On the feasibility of portfolio optimization under expected shortfall

Stefano Ciliberti, Imre Kondor, Marc Mézard

Research output: Contribution to journalArticle

19 Citations (Scopus)


We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As is well known, one can map this problem into a linear programming setting. For some values of the external parameters, when the available time series is too short, portfolio optimization is ill-posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on others. As first observed by Kondor and coworkers, this phenomenon is actually a phase transition. We investigate the nature of this transition by means of a replica approach.

Original languageEnglish
Pages (from-to)389-396
Number of pages8
JournalQuantitative Finance
Issue number4
Publication statusPublished - Aug 1 2007



  • Correlation modelling
  • Critical phenomena
  • Finance
  • Portfolio optimization
  • Quantitative finance
  • Risk measures
  • Statistical physics

ASJC Scopus subject areas

  • Finance
  • Economics, Econometrics and Finance(all)

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