I Know What You Did Last Summer

Abstract

The outperformance of smaller stocks is one of the oldest anomalies, but its existence has been questioned in recent years. We show that a simple intuitive change in definition significantly improves the performance of small stocks. In particular, we require a small cap stock to be small not just at the current rebalance, but to have been small in prior years as well. This definition removes stocks which have fallen from large cap ranks and recent additions such as IPOs, groups which typically have poor properties. Annual small cap returns rise by 65 bp with a one-year lookback and 157 bp with a three-year lookback; the increases are statistically significant. Factor analysis shows the boost comes from improvements in momentum, profitability and investment as well as alpha. We also provide a number of checks to show the robustness of our result.

Key Takeways:

• Requiring that a company be small not just in the current year but also in past years dramatically improves the return and statistical significance of the size factor.
• This requirement removes stocks which have fallen from large cap ranks and recent additions such as IPOs, groups which we document have poor properties.
• Annual returns rise by 65 bp with a one-year lookback and 157 bp with a three-year lookback, and are robust to a number of variations.

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The outperformance of smaller market capitalization (small cap) stocks is one of the oldest anomalies, dating back to Banz’s (1981) paper. Size then became incorporated into the classic Fama-French (1993) three-factor model, along with market beta and value, and it remains in their subsequent five-factor model (Fama and French 2015).

Yet in recent years, the excess returns of smaller stocks have become more muted. These lower returns have led some to claim that small size is not a factor that delivers excess returns; see for example Alquist, Israel and Moskowitz (2018).

We claim that the performance of smaller size is burdened by unfair definitions. For example, the standard Fama-French size factor, SMB, is constructed from the returns of the smaller half of stocks minus the returns of the larger half. Other Fama-French factors use the top 30% minus the bottom 30%, while many other papers use quintile or decile spreads in factor construction. Berkin and Wang (2025) show that defining a size factor by the top and bottom 30% or by quintiles greatly improves returns. They also show that removing bad actors such as stocks with poor momentum further boosts the size factor. Asness et al (2018) show that smaller stocks do better when controlling for quality.

In this paper, we also remove certain stocks from our definition of small cap. We divide small stocks into those that were also small at the previous rebalance and those that were not. The former group earns an even higher return premium, while the latter group has far weaker returns. This approach may seem similar to removing stocks with bad factor attributes, such as poor momentum. In fact, it reflects an important distinction in what it means to be a small stock. Instead of calling any stock with low market cap small, we distinguish stocks which have been small from those which have become small. Much as someone who moves to California or Texas may be a resident there on the first day, but wouldn’t be considered a true Californian or Texan until they have been there for enough time to adopt local characteristics, we take a similar approach with small caps.

This distinction in defining small caps doesn’t just improve returns, it also improves the characteristics of the drivers of those returns. Much as a newcomer to an area may have different behavior than longtime residents, stocks that are newly small have different behaviors than stocks which have been small. Stocks which have been small have higher exposures to the momentum, profitability and investment factors. They also have higher alphas as measured by regressions against standard factor models.

This paper is related to work which uses alternate definitions of small cap, as noted above. It is also related to papers which examine the negative impact of indexing on small cap returns. For example, Madhavan (2003) and Chen (2006) analyze the price impact of index changes around the annual reconstitution of the Russell indices at the end of June. More closely related to our paper, Cai and Houge (2008) show that the returns of the small cap Russell 2000 index from two to five years back beat the returns of the current index. Our paper differs from theirs in several respects. Our universe of small cap stocks is broader, consisting of all stocks smaller than the NYSE median, thus including the smallest stocks. Crucially, our universe allows us to go back to 1964, before the inception of the Russell indices in 1984[1] and even further before these indices had significant assets. Our results are not solely driven by indexing as they hold in a period before indexing took off. The results also hold for rebalancing dates at the end of all four quarters and not just June. While the old Russell 2000 universe constituents that Cai and Houge consider include stocks that have become large, we start with only small stocks and then screen out those which are new entries. Our method defines small cap stocks as those which are not just small, but also have been small, a conceptual distinction to the standard approach of what defines a small stock.

Our results give a more robust small cap premium. They also have important implications for the management of small cap portfolios. Investors need not invest in all stocks that are currently small. We know what those stocks were like a year before. Cutting out those stocks which were not small in the prior year, especially those with bad characteristics, can improve results significantly.

DATA AND METHODOLOGY

We consider all U.S. stocks listed on the NYSE, NASDAQ and AMEX exchanges with CRSP share codes 10 and 11. Market capitalization and returns come from CRSP, while accounting variables are from Compustat. Our data starts in July 1963 when broad coverage in Compustat becomes available and ends in June 2023, giving us a 60-year history. We follow the methodology of Fama and French (1993), requiring that stocks have a positive book value. Fama-French and momentum factors used in explanatory regressions, and their definitions, come from Ken French’s data library[2].

Our main analysis is done on six portfolios formed from 2×3 independent sorts on size and value, as is done in Fama and French (1993), but we perform the analysis ourselves. Size is broken into halves, while the breakpoints for value are at 30% and 70%. As is standard in the literature, the sorts to determine the breakpoints are performed only on NYSE stocks. Size is determined by market cap, while value is the ratio of book equity to market cap (book to market or B/M). To ensure data availability, B/M is measured with a six-month lag, as is standard. We also examine 25 portfolios formed by 5×5 independent sorts on size and value. Each of these 6 or 25 portfolios is cap weighted and represents a long-only portfolio of stocks with certain size and value characteristics. Alphas and factor loadings are calculated from monthly Fama-French-Carhart (FFC) regressions using the Fama-French three or five factor models (Fama and French, 1993 and 2015) augmented with momentum (Carhart, 1997). Returns are annualized geometrically (compounded), while following convention alpha is annualized arithmetically by multiplying by 12.

