Minimum sample size definition for the purpose of the loss provisions’ extrapolation under the presence of default correlation

In 2016, the Bank of Russia developed two ordinances to set forth a procedure using a limited sample of loans to conclude whether the level of loss provisions in the portfolio of uniform loans is sufficient or not and whether the bank’s capital is adequate. The existing procedure of reserve sufficiency evaluation previews as a rule considering only a part of the loan portfolio and transfer (extrapolation) of the provision thus assessed for the overall portfolio. Moreover, the acting approach to define the minimum loan sample size assumes the absence of the default correlation. Author’s contribution is the application of the known, though often neglected properties of the distribution of the sum of the correlated Bernoulli events (trials) for the novel task, namely for the provision extrapolation, which did not consider the possibility of the default correlation existence. As a result, we prove that its presence requires larger minimum sample size of loans compared with the instances of its absence. 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 legal violations) within two samples, upon the required significance levels and the levels of statistical power.