loss development factor

An age-to-age factor tells you how losses grow over one step — say 1.58 from 12 to 24 months. But you usually want the whole journey: how much will a year at 12 months grow before it is finally all paid and settled? Multiply all the remaining single-step factors together — 12-to-24, 24-to-36, 36-to-48, and so on out to the tail — and you get one number, the loss development factor (LDF), that takes an age straight to ultimate in a single multiplication.

Precisely, the LDF (also called the cumulative development factor or age-to-ultimate factor) at a given age is the product of all the selected age-to-age factors from that age onward, including any tail factor. For example, if the link ratios beyond 12 months are 1.58, 1.10, 1.04 and a 1.02 tail, then the 12-month LDF is 1.58 x 1.10 x 1.04 x 1.02 which is about 1.84. Multiply a year's age-12 losses by 1.84 to estimate its ultimate. The reciprocal, 1/1.84 which is about 0.54, is the 'percent reported' — the share of ultimate losses you expect to have already seen at 12 months. Those percentages are exactly what the Bornhuetter-Ferguson and Cape Cod methods feed on.

LDFs matter because they are the compact summary the rest of reserving uses: ultimate equals current losses times the LDF, and the implied reserve is current losses times (LDF minus 1). Two honesty points: errors compound, so a small misjudgement in an early, high-leverage factor swings the answer a lot; and the LDF for the newest, greenest years is the most leveraged of all — a factor of 1.84 means more than half of that year's ultimate is still pure projection, which is why young years are reserved with extra humility and often with the Bornhuetter-Ferguson method instead.