An Algorithmic Multifactor Extension

Anomaly-based multifactor models have become a major development in empirical asset pricing because they provide a systematic way to expand existing pricing models. This study clarifies the algorithmic logic behind that extension. Specifically, it shows how these models identify pricing errors left unexplained by the factors already included in a model and incorporate additional factors to reduce those errors. This logic matters because it explains how anomaly-based models absorb empirical anomalies while reducing dimensionality. We further show that the method for adding factors closely parallels a classical factor-extraction algorithm in statistical modeling, thereby reinforcing the statistical validity of anomaly-based models.