The ZCAPM and Large Online Datasets of Anomaly Portfolio Returns

James W. Kolari (), Wei Liu, Jianhua Z. Huang () and Huiling Liao ()
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James W. Kolari: Texas A&M University, Mays Business School
Wei Liu: Texas A&M University, Mays Business School
Jianhua Z. Huang: The Chinese University of Hong Kong, Shenzhen, School of Artificial Intelligence and School of Data Science
Huiling Liao: Illinois Institute of Technology, Department of Applied Mathematics

Chapter Chapter 5 in Asset Pricing Models and Market Efficiency, 2026, pp 93-139 from Springer

Abstract: Abstract This chapter utilizes open source datasets with over 250 anomaly portfolios constructed by Chen and Zimmerman (2022) and Jensen, Kelly, and Pedersen (2023) to conduct out-of-sample tests of prominent asset pricing models. Chen and Zimmerman found that 161-out-of-319 long-short anomalies are “clear predictors” in terms of the statistical significance of cross-sectional return predictability on an out-of-sample basis. Jensen, Kelly, and Pedersen documented that 153 long-short factors across 93 countries can be replicated over time, survive joint modeling of all factors, hold up out-of-sample after their original publication, are strengthened by the large number of factors including global evidence, and can be grouped into a smaller number of anomaly clusters. Unlike previous studies, the authors employed alphas from the CAPM to measure anomaly returns. These risk-adjusted returns yielded results different from those of raw returns – unlike declining raw returns, alphas have not decreased over time. An important inference from the Jensen et al. study is that anomaly returns contain mispricing errors that likely arise from premiums associated with their risks. As we will see in this chapter, confirming this conjecture, risk premiums associated with systematic risk factors in the ZCAPM well explain large datasets of anomaly portfolio returns. The ZCAPM is a new asset pricing model by Kolari, Liu, and Huang (2021). Because large numbers of anomalies can be explained by ZCAPM systematic risk factors (viz., market returns and market return dispersion), the market efficiency hypothesis is supported. Also, we infer that hundreds of long-short portfolio anomalies yielding relatively high abnormal returns are no longer anomalous or unexplained. If previously published anomalies are explained by the ZCAPM, further research is needed to find long-short portfolios not explained by the ZCAPM. Finally, the consistent outperformance of the ZCAPM compared to prominent multifactor modelsMultifactor models in our out-of-sample empirical tests, in many cases by large margins, suggests that the ZCAPM is a valid asset pricing model worthy of further study by researchers. Can multifactor modelsMultifactor models be enhanced to match the out-of-sample performance of the ZCAPM? Or, should extant multifactor modelsMultifactor models be scrapped by researchers to make way for future progress in the development of the ZCAPM?

Keywords: Anomalies; Artificial intelligence (AI); Market return dispersion; Machine learning (ML); Mispricing errors; Multifactor models; Out-of-sample cross-sectional regression test; ZCAPM; Zeta risk (search for similar items in EconPapers)
Date: 2026
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DOI: 10.1007/978-3-031-92901-4_5

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