We further break down these portfolios by how they were previously classified. Our main analysis rebalances portfolios annually in June, as is standard in the literature. We thus also characterize stocks by whether they were small, large, or not available the prior June. Modifications made for additional tests and analysis are discussed appropriately below as needed. Stocks may not have been available the prior year for a variety of reasons. They may have been privately held and became publicly traded through an event like an initial public offering (IPO) or through a Special Purpose Acquisition Company (SPAC). They may have been spun off from another stock. They could have not been listed on a major exchange, trading instead on over-the-counter markets like the pink sheets. Or they might have had negative book value which subsequently became positive. There are a variety of other reasons as well, such as a change in classification from a REIT to a regular common stock. Whatever the reason, we group all these new stocks into the same category both for simplicity and to ensure adequate sample size.

Exhibit 1 shows the average composition of current year small and large portfolios by their prior year status. From Panel A, we see that there is moderate turnover by count. About 88% of the names that are big were also big the year before on average, while 87% of the small names were also small the prior year. Of the large names, 8.3% were small and 3.3% were not classified the prior June. For small names, 2.2% were large and 11.0% not classified the prior year. Panel B gives results by market cap weight. Now almost 97% of large caps by weight were large the year before, reflecting the heavy weighting of the largest stocks. For small caps, almost 84% of the weight remains the same, with new stocks taking slightly more of the remaining weight than former large caps which have come down in size.

Exhibit 1: Average Composition in % of Large and Small Stocks by Prior Year Status, July 1964 – June 2023
Panel A: Count
	Last Year
Current	Small	Big	N/A
Big	8.3	88.3	3.3
Small	86.9	2.2	11.0
Panel B: Weight
	Last Year
Current	Small	Big	N/A
Big	1.5	96.9	1.6
Small	83.7	7.6	8.7
Note: The averages skip the period when NASDAQ stocks first became available, which falsely inflates the number of new stocks.Source: Bridgeway calculations, CRSP, Compustat.

I KNOW WHAT YOU DID LAST SUMMER

Returns of Size and Value Portfolios

We start by analyzing the standard case of forming size and value portfolios once a year at the end of June. Annualized returns are in Exhibit 2. Panel A gives results for all stocks. Over this 60-year period, small stocks with high B/M have the highest return at 14.91% a year. Small stocks with medium B/M have the next highest return at 13.47%. Small stocks with low value lag all other groups, however, at 8.27%. If we average the three value groups (high, medium and low), small stocks do still enjoy a 1.29% annual premium over large caps.

Exhibit 2: Cap Weight Annual Geometric Returns in %, July 1963 – June 2023
Panel A: All Stocks
		Book to Market
		Low	Med	High
Cap	Big	10.35	10.24	12.18
	Small	8.27	13.47	14.91
Panel B: Only Stocks Small Last Year
		Book to Market
		Low	Med	High
Cap	Big	10.18	11.77	14.46
	Small	9.29	13.85	15.44
Panel C: Only Stocks Large Last Year
		Book to Market
		Low	Med	High
Cap	Big	10.45	10.27	12.18
	Small	6.72	11.65	8.87
Panel D: Only Stocks Not in Universe Last Year
		Book to Market
		Low	Med	High
Cap	Big	7.24	8.10	6.31
	Small	5.32	8.13	15.03
Note: Portfolios formed annually at the end of June based on June cap and annual book equity and cap from prior December. Source: Bridgeway calculations, CRSP, Compustat.

Panel B shows returns only for stocks that were small caps the prior June. For example, stocks in the lower right group are small and high value as of the end of the most recent June and also had been classified as small (in any of the three value categories) at the end of June the year before. It is thus a subset of the stocks in the small value category of Panel A. Similarly, stocks in the upper left group are large and low value as of the most recent June but were small the year before.

Returns are higher for all three small cap portfolios compared to Panel A, with the low value one rising the most at over 1% more annually. Stocks which are not just small but have been small outperform the rest of small stocks, consisting of those which have become small. Returns are also notably higher for two of the three large cap portfolios, with large and high value particularly benefiting. The large and low value group is the only exception; returns drop by a modest 17 bp compared to its counterpart in Panel A. For large caps, these stocks which used to be small represent a relatively minor percentage of the portfolio, both by count and by weight, as seen in Exhibit 1. Large cap managers still need to hold the names which were large the year before to best represent the large cap space. But especially for large cap strategies with a value tilt, extra focus on names that have moved up from being small cap could be beneficial.

One key to understanding these results lies in the returns of Panel C, which contains only stocks which had been classified as large the prior June. For large caps, returns are quite similar to those of Panel A. This makes sense, as the very largest stocks tend to remain large, and their weights continue to dominate; Panel C stocks make up most of the weight of large caps in Panel A. Those stocks from the top row of Panel B, which have moved from small to large cap, provide a nice boost, but their weight is modest in Panel A.

But Panel C paints a different picture for small caps. Those stocks which have fallen from large cap the year before to their current status as small caps continue to have horrible returns. The former large caps which have become small of Panel C lag those which have been small in Panel B by multiple percent; 8.87% compared to 15.44% in the case of small value. This is a key reason behind our admonition to look back to the end of June the year before and slash from the portfolio those stocks which had been large but suffered bad behavior.

