Development Factor
Development Factor (link ratio or age-to-age factor) is the ratio used to project cumulative losses from one maturity age to the next, forming the building blocks of the Chain Ladder Method; chaining them together produces the Cumulative Development Factor to ultimate.
f_{n \to n{+}1} = \frac{\text{Losses at age }n{+}1}{\text{Losses at age }n}
\text{(for a single accident year)}
- Simple average: unweighted mean of all individual year factors — treats each accident year equally regardless of size
- Volume-weighted average:
\Sigma(\text{col }n{+}1) / \Sigma(\text{col }n)— gives more credibility to larger accident years; the standard default selection - Latest-
k-year average: uses only the most recentkaccident years — reduces the influence of older, potentially unrepresentative data - Medial average: drops the highest and lowest individual factors before averaging — reduces the impact of outliers without discarding recent years
Factor Selection Methods 12-to-24-month individual factors: AY 2020: 1.450, AY 2021: 1.550, AY 2022: 1.480, AY 2023: 1.520. Column sums: age-24
= 9{,}900, age-12= 6{,}600(in $000s).Answer Simple average:
(1.450 + 1.550 + 1.480 + 1.520)/4 = 1.500Volume-weighted:
9{,}900 / 6{,}600 = 1.500Latest 2-year average:
(1.480 + 1.520)/2 = 1.500Medial (drop high 1.550 and low 1.450):
(1.480 + 1.520)/2 = 1.500In this case all methods agree; in practice they diverge when individual year factors are non-uniform, and the actuary selects based on data stability and recency