Geodesic
Small perturbations with large effects on value-at-risk
Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 151-169

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We show that in the delta-normal model there exist perturbations of the Gaussian multivariate distribution of the returns of a portfolio such that the initial marginal distributions of the returns are statistically undistinguishable from the perturbed ones and such that the perturbed V@R is close to the worst possible V@R which, under some reasonable assumptions, is the sum of the V@Rs of each of the portfolio assets.
Keywords: Gaussian perturbation, value-at-risk, delta-normal model 
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Esquível, Manuel; Dimas, Luís; Mexia, João; Didier, Philippe. Small perturbations with large effects on value-at-risk. Discussiones Mathematicae. Probability and Statistics, Tome 33 (2013) no. 1-2, pp. 151-169. http://geodesic.mathdoc.fr/item/DMPS_2013_33_1-2_a9/