Aggregate Retrospective Premium Ratio as a Function of the Aggregate Incurred Loss Ratio

The aggregate premium returned to a group of individual risks that are subject to retrospective rating depends upon the retrospective rating formula, the aggregate loss ratio of the risks, and the distribution of the individual risks’ loss ratios around the aggregate. As the aggregate incurred loss ratio for a group of risks increases, the aggregate returned premium decreases, but not as rapidly as the loss ratio increases. In this paper a simple equation is developed for the relationship between the aggregate incurred loss ratio and the aggregate retrospective return premium. The equation relies on the tabular charges and savings of Table M, thereby eliminating the need to perform Monte Carlo style simulations. Using the relationship expressed in terms of Table M values, the response of several retrospective rating formulas to changes in the aggregate incurred loss ratio is determined.