Machine Learning in Asset Pricing: The Dominance of the ZCAPM

The empirical results in this book have shown that machine learning is a powerful new approach to asset pricing that can boost predictive performance of asset pricing models. The ZCAPM of Kolari, Liu, and Huang (2021) takes advantage of machine learning in estimating the empirical ZCAPM via the expectation-maximization (EM) algorithm in regression analyses. The ZCAPM contains a hidden or latent variable that determines the positive versus negative sensitivity of asset returns to changes in the cross-sectional return dispersion of assets in the market. It is unknown if a stock will be positively or negatively affected the market return dispersion at any given time. In estimating the empirical ZCAPM regression, the EM algorithm incorporates information about asset returns over the past year. From this information, it estimates a probability (or p value) that an asset or portfolio of assets will have a positive sensitivity to market return dispersion. As it turns out, from an artificial intelligence perspective, this hidden probability is crucial to the predictive success of the ZCAPM in explaining stock market anomalies in our out-of-sample cross-sectional regression tests. Without it, the model would not work in predicting anomaly portfolio returns. Here we review the material in previous chapters. Hundreds of long/short portfoliosLong/short portfolio of stock market anomalies have been constructed by researchers. Because asset pricing modelsAsset pricing model cannot explain their abnormally high average stock returns, these portfolios are considered to be anomalies. Importantly, the inability of prominent asset pricing modelsAsset pricing model to explain economically interesting anomalies strikes a major blow to the famous efficient market hypothesis (EMH)Efficient markets hypothesis (EMH) of Nobel Prize winner Professor Eugene FamaFama, E.F.. Asset prices should be related to their market risks. If systematic market risks in asset pricing modelsAsset pricing model cannot explain their prices, the EMHEfficient markets hypothesis (EMH) is rejected. In its place, behavioral theories have proposed irrational investorIrrational investors behavior grounded in inherent biases in human behavior to potentially explain stock market anomalies’ returns. Given the rising tide of anomalies, which are outpacing the ability of multifactor modelsMultifactor models in asset pricing to keep up with them, behavioralistsBehavioralists have gained a solid footing in the anomalies literature. The stock market evidence documented in this book sheds new light on the longstanding yet increasing debate between efficient marketsEfficient markets and behavioral theories of asset pricingAsset pricing. We compared the most prominent asset pricing modelsAsset pricing model in the finance literature in terms of their ability to predict in out-of-sample testsOut-of-sample tests the stock market returns of hundreds of anomaly portfoliosAnomaly portfolio. Also, we included in our tests the ZCAPMZCAPM a lesser known asset pricing modelAsset pricing model that employs expectation-maximization (EM) algorithmExpectation-maximization (EM) algorithm optimization methods to estimate a hidden signal variableHidden signal variable. Strikingly, the ZCAPM is the only model that does a good job of predicting the returns of large numbers of stock market anomaly portfoliosAnomaly portfolio (i.e., long/short portfoliosLong/short portfolio based on accounting and market characteristics of firms). Virtually all of the anomalies tested are explained by the ZCAPM on an out-of-sample basis. Our ZCAPMZCAPM evidence reverses the above mentioned trends in asset pricingAsset pricing and market efficiency. Given that the ZCAPM can explain anomalies’ abnormally high returns over time, our results strongly support the EMHEfficient markets hypothesis (EMH). In turn, behavioral explanations of anomalies are not needed. Also, since prominent multifactor modelsMultifactor models cannot predict anomalyAnomaly returns over time, the ZCAPM dominates these models in terms of asset pricingAsset pricing ability. In further tests of model validityModel validity, we confirm that the ZCAPMZCAPM has lower out-of-sample mispricing errorsMispricing error among anomaly portfoliosAnomaly portfolio than commonly-used, popular multifactor modelsMultifactor models. Important implications of our findings are discussed with respect to asset pricingAsset pricing and market efficiency in particular and the field of finance in general. Lastly, we provide closing remarks on the findings of this book.