Why Documenting Credibility Matters
A credibility indication is useful only when a reader can tell what it estimates and how the evidence was assembled. A number such as “$425 per unit” is incomplete on its own: the target might include or exclude catastrophe losses, use a particular exposure denominator, or apply only to a narrowly defined group. A well-documented assessment makes those choices visible so that the indication can be interpreted, reviewed, and updated.
This tutorial focuses on recording the scope and limitations of a credibility assessment. It does not prescribe a method for selecting a credibility weight. In the examples, the weight is supplied; the task is to document the calculation and judge whether the experience and complement represent the same target. This discipline is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
What a Complete Record Specifies
Start with the target measure, not with the observed data. The target should name the quantity, its unit, its scope, and any adjustments that define it. Examples include claim frequency per earned exposure-year, ultimate capped loss cost per vehicle-year, or a loss ratio on a stated premium basis. “Loss experience” is not precise enough to identify a target.
Next, describe the experience period and data basis. State the start and end dates or policy years, the valuation date, whether the data are paid or incurred, and whether they are developed to ultimate or otherwise adjusted. If amounts are trended, capped, excluded, or expressed at a current rate level, record that as part of the target and the data treatment. For frequency, state what counts as a claim and how exposures are measured.
Define the group in operational terms. A group definition may specify coverage, territory, class, limits, deductibles, policy form, or other inclusion rules. “Small accounts” is ambiguous unless the criteria for being a small account are stated. Also identify the complement: the broader or otherwise relevant estimate blended with the group’s own experience. Its population, period, measure, and adjustments matter just as much as those of the group data.
Finally, report the weight and its basis. In a linear credibility blend, let \(\hat\theta_E\) denote the experience estimate, \(\hat\theta_C\) the complement, and \(Z\) the credibility assigned to experience. Then
This formula applies when the stated assessment uses a linear blend of two estimates of the same target. It does not determine how \(Z\) should be chosen; that depends on the credibility approach being used. Record whether the weight was prescribed, calculated under a stated method, or selected as an assumption. Do not present an assumed weight as if it were a result established by the data.
Why the Blend Requires Alignment
The blend is a weighted average of two estimates only when both estimates refer to the same quantity and use compatible units. For example, dollars per earned vehicle-year can be blended with dollars per earned vehicle-year, but not directly with dollars per policy unless the exposure relationship has been accounted for. Likewise, a group estimate excluding catastrophe losses should not be blended without qualification with a complement that includes them.
The reason is direct: \(Z\) and \(1-Z\) are weights on alternative estimates of one target. If the estimates refer to different targets, the weighted result combines unlike quantities. A numerical answer may still be produced, but its interpretation is no longer the stated target.
Thus, the blend lies between the two input estimates when \(0\le Z\le1\), and its difference from the complement is \(Z\) times the difference between experience and complement. This identity is a useful check on arithmetic, not a test of whether the target, data, or assumptions are appropriate.
Worked Assessments
Worked Example: Recording a Frequency Indication
A hypothetical insurer evaluates ordinary liability claim frequency for a defined group of electric utility carts. The group has 46 eligible claims over 500 earned cart-years from July 1, 2022, through June 30, 2025. The claim count is complete and mature through June 30, 2026. A relevant portfolio complement is 0.082 claims per earned cart-year, and the supplied credibility weight is \(Z=0.40\). Calculate the indication and identify the information a reviewer needs.
Method. Calculate the group frequency using eligible claims divided by earned cart-years, then blend it with the complement. The target is ordinary liability claim frequency per earned cart-year. The problem states that claims are eligible and mature; no trend, catastrophe adjustment, interest rate, mortality assumption, or probability distribution is applied in this calculation.
Step 1: Calculate the group experience frequency.
Step 2: Apply the supplied weight. The complement receives weight \(1-0.40=0.60\).
Step 3: Check. The indication, 0.086, lies between 0.082 and 0.092. Its difference from the complement is \(0.086-0.082=0.004\), which equals \(0.40(0.092-0.082)=0.004\).
A useful record would state the target and unit, the three-year experience period, the valuation date and maturity basis, the group definition, the complement’s scope and period, and that the 0.40 weight was supplied. A limitation is that this calculation does not establish whether the cart-year exposure is an adequate measure of risk or whether the defined group will remain comparable in future periods.
Common mistake avoided: Reporting “0.086 claims” without the denominator or time basis. The result is a frequency per earned cart-year, not a claim count or an annual probability for an individual cart.
Worked Example: Documenting a Capped Loss-Cost Target
A hypothetical insurer estimates ultimate loss cost for a group of inland-waterway service vessels. The target is incurred loss plus allocated loss adjustment expense (ALAE), capped at $25,000 per claim, per earned vessel-year, at the current price level. After development and trend adjustments consistent with that target, the group total is $1,080,000 over 1,200 earned vessel-years. A compatible portfolio complement is $840 per earned vessel-year, and \(Z=0.25\). Calculate the indication and state what the documentation must make explicit.
Method and assumptions. Use the adjusted capped loss amount divided by earned vessel-years, then apply the supplied linear weight. The example assumes the stated development and trend adjustments are appropriate, the same cap and ALAE treatment are used for the complement, and the complement is expressed at the same price level. No interest rate, mortality assumption, or probability distribution is used.
