Refining understanding of corporate failure through a topological data analysis mapping of Altman’s Z-score model

Corporate failure resonates widely, leaving practitioners searching for understanding of default risk. Managers seek to steer away from trouble, credit providers to avoid risky loans and investors to mitigate losses. Applying Topological Data Analysis tools, this paper explores whether failing firms from the United States organise neatly along the five predictors of default proposed by the Z-score models. Each firm is represented as a point in a five-dimensional point cloud, each dimension being one of the five predictors. Visualising that cloud using Ball Mapper reveals failing firms are not always located in similar regions of the point cloud, that is they are not concentrated in an easily split out area of the space. As new modelling approaches vie to better predict firm failure, often using black boxes to deliver potentially over-fitting models, a timely reminder is sounded on the importance of evidencing the identification process. Value is added to the understanding of where in the parameter space failure occurs, and how firms might act to move away from financial distress. Further, lenders may find opportunity amongst subsets of firms that are traditionally considered to be in danger of bankruptcy, but which the Ball Mapper plots developed herein clarify actually sit in characteristic spaces where failure has not occurred.