Fat Tails, VaR and Subadditivity

Jón Daníelsson, Bjørn N. Jørgensen, Gennady Samorodnitsky, Mandira Sarma, Casper G. de Vries

Research output: Contribution to journalConference article in journalResearchpeer-review


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.
Original languageEnglish
JournalJournal of Econometrics
Issue number2
Pages (from-to)283-291
Number of pages9
Publication statusPublished - 2013
Externally publishedYes


  • Value-at-Risk
  • Subadditivity
  • Fat tailed distribution
  • Extreme value estimation

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