Another rationale for doing so lies in Panel D, containing stocks which were not in the universe the prior June, such as IPOs. Now the returns of five of the groups are lower than those for all stocks in Panel A, by over 2% to almost 6%. The one exception is returns for small value stocks, which are 12 bp higher in Panel D, but the returns of these stocks which did not exist the prior June are still lower than those in Panel B for stocks which have been small. An investor is thus well served by avoiding stocks which did not exist the year before. This result aligns with those of Ritter (1991) and Loughran and Ritter (1995), who found that IPOs lag the market. Thus, another reason to look back at what stocks were doing a year before is to avoid investing in those that did not exist. This is true for large caps, but especially apt in the small cap space where the majority of these stocks reside.

Factor Exposures

Our results above demonstrate that stocks which have been small have higher returns than stocks which have become small. But what causes this result? For more insight, we perform FFC regressions on monthly returns to see the exposures of these portfolios. Results are in Exhibits 3 and 4, for four- and six-factor models respectively. The four panels in both of these exhibits represent the same four panels of Exhibit 2: all stocks, stocks that were small the prior June, stocks that were big the prior June, and stocks that weren’t available to be ranked the prior June.

Exhibit 3: Fama-French-Carhart Four-Factor Loadings of Cap Weight Monthly Returns, July 1963 – June 2023
Panel A: All Stocks
	alpha	Mkt-RF	SMB	HML	MOM
LgLo	1.36***	1.00	-0.15	-0.28	0.00
LgMd	-0.77	0.97	-0.12	0.32	0.00
LgHi	-0.90*	1.08	0.01	0.76	-0.03***
SmLo	-2.15***	1.08	1.06	-0.25	-0.02**
SmMd	0.74*	0.97	0.83	0.34	0.00
SmHi	0.63**	1.00	0.87	0.69	0.00
Panel B: Only Stocks Small Last Year
	alpha	Mkt-RF	SMB	HML	MOM
LgLo	-1.42	1.20	0.65	-0.43	0.25***
LgMd	-2.11	1.12	0.44	0.27	0.23***
LgHi	-0.54	1.12	0.60	0.59	0.29***
SmLo	-1.79***	1.06	1.04	-0.19	0.03***
SmMd	0.77*	0.96	0.84	0.35	0.03***
SmHi	0.94***	0.98	0.88	0.68	0.03***
Panel C: Only Stocks Large Last Year
	alpha	Mkt-RF	SMB	HML	MOM
LgLo	1.51***	0.99	-0.17	-0.27	-0.01
LgMd	-0.71	0.97	-0.13	0.33	-0.01
LgHi	-0.85	1.08	-0.01	0.78	-0.04***
SmLo	-0.54	1.07	0.91	-0.14	-0.36***
SmMd	2.15	1.06	0.67	0.39	-0.37***
SmHi	-2.08	1.24	0.77	0.94	-0.41***
Panel D: Only Stocks Not in Universe Last Year
	alpha	Mkt-RF	SMB	HML	MOM
LgLo	-0.44	1.12	0.48	-0.63	0.04
LgMd	-0.46	1.06	0.07	0.10	-0.13***
LgHi	-2.25	1.05	0.15	0.38	-0.16***
SmLo	-3.34**	1.15	1.18	-0.49	-0.07***
SmMd	-2.68*	0.95	0.97	0.09	-0.01
SmHi	1.85	1.00	0.82	0.46	0.04
Note: One, two and three asterisks (*, **, and ***) denote statistical significance at the 10%, 5%, and 1% levels respectively.  Only the first and last columns are marked. The middle three columns are typically highly significant and hence not marked to reduce clutter. Source: Bridgeway calculations, CRSP, Compustat, Ken French data library.

Starting with the four-factor models in Exhibit 3, exposures to the market factor are generally similar across the four panels. Exposures to HML reflect the value classifications of high, medium and low. They do vary across the panels, but no systematic differences are obvious. We do see patterns with SMB exposure. Comparing Panels A and B, small stocks which had been small the year before have comparable size exposure as all small stocks, while formerly small stocks which become large are still smaller than other large caps. This makes sense, as small stocks are unlikely to jump into the very largest mega cap ranks. Conversely, stocks which had been big tend to be on the larger side when they fall into the small cap range. This is reflected in the lower exposure to SMB of the small stocks in Panel C compared to Panels A and B. It also aligns with Exhibit 1 where formerly big stocks make up 2.2% of the small caps by name but 7.6% by weight, showing that they tend to be on the larger side of current small caps. Because SMB returns are positive on average over time, large caps gain a return benefit from stocks that were small moving up, but the advantage is limited by their low weight in the large cap portfolio. Stocks that were large but are now small drag down returns because they reduce SMB exposure and their weight is more substantial. Finally, stocks that were not ranked at all the prior year tend to be on the smaller side, whether they debut in the small or large cap side[3].

Momentum exposures provide further important insights. Stocks that had been small but now have moved into large caps have strong positive momentum, as expected. They provide a boost to the existing large caps, but their impact is limited as they come in with modest weight. On the other hand, stocks that had been large the year before but now are small have quite poor momentum exposure, as expected. They do have an influential weight. Cutting these formerly large stocks from the small cap portfolio notably improves momentum exposure and thus returns.

The intercept or alpha term is also interesting. Despite these six portfolios being formed in the same way that determines the SMB and HML factor returns, there is significant alpha when looking at all stocks in Panel A. Small stocks with low value have significantly negative alpha, while for large low value stocks as well as small value and small medium stocks alpha is significantly positive. For the subset of small stocks that were small the prior year, alpha improves (Panel B), while for small value stocks that had been large their alpha is poor (Panel C). From Panel D, stocks which did not exist the prior year have negative alpha in five of the six buckets, with small value stocks the exception. The negative alpha of the small low and medium value groups is statistically significant and helps explain why removing them boosts small cap performance.

