Trending Entry Ratio Tables

Entry ratio tables are often a convenient mechanism for capturing information that is subject only to scale transforms. For example, the National Council on Compensation Insurance, Inc. (NCCI) stores excess loss factors (ELFs) in entry ratio tables. To determine an ELF at an attachment point, you simply divide the attachment point by the mean loss, and use that "entry ratio" value to look up the ELF in the table. A key assumption is that the underlying size of loss distribution changes only by a uniform scale transform over time (or by a transform that is close enough to a scale transform; c.f. Venter [3] for a discussion of scale adjustments and excess losses).

In fact, there can be forces at work that change the shape of size of loss distributions in ways that are not captured by scale transforms. For example, large claims might have greater trend factors than small claims (differential severity trend). Also, the frequency of small claims might decrease more than the frequency of large claims over some period of time (differential frequency trend). Not surprisingly, both of these possible effects act to stiffen "the size of loss distribution, that is, increase the probability that a claim is "large," given that a claim occurs. A surprising result of our analysis is that the adjustments to entry ratio tables to take these phenomena into account, when they occur, often work in opposite directions. When large claims have greater trend factors than small claims, it might be necessary to increase the entry ratio table ELFs for large entry ratios. But when small claim frequency declines more rapidly than large claim frequency over a period of time, it might be necessary to reduce the tabular ELFs for large entry ratios.

In this note we specify a generic, spreadsheet-friendly, format for an entry ratio table and consider the effects of differential trend and differential frequency changes. Each is illustrated by a real world Workers Compensation (WC) case study. We then describe general techniques for modifying an entry ratio table to account for not only a change in scale but also a change in the relativity between the mean and the median loss (or any fixed percentile loss) or a proportional shift in the hazard rate function of the loss distribution. The findings suggest that entry ratio tables work surprisingly well even for non-uniform trend and that in some important instances just a small adjustment can extend the shelf life of an entry ratio table.