VaR-Efficient Portfolios for a Class of Super- and Sub-Exponentially Decaying Assets Return Distributions
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their multivariate generalizations with Gaussian copulas, we offer exact formulas for the tails of the distribution $P(S)$ of returns $S$ of a portfolio of arbitrary composition of these assets. We find that the tail of $P(S)$ is also asymptotically a modified Weibull distribution with a characteristic scale $\chi$ function of the asset weights with different functional forms depending on the super- or sub-exponential behavior of the marginals and on the strength of the dependence between the assets. We then treat in details the problem of risk minimization using the Value-at-Risk and Expected-Shortfall which are shown to be (asymptotically) equivalent in this framework.
|Date of creation:||Jan 2003|
|Date of revision:|
|Publication status:||Published in Quantitative Finance 4 (1), 17-36 (2003)|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- Carlo Acerbi & Dirk Tasche, 2001.
"On the coherence of Expected Shortfall,"
cond-mat/0104295, arXiv.org, revised May 2002.
- Sornette, Didier, 1998. "Large deviations and portfolio optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 256(1), pages 251-283.
- P. Gopikrishnan & M. Meyer & L.A.N. Amaral & H.E. Stanley, 1998. "Inverse cubic law for the distribution of stock price variations," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 3(2), pages 139-140, July.
- Con Keating & Hyun Song Shin & Charles Goodhart & Jon Danielsson, 2001. "An Academic Response to Basel II," FMG Special Papers sp130, Financial Markets Group.
- Didier Sornette, 1998. "Large deviations and portfolio optimization," Papers cond-mat/9802059, arXiv.org, revised Jun 1998.
- Y. Malevergne & D. Sornette, 2002. "Multi-Moments Method for Portfolio Management: Generalized Capital Asset Pricing Model in Homogeneous and Heterogeneous markets," Papers cond-mat/0207475, arXiv.org.
- A. Johansen & D. Sornette, 1998. "Stock market crashes are outliers," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 1(2), pages 141-143, January.
- Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
- 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," Finance 0111003, EconWPA.
- Yannick Malevergne & Didier Sornette, 2003. "Testing the Gaussian copula hypothesis for financial assets dependences," Post-Print hal-00520539, HAL.
- Bekaert, Geert & Wu, Guojun, 2000.
"Asymmetric Volatility and Risk in Equity Markets,"
Review of Financial Studies,
Society for Financial Studies, vol. 13(1), pages 1-42.
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