[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Trend** ## Definition ==Trend== Trend is the systematic change in loss costs or exposures over time, used in ratemaking to project historical experience to future rating periods. ## Types of Trend ### Loss Trend Change in average claim costs over time due to: - **Inflation** - General price level changes - **Medical inflation** - Healthcare cost increases - **Severity trend** - Average claim size changes - **Social inflation** - Legal/social environment changes ### Exposure Trend Change in exposure base values: - **Payroll growth** (workers comp) - **Wage inflation** - **Property values** - **Economic factors** ### Premium Trend Change in average premium per exposure: - Reflects rate changes - Mix of business shifts - Coverage changes ## Trend Methods ### Exponential Trend (Compound) ``` Future Value = Historical Value × (1 + r)^n Where: r = annual trend rate n = number of years Example: Historical loss: $1,000 Annual trend: 5% Years: 2.5 Future: $1,000 × 1.05^2.5 = $1,131 ``` ### Linear Trend (Additive) ``` Future Value = Historical Value × (1 + r × n) Example: Historical loss: $1,000 Annual trend: 5% Years: 2.5 Future: $1,000 × (1 + 0.05 × 2.5) = $1,125 ``` ## Trend Period Calculation ``` Trend Period = Rating Period Midpoint - Historical Period Midpoint Example: Historical: AY 2023 (midpoint 7/1/2023) Rating: 1/1/2026 - 12/31/2026 (midpoint 7/1/2026) Trend Period: 3.0 years Policies earned uniformly, so: - From 7/1/2023 to 7/1/2026 = 3.0 years ``` ## Estimating Trend Rates ### Historical Analysis ``` Fit regression to historical data: - Collect loss costs by period - Fit exponential or linear model - Calculate implied annual trend ``` ### External Indices - CPI (Consumer Price Index) - Medical CPI - Wage indices - Industry benchmarks ### Judgment - Expected future conditions - Economic forecasts - Regulatory environment - Known changes ## Applications in Ratemaking ### Pure Premium Method ``` Trend both losses and exposures: Trended Losses = Historical × Loss Trend^years Trended Exposures = Historical × Exposure Trend^years Pure Premium = Trended Losses / Trended Exposures ``` ### Loss Ratio Method ``` Trend losses only: Trended Losses = Historical × Loss Trend^years On-Level Premium = Historical (adjusted for rates) Loss Ratio = Trended Losses / On-Level Premium ``` ## Example Calculation ``` Workers Compensation Rate Indication: Historical Data (AY 2023): - Ultimate Losses: $1,000,000 - Exposures: $50,000,000 payroll - Historical midpoint: 7/1/2023 Rating Period: - Effective: 1/1/2026 - Midpoint: 7/1/2026 Trend Estimates: - Loss trend: 4% annually (severity) - Exposure trend: 2% annually (wage inflation) Trend Period: 3.0 years (7/1/2023 to 7/1/2026) Trending: Loss: $1,000,000 × 1.04^3.0 = $1,124,864 Exposure: $50,000,000 × 1.02^3.0 = $53,030,401 Pure Premium: = $1,124,864 / $53,030,401 = $0.0212 per $1 of payroll = $2.12 per $100 of payroll ``` ## Related Concepts - [[Exponential Trend]] - [[Linear Trend]] - [[Loss Trend]] - [[Exposure Trend]] - [[On-Level Premium]] - [[ASOP 13 - Trending Procedures]] ## References - Werner & Modlin, Chapter 8 - ASOP 13