Are Copula-GoF-Tests of Any Practical Use? Empirical Evidence for Stocks, Commodities and FX Futures

54 Pages Posted: 23 Aug 2009 Last revised: 12 Dec 2010

See all articles by Gregor N. F. Weiss

Gregor N. F. Weiss

University of Leipzig - Faculty of Economics and Management Science

Date Written: November 23, 2010

Abstract

In this paper, the optimality of bivariate copula-VaR models and the usefulness of several goodness-of-fit tests for copulas are analysed in a comprehensive empirical study using data for stocks, commodities and FX futures. In particular, I try to answer two questions: (1) Which parametric copula is optimal for estimating the VaR and Expected Shortfall (ES) of a given portfolio consisting of linear assets? (2) How can the VaR- or ES-optimal parametric copula be identified in-sample? To answer these questions, the VaR and ES for a total of 12, 000 bivariate portfolios are estimated from 435 linear assets over eight different time windows. The results show that although copula-models with GARCH-margins yield considerably better VaR-estimates than correlation-based models, the identification of the optimal parametric copula form is a serious unsolved problem. The analysis of three state-of-the-art approaches for testing a copula-model’s goodness-of-fit showed that none of the tests is able to identify the optimal parametric form unequivocally. In addition to this result, for more than 80% of all portfolios considered, all five parametric copula models yielded worse ES-estimates than the correlation-based benchmark or underestimated actual portfolio risk. Moreover, the backtesting results show that the optimal parametric copula is both dependent on the risk measure and time-variant.

Keywords: Dependence structures, Risk management, Copulas, Goodness-of-fit-testing

JEL Classification: G11, C12, C14

Suggested Citation

Weiss, Gregor N. F., Are Copula-GoF-Tests of Any Practical Use? Empirical Evidence for Stocks, Commodities and FX Futures (November 23, 2010). 22nd Australasian Finance and Banking Conference 2009, Quarterly Review of Economics and Finance, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1459654 or http://dx.doi.org/10.2139/ssrn.1459654

Gregor N. F. Weiss (Contact Author)

University of Leipzig - Faculty of Economics and Management Science ( email )

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Leipzig, 04109
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+49 341 97 33821 (Phone)
+49 341 97 33829 (Fax)

HOME PAGE: http://www.wifa.uni-leipzig.de/nfdl

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