Multivariate Analysis to Understand Functional Relationship and Scenario Building

Abstract

Abstract This chapter demonstrates widespread applications of multivariate regression techniques in developing credit rating models. Risk analysts use multivariate techniques to forecast default risk or investment outcomes to understand the role of key contributing factors. Multivariate regression models are also used in predicting losses. It explains regression basics, estimation, and interpretation of coefficients, t-statistics, significance of factors, and its relation with the dependent variable. Various test statistics, analysis of variance, and explanatory power of the models have been explained with banking data and also using statistical package STATA. The use of matrix in estimating multiple regression equations, derivation of regression coefficients, and their functional forms has been explained. Application of multiple regressions in credit risk, operational risk as well as market risk has been illustrated with examples. Further, statistical scorecard development using multiple discriminant analysis and logistic regression techniques have been explained in step-wise manner. Interpretation of key test statistics and their usage in model development as well as post-regression estimation diagnostic tests are shown with numerous examples. Panel regression techniques in understanding determinants of bank performance and in identifying key factors contribute to refinancing by housing finance companies are demonstrated using STATA. Finally, heteroskedasticity and multicollinearity tests are explained to check robustness of the econometric findings. These tests are useful to validate the statistical results. Regression models are not only used to predict determinant of losses, but it also helps a bank to develop stress testing scenarios.