On the consistency of the Z-score to measure the bank risk

Abstract

This paper raises questions about the consistency of the Z-score, which is the most applied accounting-based measure of bank risk. In spite of its advantage, namely the concept of risk on which it relies, the traditional formula is precisely inconsistent with its own concept. The Z-score is deduced from the probability that bank’s losses exceed its capital, but under the very unrealistic assumption of normally distributed returns on assets. Consequently, we show that the traditional Z-score fails to consider correctly the distribution of banks’ returns. To make the Z-score consistent and preserve its original concept of risk, we propose more flexible distribution functions. Between skew normal and stable distributions, we prove that the latter fits the best the distribution of banks’ returns and therefore provides more reliable results for the Z-score. An application on the experience of the Central and Eastern European banks confirms this theoretical prove