Why the Grouping Period Matters
A policy can begin in one calendar year, earn premium in two calendar years, and have a claim recognized or paid in a later year. The resulting totals depend on the period used to group the amounts. A policy-year view groups business by the year the policies take effect; a calendar-year view groups amounts by the accounting year in which they are earned or recognized. The totals answer different questions, so the period basis must be clear before calculating a ratio.
This tutorial compares premium and claim amounts using earned premium and incurred claims. These measures support a consistent comparison, but their allocation rules are not identical: premium is earned as coverage is provided, while a claim is associated with a covered policy and its accounting recognition can change over time. The distinctions are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
The same policy can therefore contribute premium to more than one calendar year but belongs to only one policy-year cohort. Similarly, a claim can belong to the policy year of the covered policy while its incurred amount is recorded in more than one calendar year as the estimate changes. A calendar-year result is not simply a list of policies that started in that year.
Allocating Earned Premium Across Calendar Years
For a policy with level coverage and premium earned uniformly over a 12-month term, the earned premium for a period is the annual premium multiplied by the fraction of the term falling in that period. This assumes the policy has not been cancelled or otherwise changed and that monthly pro rata earning is appropriate. For other earning patterns, use the applicable premium recognition basis rather than automatically applying a monthly fraction.
This allocation follows from the assumption of uniform earning: each month of a 12-month term earns one-twelfth of the policy premium. If a calendar year contains \(m\) months of the term, it earns \(m\) of those monthly portions, or \(m/12\) of the premium. Across the full term, the portions sum to the total premium because the months of coverage sum to 12.
Worked Example: One Policy Spanning Two Calendar Years
A hypothetical equipment policy takes effect October 1, 2025, and provides 12 months of coverage. Its premium is $1,200, earned evenly by month. A $600 covered claim is incurred in May 2026, and there are no other claims. Calculate the earned premium in each calendar year, then compare the policy-year and 2026 calendar-year incurred loss ratios.
Method. Allocate premium by the months of coverage in each calendar year. The policy belongs to policy year 2025 because its coverage takes effect in 2025.
The monthly premium earned is $1,200 / 12 = $100. The policy covers October, November, and December 2025, so 2025 earns 3 × $100 = $300. It covers the remaining nine months, January through September 2026, so 2026 earns 9 × $100 = $900. The check is $300 + $900 = $1,200, the full policy premium.
The $600 claim is associated with this 2025 policy-year cohort, and its incurred amount falls in calendar year 2026. The policy-year incurred loss ratio, using the full-term earned premium and claim amount in this example, is $600 / $1,200 = 0.5000, or 50.00%. The 2026 calendar-year incurred loss ratio is $600 / $900 = 0.6667, or 66.67%.
The ratios differ because their denominators represent different groupings: the policy-year ratio uses the full premium for the 2025 cohort, while the calendar-year ratio uses only premium earned during 2026. This example assumes the claim amount is fully recognized in 2026 and that no other policies or claims contribute to either measure.
Policy-Year and Calendar-Year Results in a Portfolio
For a portfolio, repeat the same allocation policy by policy and add the earned amounts for the relevant period. Grouping by policy year answers how a cohort of policies is performing. Grouping by calendar year answers what premium was earned and what claim costs were recognized in that accounting year, regardless of when the policies began.
Worked Example: Two Policy Cohorts and One Calendar-Year Result
A hypothetical insurer has two policies. Policy A takes effect November 1, 2025, has a 12-month term, and has a $1,200 premium earned evenly by month. It has a $400 claim incurred in January 2026. Policy B takes effect April 1, 2026, has a 12-month term, and has a $1,800 premium earned evenly by month. It has a $300 claim incurred in August 2026. Assume no other claims and that both claim amounts are recognized in full in the stated month. At December 31, 2026, calculate 2026 earned premium and incurred claims, then calculate the 2025 and 2026 policy-year incurred loss ratios to date.
Method. First allocate the premium earned in calendar year 2026. Then group the claims and earned premium by policy-year cohort. The valuation date matters: Policy A has completed its term, while Policy B has earned only part of its term.
Policy A earns $1,200 / 12 = $100 per month. Ten months of its term fall in 2026, January through October, so it earns 10 × $100 = $1,000 in 2026. Policy B earns $1,800 / 12 = $150 per month. Nine months of its term fall in 2026, April through December, so it earns 9 × $150 = $1,350 in 2026. Thus total 2026 earned premium is $1,000 + $1,350 = $2,350.
Both claims are incurred in 2026, so 2026 incurred claims total $400 + $300 = $700. The 2026 calendar-year incurred loss ratio is $700 / $2,350 = 0.297872… = 29.79%, rounded to two decimal places.
Policy A belongs to policy year 2025. By December 31, 2026, it has earned its full $1,200 premium and has $400 of incurred claims. Its policy-year incurred loss ratio is $400 / $1,200 = 33.33%. Policy B belongs to policy year 2026. By the valuation date, it has earned $1,350 and has $300 of incurred claims, so its policy-year-to-date incurred loss ratio is $300 / $1,350 = 0.222222… = 22.22%, rounded to two decimal places.
The policy-year ratios are cohort measures at the stated valuation date; the 2026 cohort is not yet fully earned. The calendar-year ratio combines the earned premium and incurred claims recorded during 2026 across both cohorts. The check on the calendar-year totals is that $1,000 + $1,350 = $2,350 of earned premium and $400 + $300 = $700 of incurred claims.
