[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Development Factor** ## Definition ==Development Factor== A development factor (or link ratio) represents the factor by which losses are expected to increase as they mature from one evaluation point to another. ## Types ### Age-to-Age Factor ``` Factor_{n to n+k} = Losses at age n+k / Losses at age n Example: 12-24 month factor = Losses @ 24mo / Losses @ 12mo ``` ### Cumulative Development Factor (CDF) ``` CDF_{n to ultimate} = Ultimate Losses / Losses at age n Example: 12-to-ultimate CDF = Ultimate / Losses @ 12mo ``` ## Calculating Development Factors ### 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 ``` ### Volume Weighted ``` Weighted Factor = Σ(Age n+1) / Σ(Age n) For 12-24: = (750 + 825 + 900) / (500 + 550 + 600) = 2,475 / 1,650 = 1.500 ``` ## Cumulative Factors ### Calculation ``` CDF = Product of age-to-age factors If: 12-24: 1.500 24-36: 1.167 36-48: 1.057 48-Ult: 1.020 (tail) Then: 12-Ult CDF = 1.500 × 1.167 × 1.057 × 1.020 = 1.896 ``` ## Tail Factor The development factor from the end of the triangle to ultimate: - Based on industry data - Actuarial judgment - Curve fitting - Varies significantly by line ## Related Concepts - [[Loss Development Triangle]] - [[Chain Ladder Method]] - [[Cumulative Development Factor]] - [[Tail Factor]] ## References - Friedland, Chapters 3-4