of capital calls with unknown call dates and long lockups.

Other good news related to changes in private equity is that a deep market in secondaries has developed where funds can purchase existing holdings at a discount (typically around 10%, but it can be much larger in times of distress) from investors or funds that need to trade either for liquidity or asset-allocation (rebalancing) requirements. Additionally, larger private equity funds, such as the ones mentioned, are able to negotiate co-investments for a large majority of their holdings, avoiding the second layer of fees. That, along with secondaries bought at discount, can offset some or all of any acquired fund fees.

Evergreen funds allow for investment at any time and typically allow for limited liquidity (such as 5% a quarter or 10% a year). And Cliffwater has recently introduced its Cascade Private Capital CPEFX in a publicly available interval fund structure. That has the benefit of eliminating the nuisance and expense of receiving K-1s from limited partnerships, as investors receive a 1099 at the end of the year instead. And these vehicles are available on custodial platforms such as Schwab and Fidelity. While the 2/20 structure led to the fund sponsors taking all the alpha available from private equity, today’s lower fees (such as Pantheon’s 1.45% with no carry, and JPMorgan’s fee of 1% with a 10% carry) allow investors to capture the size (and takeover) premiums as well as illiquidity premiums typically found in nonpublic investments.

Words of Caution

We need to cover two last points regarding private equity. First, because private equity investments are much more volatile than public equity, it is important to make sure your allocation to private equity is highly diversified across industries and perhaps even investment firms. Second, private equity funds tend to show much lower volatility than public markets. However, do not be fooled by this “volatility laundering,” as the lower volatility arises purely because these funds do not mark to market in a timely manner. So, don’t fall for that narrative. Private equity is as least as volatile as public equity, if not more so, and it’s a lot less liquid. With that in mind, any allocation to private equity should not be considered as an allocation to alternatives. Instead, it should come from your equity allocation, specifically your small-cap allocation, and should only be made if you can allocate that amount to less liquid assets.

Larry Swedroe is the author or co-author of 18 books on investing, including his latest, Enrich Your Future: The Keys to Successful Investing.