ZETA™ Methodology and Variation in the Systemic Risk of Default: Accounting for the Effects of Type II (False Negative) Errors Variation on Lending
Authors: Stefano Olgiati , Alessandro Danovi 
Published: November 2018

Olgiati Stefano - University of Bergamo, Department of Management, Economics and Quantitative Methods.
Danovi Alessandro - University of Bergamo
The loan manager - dealing with one single borrower at a time and being responsible for that single decision to lend - is exposed to the idiosyncratic risk of default of his customer just like the physician is exposed to the risk of a wrong diagnosis with our strep throat. At the same time – if we do not expect the strep throat diagnostic test kit to change - we would still expect that physician reading that test to become more careful – or update his prior beliefs – about his diagnoses when a flu epidemic is likely to kick in with a certain estimated probability (likelihood). However, this has not been the case with loan management - there is in fact some consensus that before 2007 a reduction in the standards of idiosyncratic risk assessment by lenders - prior to risks pooling - coupled with a worsening of the systemic risk scenario, is partly to blame for the well known 2007-2008 financial crisis, with some of the blame falling also on the incapacity of actuarial mathematical models (test kits) to update worst case scenarios or be calibrated continuously on the basis of variation in the likelihood of default of the underlying risks pool.The authors of this paper argue that, on the other hand, a standard Bayesian transformation of the ZETA bankruptcy prediction methodology introduced by Altman in 1968-1977 allows for a continuous a posterioriupdate of conditional Type I and II errors due to variation in the systemic likelihood of default. The Bayesian transformation can be used both to condition the loan manager’s prior decision (generally based on Basel II-compliant Internal Rating Based system or Credit Agency’s Rating) and to update such decision on the basis of any posterior hypothesis (based on actuarial frequentist assumptions of conditional hazard rates) regarding the creditworthiness and the probability of default of an underlying pool of securities.At the same time – under a Bayesian framework - the ZETA diagnostic test can be conditioned on the new evidence introduced by other tests to increase the total sensitivity of the default prediction models (IRB ratings, TTC ratings, logit, probit, neural) to update the commercial bank’s lending decisions.A ground-state, static meta-analysis of Altman’s et al. ZETA original article (1977) reveals that the odds of the commercial bank detecting a default after the ZETA score has been introduced (post-test) is 13.2 times more effective than the a priori prediction. Under the same assumptions, the odds of the commercial bank detecting a survival after (post-test) the ZETA score has been introduced is 12.2 times more effective than the a priori. Integration of the ZETA model with other default prediction models reaches a credibility interval of CI ≥ 95% when the updated likelihood of default is equal to 60%. As expected, the Efficiency Comparison Test ECZETA=.00243 is invariant under the Bayesian transformation.