[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Exposure Trend** ## Definition ==Exposure Trend== is the systematic change in exposure base values over time, reflecting inflation or changes in the underlying risk measure. ## Common Exposure Trends ### Workers Compensation (Payroll) ``` Trend = Wage inflation Typical: 2-4% annually Reflects: - Wage increases - Salary inflation - Economic growth ``` ### Auto (Vehicles) ``` Trend = Vehicle value inflation Typical: 1-3% annually Reflects: - New vehicle prices - Vehicle mix changes ``` ### Property (Building Values) ``` Trend = Construction cost inflation Typical: 2-5% annually Reflects: - Material costs - Labor costs - Building values ``` ## Application in Pure Premium Method ``` Both losses AND exposures trended: Trended Losses = Historical × Loss Trend^years Trended Exposures = Historical × Exposure Trend^years Pure Premium = Trended Losses / Trended Exposures ``` ## Example ``` Workers Compensation: Historical payroll: $50,000,000 Historical losses: $1,000,000 Trend period: 2.5 years Loss trend: 4% annually Exposure trend (wage inflation): 3% annually Trended losses: $1,000,000 × 1.04^2.5 = $1,104,081 Trended exposures: $50,000,000 × 1.03^2.5 = $53,885,563 Pure Premium: = $1,104,081 / $53,885,563 = $0.0205 per $1 of payroll = $2.05 per $100 of payroll ``` ## Why Trend Exposures? - Exposure values inflate over time - $1 of payroll today ≠ $1 of payroll historically - Must normalize to same economic level - Ensures proper matching with losses ## Related Concepts - [[Trend#Definition]] - [[Loss Trend#Definition]] - [[Pure Premium Method#Definition]] ## References - Werner & Modlin, Chapter 8