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This paper employs a new approach to analyze potentially omitted non-diversifiable factors in the idiosyncratic risks from multi-factor asset pricing models. It is shown that if there is an omitted non-diversifiable hidden factor, the idiosyncratic risks will contain persistent cross-sectional memory. An extended Rescaled Variance test generalized from L. Giraitis, P. Kokoszaka, R. Leipus, and G. Teyssiere [1] with finite forecast horizon is provided to investigate the cross-sectional memory of forecast errors in multifactor pricing models. Under the null hypothesis that idiosyncratic risks contain only short memory when there is no hidden non-diversifiable factor, we demonstrate that the extendedT-sample Rescaled Variance test statistic approximates a functional of weighted Brownian Bridge, which is distributed asymptotically as the T-sample Watson’s statistic presented by Maag [2]. Using this approach, our empirical tests that compare forecast errors from the CAPM and Fama-French [3] model with the excess returns of 1391 firms indicate that there is a strong likelihood that the CAPM may require further identification of hidden non-diversifiable factor(s). Yet, there lacks convincing evidence that the Fama-French [3] model has an omitted non-diversifiable factor in idiosyncratic risks

Do Idiosyncratic Risks in Multi-Factor Asset Pricing Models Really Contain a Hidden Non-Diversifiable Factor? A Diagnostic Testing Approach