Why Period Selection Matters
A rate filing can use accurate records and still present a misleading picture if the records cover the wrong time window or combine unlike periods. A policy cohort may not have completed its term, claims may not have had enough time to be reported, and the business written in one year may differ from the business written in another. Selecting an experience period is therefore a substantive actuarial judgment, not merely a choice of convenient calendar years.
The selected dates must also be interpreted in relation to the proposed effective date. The experience window describes the source data; it does not, by itself, make those data representative of the period when new rates will apply. A filing should identify the dates precisely, explain the rationale for choosing them, and disclose material limitations. The principles below are aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
Keep the Period Definitions Separate
These periods are related, but they are not interchangeable. A policy written during a calendar year may remain in force into the next year. Its written premium is associated with the transaction or policy issuance, while its earned premium is allocated over the period of coverage. Exposure is likewise associated with the time coverage is provided, according to the exposure measure used. A loss period might be based on when an accident occurred, when a claim was reported, or the policies to which claims are assigned. A filing must state which basis it uses.
For example, “2024 data” is not a sufficiently precise description. It could mean policies effective in 2024, premium earned during calendar year 2024, accidents occurring during 2024, claims reported during 2024, or information valued as of a date in 2024. Those choices can produce different records and different degrees of maturity. State the period type, start and end dates, and any assignment rule.
Maturity is also specific to the type of data. A premium record may be nearly complete while a loss record for the same period is still receiving reports. A policy-effective-date cohort can be less mature than an accident-year cohort, depending on the coverage term, reporting practices, and valuation date. A practical maturity test might require a specified reporting window after policy expiration or might compare recorded claim counts with an independently selected completeness measure. The test should be described as a selection criterion; it should not be confused with a guarantee that no later information will emerge.
Relate the Experience Window to the Filing Date
The proposed effective date helps determine how current the data need to be, but it does not dictate a single correct experience period. A filing preparation process needs time to assemble and validate data, and a deliberate cutoff helps ensure that all included records were available on a consistent basis. If the newest period is incomplete, including it without qualification can give recent observations less time to develop or report than earlier observations. Conversely, excluding too much recent experience can leave the analysis less current.
A filing should therefore explain both what was selected and what was excluded. A clear rationale might say that the selected policy cohorts have completed their terms and met a stated reporting window by the valuation date, while the newest cohort was omitted because it had not met that window. If a period is retained despite a limitation, describe the limitation and how it affects interpretation. Do not imply that one maturity rule is universally required; the rule depends on the coverage, data source, and filing purpose.
Worked Example: Selecting Mature Policy Cohorts
A hypothetical insurer proposes new rates effective July 1, 2026. Its filing data cutoff is December 31, 2025. Policies are annual, assigned to policy cohorts by effective year, and claims are assigned to the policies covering the event. For this filing, the actuary requires each cohort to have completed its policy term and then had a 12-month claim-reporting window by the cutoff. Which is the newest eligible cohort, and what three-year window could be selected if older cohorts are considered comparable?
Method. Test each cohort against both conditions: the policy term must have ended, and the full 12-month reporting window must have elapsed by December 31, 2025.
The 2023 cohort’s annual policies end no later than December 31, 2024. Its 12-month reporting window ends by December 31, 2025, so it satisfies the stated test. The 2024 cohort’s annual policies may not end until December 31, 2025. At the cutoff, that cohort has no post-expiration reporting window, so it fails the test.
The newest eligible cohort is therefore 2023. If the 2021, 2022, and 2023 cohorts are also judged comparable in coverage and business mix, a three-cohort window is 2021 through 2023. This selection uses the policy effective year as the cohort basis; it does not mean that all premium was earned or all accidents occurred in those same calendar years.
Check. The 2023 cohort has completed the policy term and the required reporting window by the cutoff; the 2024 cohort has not. The common mistake is to include 2024 merely because its effective year has ended. The correction is to test term completion and reporting time separately.
