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Bank Insolvency Risk and Z-Score Measures: A Refinement

We re-examine the probabilistic foundation of the link between Z-score measures and banks’ probability of insolvency, offering an improved measure of that probability without imposing further distributional assumptions. While the traditional measure of the probability of insolvency thus provides a less effective upper bound of the probability of insolvency, it can be meaningfully reinterpreted as a measure capturing the odds of insolvency instead. We similarly obtain refined probabilistic interpretations of the commonly used simple and log-transformed Z-score measures; in particular, the log of the Z-score is shown to be negatively proportional to the log odds of insolvency.