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Statistical Papers

, Volume 60, Issue 1, pp 293–312 | Cite as

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

  • Manuel GaleaEmail author
  • Patricia Giménez
Regular Article

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.

Keywords

Local influence diagnostics First and second-order approaches Capital asset pricing model Wald test statistic 

Mathematics Subject Classification

62J05 62J20 62F03 

Notes

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Departamento de EstadísticaPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Departamento de MatemáticaUniversidad Nacional de Mar del PlataMar del PlataArgentina

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