Inferred Loss Rate as a Credit Risk Measure in the Bulgarian Banking System

The loss rate of a bank’s portfolio traditionally measures what portion of the exposure is lost in the case of a default. To overcome the difficulties involved in its computation due to, e.g., the lack of private data, one can utilize an inferred loss rate (ILR). In the existing literature, it has been demonstrated that this indicator has sufficiently close properties to the actual loss rate to facilitate capital adequacy analysis. The current study provides complete mathematical proof of an earlier-stated conjecture, that ILR can be instrumental in identifying a conservative upper bound of the capital adequacy requirement of a bank credit portfolio, using the law of large numbers and other techniques from measure-theory-based probability. The assumptions required in this proof are less restrictive, reflecting a more realistic view. In the current study, additional empirical evidence of the usefulness of the indicator is provided, using publicly available data from the Bulgarian National Bank. Despite the definite conservativeness of the capital buffer implied from the analysis of ILR, the empirical analysis suggests that it is still within the regulatory limits. Analyzing ILR together with the Inferred Rate of Default, we conclude that the indicator provides signals about a bank portfolio’s credit risk that are relevant, timely, and adequately inexpensive.