Calculating Lifetime Expected Loss for IFRS 9: Which Formula is Correct?

Banks reporting under IFRS have to build provisions for expected credit losses in their financial statement. The rules for determining loan loss provisions have been reformed in 2014 by the International Accounting Standards Board and been published under IFRS 9. A new requirement which was not present in previous regulation is the necessity to provision the expected loss over a loan's lifetime in case a borrower's credit quality deteriorates substantially. The IFRS 9 rules are formulated in a qualitative way and no explicit formulas or precise parameter estimation methods are prescribed. An established method both in academia and practice for computing lifetime expected loss is summing over discounted one-year expected credit losses calculated for each year of a loan's remaining lifetime. When comparing this approach with an exact calculation based on discounted cash flows, it turns out that this formula is not correct and is underestimating true economic expected credit loss. In addition, the impact of prepayments, different assumptions on LGD, and the IFRS 9 requirements for the choice of discount factors on loan loss provisions are analyzed in detail and accurate formulas for lifetime expected credit loss are provided.