Selecting Copulas for Risk Management
Copulas 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.
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- Yannick Malevergne & Didier Sornette, 2003.
"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.
- Y. Malevergne & D. Sornette, 2001. "Testing the Gaussian Copula Hypothesis for Financial Assets Dependences," Finance 0111003, EconWPA.
- 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.
- Philipp Hartmann & Stefan Straetmans & Casper G. de Vries, 2001. "Asset market linkages in crisis periods," Proceedings 727, Federal Reserve Bank of Chicago.
- 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.
- Berkelaar, A.B. & Kouwenberg, R.R.P., 2000.
"Optimal portfolio choice under loss aversion,"
Econometric Institute Research Papers
EI 2000-08/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Newey, Whitney K., 1984. "A method of moments interpretation of sequential estimators," Economics Letters, Elsevier, vol. 14(2-3), pages 201-206.
- 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.
- 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.
- 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.
- 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.
- 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.
- Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2001. "A new approach to measuring financial contagion," Proceedings 743, Federal Reserve Bank of Chicago.
- Kee-Hong Bae & G. Andrew Karolyi & Rene M. Stulz, 2000. "A New Approach to Measuring Financial Contagion," NBER Working Papers 7913, National Bureau of Economic Research, Inc.
- Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
- 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.
- 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.
- 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.
- Markus Junker & Alexander Szimayer & Niklas Wagner, 2004. "Nonlinear Term Structure Dependence: Copula Functions, Empirics, and Risk Implications," Econometrics 0401007, EconWPA.
- Amos Tversky & Daniel Kahneman, 1979.
"Prospect Theory: An Analysis of Decision under Risk,"
Levine's Working Paper Archive
7656, David K. Levine.
- Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
- François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
- 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.
- 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.
- 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.
- 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.
- 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.
- Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
- 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.
- 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.
- Fermanian, Jean-David, 2005. "Goodness-of-fit tests for copulas," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 119-152, July.
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