Turning to the six-factor model of Exhibit 4, the same general patterns hold for the market, size, value and momentum factors. RMW shows that stocks which have remained small tend to have better profitability than small stocks as a whole, which are dragged down by the poor profitability of stocks that weren’t in our universe a year ago. CMA shows that small caps benefit from more conservative investment among stocks that were either small or large the prior year, but they are dragged down by the weak returns of the more aggressive investment among stocks that weren’t in our universe before. These extra factors help explain some of the relative boost in alpha we saw under the four-factor model for the stocks which continued to be small[4].

Exhibit 4: Fama-French-Carhart Five-Factor + Momentum Loadings of Cap Weight Monthly Returns, July 1963 – June 2023
Panel A: All Stocks
	alpha	Mkt-RF	SMB	HML	RMW	CMA	MOM
LgLo	0.85***	1.00	-0.11	-0.25	0.15***	-0.04**	-0.01
LgMd	-1.50***	0.99	-0.08	0.26	0.09***	0.15***	-0.01
LgHi	-0.33	1.06	0.01	0.83	-0.07***	-0.15***	-0.02**
SmLo	-0.83**	1.05	1.01	-0.35	-0.22***	-0.12***	-0.01
SmMd	0.70**	0.96	0.85	0.20	0.05***	0.01	-0.01
SmHi	0.50	1.00	0.87	0.51	0.03***	0.09***	0.00
Panel B: Only Stocks Small Last Year
	alpha	Mkt-RF	SMB	HML	RMW	CMA	MOM
LgLo	0.35	1.16	0.59	-0.35	-0.22***	-0.36***	0.27***
LgMd	-2.32*	1.11	0.48	0.23	0.12**	-0.08	0.23***
LgHi	0.12	1.13	0.53	0.45	-0.21**	0.13	0.29***
SmLo	-0.93**	1.04	1.01	-0.33	-0.15***	-0.03	0.04***
SmMd	0.44	0.95	0.88	0.20	0.11***	0.04**	0.03***
SmHi	0.74**	0.98	0.89	0.48	0.04**	0.13***	0.03***
Panel C: Only Stocks Large Last Year
	alpha	Mkt-RF	SMB	HML	RMW	CMA	MOM
LgLo	0.86***	1.00	-0.12	-0.24	0.18***	-0.03	-0.01**
LgMd	-1.48***	0.98	-0.09	0.27	0.10***	0.16***	-0.01
LgHi	-0.29	1.06	-0.01	0.86	-0.06***	-0.17***	-0.03***
SmLo	-0.47	1.07	0.91	-0.35	-0.05	0.15	-0.37***
SmMd	1.74	1.07	0.69	0.19	0.02	0.22***	-0.38***
SmHi	-2.93	1.24	0.83	0.75	0.19***	0.13	-0.42***
Panel D: Only Stocks Not in Universe Last Year
	alpha	Mkt-RF	SMB	HML	RMW	CMA	MOM
LgLo	1.52	1.07	0.40	-0.54	-0.30***	-0.33***	0.06
LgMd	-0.11	1.05	0.06	0.11	-0.07	-0.04	-0.12***
LgHi	-2.66	1.04	0.21	0.38	0.15	-0.07	-0.16***
SmLo	-0.27	1.08	1.08	-0.42	-0.45***	-0.50***	-0.04
SmMd	0.19	0.89	0.84	0.13	-0.49***	-0.36***	0.02
SmHi	2.09	0.99	0.82	0.33	-0.01	-0.01	0.04
Note: One, two and three asterisks (*, **, and ***) denote statistical significance at the 10%, 5%, and 1% levels respectively.  The Mkt-RF, SMB and HML columns are typically highly significant and hence not marked to reduce clutter. Source: Bridgeway calculations, CRSP, Compustat, Ken French data library.

Modified SMB Factor

To further demonstrate the benefits of defining small as only stocks that are small at the end of both the current and prior June, we construct both a regular and an alternative SMB factor. The regular SMB is calculated by averaging the three small cap portfolio returns and subtracting the average of the three large cap portfolios, using all stocks defined by their market cap each June, as given in Panel A of Exhibit 2. Our results match those from Ken French’s data library closely: our monthly series for SMB, as well as HML, correlate with those of Fama-French at over 99%, and our average returns are within 2 bp. These factors are notoriously difficult to exactly reproduce[5], and the website itself has returns for a given date which vary over time due to reasons such as accounting rules changes, new data and restatements.

Our alternate SMB, SMB*, is formed using the three small cap portfolios from Panel B of Exhibit 2 and again subtracting the average of the three large cap portfolios from Panel A of Exhibit 2. The only difference between these two is that SMB* uses only small cap stocks which were also small cap the prior June in the formation of the small cap portfolios[6]. We also calculate their difference. Exhibit 5 shows the results, for the full period of 720 months (60 years) as well as by halves.

Exhibit 5: Monthly Statistics in %
Panel A: Full Period, July 1963 – June 2023
	SMB	SMB*	Difference
Mean	0.17	0.21	0.04
Stdev	3.07	3.06	0.40
T-stat	1.49	1.87	2.85
Panel B: 1st Half, July 1963 – June 1993
	SMB	SMB*	Difference
Mean	0.29	0.32	0.04
Stdev	2.91	2.93	0.28
T-stat	1.86	2.09	2.49
Panel C: 2nd Half, July 1993 – June 2023
	SMB	SMB*	Difference
Mean	0.06	0.11	0.05
Stdev	3.23	3.19	0.50
T-stat	0.33	0.63	1.87
Note: Annual rebalances in June. SMB has all small stocks, SMB* has only small stocks which were also small the prior June. Source: Bridgeway calculations, CRSP, Compustat.

