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Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model

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Abstract

In this paper we consider the capital asset pricing model under the multivariate normal distribution for modeling asset returns. We develop and implement local influence diagnostic techniques not based on likelihood displacement. The main interest is to consider the test of mean–variance efficiency of a given portfolio as objective function. Sensitivity of maximum likelihood estimators of slopes is also considered. For this purpose, first and second-order local influence measures are calculated under a case weights perturbation scheme. In particular, for our objective functions, which have nonzero first derivative at the critical point, the proposed second-order measures are scale invariant, unlike the normal curvature. The performance of the proposed measures is illustrated by using two real data sets as well as a simulation study and a simulated data set. Empirical results seem to indicate that the Wald test statistic is less sensitive to atypical returns than maximum likelihood estimators of the slopes. By the other hand, there is some evidence about the convenience of jointly using first and second-order influence measures, to detect months/days with outlying returns, principally in Wald test statistic.

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Acknowledgments

We would like to thank the Associate Editor and two referees for their helpful comments and suggestions, leading to improvement of the paper. Also, we acknowledge the partial financial support from Projects Fondecyt 1110318 and 1150325, Chile.

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Authors and Affiliations

  1. Departamento de Estadística, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna 4860, Santiago, Chile

    Manuel Galea

  2. Departamento de Matemática, Universidad Nacional de Mar del Plata, Funes 3350, Mar del Plata, Argentina

    Patricia Giménez

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  1. Manuel Galea
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  2. Patricia Giménez
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Correspondence to Manuel Galea.

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Galea, M., Giménez, P. Local influence diagnostics for the test of mean–variance efficiency and systematic risks in the capital asset pricing model. Stat Papers 60, 293–312 (2019). https://doi.org/10.1007/s00362-016-0838-8

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  • DOI: https://doi.org/10.1007/s00362-016-0838-8

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