Accident Year

Study guide: Exam 5

Accident Year (AY) is a data aggregation method that groups losses by the calendar year in which the loss event occurred, and matches them against the premium earned in that same year — regardless of when the policy was written, when the claim was reported, or when it was paid.

\text{AY } n \text{ Loss Ratio} = \frac{\text{Losses occurring in year } n}{\text{Premium earned in year } n}

• The occurrence date alone decides the year. A policy written 10/1/2023 with a loss on 2/4/2024 paid in 2026 is Accident Year 2024.
• Werner & Modlin set three objectives for aggregating ratemaking data: accurately match losses and premium, use the most recent data available, and minimize the cost of data collection and retrieval. AY matches premium and losses better than Calendar Year, and its claims occur over a shorter time frame than a Policy Year's, so its ultimate can be reliably estimated sooner. Friedland calls it the accepted norm for P&C insurers in the U.S. and Canada, and by far the most common grouping for the analysis of unpaid claims.
• An AY cohort is not final at year end: losses still develop as claims are reported and case reserves are re-estimated, so an AY must be brought to ultimate with a CDF before it can be compared with a mature year. See Loss Development.
• Premium and losses are only approximately matched. AY n earned premium comes partly from policies written in year n-1, whose rates and terms differ — which is why the premium must still be brought to current level (On-Leveling).
• The rows of a Development Triangle are usually accident years; diagonals are valuation dates. Insurers also compile claims by accident month, quarter and half-year.

Assigning a Claim to an Accident Year A 12-month policy is effective 10/1/2023. The insured has a loss on 11/15/2024, which is reported 12/1/2024, reserved at \$40{,}000, and paid \$52{,}000 on 3/1/2025.

Assign the claim under each aggregation basis.

Answer

Basis	Year	Driver
Accident Year	2024	occurrence date 11/15/2024
Policy Year	2023	policy effective date 10/1/2023
Report Year	2024	first notice 12/1/2024
Close Year	2025	settlement 3/1/2025
Calendar Year	2024 and 2025	\$40{,}000 incurred in CY 2024; the \$12{,}000 of adverse development lands in CY 2025

The accident-year and policy-year assignments are fixed by the occurrence and policy dates alone; the report, close and calendar years depend on when the claim was reported, settled and paid.

Why an Accident Year Loss Ratio Moves AY 2024 earned premium is \$8{,}000{,}000. Reported losses were \$4{,}400{,}000 at 12 months and \$5{,}300{,}000 at 24 months. The selected \text{CDF}_{24 \to \text{ult}} is 1.150.

Compute the loss ratio at each evaluation and at ultimate.

Answer

\begin{align*}
\text{LR at 12 mo} &= \frac{\$4{,}400{,}000}{\$8{,}000{,}000} \\
&= 55.0\% \\[4pt]
\text{LR at 24 mo} &= \frac{\$5{,}300{,}000}{\$8{,}000{,}000} \\
&= 66.3\%
\end{align*}

At ultimate:

\begin{align*}
\text{Ultimate} &= \$5{,}300{,}000 \times 1.150 \\
&= \$6{,}095{,}000 \\[4pt]
\text{Ultimate LR} &= \frac{\$6{,}095{,}000}{\$8{,}000{,}000} \\
&= 76.2\%
\end{align*}

The denominator never changes — earned premium for a closed accident year is fixed — so every movement in an AY loss ratio comes from loss development. An immature AY loss ratio always understates the ultimate answer, and quoting one without its CDF is a standard exam trap.