Incurred Claims Can Change Across Accounting Years
A claim’s incurred amount for a calendar year is not necessarily the amount paid in that year. With the usual accrual accounting identity, incurred claims equal claim payments in the year plus the ending unpaid claim estimate, less the beginning unpaid claim estimate. The change in the unpaid estimate is included because the incurred amount measures both payments and the change in the liability for claims not yet paid.
To see why, let cumulative paid claims increase by the current-year payments. At the start of the year, the unpaid estimate has already been included in prior incurred amounts. At year-end, the new unpaid estimate is included in the cumulative incurred amount. Therefore, the change in cumulative incurred claims over the year is current-year payments plus ending unpaid claims minus beginning unpaid claims. The identity assumes the stated beginning and ending unpaid estimates cover the same claim set and that there are no other adjustments omitted from the calculation.
Worked Example: A Policy-Year Claim Revised in a Later Year
A hypothetical policy takes effect July 1, 2025, provides 12 months of coverage, and has a $2,400 premium earned evenly by month. A claim occurs in November 2025, when the initial unpaid estimate is $500. During 2026, the insurer pays $400 on the claim and revises the remaining unpaid estimate to $300. Assume there are no other claims or adjustments. Calculate the claim’s incurred amount in each calendar year, the 2025 policy-year claim amount as of December 31, 2026, and the relevant loss ratios.
Method. Apply the paid-plus-ending-unpaid-minus-beginning-unpaid identity separately to each calendar year. The policy-year amount as of the valuation date is cumulative paid plus the ending unpaid estimate.
For 2025, there are no payments, the ending unpaid estimate is $500, and the beginning unpaid estimate is $0. Thus 2025 incurred claims are $0 + $500 − $0 = $500.
For 2026, payments are $400, the ending unpaid estimate is $300, and the beginning unpaid estimate is $500. Thus 2026 incurred claims are $400 + $300 − $500 = $200. This is less than the $400 paid because the unpaid estimate decreased by $200 during the year.
The policy belongs to policy year 2025. As of December 31, 2026, its cumulative claim amount is $400 paid + $300 unpaid = $700. This also reconciles to the calendar-year incurred amounts: $500 in 2025 + $200 in 2026 = $700.
The full-term premium is $2,400. It earns $200 per month, so six months of coverage in 2025 earn $1,200, and six months in 2026 also earn $1,200. The 2025 policy-year incurred loss ratio as of the valuation date is $700 / $2,400 = 0.291666… = 29.17%. The 2026 calendar-year incurred loss ratio is $200 / $1,200 = 0.166666… = 16.67%. Both percentages are rounded to two decimal places.
The check is that the policy-year claim amount equals the sum of the calendar-year incurred amounts, $500 + $200 = $700, while the calendar-year amounts reflect the timing of the claim estimate change and payment.
Common Mistake: Putting the Full Policy Premium in One Calendar Year
A frequent error is to assign the entire annual premium to the calendar year in which the policy began, then compare that amount with claims incurred in another calendar year. For the policy in the first worked example, this incorrect approach would use $1,200 as 2026 earned premium and calculate $600 / $1,200 = 50.00% as the 2026 calendar-year loss ratio. That assigns nine months of 2026 coverage to 2025, even though the policy earns $100 in each covered month.
The correction is to use the calendar-year earned premium: nine months × $100 = $900. The correct 2026 calendar-year ratio is therefore $600 / $900 = 66.67%. The 50.00% ratio is appropriate for the full policy-year cohort in that example, not for calendar year 2026. Always label the period and use matching premium and claim groupings.
Check Your Understanding
For each problem, identify the period basis before calculating. Round loss ratios to two decimal places where needed.
- A hypothetical 12-month policy takes effect October 1, 2026, with a $1,800 premium earned evenly by month. How much premium is earned in calendar year 2026, and how much in calendar year 2027? (Answer: 2026: $450; 2027: $1,350.)
- A policy takes effect November 1, 2025, has a $1,200 premium earned evenly over 12 months, and has a $360 claim fully incurred in February 2026. At the end of the policy term, what is the policy-year incurred loss ratio? What is the 2026 calendar-year incurred loss ratio, using only that policy’s 2026 earned premium? (Answer: Policy year 2025: 30.00%; calendar year 2026: 36.00%.)
- A policy takes effect July 1, 2026, has a $2,400 annual premium earned evenly, and has a $500 claim fully incurred in December 2026. Calculate its 2026 earned premium and its 2026 calendar-year incurred loss ratio. (Answer: Earned premium $1,200; incurred loss ratio 41.67%.)
- For a claim, the beginning unpaid estimate in 2026 is $800, payments during 2026 are $500, and the ending unpaid estimate is $450. Calculate 2026 incurred claims. If the claim belongs to a policy in the 2025 cohort, does the $2026 incurred amount change its policy-year assignment? (Answer: $150 incurred in 2026; no, the claim remains associated with policy year 2025.)
- A policy-year cohort has earned $3,000 of premium by the valuation date. Its associated claims have $1,100 paid and an ending unpaid estimate of $400. Calculate its incurred claims to date and its incurred loss ratio to date. (Answer: Incurred claims $1,500; incurred loss ratio 50.00%.)