Size Matters, if You Control Your Junk

Clifford S. Asness

AQR Capital Management, LLC

Andrea Frazzini

AQR Capital Management, LLC

Ronen Israel

AQR Capital Management, LLC

Tobias J. Moskowitz

University of Chicago – Booth School of Business

Lasse Heje Pedersen

New York University (NYU) – Department of Finance; Copenhagen Business School; AQR Capital Management, LLC; Centre for Economic Policy Research (CEPR); National Bureau of Economic Research (NBER)


The size premium has been challenged along many fronts: it has a weak historical record, varies significantly over time, in particular weakening after its discovery in the early 1980s, is concentrated among microcap stocks, predominantly resides in January, is not present for measures of size that do not rely on market prices, is weak internationally, and is subsumed by proxies for illiquidity. We find, however, that these challenges 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 also explains interactions between size and other return characteristics such as value and momentum.

Size Matters, if You Control Your Junk

The finding that size is related to expected returns dates back at least to Banz (1981), who found that small stocks in the U.S. (those with lower market capitalizations) have higher average returns than large stocks, a relation which is not accounted for by market beta. The relation between size and returns is important for several reasons. First, the size anomaly has become one of the focal points for discussions of market efficiency. Second, the size factor has become one of the staples of current asset pricing models used in the literature (e.g., Fama and French (1993, 2014)). Third, the size premium implies that small firms face larger costs of capital than large firms, with important implications for corporate finance, incentives to merge and form conglomerates, and broader industry dynamics. Fourth, the size effect has had a large impact on investment practice, including spawning an entire category of investment funds, giving rise to indices, and serving as a cornerstone for mutual fund classification.

Given the importance of the size effect, it has naturally come under heavy scrutiny. Considering a long sample of U.S. stocks and a broad sample of global stocks, we confirm the common criticisms of the standard size factor: a weak historical record in the U.S. and even weaker record internationally makes the size effect marginally significant at best, long periods of poor performance, concentration in extreme, difficult to invest in microcap stocks, concentration of returns in January, absent for measures of size that do not rely on market prices, and subsumed by proxies for illiquidity.

However, we find that measures of size studied by the literature load strongly and consistently negatively on a large variety of “quality” factors. At a broad level, quality is a characteristic or set of characteristics of a security that investors are willing to pay a high price for, all else equal. Asness, Frazzini, and Pedersen (2014), using the Gordon growth model, illustrate various dimensions of quality that can be measured in a number of ways – profitability, profit growth, low risk in terms of return-based measures and stability of earnings, and high payout and/or conservative investment policy. We find a strong and robust size effect when controlling for a firm’s quality or its inverse – “junk” – and we find that the results are very consistent across a variety of measures.

Controlling for quality/junk reconciles many of the empirical irregularities associated with the size premium that have been documented in the literature and resurrects a larger and more robust size effect in the data. To understand this, note that large firms tend to be high quality firms on each of the above dimensions, while small firms tend to be “junky” (i.e., have the opposite characteristics). Given that high quality stocks tend to outperform junk stocks in general, including when comparing stocks of similar size (Asness, Frazzini, and Pedersen (2014), Fama and French (2014)), this means that the size effect is fighting a headwind due to the low quality of small stocks. Said differently, 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.


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