Step 1: Calculate the group loss cost.
Step 2: Calculate the complement weight. It is \(1-0.25=0.75\).
Step 3: Check. The result is between $840 and $900. Its difference from the complement is $15, equal to \(0.25(\$900-\$840)=\$15\).
The record should preserve the cap, the inclusion of ALAE, the ultimate and trend basis, the exposure denominator, and the current price level. It should also define which vessels belong to the group and describe the complement’s population. Without these details, “$855 per vessel-year” could be mistaken for an uncapped cost, a paid cost, or a cost on a different exposure basis.
Common mistake avoided: Dividing by the number of claims rather than earned vessel-years. That would produce a severity-like measure, not the specified loss cost per exposure unit, and could not be blended directly with the stated complement.
Worked Example: Aligning the Catastrophe Treatment
A hypothetical regional property group has $600,000 of losses over 1,200 earned location-years. Of those losses, $120,000 are identified as catastrophe losses, and the target excludes catastrophe losses. The complement is $450 per earned location-year, and \(Z=0.50\). Calculate the aligned indication, then show the result of mistakenly retaining all losses.
Method and assumptions. The target is non-catastrophe loss cost per earned location-year. Assume the identified catastrophe amount is removed from the group losses, the exposure denominator remains 1,200 earned location-years, and the complement also excludes catastrophe losses. The example does not apply a probability distribution, interest rate, or mortality assumption.
Step 1: Align the loss numerator with the target.
Step 2: Calculate the aligned experience loss cost.
Step 3: Blend with the complement. Since \(Z=0.50\), each estimate receives half the weight.
Step 4: Calculate the common mistaken result. If all losses are retained, the experience figure is \(\$600{,}000/1{,}200=\$500\) per unit. Blending that mismatched value gives
Check and limitation. The aligned $425 indication is between $400 and $450; its $25 difference from the complement equals \(0.50(\$400-\$450)=-\$25\). The incorrect $475 is also an arithmetic blend, but it estimates a different scope because the group experience retains catastrophe losses while the target and complement exclude them. The record should document the catastrophe identification and exclusion rule; it should not imply that the chosen treatment resolves every question about catastrophe risk.
Common mistake avoided: Removing the catastrophe amount from the target description but not from the numerator. Align the losses before dividing and blending.
Assumptions, Limitations, and Review
An assessment should distinguish a calculation from the assumptions that make it interpretable. A compact report can use the following sequence:
State the measure, unit, coverage, loss scope, and adjustments, including any cap or exclusion.
Give the dates, valuation date, maturity or development basis, exposure denominator, and data selection rules.
State inclusion criteria and describe the complement’s population, period, measure, and adjustments.
Show the experience estimate, complement, \(Z\), source or method for the weight, and resulting indication.
Identify material dependencies, known data constraints, and reasons the result may not transfer to another period or group.
Limitations should be specific rather than boilerplate. They may concern immature data, sparse observations, changes in coverage or underwriting, exposure measures that imperfectly reflect risk, uncertain adjustments, or a complement that is only approximately comparable. Earlier material on completeness and maturity of experience and data quality checks is useful context: a credibility weight does not correct errors or make incomplete data complete. Similarly, a credible estimate is not by itself evidence that a rate is adequate.
Avoid overstating what a blend proves. The result is conditional on the target definition, data treatment, complement, and weight. It does not establish that the group is homogeneous, that past conditions will continue, or that omitted effects are immaterial. A concise limitation statement identifies those dependencies so the reader can decide whether further analysis is needed.
Check Your Understanding
For each problem, calculate the requested indication and keep the target and exposure basis aligned.
- A hypothetical class has 31 eligible claims over 400 earned exposure-years. Its complement is 0.070 claims per earned exposure-year, and the supplied weight is \(Z=0.20\). What frequency should be reported, including its unit? (Answer: 0.0715 claims per earned exposure-year.)
- A hypothetical coverage group has adjusted target losses of $950,000 over 1,000 earned units. A compatible complement is $880 per earned unit, and \(Z=0.40\). Calculate the indicated loss cost. (Answer: $908 per earned unit.)
- A hypothetical group records $540,000 of losses over 900 earned units, including $90,000 of catastrophe losses. The target and complement both exclude catastrophe losses; the complement is $520 per earned unit, and \(Z=0.30\). Calculate the aligned indication and the result if all losses are mistakenly retained. (Answer: Aligned: $514 per earned unit; all-loss calculation: $544 per earned unit.)
- A hypothetical target is eligible claim frequency per earned contract-year. The experience has 64 reported claims over 800 earned contract-years, but 8 claims are glass-only claims excluded from the target. The complement is 0.080 claims per earned contract-year, and \(Z=0.40\). Calculate the aligned indication. (Answer: 0.076 claims per earned contract-year.)
- A hypothetical group’s capped loss cost is $720 per earned unit, based on the target cap and expense treatment. The complement is $680 per earned unit but includes losses above that cap; \(Z=0.25\). Can the two figures be blended as stated? If the complement is recalculated on the target basis and becomes $700, what is the resulting indication? (Answer: No; the stated figures are not aligned. After recalibration: $705 per earned unit.)