Value at Risk and expected shortfall of firms in the main European Union stock market indexes: A detailed analysis by economic sectors and geographical situation ¬リニ

a r t i c l e i n f o Keywords: Pareto tail thickness parameter GARCH-type models Value at Risk Extreme value theory Heavy tails Stock indexes Eurozone We have analyzed extreme movements of the main stocks traded in the Eurozone in the 2000–2012 period. Our results can help future very-risk-averse investors to choose their portfolios in the Eurozone for risk management purposes. We find two main results. First, we can clearly classify firms by economic sector according to their different estimated VaR values in five of the seven countries we analyze. Specially, we find sectors in general where companies have very high (telecommunications and banking) and very low (petroleum, utilities, energy and consumption) estimated VaR values. Second, we only find differences according to the geographical situation of where the stocks are traded in two countries: (1) all firms in the Irish stock market (the only financially rescued country we analyze) have very high estimated VaR values in all sectors; while (2) in Spain all firms have very low estimated VaR values included in the banking and the telecommunication sectors. All our results are supported when we also study the expected shortfall of the firms. Although diversification in the portfolio is a well-known strategy to reduce risk, this is not a guarantee to avoid losses specially in crisis periods. All this motivates the need to have rigorous measures of risk, and specially, during extreme events. Both academics and practitioners have been trying to find determinants of extreme behaviors. For example, Cutler et al. (1989) in fact conclude that extreme values for returns happen during periods where there is no news with special relevance. The concept of financial risk is directly linked with one of the losses; however , there are different measures of risk. Value at Risk (VaR) has its origin in Riskmetrics, that was developed by JP Morgan. Moreover, VaR became a very important measure of risk specially since the Basel Committee on banking supervision declared that banks should be able to cover losses in their portfolios (see for example Dowd VaR has been applied in many different situations. This article analyzes the extreme movements of the main stocks traded in the Eurozone by sectors in the period 2000–2012. European stocks have been analyzed deeply in the literature (see e.g. main objective in this paper is to study their VaR behavior by economic sectors and if there are …