[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Loss Ratio Method** ## Definition ==Loss Ratio Method== The loss ratio method is a ratemaking approach that calculates the indicated rate change by comparing the actual loss ratio to the expected or target loss ratio. ## Formula ### Basic Loss Ratio ``` Loss Ratio = (Losses + LAE) / Earned Premium ``` ### Indicated Rate Change ``` Rate Change = (Actual Loss Ratio / Expected Loss Ratio) - 1 Or equivalently: Rate Change = (Projected Loss Ratio / Target Loss Ratio) - 1 ``` ## Components ### Actual Loss Ratio ``` Actual LR = (Ultimate Losses + Ultimate LAE) / On-Level Earned Premium Steps: 1. Develop losses to ultimate 2. Trend losses to rating period 3. On-level earned premium 4. Calculate ratio ``` ### Expected/Target Loss Ratio ``` Expected LR = 1 - Expense Ratio - Profit Provision Example: Total expenses: 30% Profit & contingency: 5% Expected LR = 1 - 0.30 - 0.05 = 0.65 or 65% ``` ## Step-by-Step Process ### Step 1: Select Experience Period - Multiple accident years for credibility - Exclude unusual years if justified - Typically 3-5 years ### Step 2: Develop Losses to Ultimate ``` Ultimate Losses = Reported Losses × LDF Example: AY 2023 @ 12 months: $500,000 LDF 12-ultimate: 2.500 Ultimate: $500,000 × 2.500 = $1,250,000 ``` ### Step 3: Trend Losses to Rating Period ``` Trended Losses = Ultimate × (1 + trend)^years Example: Ultimate: $1,250,000 Annual trend: 5% Years from midpoint: 2.0 Trended: $1,250,000 × 1.05^2.0 = $1,378,125 ``` ### Step 4: On-Level Premium ``` On-Level Premium = Earned Premium × Rate Change Factors Accounts for: - Historical rate changes - Coverage changes - Exposure changes ``` ### Step 5: Calculate Projected Loss Ratio ``` Projected LR = Trended Ultimate Losses / On-Level Premium ``` ### Step 6: Compare to Target ``` Indicated Change = (Projected LR / Target LR) - 1 ``` ## Complete Example ``` Experience Period: AY 2021-2023 Data: 2021 2022 2023 Total Earned Premium: $10M $11M $12M $33M Reported Losses: $5.5M $5.8M $4.2M $15.5M Age (months): 36 24 12 Development to Ultimate: 2021: $5.5M × 1.100 = $6.05M 2022: $5.8M × 1.250 = $7.25M 2023: $4.2M × 2.500 = $10.50M Total Ultimate: $23.80M Trending (5% annual from midpoint to rating period): 2021 (2.5 yrs): $6.05M × 1.05^2.5 = $6.84M 2022 (1.5 yrs): $7.25M × 1.05^1.5 = $7.81M 2023 (0.5 yrs): $10.50M × 1.05^0.5 = $10.76M Total Projected: $25.41M On-Leveling Premium: Rate changes: +8% in 2022, +5% in 2023 On-level factors calculated On-level Premium: $35.5M Projected Loss Ratio: = $25.41M / $35.5M = 71.6% Target Loss Ratio: 65.0% Indicated Rate Change: = (71.6% / 65.0%) - 1 = 10.2% ``` ## Advantages 1. **Simple** - Straightforward calculation 2. **Common** - Industry standard approach 3. **Stable** - No exposure trending needed 4. **Direct** - Premium-based, matches financial perspective ## Disadvantages 1. **Circular** - Rates affect premium which affects loss ratio 2. **Limited detail** - Doesn't separate frequency/severity 3. **Exposure blind** - Doesn't directly consider exposure changes 4. **Rate sensitivity** - Results depend on historical rate adequacy ## Adjustments and Refinements ### Premium Adjustments - **On-leveling** for rate changes - **Premium audit** adjustments - **Exposure changes** may require adjustment - **Coverage changes** must be reflected ### Loss Adjustments - **Development** to ultimate - **Trending** to rating period - **Large loss** treatment - **CAT losses** may be excluded/limited ### Credibility ``` Credibility-weighted change: = Z × Indicated + (1-Z) × Complement Example: Indicated: +10.2% Credibility: 75% Complement: +3.0% (industry) Final: 0.75(10.2%) + 0.25(3.0%) = 8.4% ``` ## When to Use **Preferred for:** - Mature products with rate stability - Lines where premium is good proxy for exposure - Standard ratemaking analyses - Regulatory filings **Less suitable for:** - Rapidly changing exposures - New products - Significant mix changes - When exposure data preferred ## Comparison to Pure Premium | Aspect | Loss Ratio | Pure Premium | |--------|------------|--------------| | Denominator | Premium | Exposure | | Trending | Losses only | Losses & exposures | | Simplicity | Simpler | More complex | | Exposure changes | Indirect | Direct | | Common use | More common | Less common | ## Related Concepts - [[Pure Premium Method]] - [[Trend]] - [[On-Level Premium]] - [[Loss Development Factor (LDF)]] - [[Credibility]] - [[Target Loss Ratio]] ## References - Werner & Modlin, Chapter 4 - CAS Ratemaking Principles