Recursive Partitioning via Discriminant Functions for Rating

Aim of this paper is to propose a nonparametric method for the rating of financial stocks, such as Mutual Funds, Corporates, Equities etc. To this purpose, we refer to a procedure based on the joint use of linear discriminant analysis and tree based recursive partitioning. This method is applied when dealing with large sets of within-groups correlated covariates in order to overcome the dimensionality problem. For that, multiple splits defined upon a suitable linear combination of covariates are required. We describe a methodology that builds up a treebased model which nodes splitting is due to multiple splitting, following a recursive partitioning algorithm considering a splitting criterion based on linear discriminant functions. As a result, an automated and fast procedure allows to look for multiple splits able to capture suitable directions in the variability among the sets of covariates. We identify some variables to be meant as key factor in the rating attribution process. To rate financial assets, we perform T times the recursive partitioning procedure based on discriminant functions in order to obtain a partial rating with respect to each key factor. For each stock, the final rating is obtained averaging the partial ratings associated to each key factor. Main results of the performance of the proposed method to a set of equities listed in the Eurostox 600 Index are presented.