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Feasibility of Portfolio Optimization under Coherent Risk Measures

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  • Imre Kondor
  • Istvan Varga-Haszonits

Abstract

It is shown that the axioms for coherent risk measures imply that whenever there is an asset in a portfolio that dominates the others in a given sample (which happens with finite probability even for large samples), then this portfolio cannot be optimized under any coherent measure on that sample, and the risk measure diverges to minus infinity. This instability was first discovered on the special example of Expected Shortfall which is used here both as an illustration and as a prompt for generalization.

Suggested Citation

  • Imre Kondor & Istvan Varga-Haszonits, 2008. "Feasibility of Portfolio Optimization under Coherent Risk Measures," Papers 0803.2283, arXiv.org, revised Apr 2008.
    • Handle: RePEc:arx:papers:0803.2283
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    File URL: http://arxiv.org/pdf/0803.2283
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    Cited by:

    1. Istvan Varga-Haszonits & Imre Kondor, 2008. "The instability of downside risk measures," Papers 0811.0800, arXiv.org, revised Nov 2008.
    2. Saša ŽIKOVIÆ & Randall K. FILER, 2013. "Ranking of VaR and ES Models: Performance in Developed and Emerging Markets," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 63(4), pages 327-359, August.
    3. Sasa Zikovic & Randall Filer, 2009. "Hybrid Historical Simulation VaR and ES: Performance in Developed and Emerging Markets," CESifo Working Paper Series 2820, CESifo.

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