Fat tails, VaR and subadditivity☆

By Jón Dańıelsson, Bjorn N. Jorgensen, Gennady Samorodnitsky, Mandira Sarma, Casper G. de Vries. 2013

129 citations recorded by the source corpus.

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.

Subfields: Finance

View Paper: https://www.semanticscholar.org/paper/3b21f258b85a737acdeef3c8ee1b9c8b4d6f989a

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1. M. Nieto
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Citations in the corpus

• Modeling Dependence in High Dimensions With Factor Copulas (2015, unknown): “q (j) q (j) N j (14) where q (j) = E N q jN q j j N q XN i=1 1 fUi qg”
• Frontiers in VaR forecasting and backtesting (2016, background): “However, Danielsson et al. (2013) show that, for example, Lien et al. (2014). continuous random variables, either the VaR is coherent and satisfies subadditivity or the first moment of returns does not exist.”