Why Window Design Matters
An experience rating calculation can only use the periods its rules specify. A plan might hold the experience window constant for a group of renewals, or it might move the window forward at each renewal. Those choices determine whether a period remains in the calculation, when newer experience enters, and how quickly the measured experience changes.
The distinction is about which periods are included, not about how losses are valued, how exposure is measured, or how credibility is assigned. Those elements must be defined separately and consistently. The timeline method here is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
“Fixed” does not mean that the same window must be used forever. A plan may establish a new fixed window for a later rating cycle. Likewise, “rolling” does not by itself say whether a window ends at the renewal date, at a valuation date before renewal, or at the latest completed policy period. The written plan must answer that question. For this tutorial, calendar-year and half-year intervals are stated explicitly in each example.
Put the Boundaries on a Timeline
A useful first step is to write each interval from its start date through its end date, then list the periods it contains. Under a rolling design, do this separately for every renewal. Under a fixed design, repeat the specified interval for each renewal in its defined cohort. Treat boundary dates consistently: for example, an interval from January 1, 2022 through December 31, 2024 contains calendar years 2022, 2023, and 2024.
The following schematic shows a three-calendar-year window. The fixed window is held constant for two renewals in the same rating cycle; the rolling window advances one year for the later renewal.
| Renewal | Fixed window for the cycle | Rolling three-year window |
|---|---|---|
| January 1, 2025 | 2022–2024 | 2022–2024 |
| January 1, 2026 | 2022–2024 | 2023–2025 |
The table assumes that the rolling window is defined by the three most recent calendar years ending before each renewal and that the relevant data are available. If the plan instead sets an earlier valuation cutoff, that cutoff governs. A calendar year that has started is not automatically a complete or usable experience period.
Identify the date the rating applies and, separately, the date through which experience can be used.
For a fixed window, record the common interval. For a rolling window, calculate the interval for each renewal using the plan’s stated rule.
List the periods that fall within the interval and satisfy the plan’s availability and eligibility rules.
For a rolling window, confirm which old period leaves and which new period enters. Do not assume that the change is exactly one period if renewal dates or window lengths differ.
How a Rolling Window Updates
For a simple annual design, suppose each complete calendar year has an experience measure \(x_y\), and the rolling window contains \(n\) consecutive years. If the window advances by one year, the oldest year leaves and the newest year enters. The new total is therefore the old total minus the departing value plus the entering value:
This identity follows by writing both totals as sums. If the first window contains years \(a\) through \(a+n-1\), then \(T_t=\sum_{y=a}^{a+n-1}x_y\). The next window contains years \(a+1\) through \(a+n\), so \(T_{t+1}=\sum_{y=a+1}^{a+n}x_y\). The common terms for years \(a+1\) through \(a+n-1\) cancel when the sums are compared, leaving \(T_{t+1}=T_t-x_a+x_{a+n}\). This update is valid only when both windows contain the same number of comparable periods and the stated annual measures are additive. It does not justify treating partial periods as full years or combining incomparable measures.
Worked Example: Three-Year Windows at Successive Renewals
A hypothetical contractor program assigns each completed calendar year an experience index, measured in points. The values are 90 points for 2022, 120 for 2023, 150 for 2024, and 210 for 2025. The program uses a fixed 2022–2024 window for renewals in its 2025–2026 rating cycle. Compare that window with a rolling three-year window for the January 1, 2026 renewal. The index is only a period-selection measure; no credibility or premium formula is being applied.
Method. List the calendar years in each window, then sum their stated index values. The data through 2025 are assumed available for the 2026 renewal.
Fixed window. The specified years are 2022, 2023, and 2024. The total is \(90+120+150=360\) points. The mean across the three years is \(360/3=120\) points per year.
Rolling window for January 1, 2026. The three years immediately preceding the renewal are 2023, 2024, and 2025. The total is \(120+150+210=480\) points. The mean is \(480/3=160\) points per year.
Update check. The rolling window drops 2022, worth 90 points, and adds 2025, worth 210 points. Thus its new total is \(360-90+210=480\), matching the direct sum. Its mean rises by \(160-120=40\) points per year.
Common mistake avoided. Reusing 2022–2024 for the 2026 renewal gives the fixed-window result, not the rolling-window result. The labels “three-year window” alone do not determine whether the years move; the plan’s fixed or rolling rule does.
Renewal Dates Can Change the Periods
A rolling window is defined by its dates, not merely by a count of annual labels. When renewals occur at different points in the year, a stated lookback can select different half-years or other subannual periods. The periods must be segmented and valued on the basis specified by the plan; assigning a whole calendar year to a window that contains only part of it can misstate what is included.
Worked Example: A Two-Year Lookback at Two Renewal Dates
A hypothetical equipment policy has experience recorded in six-month blocks. The values are 20 points for July–December 2022, 30 for January–June 2023, 40 for July–December 2023, 50 for January–June 2024, and 60 for July–December 2024. A fixed window for a renewal cohort is July 1, 2022 through June 30, 2024. Compare it with a rolling 24-month window ending immediately before each renewal on July 1, 2024 and January 1, 2025. Assume all listed blocks are complete and available for the relevant calculation.
Method. Match each 24-month date interval to the six-month blocks it contains, then add the values for those blocks.
