[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Age-to-Age Factor** ## Definition ==Age-to-Age Factor== (also called link ratio) is the ratio of cumulative losses at one development age to cumulative losses at the prior development age, representing the development expected between those two ages. ## Formula ``` Age-to-Age Factor = Losses at age (n+1) / Losses at age n Example: 12-24 month factor = Losses @ 24 months / Losses @ 12 months ``` ## Calculation from Triangle ``` Age (months) AY 12 24 36 2021 500 750 875 2022 550 825 950 2023 600 900 12-24 factors: 2021: 750/500 = 1.500 2022: 825/550 = 1.500 2023: 900/600 = 1.500 Selected 12-24: 1.500 ``` ## Selection Methods ### Simple Average ``` Average of all years: (1.500 + 1.500 + 1.500) / 3 = 1.500 ``` ### Volume Weighted ``` Sum of age 24 / Sum of age 12 = (750 + 825 + 900) / (500 + 550 + 600) = 2,475 / 1,650 = 1.500 ``` ### Median ``` Use middle value to reduce outlier impact ``` ### Latest Periods ``` Weight recent years more heavily Example: Average last 3 years only ``` ## Related Concepts - [[Development Factor#Definition]] - [[Link Ratio#Definition]] - [[Cumulative Development Factor#Definition]] - [[Chain Ladder Method#Definition]] ## References - Friedland, Chapter 4