Title: High Dimensional Estimation and Multi-Factor Models,
Abstract: 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.