A simulation comparison of aggregation periods for estimating correlations within operational loss data

Abstract

We investigate the differences in the values of correlations based on different aggregation periods of time series loss data. The aggregation periods considered for this study were annual, quarterly and monthly, ie, the losses were binned in one year, one quarter and one month buckets, respectively. We conducted a simulation study in order to cover a wide spectrum of frequencies (sample sizes), severity distributions and dependencies between the severities, choosing the parameters of the simulation study to obtain severity and frequency distributions popular in operational risk loss modeling. Our main conclusion is that the difference in values of the correlation coefficients calculated from aggregate loss severities only becomes material when the inherent correlation in the loss-generating process exceeds approximately 0.5. From a risk management perspective, where annual aggregation is desired due to loss horizons typically being annual, this result implies that aggregation periods shorter than annual can be used, which will increase the number of observations to improve the stability of correlation estimates, and the diversification benefit due to estimating correlation values using a shorter aggregation period will not result in a material misstatement of the diversification benefit, since the differences in the values of the correlations are minimal