Extreme movements of the main stocks and stock market indexes traded in the eurozone

Objectives. We analyze extreme movements of the main stocks traded in the Eurozone by sector (consumption sector, financial services, petroleum and energy, technologies and telecommunications, industry and construction) in the 2000´s decade. We also analyze some of the main stock market indexes in the Eurozone. Data/Methods. We use monthly data of the returns of the fifty companies traded in the Eurostoxx50 in the 2000´s decade from January 2000 until December 2009. We also analyze daily data of the main stock market indexes of France, Germany, Holland, Ireland, Italy, United Kingdom and Spain. We use econometric techniques to estimate tail indexes and Value at Risk (VaR) measures. Many alternative estimators of unconditional VaR can be found. The most traditional one was proposed by Hill (1975, Annals of Statistics), where the existence of generalized autoregressive and conditional heteroskedastic (ARCH) effects (very important when modelling financial returns; see e.g. Engle (1982, Econometrica) and Bollerslev (1986, Journal of Econometrics) for more details) can be implicitly acknowledged. Hill (2010, Econometric Theory) has shown that the Hill (1975, Annals of Statistics) estimator is robust to the existence of GARCH effects; however, there exists clear evidence in the literature of its poor finite sample properties (see e.g. Kearns and Pagan (1997, Review of Economics and Statistics) and Wagner and Marsh (2005, Journal of Empirical Finance)). In this paper, we use also an alternative estimator that is shown to have improved finite sample properties under some assumptions and it is based on the work of Berkes, Horváth and Kokoszka (2003, Econometric Theory) and it has been generalized to the case of the GJR-GARCH model of Glosten, Jagannathan and Runkle (1993, Journal of Finance) by Iglesias and Linton (2009, Working paper, University Carlos III, Madrid). Results/Expected Results. We find several patters. First, we can classify firms by sector according to their different estimated VaR values but we cannot find differences according to their geographical situation. Second, we find sectors where companies have very high (telecommunications and banking) and very low (petroleum, utilities, energy and consumption) estimated VaR values. Other sectors such as industry are very heterogeneous. Third, we get differences when we analyze the correlation between average return and VaR estimates: higher average return is found in firms with smaller risk in extreme events in the banking and consumption subsectors; however higher return with higher estimated VaR values occurs in the utilities (electricity and gas) subsector, being less attractive for very risk averse investors. Finally, our results show that very risk averse investors that are looking for high average return and low estimated VaR should choose the following firms classified by sector: Danone and Sanofi-Aventis (consumption), Bbva (financial services), Eni Spa and Iberdrola (petroleum and energy) and Telefonica (technology and telecommunications). We also show results concerning the evolution of the VaR applied to the main European stock indexes and we compare them. This improves our knowledge of the stock markets in the European countries in periods of financial crisis.