On the feasibility of portfolio optimization under expected shortfall. (English) Zbl 1190.91116

Summary: 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.


91B80 Applications of statistical and quantum mechanics to economics (econophysics)
91G10 Portfolio theory
82C99 Time-dependent statistical mechanics (dynamic and nonequilibrium)
91B84 Economic time series analysis
Full Text: DOI arXiv


[1] DOI: 10.1016/S0378-4266(02)00283-2
[2] DOI: 10.1111/1467-9965.00068 · Zbl 0980.91042
[3] DOI: 10.1016/S0378-4266(02)00265-0
[4] DOI: 10.1023/B:JOSS.0000019815.11115.54 · Zbl 1157.82377
[5] DOI: 10.1016/j.jbankfin.2006.12.003
[6] Mézard M, Spin Glass Theory and Beyond 9 (1987)
[7] Pafka S, Eur. Phys. J. 27 pp 277– (2002)
[8] Pflug GC, Probabilistic Constrained Optimization: Methodology and Applications (2000)
[9] Press WH, Numerical Recipes in C (1992)
[10] Rockafellar R, J. Risk 2 pp 21– (2000)
[11] Talagrand M, Spin Glasses: A Challenge for Mathematicians (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.