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Coherent risk measures alone are ineffective in constraining portfolio losses

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  • Armstrong, John
  • Brigo, Damiano

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.

Suggested Citation

  • Armstrong, John & Brigo, Damiano, 2022. "Coherent risk measures alone are ineffective in constraining portfolio losses," Journal of Banking & Finance, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:jbfina:v:140:y:2022:i:c:s0378426621002673
    DOI: 10.1016/j.jbankfin.2021.106315
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    References listed on IDEAS

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    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. George M. Constantinides & Michal Czerwonko & Stylianos Perrakis, 2020. "Mispriced index option portfolios," Financial Management, Financial Management Association International, vol. 49(2), pages 297-330, June.
    3. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    4. George M. Constantinides & Michal Czerwonko & Jens Carsten Jackwerth & Stylianos Perrakis, 2011. "Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence," Journal of Finance, American Finance Association, vol. 66(4), pages 1407-1437, August.
    5. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July.
    6. Armstrong, John & Brigo, Damiano, 2019. "Risk managing tail-risk seekers: VaR and expected shortfall vs S-shaped utility," Journal of Banking & Finance, Elsevier, vol. 101(C), pages 122-135.
    7. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    8. George M. Constantinides & Jens Carsten Jackwerth & Stylianos Perrakis, 2009. "Mispricing of S&P 500 Index Options," The Review of Financial Studies, Society for Financial Studies, vol. 22(3), pages 1247-1277, March.
    9. John Armstrong, 2016. "The Markowitz Category," Papers 1611.07741, arXiv.org, revised Jun 2018.
    10. Teemu Pennanen, 2011. "Convex Duality in Stochastic Optimization and Mathematical Finance," Mathematics of Operations Research, INFORMS, vol. 36(2), pages 340-362, May.
    11. Thierry Post & Iňaki Rodríguez Longarela, 2021. "Risk Arbitrage Opportunities for Stock Index Options," Operations Research, INFORMS, vol. 69(1), pages 100-113, January.
    12. Alexander, Carol, 2004. "Normal mixture diffusion with uncertain volatility: Modelling short- and long-term smile effects," Journal of Banking & Finance, Elsevier, vol. 28(12), pages 2957-2980, December.
    13. Hans Föllmer & Alexander Schied, 2002. "Convex measures of risk and trading constraints," Finance and Stochastics, Springer, vol. 6(4), pages 429-447.
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