For the full period, the standard SMB averages 17 bp/month and is not quite statistically significant. By looking back to the prior June and slashing from the small cap portfolios those stocks which were not small the year before, the alternative SMB* averages 21 bp/month. This is statistically significant. Even more impressive, the average difference between these two monthly series of 4 bp is even more statistically significant, with a t-stat of 2.85.

Breaking these results into two halves is instructive. Returns in the first half are notably higher, with SMB at 29 bp/month and SMB* at 32 bp/month. This compares with 6 bp/month and 11 bp/month in the second half. Our alternative measure SMB* is still significantly better than SMB in both halves, with the difference even improving in the second half. The improvement in returns from defining small caps as stocks which are not just small but have been small is robust across time. Furthermore, it shows that our results are not driven by indexing effects from the annual Russell reconstitution in June, since our results hold in the first half spanning 1963-1993. The Russell indices did not exist prior to 1984 and the amount indexed was much smaller through 1993.

Our alternative SMB* has a return advantage over the standard SMB which has persisted over time. Like all factors, small size has had periods where it performed strongly and others where it has been weaker, Overall, both SMB and SMB* have been positive in both halves and indeed all four quarters (not shown for brevity). The most recent 15 years has been the weakest quarter for small size, but it is still positive with traditional SMB averaging 2.5 bp/month. Our alternative SMB* returns 5.6 bp/month, which is a notable improvement. Whether one believes in excess small cap returns, managers of small cap strategies can benefit by avoiding new small caps and focusing on those stocks which are not just small now but have been small.

I KNOW WHAT YOU DID LAST YEAR

So far we have studied portfolios which rebalance annually in June. One might wonder how dependent are these results on when the rebalance occurs. There could be potential seasonality effects. The June date was chosen by Fama and French to allow for adequate time for end of year 10-K reports to become available; perhaps the reporting cycle has something to do with it. Perhaps the annual Russell reconstitution at the end of June is a cause. Historically, small caps have done best in January; maybe the choice of when to rebalance plays a role. To show robustness and gain further insight, we study what happens if we look back to other seasons by rebalancing our portfolios at the end of other quarters.

We run the exact same analysis as before, but instead have three new cases where the portfolios are rebalanced at the end of September, December, and March. We again break small caps into three groups depending on their classification as small, large or not available the year before. The same is done for large caps. For example, a rebalance in September looks back to the prior September for determining what a given stock had been classified as.

Results for the annualized returns are not shown for brevity, but qualitatively and quantitatively are quite similar to the annual rebalance in June of Exhibit 2. The same holds for the FFC regressions. We do present the alternative SMB* for these various rebalance date scenarios in Exhibit 6. We observe the same pattern that we saw in Exhibit 5. SMB* continues to provide a positive return, no matter which quarter we rebalance. Our alternate SMB* improves upon the regular SMB which uses all small stocks by 3 to 4 bp per month, and the improvement is statistically significant with t-stats over 2 (results not shown for brevity). The SMB* returns are similar for the different rebalance months. September and December rebalances do better than June by 3 bp/month, March rebalances lag by 1 bp/month. But none of these differences are statistically significant.

Exhibit 6: SMB Monthly Statistics in %,
by Rebalance Date
Full Period, July 1963 – June 2023
	June	September	December	March
Mean	0.21	0.24	0.24	0.20
Stdev	3.06	3.13	3.07	3.07
T-stat	1.87	2.07	2.09	1.77
Note: Annual rebalances at the end of different quarters. Source: Bridgeway calculations, CRSP, Compustat.

It is reassuring to see the robustness of our results to different rebalance dates. Just as important, these results show that the improvement in small cap returns is not driven by some seasonal issue such as the Russell reconstitution, the annual reporting cycle or turn of the year effects. Instead, it always pays to know what your current small caps were doing the prior year, and cutting out the ones which were not small.

I KNOW WHAT YOU DID LAST QUARTER

We have so far examined the benefits of looking back one year to determine if a stock is a true small cap. What happens if we look back one quarter instead? One might anticipate that the shorter lookback uses more timely data and thus provides additional benefits. On the other hand, perhaps the shorter lookback reduces the benefits, especially as factors such as momentum work best with a 12-month lookback.

Exhibit 7 gives results for three variations of SMB. All of the portfolios are formed quarterly, but with lookback periods of 0, 3 and 12 months. The no lookback (0 months) is similar to the classic Fama-French (1993) definition, except the portfolios are formed quarterly rather than annually. Returns are slightly better, rising by just over 1 bp/month. Results improve more with a 3-month lookback. Average returns improve by another 2 bp to 20 bp/month and are now modestly significant statistically. But the improvement is not as great as rebalancing quarterly with a 12-month lookback. Those returns rise to 23 bp/month with a t-stat of 2, in line with those of annual rebalancing at different quarters shown in Exhibit 6. Overall, we see a benefit to cutting those stocks which were not small one quarter before, but the improvement is not as great as with a 12-month lookback.

Exhibit 7: SMB Monthly Statistics in %, Quarterly Rebalance by Lookback
Full Period, July 1963 – June 2023
	0 months	3 months	12 months
Mean	0.18	0.20	0.23
Stdev	3.09	3.09	3.07
T-stat	1.60	1.71	1.99
Note: Small stocks only include those also small in the lookback period. Source: Bridgeway calculations, CRSP, Compustat.