Allocating Earned Premium and Exposure by Period
When a policy crosses a calendar boundary, its premium and exposure may need to be divided across calendar periods. The allocation depends on the stated earning convention. Under a simple straight-line daily assumption, a constant portion of the policy’s premium and exposure is earned for each day of coverage. This is an assumption for the calculation, not a universal rule for every product or exposure basis.
The justification is direct: if a total amount \(Q\) is earned uniformly over \(T\) covered days, the daily amount is \(Q/T\). An interval containing \(t\) covered days earns \(t(Q/T)=Q(t/T)\). The formula applies only when earning is uniform over the term and the period allocation is based on covered days. If premium is earned under another rule, or exposure varies seasonally or by another measure, use and document that basis instead.
Worked Example: Splitting a Policy Across Calendar Years
A hypothetical one-policy contract covers October 1, 2023 through September 30, 2024, inclusive. Its total term premium is $1,830, and its total exposure is 1.000 policy-year. Assume both premium and exposure are earned uniformly by day over the actual policy term. Allocate them to calendar years 2023 and 2024.
Method. Count covered days in each calendar year, then apply the daily allocation formula to premium and exposure. The term contains 92 covered days in 2023 (October 1 through December 31) and 274 covered days in 2024 (January 1 through September 30). Thus the actual term is \(92+274=366\) days.
The 2023 fraction is \(92/366=0.251366\ldots\), and the 2024 fraction is \(274/366=0.748634\ldots\). These fractions sum to \(366/366=1\).
For 2023, earned premium is \(1{,}830(92/366)=\$460.00\), because \(1{,}830/366=\$5\) per day and \(92(\$5)=\$460\). Earned exposure is \(1.000(92/366)=0.251366\ldots\) policy-year.
For 2024, earned premium is \(1{,}830(274/366)=\$1{,}370.00\), because \(274(\$5)=\$1{,}370\). Earned exposure is \(1.000(274/366)=0.748634\ldots\) policy-year.
Check. The premiums sum to \(\$460+\$1{,}370=\$1{,}830\), and the exposures sum to \(0.251366\ldots+0.748634\ldots=1.000\). The common mistake is to use 365 as the denominator because the policy is “one year.” This policy term includes February 29, so the stated daily earning assumption uses 366 covered days.
Check Comparability Before Combining Periods
Even mature data can be difficult to compare if the composition of the business changes. A change in geography, coverage, distribution channel, or other relevant grouping can shift the aggregate results even when the results within each group do not change. This is a period-selection concern: the actuary should decide whether the combined window represents a reasonably comparable book, or whether the differences need to be described or examined by group.
A useful diagnostic is to compare the exposure shares by group across periods. If the shares change materially, compare like with like before treating an aggregate change as evidence of a change in underlying experience. A standardized weighted average can illustrate the effect of mix, provided the groups and exposure units are comparable and the weighting rule is stated. This diagnostic does not replace the separate work required to prepare a rate indication.
Worked Example: Detecting a Business-Mix Change
A hypothetical book has two risk groups, Low and High. Exposure units are comparable across years, and both periods are equally mature. In Period A, Low has 800 units and $400,000 of losses; High has 200 units and $200,000 of losses. In Period B, Low has 400 units and $200,000 of losses; High has 600 units and $600,000 of losses. Determine whether the aggregate average loss per exposure changed within groups, and calculate each period’s aggregate average. Then compare the groups using common weights of 70% Low and 30% High.
Method. Calculate each group’s losses per exposure, the actual exposure mix, the aggregate result, and finally the common-weight comparison.
In Period A, Low’s result is \(\$400{,}000/800=\$500\) per unit, and High’s result is \(\$200{,}000/200=\$1{,}000\) per unit. Total exposure is \(800+200=1{,}000\), and total losses are \(\$400{,}000+\$200{,}000=\$600{,}000\). The aggregate average is \(\$600{,}000/1{,}000=\$600\) per unit. The mix is 80% Low and 20% High.
