Fat tails, VaR and subadditivity

Jon Danielsson, Bjørn Jørgensen, Gennady Samorodnitsky, Mandira Sarma and Casper de Vries

Journal of Econometrics, 2013, vol. 172, issue 2, 283-291

Abstract: 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.

Keywords: Value-at-Risk; Subadditivity; Fat tailed distribution; Extreme value estimation (search for similar items in EconPapers)
JEL-codes: G00 G18 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (53)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:172:y:2013:i:2:p:283-291

DOI: 10.1016/j.jeconom.2012.08.011

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