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

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. [ABSTRACT FROM AUTHOR]