Why the Grouping Date Matters
A claim has more than one relevant date. The accident date identifies when the event giving rise to the claim occurred; the payment date identifies when the insurer paid money on that claim. A payment made during one calendar year can therefore relate to an accident from an earlier year. Grouping by one date answers a different question from grouping by the other.
This distinction matters when interpreting results for a particular year. Calendar-year paid losses describe payments made during that calendar year, regardless of when the accidents occurred. Accident-year paid losses describe payments on claims arising from accidents during that year, regardless of when the payments were made, subject to the stated valuation date. All worked examples below use paid losses and hypothetical claim data. They do not treat paid losses as estimates of ultimate claim cost.
A calendar-year total follows payment transactions. An accident-year total follows the claims’ accident dates and gathers their payments across payment years. The two totals for the same named year need not be equal. Neither grouping changes the amount of a transaction; it changes the period to which that transaction is assigned.
Classifying Payments and Reconciling Totals
The safest way to calculate either result is to keep the accident date and payment date as separate fields. For each payment, use the payment date to find its calendar year and the claim’s accident date to find its accident year. Then sum the payment amounts in the requested group.
Confirm that the figures are paid losses, rather than another claim-cost measure, and state the valuation date if payments are being grouped by accident year.
For each payment, record the calendar year of payment and the accident year of the underlying claim. Do not substitute one date for the other.
For a calendar-year result, sum payments made in that year. For an accident-year result, sum payments on claims from that accident year that have been made by the valuation date.
If comparing totals over a set of years, make sure both calculations include the same payment transactions. Differences between individual period totals can be reconciled by the way payments cross year boundaries.
This reconciliation can be stated precisely. Let \(p_{a,c}\) be the amount paid on claims from accident year \(a\) during calendar year \(c\), with payments outside the observation period omitted. Then the calendar-year total for year \(c\) is the sum down that calendar-year column, while the accident-year total for year \(a\) is the sum across that accident-year row.
The reason the grand totals reconcile is that both methods sum the same payment cells. Summing the calendar-year totals across all included calendar years gives the sum of every included cell. Summing the accident-year totals across all included accident years gives that same sum:
This equality requires the comparison to cover the same payments. If a calendar-year summary includes payments made through a particular date but an accident-year summary excludes some of those payments because the associated accidents are outside its displayed years, the displayed totals will not be directly comparable. Likewise, an accident-year total at a valuation date includes only payments made by that date; later payments can change it.
Worked Example: Two Calendar Years and Two Accident Years
A hypothetical insurer records the following payments. Each claim can have more than one payment.
| Claim | Accident date | Payment date | Payment |
|---|---|---|---|
| P | December 18, 2024 | January 20, 2025 | $4,000 |
| P | December 18, 2024 | March 15, 2025 | $6,000 |
| Q | February 10, 2025 | May 1, 2025 | $3,000 |
| R | November 25, 2025 | December 20, 2025 | $2,000 |
| R | November 25, 2025 | February 10, 2026 | $5,000 |
| S | December 30, 2025 | January 15, 2026 | $7,000 |
Calculate calendar-year paid losses for 2025 and 2026, and accident-year paid losses for 2024 and 2025 through December 31, 2026.
Calendar year 2025. Include each payment with a 2025 payment date: P’s two payments, Q’s payment, and R’s December payment.
\($4,000+$6,000+$3,000+$2,000=$15,000\).
Calendar year 2026. Include R’s February payment and S’s January payment.
\($5,000+$7,000=$12,000\).
Accident year 2024. Both payments on P arose from the December 2024 accident, so the total through the stated valuation date is \($4,000+$6,000=$10,000\).
Accident year 2025. Q, R, and S arose from 2025 accidents. Include all their payments made by December 31, 2026: \($3,000+$2,000+$5,000+$7,000=$17,000\).
Check. The calendar-year totals add to \($15,000+$12,000=$27,000\). The accident-year totals add to \($10,000+$17,000=$27,000\). Both cover the same six payments. The 2025 calendar-year result is $2,000 lower than the 2025 accident-year result because the latter includes $5,000 and $7,000 paid in 2026, while the former includes $4,000 and $6,000 paid on a 2024 accident.
Method and trap avoided. This is a transaction-by-transaction classification. A common error is to assign P’s $10,000 to calendar year 2024 merely because its accident occurred in 2024. That would misclassify both payments: their payment dates are in 2025, so they belong in calendar-year 2025 paid losses.
Valuation Date and Incomplete Accident-Year Results
An accident-year paid total is always tied to a cutoff date when the claims are not fully paid. For example, an accident-year result measured at the end of the accident year usually omits payments made later. If a later valuation includes additional payments on the same claims, that accident-year paid result increases. The change reflects additional observed payments, not a change in the accident dates.
This is why an accident-year paid figure should not be described as the final cost of that year’s accidents unless the data and definition justify that conclusion. A calendar-year paid figure also has a specific scope: it records cash paid in the year, including payments on claims from earlier accident years. The result is useful for describing payments in that accounting period, but it does not by itself identify the accident cohort that generated them.
Worked Example: Comparing Results at a Year-End Cutoff
A hypothetical carrier has recorded these payments by December 31, 2025: $6,000 on claims from accidents in 2023, paid in 2024; $8,000 on claims from accidents in 2024, paid in 2024; $4,000 on claims from accidents in 2024, paid in 2025; and $5,000 on claims from accidents in 2025, paid in 2025. A further $3,000 payment on the 2025 accidents is made in 2026. Calculate calendar-year 2025 paid losses and accident-year paid losses for 2024 and 2025 as of December 31, 2025. Then update the 2025 accident-year result after the 2026 payment.
