Estimation of Expected Operational Losses : Approaches Based on Heavy Right-Tailed Distributions

This paper employs methodologies that were developed for heavy right-tailed distributions to construct the point and interval estimates of the expected operational losses in the US. These are consistent and unbiased estimates of the mean of the heavy right-tailed loss distribution, whereas those based on normal approximations are not reliable. The estimation methodologies used in this paper exploit the nature of the tail index that measures the degree of tail thickness. To eliminate the small-sample bias in the widely used Hill index estimator, this paper employs an estimator, which is the weighted average of Hill estimators. Furthermore, we employ both m out of n bootstrap and empirical likelihood methods for constructing reliable 95 per cent confidence intervals (CI) for the mean. We provide step-by-step details to show that how these methodologies are applied in practice. The results indicate that the estimates of the expected operational losses of financial institutions in the US are much bigger than the simple sample averages. The 95 per cent CI estimates of the expected losses are asymmetric and much wider than those based on normal approximations. These findings have implications for risk management and economic capital requirements