Fat tails, VaR and subadditivity
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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- Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
- Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005.
"Subadditivity Re–Examined: the Case for Value-at-Risk,"
FMG Discussion Papers
dp549, Financial Markets Group.
- Danielsson, Jon & Jorgensen, Bjørn N. & Mandira, Sarma & Samorodnitsky, Gennady & Vries, C. G. de, 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.
- Jón Daníelsson & Bjørn Jorgensen & Casper Vries & Xiaoguang Yang, 2008. "Optimal portfolio allocation under the probabilistic VaR constraint and incentives for financial innovation," Annals of Finance, Springer, vol. 4(3), pages 345-367, July.
- Yamai, Yasuhiro & Yoshiba, Toshinao, 2002. "Comparative Analyses of Expected Shortfall and Value-at-Risk: Their Estimation Error, Decomposition, and Optimization," Monetary and Economic Studies, Institute for Monetary and Economic Studies, Bank of Japan, vol. 20(1), pages 87-121, January.
- Rustam Ibragimov, 2009. "Portfolio diversification and value at risk under thick-tailedness," Quantitative Finance, Taylor & Francis Journals, vol. 9(5), pages 565-580.
- M.J.B. Hall, 1996.
"The amendment to the capital accord to incorporate market risk,"
BNL Quarterly Review,
Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
- M.J.B. Hall, 1996. "The amendment to the capital accord to incorporate market risk," Banca Nazionale del Lavoro Quarterly Review, Banca Nazionale del Lavoro, vol. 49(197), pages 271-277.
- 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.
- Geluk, J.L. & de Vries, C.G., 2004. "Weighted sums of subexponential random variables and asymptotic dependence between returns on reinsurance equities," Econometric Institute Research Papers EI 2004-47, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- De Vries, C.G., 2005. "The simple economics of bank fragility," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 803-825, April.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
- Jansen, Dennis W & de Vries, Casper G, 1991. "On the Frequency of Large Stock Returns: Putting Booms and Busts into Perspective," The Review of Economics and Statistics, MIT Press, vol. 73(1), pages 18-24, February.
- Dennis W. Jansen & Casper de Vries, 1988. "On the frequency of large stock returns: putting booms and busts into perspective," Working Papers 1989-006, Federal Reserve Bank of St. Louis.
- S. V. Stoyanov & S. T. Rachev & F. J. Fabozzi, 2007. "Optimal Financial Portfolios," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 401-436.
- René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.
- Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- HyunSong Shin, 2009. "Securitisation and Financial Stability," Economic Journal, Royal Economic Society, vol. 119(536), pages 309-332, March.
- repec:adr:anecst:y:2000:i:60:p:10 is not listed on IDEAS
- Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
- Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
- de Haan, Laurens & Resnick, Sidney I. & Rootzén, Holger & de Vries, Casper G., 1989. "Extremal behaviour of solutions to a stochastic difference equation with applications to arch processes," Stochastic Processes and their Applications, Elsevier, vol. 32(2), pages 213-224, August. Full references (including those not matched with items on IDEAS)