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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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  1. Geluk, J.L. & De Vries, C.G., 2006. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 39-56, February.
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  14. J�n Dan�elsson & Bj�rn N. Jorgensen & Casper G. de Vries & Xiaogang Yang, 2001. "Optimal Portfolio Allocation under a Probabilistic Risk Constraint and the Incentives for Financial Innovation," Tinbergen Institute Discussion Papers 01-069/2, Tinbergen Institute.
  15. Jon Danielsson & Bjørn N. Jorgensen & Sarma Mandira & Gennady Samorodnitsky & C. G. de Vries, 2005. "Subadditivity re–examined: the case for value-at-risk," LSE Research Online Documents on Economics 24668, London School of Economics and Political Science, LSE Library.
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Citations

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Cited by:
  1. 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.
  2. Antonio Di Cesare & Philip A. Stork & Casper G. de Vries, 2011. "Risk measures for autocorrelated hedge fund returns," Temi di discussione (Economic working papers) 831, Bank of Italy, Economic Research and International Relations Area.
  3. 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.
  4. 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.

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