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Fat tails, VaR and subadditivity


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


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.

Suggested Citation

  • Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
  • Handle: RePEc:eee:econom:v:172:y:2013:i:2:p:283-291
    DOI: 10.1016/j.jeconom.2012.08.011

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    References listed on IDEAS

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    Cited by:

    1. Chuancun Yin & Dan Zhu, 2015. "New class of distortion risk measures and their tail asymptotics with emphasis on VaR," Papers 1503.08586,, revised Mar 2016.
    2. Massimiliano Amarante, 2016. "A representation of risk measures," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(1), pages 95-103, April.
    3. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.
    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.
    5. Ra'ul Torres & Rosa E. Lillo & Henry Laniado, 2015. "A Directional Multivariate Value at Risk," Papers 1502.00908,
    6. Fabozzi Frank J. & Stoyanov Stoyan V. & Rachev Svetlozar T., 2013. "Computational aspects of portfolio risk estimation in volatile markets: a survey," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 17(1), pages 103-120, February.
    7. Imre Kondor, 2014. "Estimation Error of Expected Shortfall," Papers 1402.5534,
    8. Antonio Di Cesare & Philip A. Stork & Casper G. de Vries, 2015. "Risk Measures for Autocorrelated Hedge Fund Returns," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 13(4), pages 868-895.
    9. Charles-Olivier Amédée-Manesme & Fabrice Barthélémy & Donald Keenan, 2015. "Cornish-Fisher Expansion for Commercial Real Estate Value at Risk," The Journal of Real Estate Finance and Economics, Springer, vol. 50(4), pages 439-464, May.
    10. Frantisek Cech & Jozef Barunik, 2017. "Measurement of Common Risk Factors: A Panel Quantile Regression Model for Returns," Papers 1708.08622,
    11. 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.
    12. Marcelo Brutti Righi & Paulo Sergio Ceretta, 2015. "Shortfall Deviation Risk: An alternative to risk measurement," Papers 1501.02007,, revised May 2016.
    13. Dominique Guegan & Bertrand Hassani, 2016. "Combining risk measures to overcome their limitations - spectrum representation of the sub-additivity issue, distortion requirement and added-value of the Spatial VaR solution: An application to Regul," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01391103, HAL.
    14. 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.
    15. Torres, Raúl & Lillo, Rosa E. & Laniado, Henry, 2015. "A directional multivariate value at risk," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 111-123.
    16. Dominique Guegan & Bertrand K. Hassani, 2016. "Combining risk measures to overcome their limitations - spectrum representation of the sub-additivity issue, distortion requirement and added-value of the Spatial VaR solution: An application to Regul," Documents de travail du Centre d'Economie de la Sorbonne 16066, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    17. Ho Hwang, Jong, 2013. "A proposal for an open-source financial risk model," LSE Research Online Documents on Economics 59298, London School of Economics and Political Science, LSE Library.
    18. Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
    19. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    20. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    21. 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.
    22. Berger, T. & Missong, M., 2014. "Financial crisis, Value-at-Risk forecasts and the puzzle of dependency modeling," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 33-38.

    More about this item


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

    JEL classification:

    • G00 - Financial Economics - - General - - - General
    • G18 - Financial Economics - - General Financial Markets - - - Government Policy and Regulation


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