Regression analysis explains the reduced improvement of a quarterly compared to an annual lookback[7]. Alpha in the small cap portfolios does improve modestly when we move from a 12-month lookback to 3 months. This is reasonable, since the FFC factors we use as explanatory variables are based upon annual rebalancing, with the exception of momentum. However, the 3-month lookback has less improvement than the 12-month lookback because the momentum, profitability and conservative investment exposures are all lower. This is intuitive, as momentum has a 12-month formation period, while profitability and investment use annual reporting data. Thus, while knowing whether a stock was small 3 months ago helps, knowing what it did the year before provides greater improvement.

I ALSO KNOW WHAT YOU DID THE LAST FEW SUMMERS

We just showed that looking back one year to screen out stocks that were not small performs better than looking back just one quarter. What happens if we look back for longer periods? While a one-year lookback matches with removing poor momentum stocks, we also saw that profitability (RMW) and investment (CMA) improve, and these tend to be more persistent characteristics. IPO stocks tend to lag for three to five years (Ritter, 1991; Loughran and Ritter, 1995), so excluding IPOs from further back than just one year should help. Cai and Houge (2008) found that the small cap Russell 2000 of up to five years before outperformed the current Russell 2000.

We therefore examine longer lookback periods of up to five years. For each of these longer lookback periods we again construct three sets of portfolios, just as in the one-year lookback case. One set is the stocks which were small in all of the prior years. For example, with a two-year lookback, the “were small” stocks must be small both one and two years ago[8]. A second set is stocks which have been in existence for all of the lookback periods, but were not small in at least one of them. The third set is stocks which did not exist in at least one of the lookback periods. For each of these three sets we again create six portfolios based on their current status, corresponding to high, mid and low B/M for both large and small stocks. Portfolios are rebalanced annually in June.

Exhibit 8 shows the returns of the three small cap portfolios and their average for the set of stocks which have been small for all lookback years. These stocks are the main focus of this paper, and their average forms the small leg of our adjusted SMB* factor[9]. While not shown for brevity, we’ll also briefly discuss the other portfolios below.

Exhibit 8: Cap Weight Annual Geometric Returns in %, July 1963 – June 2023, Lookback of Different Years
	Only Stocks Small All Years
	Book to Market
Lookback	Low	Med	High	Average
None	8.27	13.47	14.91	12.22
1 Year	9.29	13.85	15.44	12.86
2 Years	10.24	14.00	15.79	13.35
3 Years	10.97	14.29	16.09	13.79
4 Years	11.24	14.19	16.07	13.83
5 Years	11.13	14.05	15.95	13.71
Note: Annual rebalances at the end of June. Stocks must be small in all years of the lookback period. Source: Bridgeway calculations, CRSP, Compustat.

The first two rows of Exhibit 8 are the same returns found in Exhibit 2, showing that small stocks which were also small the prior year outperform the full set of current small stocks. We now see that this pattern holds for lookback periods of two and three years. Eliminating stocks which were not small for each year of the lookback period provides higher returns for two and three years; there is no additional improvements for longer lookback periods. The average across the three small different B/M portfolios gives an annual return which rises from 12.22% to 13.79% as we go from no lookback to a lookback period of three years. This increase in small cap returns gives an SMB* of 2.86% annually with a three-year lookback, more than double the SMB of 1.29% from the standard calculation with no lookback. At a monthly level (not shown), the SMB premium rises from 17 bp as seen in Exhibit 5 to 28 bp for a three-year lookback, which is now statistically significant with a t-stat of 2.46. The difference of this modified SMB* from the traditional SMB becomes even more statistically significant, peaking at a t-stat of 3.98 for the three-year lookback.

To see what drives these improved returns, we again run FFC factor regressions. Results are not shown for brevity. Exposures to market beta, value (HML) and size (SMB) stay roughly the same as the lookback increases. Momentum, profitability (RMW) and conservative investment (CMA) all continue to increase with the lookback period, helping returns. Alpha also increases; there is a benefit to a longer lookback independent of factor exposure.

We can also gain insight by examining the returns of the other portfolios. For stocks which were small in each of the lookback years but are now big, their return is greater than that of other large cap stocks for lookbacks up to three years, but then is smaller for four and five years. Some caution is warranted here, as the number of stocks becomes fewer and less representative with longer lookback[10]. Stocks which are now big and were also big in one or more of the lookback periods have returns similar to all big stocks (no lookback) for all lookbacks. Due to cap weighting, these portfolios are dominated by the very largest stocks, which tend to have been large for many years in a row. Meanwhile, stocks which are now small but had been large at some point in the past have returns which are consistently weaker than stocks which have always been small, but the difference moderates with longer lookback. Lastly, stocks which did not exist at some point in the lookback period have uniformly worse returns whether small or large, although they lag less with longer lookback. Overall, we see that the pure small cap stocks benefit by removing both formerly large and newer stocks, with this boost peaking at a three-year lookback.

SIZE BY QUINTILE SPREAD

It is common in the literature to define factors or anomalies by their quintile or decile spread. The Fama-French factors are mainly defined by taking the difference between the highest and lowest 30%. The one exception is SMB, which is defined as the smallest half minus the largest half. In fact, because these portfolios are cap weighted, SMB essentially becomes the difference between the largest decile and the sixth largest decile. Such a comparison would drastically weaken most if not all factors. To make a more even playing field when examining size, we therefore look at the quintile spread (see also Berkin and Wang, 2025).

In this section we form 25 portfolios annually in June, based on 5×5 independent sorts on market cap and B/M. We then average the returns of the five B/M portfolios in the smallest and largest quintiles and take their difference to get a quintile-based SMB₅. We next look back a year to the prior June to see which stocks were in the smallest quintile then. Only stocks which are in the current smallest quintile and which were also in the smallest quintile the prior year are kept, to form a modified SMB*₅. In the spirit of slashing poor behavers from the portfolio, we also form additional versions labeled SMB_5xL and SMB*_5xL, where we omit the worst performing low value quintile from both small and large caps, thus averaging over the other four value quintiles[11].

