Analyzing Loss Reserves

Workflow

1. Validate triangle integrity

   • Confirm triangles are on a consistent basis (paid vs. incurred, cumulative vs. incremental)
   • Check that the latest diagonal ties to the balance sheet carried amounts
   • Identify any triangle adjustments (large-loss caps, commutation removals, currency conversions) and note their impact

2. Calculate age-to-age development factors

   • Compute link ratios for each development period across all accident years
   • Examine simple average, volume-weighted average, and medial (excluding high/low) selections
   • Identify accident years with unusually high or low factors — flag potential large-loss distortion, reserve strengthening, or claim settlement pattern changes

3. Apply standard actuarial projection methods

   • Chain Ladder (Development): Apply selected LDFs to the latest cumulative values; most reliable for mature, stable lines
   • Bornhuetter-Ferguson (BF): Blend development projection with an a priori expected loss ratio; preferred for immature accident years or volatile lines
   • Cape Cod (Stanard-Buhlmann): Use exposure-weighted expected losses; useful when loss ratios are expected to be stable across years
   • Frequency-Severity: Where claim count and average severity data are available, project separately; valuable for lines with known count trends
   • Select tail factors for development beyond the triangle's observed maturity [VERIFY: tail factor assumptions are highly judgment-dependent — confirm basis and reasonableness]

4. Develop ultimate loss estimates and ranges

   • Produce point estimates from each method by accident year
   • Weight or select among methods based on data credibility, line characteristics, and maturity
   • Construct a reasonable range (e.g., low/central/high) reflecting parameter uncertainty
   • Compare to the company's carried reserves — quantify redundancy or deficiency by accident year and in total

5. Analyze reserve development trends

   • Track prior-year development (favorable or adverse) over multiple calendar periods
   • Identify whether development is concentrated in specific accident years or lines
   • Assess whether development patterns indicate systematic under- or over-reserving
   • Consider external drivers: legal environment changes, inflation, claim handling practice shifts

6. Benchmark and stress test

   • Compare company LDFs and ultimate loss ratios to industry benchmarks for the same line and maturity
   • Test sensitivity to alternative tail factors, LDF selections, and expected loss ratio assumptions
   • Quantify the reserve impact of plausible adverse scenarios (e.g., social inflation, latent exposure emergence)

Output

Structure the analysis report as follows:

• Executive Summary: Overall reserve adequacy conclusion (adequate / likely deficient / likely redundant), magnitude of estimated surplus or shortfall, key risk factors
• Data and Scope: Lines of business, accident years, triangle basis, and any data limitations
• Development Factor Analysis: Table of age-to-age factors with selected factors and basis for selection; highlight anomalies
• Ultimate Loss Projections: Table by accident year showing results from each method, selected ultimates, and comparison to carried reserves
• Reserve Adequacy Assessment: Quantified redundancy/deficiency by year and total; confidence range; discussion of key judgment areas
• Development History: Summary of favorable/adverse development trends and their implications
• Sensitivity Analysis: Impact of alternative assumptions on the adequacy conclusion
• Limitations and Caveats: Data gaps, areas of high uncertainty, reliance on third-party information

Quality Checks

• Confirm all triangle arithmetic is internally consistent (incremental values sum to cumulative; latest diagonal matches reported data)
• Verify that selected LDFs fall within a reasonable range relative to historical averages and industry benchmarks — outlier selections require explicit justification
• Ensure BF and Cape Cod a priori loss ratios are sourced and documented, not assumed without basis
• Check that tail factors are reasonable for the line's claim closure characteristics [VERIFY: long-tail lines like workers' comp or environmental liability may need tails extending 20+ years]
• Confirm the analysis addresses both paid and incurred bases — significant divergence between paid and incurred projections should be explained
• Validate that large losses or one-time events are identified and their treatment (capped, excluded, separately developed) is clearly stated
• Ensure the adequacy conclusion accounts for discount effects if reserves are on a present-value basis [VERIFY: confirm whether reserves are discounted and the applicable discount rate/standard]
• Flag any areas where actuarial judgment materially drives the result and a qualified actuary should review