Complexity in factor pricing models

We theoretically characterize the behavior of machine learning asset pricing models. We prove that expected out-of-sample model performance---in terms of SDF Sharpe ratio and test asset pricing errors---is improving in model parameterization (or "complexity''). Our empirical findings verify the theoretically predicted "virtue of complexity'' in the cross-section of stock returns. Models with an extremely large number of factors (more than the number of training observations or base assets) outperform simpler alternatives by a large margin