Why External Benchmarks Can Inform a Tail Selection
At mature development ages, an insurer’s own observed link ratios may be sparse, unstable, or absent. External benchmarks can provide evidence about the remaining development, but a published or supplied factor is not automatically suitable for a different portfolio. Its usefulness depends on whether the benchmark describes losses that develop in a sufficiently similar way.
This tutorial focuses on evaluating and selecting an external tail benchmark. It does not replace the earlier material on extrapolating unobserved link ratios or fitting exponential and power curves. An external benchmark is another source of evidence; the actuary still needs to establish what it measures and why it applies. This judgment is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
A tail factor must be tied to its starting age and loss basis. A factor from 36 months to ultimate cannot be applied directly to 24-month losses unless the development from 24 to 36 months is also included. Likewise, a paid-loss benchmark is not automatically a suitable factor for incurred losses. Before selecting a number, identify the benchmark’s coverage, loss measure, development age, maturity, and operational setting.
What Makes a Benchmark Relevant?
A useful benchmark is not necessarily the one with the largest data set or the most precise-looking decimal. It is the benchmark whose development behavior is most transferable to the portfolio being evaluated. Review the dimensions below and document material differences.
| Dimension | Questions to ask | Why it matters |
|---|---|---|
| Coverage and policy terms | Are limits, deductibles, covered events, and policy forms similar? | Coverage design can change claim size, settlement patterns, and the amount of late development. |
| Claim and loss basis | Does the benchmark use paid, incurred, or another defined loss measure? Are loss adjustment expenses included? | Different measures can have different emergence and settlement patterns. |
| Development age and maturity | Does the benchmark begin at the same age? Are its ultimate estimates based on sufficiently mature experience? | A factor from a different starting age does not represent the same remaining development. Immature benchmark ultimates may be unreliable. |
| Claims and exposure mix | Are claim types, severity, limits, jurisdictions, and exposure characteristics comparable? | A different mix may create a different proportion of claims that emerge or change at late ages. |
| Operations and external environment | Have claim handling, settlement practices, case reserving, law, or reporting systems changed? | Operational or environmental differences can alter observed development even when coverage appears similar. |
The comparison should be specific. “Similar line of business” is not a complete rationale if the benchmark has materially different policy limits, claim-handling practices, or development age. Conversely, a benchmark from a different organization may still be informative when the underlying coverage, claims, and operational conditions are well matched.
Deriving and Applying a Benchmark Tail
The ratio \(U/B_a\) follows directly from the meaning of a multiplicative development factor. If the benchmark’s losses at age \(a\) are multiplied by \(T_a\) to reach ultimate, then \(B_aT_a=U\). Solving for the factor gives \(T_a=U/B_a\). If the current portfolio is expected to have the same proportional remaining development, multiplying its current losses \(C_a\) by this factor estimates its ultimate.
This transfer assumes that the benchmark’s proportional development from age \(a\) to ultimate is relevant to the current portfolio. It does not require the benchmark and current portfolio to have the same dollar volume: the ratio removes the benchmark’s scale. But scale cancellation does not remove differences in coverage, mix, maturity, or operations. If the transfer assumption is weak, the benchmark should be qualified, used only as a reasonableness check, or not selected.
State the current portfolio’s loss basis and exact development age for which a tail factor is needed.
Confirm how its factor was calculated, including its starting age, ultimate definition, coverage, and whether it is paid or incurred.
Compare coverage, claim mix, maturity, and operating conditions. Identify differences that could raise or lower remaining development.
Choose a benchmark only when its relevance is supportable. Record the reason for choosing it, limitations, and any factor-age conversion needed.
Multiply losses at the matching age by the selected factor. Confirm that the result is at least the current losses when the selected tail factor is at least 1.
Worked Benchmark Selections
Worked Example: Selecting a Closely Matched Benchmark
A hypothetical insurer needs a tail factor from 48 months to ultimate for a specialty equipment portfolio. Its current incurred losses at 48 months are $12,400,000. Two hypothetical external studies report: Study A, a 48-to-ultimate factor of 1.031, based on similar equipment coverage and limits, mature claims, and comparable claim handling; Study B, a factor of 1.018, based on a broader property portfolio with lower limits and different settlement practices. Select a benchmark and calculate estimated ultimate losses. All amounts are nominal and undiscounted; no interest rate, mortality assumption, or probability distribution is used.
Method. Compare the benchmark characteristics first, then apply the selected factor at the matching development age.
Step 1: Confirm age and basis. Both factors run from 48 months to ultimate, and both are described as incurred-loss factors. Their starting ages and broad loss bases are therefore compatible with the target.
Step 2: Compare transferability. Study A matches the equipment coverage, limits, claim maturity, and claim-handling context more closely. Study B’s broader property mix and lower limits make it less comparable. Select Study A’s 1.031 factor; do not select the numerically smaller factor merely because it appears more conservative.
Step 3: Apply the factor.
The implied tail development is \(\$12{,}784{,}400-\$12{,}400{,}000=\$384{,}400\). The factor adds 3.1% of the current 48-month incurred amount.
Check. The selected factor exceeds 1, so ultimate losses exceed current losses. The calculated increase is 3.1% of $12,400,000, or $384,400, as shown. The common mistake avoided is choosing a benchmark by its numerical value without checking whether its underlying business resembles the target.
