[en] Economic and financial crises are characterised by unusually large events. These tail events co-move because of linear and/or nonlinear dependencies. We introduce TailCoR, a metric that combines (and disentangles) these linear and non-linear dependencies. TailCoR between two variables is based on the tail inter quantile range of a simple projection. It is dimension-free, and, unlike competing metrics, it performs well in small samples and no optimisations are needed. Indeed, TailCoR requires a few lines of coding and it is very fast. A Monte Carlo analysis confirms the goodness of the metric, which is illustrated on a sample of 21 daily financial market indexes across the globe and for 20 years. The estimated TailCoRs are in line with the financial and economic events, such as the 2008 great financial crisis and the 2020 pandemic.
Disciplines :
Mathematics Business & economic sciences: Multidisciplinary, general & others
Author, co-author :
Babić, Sladana; LeasePlan, Amsterdam, The Netherlands
LEY, Christophe ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Ricci, Lorenzo; European Stability Mechanism, Luxembourg, Luxembourg
Veredas, David; Centre for Sustainable Finance and Department of Economics, Vlerick Business School and Ghent University, Brussels, Belgium
External co-authors :
yes
Language :
English
Title :
TailCoR: A new and simple metric for tail correlations that disentangles the linear and nonlinear dependencies that cause extreme co-movements.
SB was supported by a grant (165880) as a PhD Fellow of the Research Foundation- Flanders (FWO, https://www.fwo.be). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Kiriliouk A, Rootzen H, Wadsworth J, Segers J. The meta-elliptical distributions with given marginals. Journal of Multivariate Analysis. 2019; 82:1–16.
Rootzen H, Segers J, Wadsworth J. Multivariate generalized Pareto distributions: parametrizations, representations, and properties. Journal of Multivariate Analysis. 2018; 165:117–131. https://doi.org/10.1016/j.jmva.2017.12.003
Joe H. Multivariate Models and Dependence Concepts. New York: Chapman & Hall/CRC; 1997.
Embrechts P, de Haan L, Huang X. Modeling multivariate extremes. In: Embrechts P, editor. Extremes and Integrated Risk Management. London: Risk books; 2000. p. 59–67.
Beirlant J, Goegebeur Y, Segers J, Teugels J. Statistics of Extremes. Theory and Applications. New Jersey: John Wiley & Sons; 2004.
McNeil AJ, Frey R, Paul E. Quantitative Risk Management: Concepts, Techniques, and Tools. Princeton University Press; 2005.
Chollete L, de la Pena V, Lu CC. International diversification: A copula approach. Journal of Banking and Finance. 2011; 35:403–417. https://doi.org/10.1016/j.jbankfin.2010.08.020
Hartmann P, Straetmans S, de Vries C. Asset Market Linkages in Crisis Periods. Review of Economics and Statistics. 2004; 86:313–326. https://doi.org/10.1162/003465304323023831
Longin F, Solnik B. Extreme Correlation of International Equity Market. Journal of Finance. 2001; 56:649–676. https://doi.org/10.1111/0022-1082.00340
Cizeau P, Potters M, Bouchaud JP. Correlation Structure of Extreme Stock Returns. Quantitative Finance. 2001; 1:217–222. https://doi.org/10.1080/713665669
Straetmans S, Verschoor W, Wolf C. Extreme US stock market fluctuations in the wake of 9/11. Journal of Applied Econometrics. 2008; 23:17–42. https://doi.org/10.1002/jae.973
Ledford A, Tawn J. Statistics for near independence in multivariate extreme values. Biometrika. 1996; 83:169–187. https://doi.org/10.1093/biomet/83.1.169
Hartmann P, Straetmans S, de Vries C. Banking System Stability: A Cross-Atlantic Perspective. In: Carey M, Stulz RM, editors. Risk of Financial Institutions. Chicago: The University of Chicago Press; 2005. p. 133–193.
Poon SH, Rockinger M, Tawn J. Extreme Value Dependence in Financial Markets: Diagnosis, Models, and Financial Implications. Review of Financial Studies. 2004; 17:581–610. https://doi.org/10.1093/rfs/ hhg058
Babić S, Ley C, Veredas D. Comparison and Classification of Flexible Distributions for Multivariate Skew and Heavy-Tailed Data. Symmetry. 2019; 11:1216. https://doi.org/10.3390/sym11101216
Forbes F, Wraith D. Location and scale mixtures of Gaussians with flexible tail behaviour: Properties, inference and application to multivariate clustering. Statistics and Computing. 2015; 90:61–73. https://doi.org/10.1016/j.csda.2015.04.008
Fang HB, Fanga KT, Kotz S. The meta-elliptical distributions with given marginals. Journal of Multivariate Analysis. 2002; 82:1–16. https://doi.org/10.1006/jmva.2001.2017
Lee TH, Long X. Copula-based Multivariate GARCH Models with Uncorrelated Dependent Errors. Journal of Econometrics. 2019; 150:207–218. https://doi.org/10.1016/j.jeconom.2008.12.008
Sherman S. A theorem on convex sets with applications. The Annals of Mathematical Statistics. 1955; 26:763–767. https://doi.org/10.1214/aoms/1177728435
Berkes I, Hörmann S, Schauer J. Asymptotic Results for the Empirical Process of Stationary Sequences. Stochastic Processes and their Applications. 2009; 119:1298–1324. https://doi.org/10.1016/j.spa.2008.06.010
Hashorva E. Tail asymptotic results for elliptical distributions. Insurance: Mathematics and Economics. 2008; 43:158–164.
Hashorva E. On the residual dependence index of elliptical distributions. Statistics & Probability Letters. 2010; 80:1070–1078. https://doi.org/10.1016/j.spl.2010.03.001
McCulloch J. Simple consistent estimators of stable distribution parameters. Commun Statist Simula. 1986; 15:1109–1136. https://doi.org/10.1080/03610918608812563
Lindskog F, McNeil A, Schmock U. Kendall’s tau for Elliptical Distributions. In: Bol G, Gholamreza Nakhaeizadeh TR Svetlozar T Rachev, Vollmer KR, editors. Credit Risk—Measurement, Evaluation and Management. Physica–Verlag HD; 2003.
Longin FM, Solnik B. Extreme Correlations of International Equity Markets. Journal of Finance. 2001; 24:1097–1130.
Dominicy Y, Ilmonen P, Veredas D. Multivariate Hill Estimators. International Statistical Review. 2017; 85:108–142. https://doi.org/10.1111/insr.12120
IMF. Financial Integration in Latin America. Staff Report. 2016.
Acharya VV, Richardson M. Restoring Financial Stability. New Jersey: John Willey & Sons; 2009.
Boudt K, Danielsson J, Laurent S. Robust Forecasting of Dynamic Conditional Correlation GARCH Models. International Journal of Forecasting. 2013; 29:244–257. https://doi.org/10.1016/j.ijforecast.2012.06.003
Klüppelberg C, Kuhn G, Peng L. Semi-parametric models for the multivariate tail dependence function – the asymptotically dependent case. Scandinavian Journal of Statistics. 2008; 35:701–718. https://doi.org/10.1111/j.1467-9469.2008.00602.x
Krajina A. A method of moments estimator of tail dependence in meta-elliptical models. Journal of Statistical Planning and Inference. 2012; 142:1811–1823. https://doi.org/10.1016/j.jspi.2012.01.020