Exhibit 9 shows the returns for these 5×5 sorts. Panel A gives results for all stocks according to their current classification. In the smallest quintile, stocks with the highest B/M have the best returns of all 25 portfolios, while stocks with the lowest B/M have the worst. Panel B gives returns for the stocks which were in the smallest quintile the prior year, according to where they are in the current year. There are no returns for the top row, as no stocks from the smallest quintile in one year made it all the way to the biggest quintile the next year. One should be cautious about the next biggest and middle quintiles of Panel B, as they can have sparse representation in some years. Our main focus is on Panel B’s smallest quintile in the bottom row. Returns are uniformly better for all five of the B/M slices. Consistent with our thesis for the 3×2 case, keeping only small stocks which were also small the year before notably improves returns.

Exhibit 9: Cap Weight Annual Geometric Returns in %,
July 1963 – June 2023
Portfolios formed annually at the end of June based on June cap and annual book equity and cap from prior December
Panel A: All Stocks
		Book to Market
		Low	2	Med	4	High
Market Cap	Big	10.41	10.10	10.31	9.76	10.22
	2	10.49	10.74	11.81	13.29	13.39
	Mid	8.17	12.58	12.23	14.09	14.58
	4	7.87	11.67	13.52	14.02	14.53
	Small	3.65	10.48	11.88	14.05	16.06
Panel B: Stocks in Smallest Quintile Last Year
		Book to Market
		Low	2	Med	4	High
Market Cap	Big	NaN	NaN	NaN	NaN	NaN
	2	-2.62	-2.24	-0.93	-0.14	-3.31
	Mid	1.59	-6.97	-6.96	-3.19	1.03
	4	5.27	9.77	11.11	13.48	11.22
	Small	5.02	11.41	13.01	14.76	17.11
Panel C: Stocks Not in Smallest Quintile Last Year
		Book to Market
		Low	2	Med	4	High
Market Cap	Big	10.44	10.17	10.32	9.94	10.17
	2	11.07	10.58	11.99	13.36	13.68
	Mid	8.59	12.65	12.60	14.10	15.08
	4	10.00	12.20	14.13	13.97	14.65
	Small	2.28	7.36	8.92	9.20	12.94
Panel D: Stocks N/A Last Year
		Book to Market
		Low	2	Med	4	High
Market Cap	Big	3.17	-3.63	3.28	-0.52	7.43
	2	3.34	12.28	3.06	4.33	4.73
	Mid	6.51	7.40	4.08	7.81	4.47
	4	5.86	7.64	6.91	10.84	15.36
	Small	-0.29	7.14	3.81	10.47	10.72
Note: NaN refers to portfolios which never had any stocks. Source: Bridgeway calculations, CRSP, Compustat.

Panels C and D help explain why our thesis holds. Panel C consists of stocks which existed but were not in the smallest quintile the year before. The bottom row returns are now uniformly lower than in Panels A and B, typically by several percent. Stocks which have fallen into the smallest quintile over the past year do poorly, and our definition screens them out. FFC regressions (not shown for brevity) reveal the main culprit to be far worse momentum exposure, not surprising for stocks that have dropped into the smallest size quintile. Panel D consists of stocks which did not exist the prior year. These also have consistently lower returns, and not just in the smallest stocks. FFC regressions show that these newcomers have much lower alpha, especially among smaller caps. Just as in the standard case of size defined by halves, returns improve when slashing stocks were not in the smallest quintile the year before.

Exhibit 10 gives results for versions of SMB formed from the 5×5 sorts. The first two columns also give SMB and SMB* derived from the 2×3 sorts for comparison. Using all stocks, the quintile spread SMB₅ has an average monthly return of 18 bp, a modest improvement on the 17 bp of the standard SMB. If we only include stocks which were also in the smallest quintile the prior June, SMB*₅ rises to 26 bp, a notable improvement over the 21 bp of SMB*. The smallest quintile of stocks is plagued by stocks which have become small. Remove them to consider only those stocks which have been in the smallest quintile and the true small size premium reveals itself. This result is further confirmation that defining size as stocks which have been small improves the size premium.

Exhibit 10: Monthly Statistics in %
Full Period, July 1963 – June 2023
	SMB	SMB*	SMB5	SMB*5	SMB5xL	SMB*5xL
Mean	0.17	0.21	0.18	0.26	0.31	0.37
Stdev	3.07	3.06	4.46	4.45	4.30	4.33
T-stat	1.49	1.87	1.10	1.57	1.91	2.31
Note: Annual rebalances in June. SMB has all small and large stocks, SMB* has only small stocks which were also small the prior June. SMB5 has all stocks in the smallest and largest quintiles, SMB*5 has only smallest quintile stocks which were also in the smallest quintile the prior June. SMB5xL and SMB*5xL are similar to SMB5 and SMB*5 but omit the lowest value quintile stocks. Source: Bridgeway calculations, CRSP, Compustat.

Now consider what happens when we also remove the lowest value quintile from both small and large caps. SMB_5xL rises to 31 bp/month, a dramatic improvement. The results are even better for SMB*_5xL with a monthly return of 37 bp. Cutting small caps which were either not small the prior year or have poor value leads to a size premium which is significant both economically and statistically.

