High Dimensional Estimation and Multi-Factor Models

This paper re-investigates the estimation of multiple factor models relaxing the convention that the number of factors is small and using a new approach for identifying factors. We first obtain the collection of all possible factors and then provide a simultaneous test, security by security, of which factors are significant. Since the collection of risk factors is large and highly correlated, high-dimension methods (including the LASSO and prototype clustering) have to be used. The multi-factor model is shown to have a significantly better fit than the Fama-French 5-factor model. Robustness tests are also provided.