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Statistical Inferences with Specification Tests

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Empirical Asset Pricing Models

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Abstract

The author discusses the methodologies that are currently applied to empirical asset pricing models on asset returns, including up-to-date coverage on theoretical setting and model specification tests. For instance, factor analysis and (asymptotic) principal component analysis are provided for searching for these pricing cores or kernels of asset returns. Unfortunately, these earlier studies incur the difficulty of observability of these factors and of (economic) interpretation of the principal components. In essence, the application of multi-factor asset pricing models with observed/presumed factors becomes an alternative in the search for the systematic components of asset returns.

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Notes

  1. 1.

    Since x is an n-dimensional vector, the moment condition is applied to each element of the vector. The same assumption holds for the price vector q as well.

  2. 2.

    The time subscript is suppressed for simplicity of expression.

  3. 3.

    The time sub-index is suppressed for simplicity.

  4. 4.

    Later work in Shanken and Zhou (2007) relaxes the assumption of correct specification of factor premiums by introducing a residual or pricing error in the expected returns. However, the analysis is still based on the correct identification of factor structure.

  5. 5.

    In fact, this setting is identical to Chamberlain and Rothschild (1983) and Ingersoll (1984) in approximate factor structure.

  6. 6.

    Notice that the notation “−∞” does not necessarily mean there are negative infinite observations. It only depicts the possible initial observations of cross-sectional idiosyncratic risk that are distant from the present collections.

  7. 7.

    Implicitly, their work assumes that the \(\frac {T}{2}\) is an integer already so that the inter-temporal differences are always feasible.

  8. 8.

    This condition is to ensure that asymptotic variance of the cumulative sum of these squared idiosyncratic risks exists and is finite under the null hypothesis.

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Authors and Affiliations

  1. School of Business and Management, Azusa Pacific University, Stevenson Ranch, CA, USA

    Jau-Lian Jeng

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Jeng, JL. (2018). Statistical Inferences with Specification Tests. In: Empirical Asset Pricing Models. Palgrave Macmillan, Cham. https://doi.org/10.1007/978-3-319-74192-5_2

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  • DOI: https://doi.org/10.1007/978-3-319-74192-5_2

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  • Publisher Name: Palgrave Macmillan, Cham

  • Print ISBN: 978-3-319-74191-8

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