http://repub.eur.nl/res/aut/14687/ List of Publications en http://repub.eur.nl/static-eur/img/logo.png http://repub.eur.nl http://repub.eur.nl/res/pub/37654/ 2012-09-19T00:00:00Z Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not globally subadditive. First, we theoretically show that the VaR portfolio measure is subadditive in the relevant tail region if asset returns are multivariate regularly varying, thus allowing for dependent returns. Second, we note that VaR estimated from historical simulations may lead to violations of subadditivity. This upset of the theoretical VaR subadditivity in the tail arises because the coarseness of the empirical distribution can affect the apparent fatness of the tails. Finally, we document a dramatic reduction in the frequency of subadditivity violations, by using semi-parametric extreme value techniques for VaR estimation instead of historical simulations. http://repub.eur.nl/res/pub/12365/ 2006-08-01T00:00:00Z In this paper we study some prominent downside risk measures for heavy tailed distribution. Using the notion of regular variation to define heavy tailed distributions we provide approximations of the risk measures in the tail region. We show that the downside risk measures produce similar and consistent ranking of risk. However, Expected Shortfall may not always distinguish between the differing risk levels of assets.