A minimum sample size definition for the purpose of loss provision extrapolation in the presence of default correlation

In 2016 the Bank of Russia developed two ordinances setting forth a procedure that uses a limited sample of loans to determine whether or not the level of loss provision for a portfolio of uniform loans is sufficient and whether the bank’s capital is adequate. The procedure for assessing the adequacy of reserves, as a rule, involves considering only a part of the loan portfolio and extrapolating the reserves calculated in this way to the entire portfolio. Moreover, the procedure for determining the minimum sample size of loans assumes there is no default correlation. The contribution of our paper is the application of well-known, though often ignored, properties of the Bernoulli distribution of the total number of correlated events to a novel problem: an extrapolation of the capital provision that does not take into account the possible existence of a default correlation. As a result, we prove that the presence of a default correlation requires a larger minimum sample size of loans than when it is absent. More specifically, we justify how the minimum sample size of loans depends upon the absolute and relative differences in default rates (provision rates, rate of regulatory noncompliance) of two samples, the required significance levels and statistical power.