Selecting Copulas for Risk Management
AbstractCopulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favour of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 5652.
Date of creation: Apr 2006
Date of revision:
Contact details of provider:
Postal: Centre for Economic Policy Research, 77 Bastwick Street, London EC1V 3PZ
Phone: 44 - 20 - 7183 8801
Fax: 44 - 20 - 7183 8820
Other versions of this item:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-05-06 (All new papers)
- NEP-BEC-2006-05-06 (Business Economics)
- NEP-ECM-2006-05-06 (Econometrics)
- NEP-FIN-2006-05-06 (Finance)
- NEP-FMK-2006-05-06 (Financial Markets)
- NEP-RMG-2006-05-06 (Risk Management)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- P. Hartmann & S. Straetmans & C.G. de Vries, 2001.
"Asset Market Linkages in Crisis Periods,"
Tinbergen Institute Discussion Papers
01-071/2, Tinbergen Institute.
- de Vries, Casper G & Hartmann, Philipp & Straetmans, Stefan, 2001. "Asset Market Linkages in Crisis Periods," CEPR Discussion Papers 2916, C.E.P.R. Discussion Papers.
- Hartmann, Philipp & Straetmans, Stefan & de Vries, Casper, 2001. "Asset market linkages in crisis periods," Working Paper Series 0071, European Central Bank.
- Hartmann, P. & Straetmans, S. & De Vries, C.G., 2001. "Asset Market Linkages in Crisis Periods," Papers 71, Quebec a Montreal - Recherche en gestion.
- Kahneman, Daniel & Tversky, Amos, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Econometric Society, vol. 47(2), pages 263-91, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- Jon DANIELSSON & Casper G. DE VRIES, 2000.
"Value-at-Risk and Extreme Returns,"
Annales d'Economie et de Statistique,
ENSAE, issue 60, pages 239-270.
- Huisman, Ronald, et al, 2001. "Tail-Index Estimates in Small Samples," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 208-16, April.
- Y. Malevergne & D. Sornette, 2001.
"Testing the Gaussian Copula Hypothesis for Financial Assets Dependences,"
- Y. Malevergne & D. Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Quantitative Finance, Taylor & Francis Journals, vol. 3(4), pages 231-250.
- Y. Malevergne & D. Sornette, 2001. "Testing the Gaussian Copula Hypothesis for Financial Assets Dependences," Papers cond-mat/0111310, arXiv.org.
- Yannick Malevergne & Didier Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Post-Print hal-00520539, HAL.
- Longin, Francois M, 1996. "The Asymptotic Distribution of Extreme Stock Market Returns," The Journal of Business, University of Chicago Press, vol. 69(3), pages 383-408, July.
- Arjan B. Berkelaar & Roy Kouwenberg & Thierry Post, 2004.
"Optimal Portfolio Choice under Loss Aversion,"
The Review of Economics and Statistics,
MIT Press, vol. 86(4), pages 973-987, November.
- Kee-Hong Bae & G. Andrew Karolyi & René M. Stulz, 2003.
"A New Approach to Measuring Financial Contagion,"
Review of Financial Studies,
Society for Financial Studies, vol. 16(3), pages 717-763, July.
- Rachel Campbell & Catherine S. Forbes & Kees Koedijk & Paul Kofman, 2003. "Diversification Meltdown or the Impact of Fat tails on Conditional Correlation?," Monash Econometrics and Business Statistics Working Papers 18/03, Monash University, Department of Econometrics and Business Statistics.
- Jansen, Dennis W. & Koedijk, Kees G. & de Vries, Casper G., 2000. "Portfolio selection with limited downside risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 247-269, November.
- Brooks, C. & Clare, A.D. & Dalle Molle, J.W. & Persand, G., 2005. "A comparison of extreme value theory approaches for determining value at risk," Journal of Empirical Finance, Elsevier, vol. 12(2), pages 339-352, March.
- Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
- Shlomo Benartzi & Richard H. Thaler, 1993.
"Myopic Loss Aversion and the Equity Premium Puzzle,"
NBER Working Papers
4369, National Bureau of Economic Research, Inc.
- Benartzi, Shlomo & Thaler, Richard H, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, MIT Press, vol. 110(1), pages 73-92, February.
- Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
- Giesecke, Kay, 2004. "Correlated default with incomplete information," Journal of Banking & Finance, Elsevier, vol. 28(7), pages 1521-1545, July.
- Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
- Junker, Markus & Szimayer, Alex & Wagner, Niklas, 2006. "Nonlinear term structure dependence: Copula functions, empirics, and risk implications," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1171-1199, April.
- Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
- Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value-at-Risk with Heavy-Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269.
- Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
- Tversky, Amos & Kahneman, Daniel, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 1039-61, November.
- Valdez, Emiliano A. & Chernih, Andrew, 2003. "Wang's capital allocation formula for elliptically contoured distributions," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 517-532, December.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- Yanqin Fan & Xiaohong Chen & Andrew Patton, 2004. "(IAM Series No 003) Simple Tests for Models of Dependence Between Multiple Financial Time Series, with Applications to U.S. Equity Returns and Exchange Rates," FMG Discussion Papers dp483, Financial Markets Group.
- Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.