This paper reconsiders the Beta Binomial approach for modeling default risk in homogenous credit portfolio. It first introduces a new parameterization of the Beta Mixing Distribution that is now a function of the common default probability and the common default correlation. It then focuses on the correlation parameter and derives closed-form expressions for sensitivities of key credit risk indicators. Results of the sensitivity and elasticity analysis show that the common default correlation impacts on the credit at risk and expected shortfall quite differently. One also performs an application on CDOs to highlight the key role of the common default correlation on the different tranches