Calendar Year

Study guide: Exam 5

Calendar Year (CY) is a data aggregation method that groups every transaction by the calendar year in which it is booked — premium as it is earned, losses as they are paid or as case reserves change — without regard to the policy's effective date or the claim's accident date.

\text{CY Earned Premium} = \text{Written Premium} - \Delta\text{UEP}

\text{CY Reported Losses} = \text{Paid} + \Delta\text{Case Reserves}

\text{CY Incurred Losses (finance)} = \text{Paid} + \Delta\text{Case Reserves} + \Delta\text{IBNR}

• \Delta\text{UEP} is the change in the unearned premium reserve over the year; \Delta terms are ending balance minus beginning balance.
• Werner & Modlin and Friedland both define calendar-year reported losses as paid losses plus the change in case reserves. The IBNR-inclusive form is the finance department's "incurred" figure (Friedland).
• CY is the financial reporting basis: most insurers report financially by calendar year, so the data is available quickly once the year ends and costs nothing extra to aggregate for ratemaking.
• A calendar year never develops — it is closed and fixed the moment the books close. Friedland counts that as an advantage and also as a disadvantage: calendar-year data cannot address development.
• CY incurred losses mix accident years: a CY 2024 figure contains payments and reserve changes on claims from 2024 and from every prior year. A single large reserve strengthening on a 2018 claim lands entirely in CY 2024 and contaminates the CY 2024 loss ratio.
• Because of that mismatch, Werner & Modlin say calendar-year aggregation for ratemaking may be most appropriate for lines or coverages whose losses are reported and settled relatively quickly, such as homeowners. Accident Year aggregation matches premium and losses better, and Policy Year best — see Ratemaking Data Organization.
• Accident-year aggregation takes its premium and exposures on the calendar-year basis — Werner & Modlin note the method is often called calendar-accident year — and Friedland observes that actuaries often use calendar-year exposures with accident-year claims. Policy Year premium is aggregated differently, by policy effective date.

Calendar Year Earned Premium from Written Premium An insurer writes \$5{,}000{,}000 of 12-month policies during calendar year 2024. The unearned premium reserve was \$1{,}800{,}000 at 12/31/2023 and \$2{,}400{,}000 at 12/31/2024.

Calculate CY 2024 earned premium, and explain what the change in UEP says about the book.

Answer

\begin{align*}
\text{CY 2024 EP} &= \text{WP} - (\text{UEP}_{\text{end}} - \text{UEP}_{\text{begin}}) \\
&= \$5{,}000{,}000 - (\$2{,}400{,}000 - \$1{,}800{,}000) \\
&= \$5{,}000{,}000 - \$600{,}000 \\
&= \$4{,}400{,}000
\end{align*}

Written premium exceeds earned premium because the unearned reserve grew: the book is growing (or prices rose). In a shrinking book the UEP falls and earned premium exceeds written premium.

How a Prior-Year Reserve Change Distorts the Calendar Year An insurer's CY 2024 results: paid losses \$7{,}200{,}000; case reserves \$5{,}000{,}000 at 12/31/2023 and \$6{,}100{,}000 at 12/31/2024; IBNR \$3{,}000{,}000 at 12/31/2023 and \$3{,}400{,}000 at 12/31/2024. Of the reserve movement, \$900{,}000 is adverse development on accident years 2021 and prior. Earned premium is \$12{,}000{,}000.

Compute the CY 2024 loss ratio and comment on its use for ratemaking.

Answer

\begin{align*}
\text{CY incurred} &= 7{,}200{,}000 + (6{,}100{,}000 - 5{,}000{,}000) \\
&\quad + (3{,}400{,}000 - 3{,}000{,}000) \\
&= \$8{,}700{,}000 \\[4pt]
\text{CY 2024 LR} &= \frac{\$8{,}700{,}000}{\$12{,}000{,}000} \\
&= 72.5\%
\end{align*}

Stripping the prior-year strengthening:

\frac{\$8{,}700{,}000 - \$900{,}000}{\$12{,}000{,}000} = 65.0\%

The 7.5 point gap is entirely about accident years 2021 and prior. Using 72.5\% to set 2026 rates would charge today's policyholders for a five-year-old reserving miss — the reason a rate indication is built on accident-year losses developed to ultimate, not on the calendar year the accountants report.