Measuring risk with ordinal variables

Silvia Figini and Paolo Giudici

Journal of Operational Risk

Abstract: ABSTRACT In this paper we propose a novel approach for measuring risks when the data available is expressed on an ordinal scale. As a result we obtain a new index of risk bounded between 0 and 1, which leads to a risk ordering that is consistent with a stochastic dominance approach. The proposed measure, being nonparametric, can be applied to a wide range of problems, where data is 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 nonparametric framework. In order to evaluate the actual performance of what we propose, we analyze a database provided by a telecommunications company, with the final aim of measuring operational risks, starting from a self-assessment questionnaire.

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