We specialize the established justification for using Z-scores as a risk measure reflecting a bank's probability of insolvency to the case where the bank's distribution of returns is unimodal, obtaining a refined upper bound of the probability of insolvency for this potentially useful special case.

We discuss to what extent existing approaches to the construction of aggregate Z-score measures capture the notion of systemic soundness, propose some alternative ones that could be just as informative and have potential complementary value, and illustrate how these different approaches compare...