Calendar-year 2025. The payments made during 2025 are $4,000 on 2024 accidents and $5,000 on 2025 accidents.
\($4,000+$5,000=$9,000\).
Accident year 2024 at December 31, 2025. Include both payments on 2024 accidents made by the cutoff: \($8,000+$4,000=$12,000\).
Accident year 2025 at December 31, 2025. Only the $5,000 payment has occurred by this valuation date, so the paid total is $5,000. The later $3,000 payment is not included as of this cutoff.
Update after the 2026 payment. The 2025 accident-year paid total becomes \($5,000+$3,000=$8,000\) at a valuation date after that payment. Calendar-year 2025 remains $9,000 because a payment made in 2026 does not become a 2025 payment.
Check. By the end of 2025, all recorded payments made in 2024 and 2025 sum to \($6,000+$8,000+$4,000+$5,000=$23,000\). The calendar-year totals are $14,000 for 2024 and $9,000 for 2025, also totaling $23,000. The $6,000 payment from 2023 accidents is included in calendar year 2024 but not in either the 2024 or 2025 accident-year total. Its accident year must be included for the accident-year grand total to reconcile.
Method and trap avoided. The valuation date determines which payments are observable in an accident-year total. Do not add the future $3,000 payment to the result as of December 31, 2025, and do not move it into calendar year 2025 when it is later paid.
Reading a Cross-Classification
A compact way to compare the two groupings is a table with accident years as rows and calendar years as columns. Each cell contains payments on claims from the row’s accident year that were made in the column’s calendar year. Row sums produce accident-year totals over the displayed payment years; column sums produce calendar-year totals over the displayed accident years.
Worked Example: Finding Period Totals From a Payment Table
A hypothetical specialty insurer summarizes its payments, in thousands of dollars, as follows. All listed payments are included, and the table covers calendar years 2024 through 2026.
| Accident year | Calendar year 2024 | Calendar year 2025 | Calendar year 2026 | Accident-year total |
|---|---|---|---|---|
| 2024 | 12 | 8 | 0 | 20 |
| 2025 | 0 | 15 | 5 | 20 |
| 2026 | 0 | 0 | 9 | 9 |
| Calendar-year total | 12 | 23 | 14 | 49 |
Calculate the 2025 calendar-year paid losses and the 2025 accident-year paid losses through calendar year 2026.
Calendar year 2025. Sum the 2025 column: \($8,000+$15,000=$23,000\), since the table is in thousands.
Accident year 2025 through 2026. Sum the 2025 row: \($15,000+$5,000=$20,000\).
Check. The full calendar-year totals are $12,000, $23,000, and $14,000, which sum to $49,000. The accident-year totals are $20,000, $20,000, and $9,000, also summing to $49,000. The 2025 figures differ because the 2025 calendar-year column contains $8,000 from 2024 accidents, while $5,000 from 2025 accidents is paid in 2026.
Method and trap avoided. Read across a row for an accident-year total and down a column for a calendar-year total. Do not label the $23,000 column sum as the cost of 2025 accidents; $8,000 of it arose from 2024 accidents.
Common Interpretation Errors
The distinction is straightforward once the date used for grouping is explicit, but several errors can make a comparison misleading.
- Using accident date to classify calendar-year payments. Calendar-year paid losses follow the payment date. A payment on an older claim still belongs to the calendar year in which it was paid.
- Using payment date to classify accident year. Accident-year paid losses follow the accident date. A payment made in a later year remains attached to the year of the accident.
- Leaving out the valuation date. An accident-year paid result can change as additional payments are made. State the cutoff so the total has a clear meaning.
- Comparing different sets of transactions. Grand totals reconcile only when both aggregations cover the same payments and the relevant accident years and payment years are included.
- Treating paid losses as ultimate losses. A paid total is the amount paid by the cutoff. It is not, by definition, a projection of all eventual payments.
Check Your Understanding
For each problem, distinguish the payment year from the accident year and use the stated valuation date.
- A claim from an accident in 2024 is paid $2,400 in March 2025. A claim from an accident in 2025 is paid $1,600 in December 2025 and $900 in January 2026. Find calendar-year 2025 paid losses and accident-year 2024 and 2025 paid losses through December 31, 2026. (Answer: CY 2025 = $4,000; AY 2024 = $2,400; AY 2025 = $2,500.)
- Payments are $3,000 on 2023 accidents in 2024, $7,000 on 2024 accidents in 2025, and $4,000 on 2025 accidents in 2025. Find CY 2025 paid losses and AY 2025 paid losses through December 31, 2025. (Answer: CY 2025 = $11,000; AY 2025 = $4,000.)
- A table reports payments, in thousands: AY 2024 has 5 in CY 2024 and 6 in CY 2025; AY 2025 has 0 in CY 2024, 8 in CY 2025, and 2 in CY 2026. Find CY 2025 paid losses and AY 2024 paid losses across the displayed years. (Answer: CY 2025 = $14,000; AY 2024 = $11,000.)
- By December 31, 2025, a carrier has paid $9,000 on 2024 accidents during 2024 and $4,000 on those accidents during 2025. It has also paid $6,000 on 2025 accidents during 2025. A further $3,000 on the 2025 accidents is paid in 2026. Find CY 2025 paid losses and AY 2025 paid losses at December 31, 2025, then after the 2026 payment. (Answer: CY 2025 = $10,000; AY 2025 at December 31, 2025 = $6,000; AY 2025 after the payment = $9,000.)
- Across all included transactions, calendar-year totals are $18,000 for 2024 and $22,000 for 2025. The same transactions are grouped by accident year, with all relevant accident years included. What must the sum of the accident-year totals be? (Answer: $40,000.)