Fixed window. July 1, 2022 through June 30, 2024 contains four blocks: July–December 2022, January–June 2023, July–December 2023, and January–June 2024. The total is \(20+30+40+50=140\) points. The mean per six-month block is \(140/4=35\) points.
Rolling window ending July 1, 2024. Its interval is also July 1, 2022 through June 30, 2024, so it contains the same four blocks and totals \(140\) points, or \(140/4=35\) points per block.
Rolling window ending January 1, 2025. Its interval is January 1, 2023 through December 31, 2024. It contains the blocks valued at 30, 40, 50, and 60 points. The total is \(30+40+50+60=180\) points, and the mean is \(180/4=45\) points per block.
Check. From the first rolling window to the second, the July–December 2022 block leaves and the July–December 2024 block enters. The updated total is \(140-20+60=180\), as calculated directly.
Common mistake avoided. Calling both calculations “the last two years” and then counting whole calendar years would obscure the exact half-year boundaries. The date intervals show that January 2025’s rolling window includes only the 2023 and 2024 calendar years, not the fixed window’s 2022–2024 span.
Data Cutoffs and Incomplete Periods
A window rule and a data cutoff answer different questions. The rule selects the period; the cutoff determines whether the required information for that period is available for rating. A plan might define a rolling interval ending at a valuation date that precedes renewal, or it might specify the latest completed periods available by a stated date. Those rules can produce different included periods.
Do not silently substitute an older period for an incomplete newer one. If the stated rolling window includes a period for which data are not yet available, the plan needs a defined response—for example, an earlier stated cutoff, a later rating decision, or an explicit rule for incomplete periods. The result should be described as the window the plan actually uses, rather than as a complete rolling window if it is not one.
Worked Example: Applying a Stated Valuation Cutoff
A hypothetical renewal takes effect January 1, 2025. The plan specifies a three-calendar-year experience window ending on the latest December 31 for which complete data are available at the October 1, 2024 valuation cutoff. The complete annual index values available are 70 points for 2021, 100 for 2022, and 130 for 2023. The 2024 value is currently 75 points through September 30 and is incomplete. Determine the selected window and its total and mean.
Method. Apply the cutoff rule before selecting the three-year interval. The latest completed December 31 at the cutoff is December 31, 2023.
The three complete calendar years ending on that date are 2021, 2022, and 2023. Their total is \(70+100+130=300\) points. The mean is \(300/3=100\) points per year.
The 2024 partial value of 75 points is excluded: it covers only nine months and is not a complete annual value under the stated rule. The January 1, 2025 effective date does not make the 2024 experience complete or available at the earlier valuation cutoff.
Common mistake avoided. Including 75 and calculating \(70+100+130+75\) mixes a partial year with complete annual values and also creates a four-period total. Replacing 2021 with the partial 2024 value would be wrong as well, because the plan expressly requires complete years at the cutoff.
Practical Checks and Exam Traps
The choice between fixed and rolling windows affects responsiveness and stability. A fixed window makes period selection consistent across renewals in its defined cycle, but newer experience does not enter until the plan resets that window. A rolling window brings newer periods into each update and removes older ones, so the selected experience changes over time. Neither design is inherently correct for every program; the choice depends on plan objectives and operational rules.
When asked to compare windows, show the actual periods rather than relying on labels such as “three years of experience.” Then verify the calculation against the timeline. A concise audit is to count included periods, identify the departing and entering periods where relevant, and confirm the data cutoff.
- Do not confuse fixed with permanently fixed. A fixed interval can be replaced at the next rating-cycle reset.
- Do not assume a rolling window ends at renewal. It may end at a separate valuation date specified by the plan.
- Do not count incomplete periods as complete. Apply the stated availability rule before calculating totals or averages.
- Do not compare totals with different numbers of periods as if they were averages. State whether the result is a total or a per-period measure.
- Do not update by adding the newest period alone. A full rolling window also removes the oldest included period.
Check Your Understanding
For each problem, identify the included periods before calculating. All scenarios are hypothetical.
- A plan uses a fixed 2021–2023 window for two renewals in one cycle. Annual experience values are 40, 60, 80, and 100 points for 2021 through 2024. What total does the fixed window use at each renewal? (Answer: 180 points at each renewal.)
- A four-year rolling window for a January 1, 2025 renewal includes 2021–2024. Annual values are 55, 65, 75, and 85 points. Find the total and annual mean. (Answer: Total 280 points; mean 70 points per year.)
- A three-year rolling window totals 410 points. It drops a year valued at 95 points and adds a newly available year valued at 125 points. Find the updated total and explain the change. (Answer: 440 points; the total increases by 30 points.)
- A plan’s fixed window is April 1, 2022 through March 31, 2024. A rolling 24-month window is calculated at April 1, 2025. Which interval does the rolling window use, and which calendar-year labels does it touch? (Answer: April 1, 2023 through March 31, 2025; it touches calendar years 2023, 2024, and 2025.)
- A plan requires the latest three complete calendar years available at a June 30, 2025 cutoff. Values for 2022, 2023, and 2024 are 90, 110, and 130 points; 2025 has 50 points through June. State the selected window, total, and mean. (Answer: 2022–2024; total 330 points; mean 110 points per year. Exclude the incomplete 2025 value.)