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Fat tails, VaR and subadditivity

Danielsson, Jon and de Vries, Casper G. and Jorgensen, Bjorn and Samorodnitsky, Gennady and Mandira, Sarma (2012) Fat tails, VaR and subadditivity. Jon Danielsson.

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Abstract

Financial institutions rely heavily on Value-at-Risk (VaR) as a risk measure, even though it is not 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.

Item Type: Monograph (Working Paper)
Official URL: http://www.riskresearch.org/
Additional Information: © 2012 The Authors
Subjects: H Social Sciences > HB Economic Theory
H Social Sciences > HG Finance
JEL classification: G - Financial Economics > G0 - General > G00 - General
G - Financial Economics > G1 - General Financial Markets > G18 - Government Policy and Regulation
Sets: Departments > Finance
Collections > Economists Online
Research centres and groups > Financial Markets Group (FMG)
Collections > LSE Financial Markets Group (FMG) Working Papers
Date Deposited: 16 Apr 2012 15:22
Last Modified: 27 Feb 2014 15:35
URI: http://eprints.lse.ac.uk/id/eprint/43138

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