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Fact, Fiction, and the Size Effect

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Fact, Fiction, and the Size Effect VOLUME 45, NUMBER 1 jpm.iprjournals.com FALL 2018 Fact, Fiction, and the Size Effect RON ALQUIST, RONEN ISraEL, AND TOBIAS MOSKOWITZ Fact, Fiction, and the Size Effect RON ALQUIST, RONEN ISraEL, AND TOBIAS MOSKOWITZ permission. Publisher without RON ALQUIST fter confronting the myths sur- a second source of priced risk beyond the is a vice president at AQR rounding momentum investing1 market. According to this view, both a stock’s Capital Management in 2 electronically and value investing, we realized market beta and its size were now required Greenwich, CT. post [email protected] two things: 1) We had passed over to understand its expected returns. As long to Athe first anomaly discovered in academic as size was correlated with a fundamental or RONEN ISraEL finance and the one that had been around source of risk, rational investors needed to be user, is a principal at AQR the longest—size, and 2) despite its longevity compensated for holding assets more exposed Capital Management in and the attention it has received, there is still to that risk. Other scholars interpreted the Greenwich, CT. much confusion and debate surrounding the evidence of a size premium as a more fun- [email protected] unauthorized size anomaly. damental conceptual challenge to market an TOBIAS MOSKOWITZ The size effect is the phenomenon in efficiency, in which small stocks relative to to is the Dean Takahashi which small stocks (i.e., those with lower large stocks were simply mispriced, having professor of finance market capitalizations), on average, outper- nothing to do with compensation for risk. forward and economics at Yale form large stocks (i.e., those with higher The size premium, therefore, represented the University, a research article, associate at the NBER, market caps) over time. The size premium first true market anomaly. this and a principal at AQR is the return achieved by buying (being long Yet, despite size’s legacy and its subse- of Capital Management in in an absolute sense or overweight relative quent prominence in the field, there remains Greenwich, CT. to a benchmark) small stocks and selling much debate about the size effect, including copies [email protected] (shorting or underweighting) large ones. The its reliability. The very existence of a size size effect was first documented by several premium, for example, turns out to be a academic papers in the early 1980s,3 and it less well-established empirical fact than its unauthorized quickly became the first real challenge to the younger cousins, value and momentum (and make field’s preeminent asset pricing framework, defensive and quality premiums as well)— to the capital asset pricing model (CAPM). something we will investigate in depth in illegal Broadly speaking, researchers responded this article. is It to its discovery in two ways. On one hand, This article is organized around a proponents of market efficiency argued that number of facts and fictions about the size this evidence simply indicated that the CAPM effect that warrant clarification. The facts was misspecified and that size was related to we present include the following: that the size effect diminished shortly after its dis- covery and publication; that it is dominated 1 Asness et al. 2014. 2 Asness et al. 2015a. by a January seasonal effect; that it is not 3 See Banz 1981, Keim 1983, and Roll 1983. applicable or does not work for other asset Fall 2018 The Journal of Portfolio Management 3 E XHIBIT 1 Original Size Anomaly Sample Period $QQXDO $OSKD $QQXDO $QQXDO 5DZ 6KDUSH $OSKDYV W6WDWYV ,5YV 5HWXUQ 9RO W6WDW 5DWLR &$30 &$30 &$30 6WDUW'DWH (QG'DWH 60% ± ± ± 'HFLOH± permission. classes outside of individual equities; that it can be made Based on the facts we uncover, size does not appear much stronger when looked at in conjunction with other to be on equal footing with other prominent factors, such factors (namely, defensive/quality factors); that the size as value, momentum, and defensive/quality investing. Publisher premium mostly comes from microcap stocks and is dif- The returns to size are far less stable, less persistent, and ficult to implement in practice; and, finally, that the size less robust than these other factors. Although we do without effect continues to receive a disproportionate amount not completely deny the existence of a size effect, and of attention relative to other factors with similar or we certainly do not advocate actively betting against or stronger evidence behind them. The fictions we attempt shorting it, we also do not believe that size on its own electronically to clarify include that the size effect is a strong anomaly; is a key factor for constructing portfolios. We believe post that other factors performing better among