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On the feasibility of portfolio optimization under expected shortfall

[journal article]

Ciliberti, Stefano; Kondor, Imre; Mézard, Marc

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Abstract We address the problem of portfolio optimization under the simplest coherent risk measure, i.e. the expected shortfall. As it 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, the portfolio optimization is ill posed because it leads to unbounded positions, infinitely short on some assets and infinitely long on some 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.
Classification Financial Planning, Accountancy; Economic Statistics, Econometrics, Business Informatics
Free Keywords Statistical physics; Finance; Portfolio optimization; Quantitative finance; Correlation modelling; Critical phenomena; Risk measures
Document language English
Publication Year 2007
Page/Pages p. 389-396
Journal Quantitative Finance, 7 (2007) 4
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)