What a Policy-Year Row Represents
A loss triangle needs an origin period: the rule that determines which row receives each claim. In a policy-year triangle, the origin period is determined by the effective date of the policy period covering the loss. Consequently, the loss date and the date the claim is reported do not, by themselves, determine the row.
This basis is useful when the analyst wants losses associated with policies that began during a particular period. A policy effective late in one calendar year may cover losses occurring in the next calendar year. Those covered losses still belong to the policy-year row selected by the policy effective date.
The policy period, rather than the broader customer relationship, is the relevant unit. If a contract renews, the renewal creates a new policy period with a new effective date. A loss is matched to the period that covered its occurrence, subject to the policy terms and the data definitions being used. A claim that is reported later remains associated with that same covering period.
A policy-year row is not a claim-date-year total. It can contain losses that occurred in more than one calendar year, and it may not contain every loss that occurred in its named calendar year. These features follow directly from the assignment rule.
Assigning Claims and Building Rows
A reliable construction begins with the policy record, not with the claim’s calendar year. For each claim, identify the policy period that covered the loss, verify its effective date, and use that date to select the origin row. Then aggregate the chosen measure, such as claim count, paid loss, or incurred loss, by row.
Use the coverage records and loss date to identify the policy period that applies. Do not choose a policy period solely because its dates are near the report date.
Use the effective date of the matched policy period, including the renewal effective date if the loss occurred during a renewal term.
Apply the stated policy-year boundary convention to the effective date. For calendar policy years, a policy period effective in 2022 is assigned to policy year 2022.
Add the relevant claim amounts or counts to the assigned row. For a development triangle, also determine the development age at each valuation date using one consistent convention.
Worked Example: Assigning Claims to Policy-Year Rows
A hypothetical insurer groups policies into calendar policy years. All listed claims are covered, and each policy term is annual. Assign each claim to a policy year, then calculate the claim count and total loss for each year.
| Claim | Policy effective date | Loss date | Loss amount |
|---|---|---|---|
| A | September 1, 2021 | August 20, 2022 | $12,400 |
| B | May 15, 2022 | May 1, 2023 | $8,600 |
| C | November 20, 2022 | November 30, 2022 | $3,100 |
| D | January 10, 2023 | December 20, 2023 | $5,400 |
Claim A. Its policy became effective in 2021, so it belongs to policy year 2021. The loss occurred in 2022, but that does not change the origin row.
Claims B and C. Both policies became effective in 2022, so both claims belong to policy year 2022. Claim B’s loss occurred in 2023 during the stated annual policy term; it remains in the 2022 policy-year row.
Claim D. Its policy became effective in 2023, so it belongs to policy year 2023.
The resulting row totals are:
Check. The row counts sum to \(1+2+1=4\), matching the four claims. The row losses sum to \(\$12{,}400+\$11{,}700+\$5{,}400=\$29{,}500\), equal to the total of the four listed losses. The method is policy-effective-date assignment; the mistake avoided is placing Claim B in policy year 2023 merely because its loss occurred in 2023.
From Policy-Year Rows to Triangle Cells
A policy-year row can be used in a paid or incurred loss triangle. A triangle cell then summarizes the chosen loss measure for an origin row at a particular development age and valuation date. The row assignment rule is unchanged: determine policy year from the effective date of the policy period covering each claim. Development age is a separate dimension and must follow a stated convention.
For a simple annual illustration, define age 12 as the valuation at the end of the first calendar year following the end of the origin policy year, age 24 as the next year-end, and so on. This is an explicit convention for the example, not a claim that every data source uses precisely these labels. Other systems may use different valuation or maturity conventions; the analyst must document the chosen one.
Worked Example: Constructing a Cumulative Paid Policy-Year Triangle
A hypothetical insurer uses calendar policy years and values cumulative paid losses at calendar year-end. For this example, age 12 for policy year \(y\) is December 31 of \(y+1\), and age 24 is December 31 of \(y+2\). All amounts are in thousands of dollars.
For claims assigned to policy year 2022, payments made by December 31, 2023 are \(50\), \(30\), and \(20\). The first two claims receive further payments of \(10\) and \(15\), respectively, during 2024; the third receives no further payment during 2024. For claims assigned to policy year 2023, payments made by December 31, 2024 are \(45\), \(25\), and \(35\). There are no other payments in the data provided.
Policy year 2022, age 12. The valuation date is December 31, 2023. Add the payments accumulated by that date:
Thus the cumulative paid amount is \(100\) thousand dollars. During 2024, the additional payments are \(10+15+0=25\) thousand dollars. Therefore, at age 24:
Policy year 2023, age 12. The valuation date is December 31, 2024. The cumulative payments provided for that date total:
The resulting observed triangle is:
| Policy-year origin | Age 12 | Age 24 |
|---|---|---|
| 2022 | 100 | 125 |
| 2023 | 105 | Not yet observed |
The age-24 cell for policy year 2023 is not zero: it is unavailable at the stated valuation because that development age has not yet been reached. The row assignment and the age calculation are distinct operations. The method avoids treating a later, not-yet-valued cell as an observed zero.
