This thesis examines the differences between Value at Risk (VaR) and Expected Shortfall (ES) in legal, regulatory and in the context of static credit portfolios, where the emphasis is on modelling the dependency between borrower defaults. Basel II, III and IV provide guidelines for risk management, introducing VaR and ES as methods for credit risk management. The study will therefore analyse that, despite their similarities, VaR and ES produce different results in capturing extreme market events and tail risks. The study employs a Beta Mixture model to capture the dependence between defaults, which is crucial for accurately assessing portfolio credit risk.