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IMPLICATIONS AND CONCLUSION

Common definitions of small cap stocks typically rebalance infrequently, often once a year towards the end of June. In this paper, we make a modest modification to that definition, requiring that stocks not only be small at the current time but also in prior years. This eliminates stocks that had recently been large or nonexistent, categories with poor characteristics. Slashing these stocks with poor behavior significantly improves small cap returns. It is robust to different quarter ends, various lookback periods, and using quintile spread rather than halves.

Our paper has implications for both academics and practitioners. Academics have struggled with what appears to have become a weak size premium. Our paper asks what defines when a stock becomes small. Is it immediately when it falls into the lower half of stocks by market cap? Most would say no, changes on a daily or weekly horizon would be too frequent. But the academic standard of defining small by the market cap at the end of the most recent June is also arbitrary. In this paper we require that a stock not just be small at the end of June, but also that it was small at the end of the prior June. That is, a stock must have been small, rather than becoming small. This difference in definition leads to a greatly improved small size premium.

For portfolio managers, one potential implication is to simply not hold any small cap stocks which were also not small the year before. There are reasons why this step may be too extreme for many, with risk control chief among them. But a simple step is to understand why a stock has become small cap. The stocks which moved from large to small cap in the past year tended to have poor characteristics, such as low momentum, weak profitability and too aggressive investment. These formerly large stocks also had negative alpha not captured by these factors, and investors should be careful. And all investors should be wary of stocks that did not exist the year before, as their returns are especially poor.

For allocators, an important implication is that an allocation to small cap stocks is still well warranted. They have always provided diversification. Our results show that small caps also continue to have the potential to deliver a return premium over large caps, especially if one cuts the poor behavers from the portfolio. This is especially true for smaller portfolios within this space. And for those who believe in mean reversion, either of returns or valuation, an increased allocation to small caps may be rewarding now.

There has been much talk about the death of the small size premium, or that it never existed. Our results show that it is alive and well, if one defines small appropriately. Those stocks which have entered into the ranks of smaller capitalization stocks behave differently from stocks which have been small. Keeping the latter while slashing the former can lead to significantly improved returns for your small cap portfolio.

REFERENCES

Akey, Pat, Adriana Z. Robertson, and Mikhail Simutin. 2023. “Noisy Factors.” Working paper.

Alquist, Ron, Ronen Israel, and Tobias J. Moskowitz. 2018. “Fact, Fiction, and the Size Effect.” Journal of Portfolio Management 45 (1): 34-61.

Asness, Clifford, Andrea Frazzini, Ronen Israel, Tobias J. Moskowitz, and Lasse H. Pedersen. 2018. “Size Matters, If You Control Your Junk.” Journal of Financial Economics 129 (3): 479-509.

Banz, Rolf W. 1981. “The Relationship Between Return and Market Value of Common Stocks.” Journal of Financial Economics 9 (1): 3-18.

Berkin, Andrew L., and Christine L. Wang. 2025. “The Incredible Structural Alpha.” Journal of Beta Investment Strategies to appear.

Cai, Jie, and Todd Houge. 2008. “Long-Term Impact of Russell 2000 Index Rebalancing.” Financial Analysts Journal 64 (4): 76-91.

Carhart, Mark M. 1997. “On Persistence in Mutual Fund Performance.” The Journal of Finance 52 (1): 57-82.

Chen, Hsiu-Lang. 2006. “On Russell Index Reconstitution.” Review of Quantitative Finance and Accounting, 26 (4): 409–430.

Fama, Eugene F., and Kenneth R. French. 1993. “Common Risk Factors in the Returns on Stocks and Bonds.” Journal of Financial Economics 33 (1): 3-56.

——. 2015. “A Five-Factor Asset Pricing Model.” Journal of Financial Economics 116 (1): 1-22.

——. 2023. “Production of U.S. SMB and HML in the Fama-French Data Library.” Working paper.

Loughran, Tim, and Jay R. Ritter. 1995. “The New Issues Puzzle.” Journal of Finance, 50 (1): 23–51.

Madhavan, Ananth. 2003. “The Russell Reconstitution Effect.” Financial Analysts Journal, 59 (4): 51–64.

Ritter, Jay R. 1991. “The Long-Run Performance of Initial Public Offerings.” Journal of Finance, 46 (1): 3–27.

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[1] The Russell indices started in 1984, but their constituents were backfilled to 1979.

[2] https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

[3] Although not shown for brevity, the factor exposures align with characteristics. For example, among the small stocks on our final date of June 30, 2023, the stocks which were big the prior year had an average market cap of $2.77 billion, compared to $634 million for the stocks which were small the prior year and $445 million for stocks that were not in the universe the prior year.

[4] These results align with Asness et al (2018), who find that controlling for quality improves the returns of smaller stocks.

[5] See Akey, Robertson, and Simutin (2023) and Fama and French (2023).

[6] We could also look at a version where the large caps only include those stocks which were also large the prior June, but the difference is minimal since very little weight is given to the newcomers.

[7] The results are not shown for brevity but are available upon request.

[8] This definition is closest to our concept that a stock is truly small only if it has been small in the past. One could use further delineations, such as small then large and now small, but the permutations grow rapidly with longer lookback, and there are fewer stocks in each of these variations.

[9] Recall that we keep the long leg of SMB as all stocks which are currently large. Due to the dominance of the largest stocks these returns are similar even if we used a lookback to define them.

[10] By this classification, at a five-year lookback a stock would have had to be small for each of the ends of June through five years ago and then large in the current year.

[11] Monthly returns for the lowest value stocks in the largest quintile are comparable to the returns of other value quintiles when B/M is used to measure value. But if other metrics are also used to measure value, then the lowest value quintile has the worst returns even among the largest stocks (Berkin and Wang, 2025).