Development factor selection

Open the working file of any triangle-based reserve review: under each column of age-to-age factors sit six or eight rows of averages, and one row marked "selected" that matches none of them. Development factor selection is the choice of that row, column by column. Jacqueline Friedland gives the usual catalog in the Casualty Actuarial Society text on basic techniques (2010). Simple average, volume-weighted average (the sum of one column over the sum of the previous one), average excluding high and low, geometric average. Each is taken over all years, the latest five or the latest three. The volume-weighted average is the one that Mack's chain ladder reproduces exactly, and it follows the large years. The simple average treats a 2 million year and a 40 million year alike. The latest three years pick up a recent change in development speed, at the cost of stability; excluding the extremes neutralizes a single large loss, at the risk of discarding a signal. When the triangle is too thin, an external benchmark steps in, market factors or those of a neighboring line. The choice is documented. A selected factor with no record of why that one and not the neighboring average does not survive an independent review. The gap between two defensible selections already gives an honest sense of the reserve uncertainty. The classic trap: carrying forward last closing's selection when claims handling has changed pace, which the raw factors often show before anyone else does. Not to be confused with the tail factor, set beyond the triangle, or with the LDF itself, the observed ratio before any choice is made.