{"title":"Bank insolvency risk, Z-score measures and unimodal returns: A refinement","authors":"Mathieu Mercadier , Frank Strobel","doi":"10.1016/j.qref.2024.101919","DOIUrl":null,"url":null,"abstract":"<div><p>We develop refined probability bounds for bank insolvency risk measures based on the Z-score, analogous to those given by Cantelli’s inequality under the additional assumption of unimodality of returns, drawing on the one-sided Vysochanskii-Petunin inequality. Illustrating empirically for US banks, we argue that (i) unimodality of returns is not an overly restrictive assumption in this context, and (ii) the refined measures provide a less conservative alternative to insolvency probability bounds drawing on the (two-sided) Vysochanskii-Petunin inequality, particularly for banks with higher levels of insolvency risk.</p></div>","PeriodicalId":47962,"journal":{"name":"Quarterly Review of Economics and Finance","volume":"98 ","pages":"Article 101919"},"PeriodicalIF":2.9000,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S106297692400125X/pdfft?md5=1da907565b2e147df500a339c7581a80&pid=1-s2.0-S106297692400125X-main.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quarterly Review of Economics and Finance","FirstCategoryId":"96","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S106297692400125X","RegionNum":3,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
We develop refined probability bounds for bank insolvency risk measures based on the Z-score, analogous to those given by Cantelli’s inequality under the additional assumption of unimodality of returns, drawing on the one-sided Vysochanskii-Petunin inequality. Illustrating empirically for US banks, we argue that (i) unimodality of returns is not an overly restrictive assumption in this context, and (ii) the refined measures provide a less conservative alternative to insolvency probability bounds drawing on the (two-sided) Vysochanskii-Petunin inequality, particularly for banks with higher levels of insolvency risk.
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