We propose multiple advanced learning methods to deal with the “”curse of dimensionality””
challenge in the cross-sectional stock returns. Our purpose is to predict the one-month-ahead
stock returns by the rm characteristics which are so-called “”anomalies””. Compared with
the traditional methods like portfolio sorting and Fama Factor models, we focus on using
all existing machine learning methods to do the prediction rather than the explanation. To
alleviate the concern of excessive data mining, we use several regularization penalties that
can lead to a sparse and robust model. Our method can identify the return predictors with
incremental pricing information and learn the interaction effects by applying to a hierarchical
structure. Our best method can achieve much higher out of sample R2 and portfolio Sharp
Ratios than traditional linear regression method.