Copula-based extreme market comovements in the EU

Copula-Based Extreme Market Comovements in the EU

 

Joseph McCarthy

Professor of Finance

Bryant University

1150 Douglas Pike

Smithfield, RI 02917

401-232-6446

mccarthy@bryant.edu

 

Alexei G. Orlov

Associate Professor of Economics

Radford University

Radford, VA 24142

540-831-5889

aorlov@radford.edu

 

 

April 2013

Abstract

This paper models extreme financial interdependence in the European financial markets using a copula approach. Copula functions allow us to capture nonlinearities in the market comovements, time-varying financial dependence, as well as dependence persistence. Copula methodology is flexible enough to permit testing for tail dependence v. independence (i.e., whether the comovements are limited to extreme events) and for any asymmetries between lower and upper tail dependencies (i.e., during the financial downturn vis-à-vis an upswing). Copulas also allow for multivariate association of non-normal marginal distributions, which is a useful feature in light of the well-known fact that equity returns deviate from a normal distribution.

We fit several theoretical copulas, such as Student-t, Frank, Gumbel and Clayton, to the data on European stock market indexes. We use daily data on MSCI international equity market indexes for EU economies  beginning with the introduction of the Euro (January 1, 1999)  through Nov. 1, 2012 downloaded from Datastream. These US$ indexes allow us to construct free float-weighted market capitalization returns to judge the performance of each country’s equity market.

We model and compare financial interdependence for several groups of European economies: PIIGS, non-PIIGS, Euro-member and Eurozone. We also analyze how the best-fit distributions react after the onset of the most recent financial crisis. It is particularly beneficial to use copulas in this context, as European stock markets have been and likely will continue to be  affected to differing degrees by the financial crisis and excessive debt. Copulas are particularly appropriate in such complex analysis as they transform  multiple dimension functions into a one dimensional function. Also, different copulas have differing degrees of tail dependence allowing for a more robust analysis of extreme events.

Our results let us  assess the impact of the debt crisis in the EU and the degree of dependence among the key groups of countries. Our study has important implications for risk and portfolio management, as well as for the resolution of the on-going European debt crisis.