Instability of Portfolio Optimization under Coherent Risk Measures

It is shown that the axioms for coherent risk measures imply that whenever there is a pair of portfolios such that one of them dominates the other one in a given sample (which happens with finite probability even for large samples), then there is no optimal portfolio 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 springboard for generalization. Key Words: Coherent Risk Measures, Portfolio Optimization, Expected Shortfall, Estimation of Risk JEL Classification: G11, C13, D81 

• Type: Journal
• Year: 2010
• Where: ADVCS
• Authors: Imre Kondor, István Varga-Haszonits
• Keywords: ADVCS 2010, Coherent Measure, Coherent Risk, Risk Measures