A Goodness-of-Fit Test with Focus on Conditional Value at Risk

Brazilian Finance Review, Vol. 6, No. 2, pp. 139-155, 2008

17 Pages Posted: 4 May 2007 Last revised: 4 Dec 2008

See all articles by José Fajardo

José Fajardo

Getulio Vargas Foundation

Aquiles Farias

Government of the Federative Republic of Brazil - Central Bank of Brazil

Jose Renato Haas Ornelas

Banco Central do Brasil

Date Written: June 30, 2008

Abstract

To verify whether an empirical distribution has a specific theoretical distribution, several tests have been used, for example: Kolmogorov-Smirnov and Kuiper. These tests try to analyze if all parts of the empirical distribution has a specific theoretical shape. But, in a Risk Management framework, the focus of analysis should be on the tails of the distributions, since we are interested on the extreme returns of financial assets. This paper proposes a new goodness-of-fit hypothesis test with focus on the tails of the distribution. The new test is based on the Conditional Value at Risk measure. Then we use Monte Carlo Simulations to assess the power of the new test with different sample sizes, and then compare with the Crnkovic and Drachman, Kolmogorov-Smirnov and the Kuiper tests. Results showed that the new distance has a better performance than other distances on small samples. We also performed hypothesis tests using financial data. We have tested thehypothesis that the empirical distribution has a Normal, Scaled Student-t, Generalized Hyperbolic, Normal Inverse Gaussian and Hyperbolic distributions, based on the new distance proposed on this paper.

Keywords: Goodness-of-Fit, Conditional Value at Risk, Risk Management

JEL Classification: C12, C13, C15, C16

Suggested Citation

Fajardo, José and Farias, Aquiles and Ornelas, Jose Renato Haas, A Goodness-of-Fit Test with Focus on Conditional Value at Risk (June 30, 2008). Brazilian Finance Review, Vol. 6, No. 2, pp. 139-155, 2008. Available at SSRN: https://ssrn.com/abstract=984041 or http://dx.doi.org/10.2139/ssrn.984041

José Fajardo

Getulio Vargas Foundation ( email )

Brazil
55213799 5781 (Phone)

HOME PAGE: http://www.josefajardo.com

Aquiles Farias

Government of the Federative Republic of Brazil - Central Bank of Brazil ( email )

P.O. Box 08670
SBS Quadra 3 Bloco B - Edificio-Sede
Brasilia DF 70074-900, Distr. Federal 70074-900
Brazil

Jose Renato Haas Ornelas (Contact Author)

Banco Central do Brasil ( email )

P.O. Box 08670
SBS Quadra 3 Bloco B - Edificio-Sede
Brasilia, Distrito Federal 70074-900
Brazil

HOME PAGE: http://www.bcb.gov.br

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