[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **On-Level Premium** ## Definition ==On Level Premium== On-level premium is historical earned premium adjusted to the current rate level, eliminating the impact of rate changes during the experience period. ## Purpose - Match premium to losses at consistent rate level - Remove distortion from rate changes - Calculate accurate loss ratios - Support rate indications ## On-Leveling Process ### Step 1: Identify Rate Changes ``` Document all rate changes during experience period: - Effective date - Rate change percentage - Portion of premium affected ``` ### Step 2: Calculate On-Level Factors ``` On-Level Factor = Current Rate / Historical Rate If rates increased 10%: On-Level Factor = 1.10 / 1.00 = 1.10 ``` ### Step 3: Apply to Earned Premium ``` On-Level Premium = Historical Earned × On-Level Factor ``` ## Example ``` Calendar Year 2024 Premium: Written: $1,000,000 (1/1/2024) Rate change: +10% effective 7/1/2024 Earned premium by rate level: Jan-Jun (old rate): $500,000 Jul-Dec (new rate): $550,000 Total CY earned: $1,050,000 On-leveling to 12/31/2024 rate: Jan-Jun: $500,000 × 1.10 = $550,000 Jul-Dec: $550,000 × 1.00 = $550,000 On-level premium: $1,100,000 On-level factor: $1,100,000 / $1,050,000 = 1.048 ``` ## Parallelogram Method For accident year premium with mid-year rate change: ``` AY 2024 with 7/1/2024 rate change of +10%: Premium at old rate: - 6 months of AY 2024 policies - 6 months of AY 2023 policies = 6/12 × 1.00 = 0.50 Premium at new rate: - 6 months of AY 2024 policies - 6 months of AY 2025 policies = 6/12 × 1.10 = 0.55 Weighted average rate level = 1.05 On-level factor to current = 1.10 / 1.05 = 1.048 ``` ## Related Concepts - [[Earned Premium]] - [[Rate Change]] - [[Loss Ratio Method]] ## References - Werner & Modlin, Chapter 7