Leira, Carolina Lopes2026-02-242026-02-242026http://hdl.handle.net/10400.5/117270Trabalho de Projeto de Mestrado, Matemática Aplicada à Economia e Gestão, 2026, Universidade de Lisboa, Faculdade de CiênciasOne of the most commonly used techniques to determine the discriminatory power of a PD model is the Gini coefficient, a metric that measures the absolute difference in the distribution of customers in the portfolio/sample by risk grade. However, when Gini is applied to portfolios with a small number of customers and/or few high-risk customers, i.e. Low Default Portefolios (LDP), it may not be as reliable, creating the need to determine a confidence interval associated with the Gini. This work aims to address this issue and identify methods for estimating the uncertainty of the Gini, in order to provide more information on the performance of LDPs. Several methods for determining Gini uncertainty are explored, namely Bootstrap, Mann-Whitney, and F-Gini, applied to randomly generated samples and real portfolios from a Bank. Additionally, another method inspired by F-Gini was developed: MS-Gini. The study concludes that the most reliable methods for determining Gini uncertainty, among those analyzed, are Mann-Whitney and F-Gini, as they accurately describe the sensitivity of Gini in LDPs, increasing Gini uncertainty in portfolios with a small number of customers, few high-risk customers, or poor customer distribution. The F-Gini method can be applied to any portfolio; however, it requires some computation time. The Mann-Whitney method has only one restriction: it cannot be applied to portfolios with only one bad client. The Bootstrap method proved inadequate for calculating reliable uncertainty, and the MS-Gini method shows a bias in Gini uncertainty for samples with a small number of clients and many bad clients, resulting from the method’s construction itself, making it unreliable in these cases.application/pdfporGiniDiscriminatory PowerDefaultProbability of Default (PD)master thesis