small stocks the size effect captures part of a broader effect—an illi- to or is evidence of a size effect; that the size effect is robust quidity premium—that can add value at the margin in to the chosen method of measurement; that it works in conjunction with other factors, but in which it is also (by user, other markets and settings; and that it seems to be more definition) more difficult and expensive to trade. On its than just an illiquidity premium. own, a size factor is not a particularly strong source of Finally, we will address fictional theories that pro- expected returns in practice, despite its prominence in unauthorized pose an economic story, unrelated to liquidity, in which the literature and the attention it has received from the an to small stocks should deserve a marginal premium over investment world. their other risk characteristics and in which a size pre- forward mium is consistent with a risk-based efficient markets FICTION: THE SIZE EFFECT IS ONE view of the world. Although a size premium can cer- OF THE STRONGEST DOCUMENTED article, tainly occur in a world of efficient or inefficient markets, ANOMALIES/FACTORS this we find economic stories, other than as a proxy for illi- of quidity, regarding why the size of a firm should matter Given its pedigree, you would be forgiven for copies for pricing to be puzzling. thinking that the size factor is one of the strongest and As done in our prior papers, we address the facts most robust anomalies in finance. In fact, it is one of and fictions of the size effect using published and peer- the weakest. It is significantly weaker than other well- reviewed academic papers and conduct tests using the known anomalies such as value, momentum, profit- unauthorized most well-known and straightforward publicly avail- ability, and defensive/quality or low volatility. make able data.4 Size has never been a very strong effect. Let’s start to by examining the original study on the size effect. Banz illegal (1981) documented that small stocks outperformed large is It 4 Kenneth French’s data library (http://mba.tuck.dartmouth. stocks over his sample period, which spanned January edu/pages/faculty/ken.french/data_library.html) provides returns 1936 to December 1975. Exhibit 1 attempts to repli- for market (RMRF), small (SMB), value (HML), momentum cate his results using the same sample period. It reports (UMD), and profitability (RMW) factors, including returns for the annualized mean, volatility, t-statistic of the mean, the long and short sides separately, and for both large- and small- capitalization securities separately, all of which we use in this article. Sharpe ratio, annual alpha, t-statistic of the alpha, and AQR’s data library (https://www.aqr.com/library/data-sets) pro- information ratio (alpha divided by residual standard vides returns for a betting against beta (BAB) factor from Frazzini deviation) from a regression of the size factor’s returns on and Pedersen (2014), which we use in this article. 4 Fact, Fiction, and the Size Effect Fall 2018 the market portfolio (CAPM). All statistics are computed If a strategy works only because it has a bigger market using monthly returns, but the numbers reported are beta, then a more efficient and reliable way to capture annualized. We use two specifications of long–short those returns is simply to allocate more to the market portfolios that seek to capture the size premium: The factor itself. This point applies with particular force to first is Fama and French’s small minus big (SMB) factor, the size premium. Because small stocks typically have which is constructed from the six size/book-to-market larger market betas than large stocks, part, or even all, benchmark portfolios and is long the smallest half of of the size premium may simply be the equity market stocks (based on NYSE breakpoints) and short the largest risk premium in disguise. The CAPM alphas account for half. By construction, then, it is composed of half growth the beta difference between small and large stocks. As and half value stocks. The second portfolio is long the Exhibit 1 shows, SMB has zero (in fact, slightly negative) permission. smallest decile of stocks (based on NYSE breakpoints) alpha with respect to the market when controlling for and short the largest. Banz’s (1981) original study used the betas, and the decile spread portfolio has a positive Publisher Fama and MacBeth (1973) regressions to show a size alpha (2.5%) that is statistically indistinguishable from premium, which is probably closer to the decile portfolio zero (t-statistic of 0.66). These results suggest that the without returns approach.5 size premium in its original sample is not only weak but As Exhibit 1 shows, over the 1936 to 1975 period, seems to be captured by general market exposure. the evidence in favor of a strong size premium is weak.
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