The Effect of Dependence on European Market Risk. A Nonparametric Time Varying Approach

Abstract

Multivariate dependence measures are crucial for risk management, where variables usually have heavy tails and non-Gaussian distributions. We propose a multivariate time varying Kendall’s tau estimator in a nonparametric context, allowing for local stationary variables. Consistency and asymptotic normality of the estimator are provided. A simulation study is conducted which supports the idea of better performance than other related methods in many complex scenarios. The proposal is used to draw up a daily estimation of the dependence between European financial market indexes. Nonparametric conditional quantiles are estimated to detect any influence of the degree of dependence on the market returns. That dependence emerges as an important factor in the Euro Stoxx distribution. It is noteworthy that the Kendall’s tau only depends on the multivariate copula, so the effect is not due to hidden effects of the marginals. Local Granger causality is tested and evidence is found that the degree of dependence affects the Euro Stoxx returns in the left tail of the distribution. We believe that these results encourage further research into the effect of diversification in quantiles, linked to the factors behind systemic risk. Additionally, there is a noteworthy increase in dependence following the outbreak of COVID-19.

Keywords:

• Local stationarity
• Multivariate Kendall’s tau
• Nonparametric estimator
• Time varying copula

Supplementary Materials

The online supplementary materials contain the proofs of the thorems (Appendix A) and additional results related to the simulation study (Appendix B).

Acknowledgments

We are grateful to the editors and two anonymous referees for their constructive comments and helpful suggestions, which helped us to improve the quality of the article.

Additional information

Funding

This work was supported by the Spanish Ministry of the Economy and Competitiveness under grant ECO2014-51914-P; the UPV/EHU under grants BETS-UFI11/46, MACLAB-IT93-13 and PES20/44; and the Basque Government under BiRTE-IT1336-19. The first author also acknowledges financial support under PIF16/87 from UPV/EHU.