A Model to Test for and Accommodate Reserving Cycles

In recent years several commentators have noted evidence for a “reserving cycle” linked to the underwriting cycle. It seems that in many classes of non-life insurance, when premium rates are relatively low, claim development patterns tend to be longer-tailed than when premium rates are high. If this is the case, then traditional reserving methods based on an assumption that the development pattern is the same for all origin years will tend to overstate reserves for periods where premium rates were high, and understate reserves for periods where premium rates were low. The present paper reviews the evidence for a reserving cycle and discusses possible causes. A mathematical model is then proposed that accommodates the main possible causes. The purpose of this model is three-fold: (a) to test for the existence of reserving cycle effects, (b) to help identify the causes, and (c) to produce improved reserve estimates. An example analysis is presented using the proposed model. The evidence for the existence of reserving cycles is now sufficiently strong that, in the author’s opinion, it is important for reserving actuaries to be aware of the possibility of cyclical effects, to investigate evidence for such effects in any reserving exercise, and (where there is strong evidence) to adjust reserve estimates accordingly. The model proposed in the present paper can be implemented in Excel and will often be a useful tool for these purposes.

Keywords. Reserving cycle, underwriting cycle, development patterns, curve fitting, least squares, premium rate indices.