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Recent studies advocate two new benchmark models (the Fama-French five-factor model and the Hou, Xue and Zhang four-factor model) with monthly data. Our daily data approach provides considerable supplement to the monthly data approach presented in recent studies. We adopt the advanced bootstrap methodology by replicating the original data sample, and this approach should effectively alleviate the problem of too much noise in the data of daily return. A two-pass cross-sectional regression and GMM with several useful testing statistics are used to more thoroughly diagnose the specifications of the model. The following consistency is observed when using different frequencies of sample data: the evidence indicates that the two newer benchmark models (the Fama-French five-factor model and the Hou, Xue and Zhang four-factor model) outperform the Fama-French three-factor model in estimating a few well-known portfolios (formed on different anomalies). However, several specification tests do not robustly accept the correct specifications of the Fama-French five-factor model and the Hou, Xue and Zhang four-factor model.

The evaluation and comparison of three benchmark asset pricing models with daily data: supplementary evidence