Measuring risk with ordinal variables

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.