Worked Example: Converting a Benchmark to the Required Age
A hypothetical benchmark reports a 36-to-ultimate factor of 1.027. The target portfolio requires a 24-to-ultimate tail. The benchmark’s 24-to-36 development factor is 1.014, and the current portfolio has $8,000,000 of losses at 24 months. Assume the benchmark is otherwise comparable in coverage, loss basis, maturity, and claims operations. Determine the benchmark factor from 24 months to ultimate and apply it. All amounts are nominal and undiscounted; no interest rate, mortality assumption, or probability distribution is used.
Method. Chain the 24-to-36 factor with the 36-to-ultimate factor. Both factors must apply to the same benchmark and compatible loss basis.
Step 1: Align the starting age. A 24-month loss amount develops first to 36 months and then from 36 months to ultimate. Therefore, the factors multiply:
Step 2: Apply the age-aligned factor.
The estimated development after 24 months is \(\$8{,}331{,}024-\$8{,}000{,}000=\$331{,}024\).
Check. The chained factor is greater than either component, as both factors exceed 1. The result includes both the 24-to-36 development and the 36-to-ultimate tail. The common mistake avoided is applying 1.027 directly to 24-month losses, which would omit the 24-to-36 interval and produce $8,216,000 instead of the age-aligned estimate.
Worked Example: Rejecting a Stale Operational Benchmark
A hypothetical liability portfolio has $20,000,000 of incurred losses at 60 months. An older external study reports a 60-to-ultimate factor of 1.028, but it reflects a claims system that closed many files earlier and a case-reserving practice that differs from the current insurer’s. A newer comparable study, using the same coverage and 60-month starting age and reflecting current claim-handling practices, reports 1.041. The newer study’s claims are sufficiently mature for its ultimate estimate. Select a factor and calculate ultimate losses. All amounts are nominal and undiscounted; no interest rate, mortality assumption, or probability distribution is used.
Method. Give greater weight to operational comparability when the difference is directly relevant to development. Select the newer benchmark because it reflects the current claims process and is otherwise comparable. The older factor is not a sound default simply because it is available.
Step 1: Apply the selected factor.
The selected tail adds \(\$20{,}820{,}000-\$20{,}000{,}000=\$820{,}000\).
Step 2: Quantify the stale-factor impact. Applying 1.028 instead would give:
That result is $260,000 below the selected estimate, because \(\$20{,}000{,}000\times(1.041-1.028)=\$260{,}000\).
Check. The selected ultimate exceeds the current 60-month incurred amount by $820,000, equal to 4.1% of that amount. The common mistake avoided is treating an old operational regime as comparable solely because it has the same nominal development age.
Common Traps and Documentation
External benchmarks can give a selection useful context, but an unsupported adjustment does not make a mismatched benchmark comparable. Do not add or subtract an arbitrary percentage because a difference “feels material.” First determine whether the difference plausibly affects late development, then seek evidence for its direction and magnitude. If that evidence is not available, state the limitation rather than implying a precise adjustment.
- Wrong starting age: Applying a 36-to-ultimate factor to losses at 24 months omits development from 24 to 36 months. Use an age-aligned factor or include the missing interval.
- Different loss basis: A paid benchmark and an incurred target do not become comparable just because both factors are labelled “tail.” Confirm the basis before use.
- Immature benchmark ultimates: A ratio can be calculated from immature data, but that does not establish that its ultimate denominator is reliable.
- False precision: A factor reported to three decimal places does not prove the benchmark is more relevant than a less precise but better-matched source.
- Undocumented differences: Recording only the selected number makes later review difficult. State the benchmark population, age, loss basis, key similarities, and limitations.
Check Your Understanding
For each problem, use the stated benchmark assumptions and show the age alignment before applying a factor.
- A hypothetical benchmark has losses of $50,000,000 at 48 months and estimated ultimate losses of $51,250,000. The benchmark matches the target portfolio’s coverage, loss basis, maturity, and operations. What is the 48-to-ultimate factor? (Answer: 1.025)
- A comparable benchmark has a 60-to-ultimate factor of 1.018. Current losses at 60 months are $9,500,000. Calculate estimated ultimate losses and tail development. (Answer: Ultimate $9,671,000; development $171,000)
- A benchmark has a 24-to-36 factor of 1.012 and a 36-to-ultimate factor of 1.015. The current portfolio has $6,000,000 at 24 months, and the benchmark is otherwise comparable. Calculate the age-aligned factor and estimated ultimate losses. (Answer: Factor 1.02718; ultimate $6,163,080)
- A study reports a 48-to-ultimate factor of 1.032 for coverage with substantially higher limits than the target. A second study reports 1.024 for matching coverage and limits, mature claims, and comparable operations. The target has $15,000,000 of losses at 48 months. Which benchmark is better supported, and what ultimate does it imply? (Answer: Select 1.024; ultimate $15,360,000)
- A current portfolio has $18,000,000 of incurred losses at 60 months. A benchmark factor of 1.030 is based on a different claim-handling process, while a factor of 1.037 is based on comparable coverage, maturity, and current operating practices. Select the better-supported factor and calculate the indicated ultimate and development. (Answer: Select 1.037; ultimate $18,666,000; development $666,000)