On the Sensitivity of a Dynamic Measure of Financial Inequality

In the present work, we investigate the sensitivity of the dynamic Theil index computed under a Markov reward model with respect to structured perturbations affecting the underlying Markov process. The model is applied to the sovereign credit spread evolution as a proxy for financial risk, which are driven by the sovereign credit rating dynamic. The introduction of such perturbations allows to evaluate the sensitivity of the inequality of the financial risk in a given group of financial entities with respect to the uncertainty in the rating dynamics. To this end we perform a simulation based sensitivity analysis. The methodology is applied to real data concerning sovereign credit ratings and long-term interest rates on government bonds of 24 European countries. Obtained results suggest different sensitivity of the inequality measure to the 12 scenarios built supposing different ways the perturbations could affect the rating process.