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Historically, small-cap stocks have had higher average returns than large-cap stocks; however, this size premium hasn’t appeared across all small caps. In this paper, we analyze stock return data going back to the 1920s and the returns of different segments of the small-cap universe to better understand the returns of small-cap relative to large-cap stocks.
Different stocks generally don’t have the same expected return. For example, some investors may see some stocks as having greater risk than others and, in turn, demand a higher expected return to be compensated for the perceived risk. Others may express a preference for stocks that meet criteria specific to their personal goals and, consequently, expect a distinct return profile from such investments. But if there’s a range in expected returns across stocks, how can we reliably identify the differences?
A stock’s current price reflects information about future cash flows discounted by the expected stock return: A higher expected return implies a lower stock price. Two price metrics have been shown to contain reliable information about differences in expected returns: company size, defined as price times shares outstanding, and relative price, defined as price scaled by a fundamental accounting variable, such as book value. Numerous studies, using data covering over 40 countries and spanning close to a century, show that these price variables, combined with cash flow variables such as profitability,¹ contain reliable information about the cross-section of expected stock returns.
To examine the existence of a size premium in the United States, we’ll look at the historical performance of the Fama/ French U.S. Small and Large Cap portfolios, as they go back almost a hundred years. Comparing the annualized compound returns of the Fama/French U.S. Small Cap portfolio and the Fama/French U.S. Large Cap portfolio, we find that small-cap stocks have outperformed large caps since the 1920s.
To examine the size premium in context with other premiums, we looked at the average returns of the equity, size, and relative price premiums from January 1927 to December 2017 and January 1964 to December 2017; the latter period also includes the profitability premium. For the whole period, the size premium in the United States was 21 basis points (bps) per month on average and reliably different from zero (t-statistic: 2.21). From 1964 to 2017, the magnitude of the size premium was similar (23bps per month on average), but no longer reliably different from zero (t-statistic: 1.87).
To further investigate the presence of the size premium in the 1964 to 2017 period, we next approach the issue from a different angle, looking at the interaction between the size premium and the other equity premiums.
As first reported by Fama/French (1993)—and further documented in Clark/Rodríguez (2010), Rizova (2012), and Fama/French (2015), among others—small-cap growth stocks have historically failed to deliver the size premium and underperformed their large-cap growth counterparts.² For that reason, it makes sense to isolate small-cap growth stocks from the rest of the small-cap universe and consider their performance separately.
To do this, we looked at the size premium in the United States for the growth and nongrowth (neutral and value) segments of the market. Once again, we looked at the whole sample period from 1927 to 2017 and 1964 to 2017. From 1927 to 2017, on the growth side of the market, the size premium was 8bps per month on average, an estimate that wasn’t reliably different from zero (t-statistic: 0.61). On the nongrowth side, on the other hand, the premium was 35bps per month on average and reliably different from zero (t-statistic: 3.44).
From 1964 to 2017, the size premium among growth stocks was 3bps per month on average, but, again, not reliably different from zero (t-statistic: 0.17), while the size premium among nongrowth stocks was 36bps per month on average, positive, and again, reliably different from zero (t-statistic: 2.30).
What does this tell us? We take it to mean that the growth segment of the small-cap universe is what drove the size premium to be unreliably different from zero in the United States from 1964 to 2017. Considering the interaction between small-cap growth stocks and the profitability dimension of expected returns allows us to isolate the underperformers among small-cap growth stocks more systematically.
To do this, we looked next at U.S. small-cap growth stocks and separated those with low profitability from those without it. Small-cap growth, low-profitability stocks greatly underperformed from 1964 to 2017.³ Furthermore, the difference in performance between those groups—45bps per month, on average, from 1964 to 2017—was reliably different from zero (t-statistic: 3.14).
Between 1964 and 2017, a small-cap strategy that excluded small-cap growth, low-profitability stocks would have returned a 36bps monthly premium over a large-cap strategy, as measured by the Fama/French U.S. Small portfolio ex-Low Profitability Growth and the Fama/French U.S. Large portfolio, respectively. The premium would have been reliably different from zero (t-statistic: 3.14).
The existence of a size premium (excepting small-cap growth, low-profitability stocks) doesn’t mean that small caps will outperform large caps every month or year. If that were the case, no one would want to hold large-cap stocks. The size premium is volatile (as are the market, value, and profitability premiums). Given that volatility and everything else we’ve addressed, how should we think about structuring an allocation to small-cap stocks and their role in a broadly diversified portfolio?
Small caps play a role in a total market portfolio. They behave differently from large caps and consequently provide important diversification benefits to portfolios of large-cap stocks. As we’ve shown, an additional potential benefit of small-cap stocks is that, over time, they’re expected to earn a premium over large-cap stocks.
What, then, is a sensible way of structuring an allocation to small-cap stocks? The first thing to realize is that the premiums are more or less driven by stock migration—stocks that move across market capitalization and relative price portfolios from one period to the next. The size premium is primarily driven by the positive performance of a random subset of small-cap stocks that unpredictably moves to the mid- or large-cap space.
This unpredictable migration has important implications for investors because it highlights the importance of diversification in the design of robust investment solutions. As Fama and French (2007), among others, have shown, not all securities contribute equally to the premiums each year.⁴ Some securities do extremely well, while others have average returns or perform poorly. Research has also shown that it’s not possible to reliably predict which of those securities sharing common characteristics and similar expected returns are going to do well.⁵ Concentrated portfolios may inadvertently exclude companies that ultimately generate most of those premiums, whereas broadly diversified portfolios are more likely to include those securities and capture those premiums.
Also, as shown above, the premiums interact with one another and there are trade-offs among the premiums, diversification, and costs. In an allocation to small caps, with no style bias, it’s still important to take into account relative price and profitability characteristics. Small-cap growth stocks with low profitability haven’t delivered the size premium, so excluding them from any strategy that seeks to capture the size premium would make sense. In our analysis, this group of stocks has historically made up approximately 15% of the aggregate market cap of the overall small-cap universe. Given that ratio, the cost of excluding these stocks in terms of reduced diversification is small relative to the expected benefit of a higher expected return.
What implications does this have for executing a strategy? Diversification, a consistent focus on known dimensions of expected return, and accounting for interaction between premiums can all increase the reliability of outcomes and the likelihood of capturing different market premiums on a daily basis.
1 Profitability is measured by the profits-to-book ratio, with profits defined as operating income before depreciation and amortization minus interest expense. 2 “The Performance of Small Cap Growth Stocks,” Quarterly Institutional Review, Dimensional Fund Advisors, 2010; “The Performance of International Small Cap Growth Stocks,” Quarterly Institutional Review, Dimensional Fund Advisors, 2012; and “A Five-Factor Asset Pricing Model,” Journal of Financial Economics, 2015. 3 Annual returns for the profitability premium in the United States go back to 1964. For that reason, the analysis that incorporates profitability in the U.S. data starts in 1964. 4 “Migration,” Financial Analysts Journal, 2007. 5 For more information on the performance of mutual fund managers, see, for instance, “The Performance of Mutual Funds in the Period 1945–1964,” Journal of Finance, 1968; “Luck vs. Skill in the Cross-Section of Mutual Fund Returns,” Journal of Finance, 2010; and “Mutual Fund Performance through a Five-Factor Lens,”my.dimensional.com/insight/purely_ academic/193867/, August 2016.