[[Actuarial Notes Wiki|Wiki]] / [[Exam 5 (CAS)]] / **Cape Cod Method** ## Definition ==Cape Cod Method== The Cape Cod method (also called Stanard-Bühlmann) is a reserving technique that estimates expected loss ratios from the data itself, using reported losses and exposure to iteratively determine ultimate losses. ## Formula ``` ELR = Σ(Reported Losses) / Σ(Exposures × % Reported) Ultimate_i = ELR × Exposure_i IBNR_i = Ultimate_i - Reported_i Where: % Reported = 1 / CDF ``` ## Comparison to BF Method ### Bornhuetter-Ferguson - Requires **a priori** expected loss ratio - External estimate needed - Fixed ELR for all years ### Cape Cod - **Derives** expected loss ratio from data - Internal estimate from reported losses - Single ELR estimated from all years combined ## Methodology ### Step 1: Calculate % Reported ``` % Reported = 1 / CDF_to_ultimate Example: 12-month CDF: 1.896 % Reported at 12 months: 1/1.896 = 52.7% ``` ### Step 2: Calculate Expected Loss Ratio ``` ELR = Total Reported / Σ(Exposures × % Reported) ``` ### Step 3: Calculate Ultimate Losses ``` Ultimate = ELR × Exposure (for each year) ``` ### Step 4: Calculate IBNR ``` IBNR = Ultimate - Reported ``` ## Complete Example ``` Given Data: AY Exposure Reported Age CDF % Rptd 2020 $5M $2,800 60mo 1.010 99.0% 2021 $5.5M $2,900 48mo 1.033 96.8% 2022 $6M $2,850 36mo 1.084 92.2% 2023 $6.5M $2,600 24mo 1.264 79.1% 2024 $7M $1,750 12mo 1.896 52.7% Step 1: Calculate weighted exposures AY 2020: $5M × 0.990 = $4.95M AY 2021: $5.5M × 0.968 = $5.32M AY 2022: $6M × 0.922 = $5.53M AY 2023: $6.5M × 0.791 = $5.14M AY 2024: $7M × 0.527 = $3.69M Total: $24.63M Step 2: Calculate ELR Total Reported: $12,900 ELR = $12,900 / $24.63M = 52.38% Step 3: Calculate ultimates AY 2020: $5M × 0.5238 = $2,619 (vs reported $2,800) AY 2021: $5.5M × 0.5238 = $2,881 AY 2022: $6M × 0.5238 = $3,143 AY 2023: $6.5M × 0.5238 = $3,405 AY 2024: $7M × 0.5238 = $3,667 Total Ultimate: $15,714 Step 4: Calculate IBNR Total IBNR = $15,714 - $12,900 = $2,814 ``` ## When to Use **Preferred when:** - No reliable a priori expected loss ratio - Want to derive ELR from data - Exposure levels vary significantly - Mix of business changing **Less appropriate when:** - Strong external information available - Known changes not reflected in data - Very immature years dominate ## Related Concepts - [[Bornhuetter-Ferguson Method]] - [[Expected Loss Method]] - [[Development Factor]] ## References - Friedland, Chapter 5