Influence diagnostics for the structural sharpe model under normal/independent distributions

ABSTRACT

A method is proposed in this paper to assess the local influence of minor perturbations for the Sharpe model when the normal distribution is replaced by normal/independent (NI) distributions. The family of NI distributions is an attractive class of symmetric heavy-tailed densities that includes as special cases the normal, t-Student, slash, and the contaminated normal distributions. Since the returns of the market are not observable, the statistical analysis is carried out in the context of an errors-in-variables model. An influence analysis for detecting influential observations (atypical returns) is developed to investigate the sensitivity of the maximum likelihood estimators. Diagnostic measures are obtained based on the conditional expectation of the complete-data log-likelihood function. The results are illustrated by using a set of shares of companies traded in the Chilean stock market.

KEYWORDS:

• Diagnostics
• EM-algorithm
• Errors-in-variables models
• Normal/independent (NI) distributions
• Portfolios
• Sharpe’s model.

MATHEMATICS SUBJECT CLASSIFCATION:

• 62F35

Acknowledgements

We acknowledge the partial financial support from Fapesp, Fapemig and CNPq, Brazil, and Project Fondecyt 1150325, Chile.

Additional information

Funding

Conselho Nacional de Desenvolvimento Científico e Tecnológico. Fundação de Amparo à Pesquisa do Estado de Minas Gerais. Fundação de Amparo à Pesquisa do Estado de São Paulo. Projects Fondecyt.