Bank insolvency risk and Z-score measures: A refinement

- Re-examine link between Z-score measures and banks' probability of insolvency.
- Improve on measure of that probability without further distributional assumptions.
- Log of Z-score is shown to be negatively proportional to the log odds of insolvency.

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.