Taking the Twists into Account: Predicting Firm Bankruptcy Risk with Splines of Financial Ratios

We demonstrate improvements in predictive power when introducing spline functions to take account of highly non-linear relationships between firm failure and earnings, leverage, and liquidity in a logistic bankruptcy model. Our results show that modeling excessive non-linearities yields substantially improved bankruptcy predictions, on the order of 70 to 90 percent, compared with a standard logistic model. The spline model provides several important and surprising insights into non-monotonic bankruptcy relationships. We find that low-leveraged and highly profitable firms are riskier than given by a standard model. These features are remarkably stable over time, suggesting that they are of a structural nature.