Check. The 2022 cumulative amount does not decrease: \(125\geq100\), as expected for cumulative paid losses when payments are nonnegative. Each displayed amount is the sum of the payments stated for its policy year through its valuation date.
Why the Effective-Date Rule Works
The row total is an aggregation over the claims whose covering policy periods began during the origin period. This makes the assignment rule precise: each included claim contributes to one policy-year row, and its loss amount is not moved to another row just because its loss or report date falls in another year.
Here, \(L_y\) is the aggregate loss assigned to policy year \(y\), \(X_j\) is the loss amount for claim \(j\), and the indicator is 1 when the condition in braces is true and 0 otherwise. Each claim contributes \(X_j\) to the sum for exactly the policy year that contains the effective date of its covering period. If the effective date is not in year \(y\), the indicator is 0 and that claim contributes nothing to \(L_y\). This is why the row groups losses by policy-period inception rather than by loss date.
Worked Example: A Policy Period Crossing Calendar Years
A hypothetical commercial equipment policy is effective October 1, 2022 and expires October 1, 2023. It covers a loss occurring September 20, 2023, reported January 8, 2024, with an ultimate loss amount of $18,000. The insured renews the coverage effective October 1, 2023, and a separate covered loss of $7,000 occurs November 12, 2023 during the renewed term.
First loss. September 20, 2023 falls within the policy period effective October 1, 2022. Its row is therefore policy year 2022. Reporting the claim in January 2024 does not change the row.
Second loss. November 12, 2023 falls during the renewal policy period effective October 1, 2023. Its row is policy year 2023. The renewal’s effective date, not the original contract’s start date, determines the row for this new policy period.
The two losses contribute \(18{,}000\) to policy year 2022 and \(7{,}000\) to policy year 2023. Their combined amount is \(18{,}000+7{,}000=\$25{,}000\). The first policy period crossed from calendar year 2022 into calendar year 2023, so the loss in September 2023 still belongs to policy year 2022. The method avoids carrying the original effective date forward into a separately effective renewal period.
Common Mistake and Practical Checks
A frequent error is to assign every loss to the year in which the loss occurred. That creates calendar-year grouping, not policy-year grouping. For the first loss in the preceding example, the incorrect calculation would place the $18,000 in policy year 2023 because the loss date is in 2023. The correction is to match the loss to the policy period covering September 20, 2023: that period became effective October 1, 2022, so the $18,000 belongs in policy year 2022.
Another error is to use a claim’s report date. Reporting delay can move the report date into a later calendar year without changing which policy period covered the loss. A report-year view uses a different grouping basis; it should not be substituted for policy year. Similarly, a policy-year triangle cell that has not reached its valuation age is unavailable, not a zero-loss observation.
Before relying on a policy-year triangle, confirm that the data consistently identify the covering policy period, that renewals have their own effective dates, and that the policy-year boundary and development-age conventions are documented. Also reconcile row totals to the underlying claim records. These checks help distinguish an assignment error from a genuine difference in losses or maturity.
Check Your Understanding
For each problem, apply the stated policy-year definition and keep effective date, loss date, and report date distinct.
- A calendar policy-year triangle contains a covered claim under a policy effective December 15, 2024. The loss occurs January 8, 2025 and is reported February 2, 2025. Which policy-year row receives the claim? (Answer: Policy year 2024.)
- Three covered claims have policy effective dates in 2023, 2023, and 2024, and loss amounts of $2,400, $3,600, and $5,000, respectively. What are the claim count and aggregate loss in each represented policy-year row? (Answer: Policy year 2023 has 2 claims and $6,000; policy year 2024 has 1 claim and $5,000.)
- For policy year 2021, cumulative paid losses are $72 thousand at age 12. Payments made between the age-12 and age-24 valuations are $9 thousand and $14 thousand. What is the cumulative paid amount at age 24? (Answer: $95 thousand.)
- A policy is effective July 1, 2022 and expires July 1, 2023. A covered loss occurs June 20, 2023, is reported August 5, 2023, and has a loss amount of $11,200. Under calendar policy years, which row receives the loss, and how much is added to that row? (Answer: Policy year 2022; $11,200.)
- A policy effective November 1, 2022 renews November 1, 2023. One covered loss of $4,500 occurs in October 2023, and another covered loss of $6,500 occurs in December 2023 during the renewal term. What are the total losses assigned to policy years 2022 and 2023? (Answer: Policy year 2022 receives $4,500; policy year 2023 receives $6,500.)