 Coherent risk measures alone are ineffective in constraining portfolio lossesJohn Armstrong and Damiano Brigo Journal of Banking & Finance, 2022, vol. 140, issue C Abstract: We show that coherent risk measures alone are ineffective in curbing the behaviour of investors with limited liability or excessive tail-risk seeking behaviour if the market admits statistical arbitrage opportunities which we term ρ-arbitrage for a risk measure ρ. We show how to determine analytically whether such ρ-arbitrage portfolios exist in complete markets and in the Markowitz model. We also consider realistic numerical examples of incomplete markets and determine whether Expected-Shortfall arbitrage exists in these markets. We find that the answer depends heavily upon the probability model selected by the risk manager but that it is certainly possible for expected shortfall constraints to be ineffective in realistic markets. Since value at risk constraints are weaker than expected shortfall constraints, our results can be applied to value at risk. Keywords: Ineffective risk measures; ρ-Arbitrage; Limited liability; Tail-risk seeking behaviour; Coherent risk measures; Positive homogeneity; S-shaped utility; Classic utility risk limit; Markowitz model; Incomplete markets (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jbfina:v:140:y:2022:i:c:s0378426621002673 DOI: 10.1016/j.jbankfin.2021.106315 Access Statistics for this article Journal of Banking & Finance is currently edited by Ike Mathur More articles in Journal of Banking & Finance from Elsevier |
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