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Measuring risk with ordinal variables

Author

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  • Silvia Figini

    (Department of Economics and Management, University of Pavia)

  • Paolo Giudici

    (Department of Economics and Management, University of Pavia)

Abstract

In this paper we propose a novel approach to measure risks, when the data available are expressed in an ordinal scale. As a result we obtain a new index of risk bounded between 0 and 1, that leads to a risk ordering that is consistent with a stochastic dominance approach. The proposed measure, being non parametric, can be applied to a wide range of problems, where data are ordinal and where a point estimate of risk is needed. We also provide a method to calculate confidence intervals for the proposed risk measure, in a Bayesian non parametric framework. In order to evaluate the actual performance of what we propose, we analyse a database provided by a telecommunication company, with the final aim of measuring operational risks, starting from a self-assessment questionnaire.

Suggested Citation

  • Silvia Figini & Paolo Giudici, 2013. "Measuring risk with ordinal variables," DEM Working Papers Series 032, University of Pavia, Department of Economics and Management.
    • Handle: RePEc:pav:demwpp:032
    as

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    File URL: http://dem-web.unipv.it/web/docs/dipeco/quad/ps/RePEc/pav/demwpp/DEMWP0032.pdf
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    References listed on IDEAS

    as
    1. Jean, William H, 1980. "The Geometric Mean and Stochastic Dominance," Journal of Finance, American Finance Association, vol. 35(1), pages 151-158, March.
    2. Levy, Haim, 1973. "Stochastic Dominance Among Log-Normal Prospects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 601-614, October.
    3. Jean, William H, 1984. "The Harmonic Mean and Other Necessary Conditions for Stochastic Dominance," Journal of Finance, American Finance Association, vol. 39(2), pages 527-534, June.
    4. 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.
    5. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(5), pages 849-866, December.
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    Cited by:

    1. Silvia Facchinetti & Paolo Giudici & Silvia Angela Osmetti, 2020. "Cyber risk measurement with ordinal data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(1), pages 173-185, March.
    2. Clive Hunt & Ross Taplin, 2019. "Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation," Risks, MDPI, vol. 7(4), pages 1-14, October.
    3. Lee, Byung Kwon & Zhou, Rong & de Souza, Robert & Park, Jaehun, 2016. "Data-driven risk measurement of firm-to-firm relationships in a supply chain," International Journal of Production Economics, Elsevier, vol. 180(C), pages 148-157.

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    More about this item

    Keywords

    Risk measurement; Ordinal variables; Operational risk;
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