The purpose of this paper is to re-investigate the estimation of multiple factor models by relaxing the convention that the number of factors is small  . We first obtain the collection of all possible factors and we provide a simultaneous test, security by security, of which factors are significant. Since the collection of risk factors selected for investigation is large and highly correlated, we use dimension reduction methods , including the Least Absolute Shrinkage and Selection Operator (LASSO ) and prototype clustering , to perform the investigation. For comparison with the existing literature, we compare the multi-factor model 's performance with the Fama-French 5-factor model. We find that both the Fama-French 5-factor and the multi-factor model are consistent with the behavior of "large-time scale" security returns. In a goodness-of-fit test comparing the Fama-French 5-factor with the multi-factor model, the multi-factor model has a substantially larger adjusted R^{2 . Robustness tests confirm that the multi-factor model provides a reasonable characterization of security returns .
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 .
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