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Fat tails, VaR and subadditivity

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

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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 172 (2013)
Issue (Month): 2 ()
Pages: 283-291

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Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:283-291

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Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Value-at-Risk; Subadditivity; Fat tailed distribution; Extreme value estimation;

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References

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Citations

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Cited by:
  1. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
  2. Dominique Guegan & Bertrand Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00969242, HAL.
  3. Antonio Di Cesare & Philip A. Stork & Casper G. de Vries, 2011. "Risk Measures for Autocorrelated Hedge Fund Returns," Tinbergen Institute Discussion Papers 11-084/2/DSF 23, Tinbergen Institute.
  4. Buch, Arne & Dorfleitner, Gregor & Wimmer, Maximilian, 2011. "Risk capital allocation for RORAC optimization," Journal of Banking & Finance, Elsevier, vol. 35(11), pages 3001-3009, November.
  5. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534, arXiv.org.
  6. Asche, Frank & Dahl, Roy Endre & Oglend, Atle, 2013. "Value-at-Risk: Risk assessment for the portfolio of oil and gas producers," UiS Working Papers in Economics and Finance 2013/3, University of Stavanger.

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