In Period B, Low’s result is \(\$200{,}000/400=\$500\) per unit, and High’s result is \(\$600{,}000/600=\$1{,}000\) per unit. Total exposure is \(400+600=1{,}000\), and total losses are \(\$200{,}000+\$600{,}000=\$800{,}000\). The aggregate average is \(\$800{,}000/1{,}000=\$800\) per unit. The mix is 40% Low and 60% High.
The within-group results are unchanged. Using the common 70%/30% weights gives \(0.70(\$500)+0.30(\$1{,}000)=\$650\) per unit in either period. The aggregate averages differ because the actual exposure mix changed: Period A is weighted 80%/20%, while Period B is weighted 40%/60%.
Check. Each period has 1,000 units, and the group losses add to the stated totals. The common mistake is to interpret the change from $600 to $800 as a within-group deterioration. The group calculations show that, under the assumptions given, the aggregate difference is explained by mix.
Document the Selection and Its Limitations
A filing record should make it possible for a reviewer to reproduce the experience window and understand why it was selected. The documentation should not rely on a label such as “latest three years” without specifying what years and what data basis that label means.
Identify the proposed effective date and the data cutoff used to assemble the filing.
Give the start and end dates for policy, premium, exposure, and loss data, and state how losses are assigned to policies or periods.
Describe the valuation date, reporting or completeness criterion, and periods excluded because they did not meet it.
Review material changes in coverage, group composition, exposure definitions, or data practices that could affect comparisons.
Explain material gaps, unusual cutoff constraints, or assumptions used to allocate records across periods.
Several exam and practice traps follow from these distinctions. “Written in the year” is not the same as “earned in the year.” A calendar-year label does not identify whether losses are selected by occurrence, report, or policy assignment. A mature premium record does not prove that the corresponding losses are equally mature. Finally, a recent period is not automatically preferable: recency must be balanced against completeness and comparability.
Check Your Understanding
For each problem, identify the relevant period or calculation and check your answer against the result shown.
- A filing has a November 30, 2025 cutoff and requires 12 months of reporting time after a policy cohort’s latest possible expiration. Annual policies effective during 2023 can expire as late as December 31, 2024; annual policies effective during 2022 can expire as late as December 31, 2023. Which is the newest cohort that meets the requirement? (Answer: 2022; the 2023 cohort has only 11 months after its latest expiration by the cutoff.)
- A hypothetical six-month policy has $900 of premium and 1.000 policy-year of exposure. It covers January 1 through June 30, with uniform daily earning, and the experience period includes only January through March. How much premium and exposure are earned in that period? (Answer: 90 of 181 days; premium \(900(90/181)=\$447.51\) to the cent, and exposure \(90/181=0.4972\) policy-year to four decimals.)
- Two groups have unchanged loss costs of $400 and $900 per exposure unit. Period A’s exposure mix is 75% first group and 25% second group; Period B’s is 50%/50%. What are the two aggregate averages, and what do they indicate? (Answer: Period A, \(0.75(400)+0.25(900)=\$525\); Period B, \(0.50(400)+0.50(900)=\$650\). The difference can arise from the mix change despite unchanged group results.)
- A filing extract includes premiums for policies written in 2024, losses for accidents occurring in 2024, and claims valued as of March 31, 2025. Is “2024 experience” a precise description? Name what must be clarified. (Answer: No. State the premium basis and dates, the loss occurrence basis and dates, the valuation date, and the data cutoff; these are distinct period definitions.)
- A policy’s 365-day term has $1,460 premium and 1.000 exposure-year, earned uniformly by day. Exactly 100 covered days fall in one calendar year and the remaining 265 in the next. Allocate both measures and check the totals. (Answer: First year: \(1{,}460(100/365)=\$400\) and \(100/365=0.2740\) exposure-year; next year: \(1{,}460(265/365)=\$1{,}060\) and \(265/365=0.7260\) exposure-year. Totals are $1,460 and 1.0000.)