Finance academics have started to take replication studies seriously. As hundreds of factors have been documented in recent decades, the concern over p-hacking has become especially acute. In a pioneering meta-study, Harvey, Liu, and Zhu (2016) introduce a multiple testing framework into empirical asset pricing. The threshold t-cutoff increases over time as more factors have been data-mined. A new factor today should have a t-value exceeding 3.
Reevaluating 296 significant factors in published studies, Harvey et al. report that 80-158 (27%-53%) are false discoveries. Two publication biases are likely responsible for the high percentage of false positives. First, it is difficult to publish a negative result in top academic journals. Second, more subtly, it is difficult to publish replication studies in finance, while in many other disciplines replications routinely appear in top journals. As a result, finance and accounting academics tend to focus on publishing new factors rather than rigorously verifying the validity of published factors.
Harvey (2017) elaborates the complex agency problem behind the publication biases. Journal editors compete for citation-based impact factors, and prefer to publish papers with the most significant results. In response to this incentive, authors often file away papers with results that are weak or negative, instead of submitting them for publication. More disconcertingly, authors often engage in, consciously or subconsciously, p-hacking, i.e., selecting sample criteria and test procedures until insignificant results become significant. The outcome is an embarrassingly large number of false positives that cannot be replicated in the future.
We conduct a massive replication of the published factors by compiling a largest-to-date data library with 447 variables. The list includes 57, 68, 38, 79, 103, and 102 variables from the momentum, value-versus-growth, investment, profitability, intangibles, and trading frictions categories, respectively. We use a consistent set of replication procedures throughout. To control for microcaps (stocks that are smaller than the 20th percentile of market equity for New York Stock Exchange, or NYSE, stocks), we form testing deciles with NYSE breakpoints and value-weighted returns. We treat a variable as a replication success if its average return spread is significant at the 5% level.
Our replication indicates rampant p-hacking in the published literature. Out of 447 factors, 286 (64%) are insignificant at the 5% level. Imposing the t– cutoff of 3 per Harvey, Liu, and Zhu (2016) raises the number of insignificance to 380 (85%).
The biggest casualty is the liquidity literature. In the trading frictions category, 95 out of 102 variables (93%) are insignificant. Prominent variables that do not survive our replication include Jegadeesh’s (1990) short-term reversal; Datar-Naik-Radcliffe’s (1998) share turnover; Chordia-Subrahmanyam-Anshuman’s (2001) coefficient of variation for dollar trading volume; Amihud’s (2002) absolute return-to-volume; Acharya-Pedersen’s (2005) liquidity betas; Ang-Hodrick-Xing-Zhang’s (2006) idiosyncratic volatility, total volatility, and systematic volatility; Liu’s (2006) number of zero daily trading volume; and Corwin-Schultz’s (2012) high-low bid-ask spread. Several recent friction variables that have received much attention are also insignificant, including Bali-Cakici-Whitelaw’s (2011) maximum daily return; Adrian-Etula-Muir’s (2014) intermediary leverage beta; and Kelly-Jiang’s (2014) tail risk.
The much researched distress anomaly is virtually nonexistent. Campbell-Hilscher-Szilagyi’s (2008) failure probability, the O-score and Z-score in Dichev (1998), and Avramov-Chordia-Jostova-Philipov’s (2009) credit rating all produce insignificant average return spreads.
Other influential but insignificant variables include Bhandari’s (1988) debt-to-market; Lakonishok-Shleifer-Vishny’s (1994) five-year sales growth; several of Abarbanell-Bushee’s (1998) fundamental signals; Diether-Malloy-Scherbina’s (2002) dispersion in analysts’ forecast; Gompers-Ishii-Metrick’s (2003) corporate governance index; Francis-LaFond-Olsson-Schipper’s (2004) earnings attributes, including persistence, smoothness, value relevance, and conservatism; Francis et al.’s (2005) accruals quality; Richardson-Sloan-Soliman-Tuna’s (2005) total accruals; and Fama-French’s (2015) operating profitability, which is a key variable in their 5-factor model.
Even for significant anomalies, their magnitudes are often much lower than originally reported. Famous examples include Jegadeesh-Titman’s (1993) price momentum; Lakonishok-Shleifer-Vishny’s (1994) cash flow-to-price; Sloan’s (1996) operating accruals; Chan-Jegadeesh-Lakonishok’s (1996) standardized unexpected earnings, abnormal returns around earnings announcements, and revisions in analysts’ earnings forecasts; Cohen-Frazzini’s (2008) customer momentum; and Cooper-Gulen-Schill’s (2008) asset growth.
Why does our replication differ so much from the original studies? The key word is microcaps. Microcaps represent only 3% of the total market capitalization of the NYSE-Amex-NASDAQ universe, but account for 60% of the number of stocks. Microcaps not only have the highest equal-weighted returns, but also the largest cross-sectional standard deviations in returns and anomaly variables. Many studies overweight microcaps with equal-weighted returns, and often together with NYSE-Amex-NASDAQ breakpoints, in portfolio sorts.
Hundreds of studies use cross-sectional regressions of returns on anomaly variables, assigning even higher weights to microcaps. The reason is that regressions impose a linear functional form, making them more susceptible to outliers, which most likely are microcaps. Alas, due to high costs in trading these stocks, anomalies in microcaps are more apparent than real. More important, with only 3% of the total market equity, the economic importance of microcaps is small, if not trivial.
Our low replication rate of only 36% is not due to our extended sample relative to the original studies. Repeating our replication in the original samples, we find that 293 (66%) factors are insignificant at the 5% level, including 24, 44, 13, 38, 81, and 93 across the momentum, value-versus-growth, investment, profitability, intangibles, and trading frictions categories, respectively. Imposing the t-cutoff of three raises the number of insignificance to 387 (86.6%). The total number of insignificance at the 5% level, 293, is even higher than 286 in the extended sample. In all, the results from the original samples are close to those from the full sample.
We also use the Hou, Xue, and Zhang (2015) q-factor model to explain the 161 significant anomalies in the full sample. Out of the 161, the q-factor model leaves 115 alphas insignificant (150 with t<3). In all, capital markets are more efficient than previously recognized.
Kewei Hou is Fisher College of Business Distinguished Professor of Finance at The Ohio State University. Chen Xue is Assistant Professor of Finance at University of Cincinnati. Lu Zhang is the John W. Galbreath Chair, Professor of Finance, at The Ohio State University. Correspondence about this blog should be addressed to Lu Zhang at firstname.lastname@example.org.
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