We extend asset pricing studies by comparing the ability of multifactor models to explain large numbers of anomalous portfolio returns. Surprisingly, standard Fama and MacBeth (1973) cross-sectional regression tests show that a lesser known two-factor
model, dubbed the ZCAPM by Kolari, Liu, and Huang (2021), well outperforms prominent multifactor models in terms of explaining anomaly returns on an out-of-sample basis. In empirical tests, we utilize online databases of anomalies recently made available by researchers. Chen and Zimmerman (2022) provided an open source database with 161 long/short anomalies in the U.S. stock market. Also, Jensen, Kelly, and Pedersen (2023) furnished an online database containing 153 long/short anomalies in 93 countries, including the U.S. Based on 133 anomalies in the former study and 153 anomalies in the latter study with return series available from July 3, 1972 to December 31, 2021, we investigate a combined dataset off 286 anomalies. We find that, with the exception of the ZCAPM, prominent multifactor models do not explain anomalous portfolio returns. In contrast, the ZCAPM does a much better job of explaining them. In standard Fama and MacBeth (1973) cross-sectional regression tests, factor loadings for the ZCAPM are more significant than well-known multifactor models. Also, the goodness-of-fit , as estimated by R2 values, are much higher for the ZCAPM than other models. Further graphical tests compare the mispricing errors of different models with respect to anomalous portfolios. We find that the ZCAPM exhibits much lower mispricing errors than other models. We conclude that anomalous returns are anomalous for the most part with respect to prominent multifactor models but not the ZCAPM.
By implication, our evidence supports the efficient-market hypothesis of Fama (1970, 2013) rather than the behavioral hypothesis. As such, stock returns are closely related to systematic market risks.