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Minimizing Conditional Value-at-Risk under Constraint on Expected Value

  • Li, Jing
  • Xu, Mingxin

Conditional Value-at-Risk (CVaR) measures the expected loss amount beyond VaR. It has vast advantage over VaR because of its property of coherence. This paper gives an analytical solution in a complete market setting to the risk reward problem faced by a portfolio manager whose portfolio needs to be continuously rebalanced to minimize risk taken (measured by CVaR) while meeting the reward goal (measured by expected return). The optimal portfolio is identified whenever it exists, and the associated minimal risk is calculated. An example in the Black-Scholes framework is cited where dynamic hedging strategy is calculated and the efficient frontier is plotted.

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File URL: http://mpra.ub.uni-muenchen.de/26342/1/MPRA_paper_26342.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 26342.

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Date of creation: 22 Feb 2009
Date of revision: 25 Oct 2010
Handle: RePEc:pra:mprapa:26342
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  1. Acerbi Carlo & Simonetti Prospero, 2002. "Portfolio Optimization with Spectral Measures of Risk," Papers cond-mat/0203607, arXiv.org.
  2. Kramkov, D.O., 1994. "Optional decomposition of supermartingales and hedging contingent claims in incomplete security markets," Discussion Paper Serie B 294, University of Bonn, Germany.
  3. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  4. Alexander Schied, 2004. "On the Neyman-Pearson problem for law-invariant risk measures and robust utility functionals," Papers math/0407127, arXiv.org.
  5. Kondor, Imre & Pafka, Szilard & Nagy, Gabor, 2007. "Noise sensitivity of portfolio selection under various risk measures," Journal of Banking & Finance, Elsevier, vol. 31(5), pages 1545-1573, May.
  6. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September.
  7. Birgit Rudloff, 2007. "Convex Hedging in Incomplete Markets," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 437-452.
  8. Consigli, Giorgio, 2002. "Tail estimation and mean-VaR portfolio selection in markets subject to financial instability," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1355-1382, July.
  9. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
  10. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, EconWPA, revised 08 Oct 2005.
  11. Rockafellar, R. Tyrrell & Uryasev, Stanislav, 2002. "Conditional value-at-risk for general loss distributions," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1443-1471, July.
  12. Jun Sekine, 2004. "Dynamic Minimization of Worst Conditional Expectation of Shortfall," Mathematical Finance, Wiley Blackwell, vol. 14(4), pages 605-618.
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