In this paper we use Ching's multivariate Markov chain model to model the dependency of rating transitions of several credit entities. The model is an enhancement of the multivariate Markov chain model for ratings considered by Siu et al. Our model is more parsimonious, flexible and empirically competent than the model used by Siu et al. We adopt an efficient method to calibrate the model parameters and formulate the estimation problem as a linear programming problem that can easily be solved using spreadsheets. We compare the estimation results and the computational efficiency of the enhanced model with that also empirically investigate the effect of incorporating both positive and negative associations on portfolio credit risks.