Why Date Alignment Matters
On-leveling compares premium earned at different rate levels. Before making that comparison, an actuary must determine which rate level applies to each policy and how much of its premium was earned within the experience period. The dates involved answer different questions: the policy effective date identifies when a policy term begins, the rate effective date identifies when a new rate may apply, and the experience-period boundaries identify which earned premium is included.
A rate change during an experience period does not necessarily split every policy’s premium between the old and new levels. If rates apply to policies based on their effective or renewal dates, a policy already in force may keep its original rate until renewal. Conversely, a policy starting after the rate change may be entirely at the new level, even if only part of its premium is earned during the experience period. This date-mapping skill is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
A Consistent Calendar Convention
Represent a period from date \(A\) through the end of the day before date \(B\) as \([A,B)\). This half-open interval includes its start date and excludes its end date. For example, calendar year 2025 is \([January\ 1,\ 2026)\) starting from January 1, 2025: it includes January 1 through December 31, but not January 1, 2026. Using this convention makes adjacent periods meet without double-counting a boundary date.
For a policy with term \([s,e)\), annual premium \(P\), and uniform earning over the term, the earned premium within experience period \([A,B)\) is proportional to the overlap. Define the overlap as the part of the policy term that also lies in the experience period. When using months for a 12-month policy, count the overlapping months and divide by 12. For actual records, use the stated earning basis; if it is daily, use the number of overlapping days divided by the policy-term days.
This proportional formula assumes premium is earned uniformly over the policy term and that the premium remains fixed for that term. It does not automatically apply to a midterm endorsement that changes premium, a cancellation with a different earning rule, or a policy whose premium is not earned uniformly. In those cases, split the policy into the relevant premium segments or use the applicable exposure and earning records.
Map the Dates Before Calculating
A reliable calculation starts by laying out the experience period, policy terms, and rate effective dates on one timeline. Then identify the rule governing how the rate change applies. A change may apply to all policies in force on its effective date, only to new business, or only when a policy renews. The applicable rule—not the calendar date alone—determines whether a policy’s premium changes.
Write the exact start and end boundaries, using one consistent convention such as \([A,B)\).
For each policy, record its effective date and expiration or renewal date. A policy can contribute only during the overlap with the experience period.
Determine whether a new rate applies immediately, to new business, or at renewal. Assign each policy term the correct rate level.
Prorate premium for the overlap and place the result in the rate-level category that applies to that term.
The reason overlap prorating works under uniform earning is direct: each equal unit of time earns an equal fraction of the policy premium. If a 12-month term earns uniformly, one month earns \(1/12\) of its premium. Therefore, if \(m\) months fall inside the experience period, the earned portion is \(P(m/12)\). If the period is partitioned into non-overlapping pieces, the pieces’ durations add to the total overlap, so their earned-premium amounts also add to the same total.
This also explains why date boundaries must be handled consistently: assigning a boundary month or day to two adjacent periods would count its earned premium twice, while omitting it from both would leave premium out.
Worked Examples
Worked Example: Two Rate Levels Within a Calendar Experience Year
A hypothetical insurer has annual policies with uniform monthly earning. Rates increase by 10% effective July 1, 2025, and the change applies to policies effective on or after that date. A group contains four policies effective January 1, April 1, July 1, and October 1, 2025. The annual premium is $1,200 at the earlier rate level and $1,320 at the later level. Determine the earned premium in calendar year 2025 by rate level.
Method and date map. Calendar 2025 is January 1 through December 31. Each policy earns for the part of its 12-month term that falls in that interval. The rate change applies by policy effective date, so the January and April policies are at the earlier level; the July and October policies are at the later level.
January 1 policy. Its full 12-month term falls in 2025. Earned premium is \(1{,}200(12/12)=\$1{,}200\), at the earlier level.
April 1 policy. Its term runs through March 31, 2026, so 9 of its 12 months fall in 2025. Earned premium is \(1{,}200(9/12)=\$900\), at the earlier level.
July 1 policy. Six months fall in 2025. Earned premium is \(1{,}320(6/12)=\$660\), at the later level.
October 1 policy. Three months fall in 2025. Earned premium is \(1{,}320(3/12)=\$330\), at the later level.
The earlier-level earned premium is \(\$1{,}200+\$900=\$2{,}100\). The later-level earned premium is \(\$660+\$330=\$990\). Total earned premium is \(\$2{,}100+\$990=\$3{,}090\). The check against the four policy calculations gives \(\$1{,}200+\$900+\$660+\$330=\$3{,}090\), so the level totals reconcile. The key mistake avoided is treating July 1 as though it changes the rate on policies already effective before that date.
Worked Example: A Renewal-Only Rate Change
A hypothetical annual policy begins October 1, 2024, with an annual premium of $1,800. A 8% rate increase takes effect April 1, 2025, but the insurer applies it only at renewal. The policy renews October 1, 2025. The experience period is calendar year 2025, and coverage continues at renewal. Find the earned premium in the period.
Method and date map. The original term runs October 1, 2024, through September 30, 2025. The April 1 rate date falls inside that term, but the stated rule is renewal-only. Thus the original term remains at $1,800 for its full duration. The renewal term starts October 1, after the rate change, so its annual premium is \(1{,}800(1.08)=\$1{,}944\).
Original term. January through September 2025 contributes 9 months. Earned premium is \(1{,}800(9/12)=\$1{,}350\).
Renewal term. October through December contributes 3 months. Earned premium is \(1{,}944(3/12)=\$486\).
Total earned premium in 2025 is \(\$1{,}350+\$486=\$1{,}836\). As a check, the original term contributes nine-twelfths of its annual premium and the renewal contributes three-twelfths of its increased annual premium; the periods cover all 12 months of the calendar year without overlap.
Common mistake avoided. Applying the 8% increase to the original policy beginning April 1 would incorrectly treat a renewal-only change as an immediate midterm change. For example, that mistake would produce \(\$450\) for January–March, \(1{,}944(6/12)=\$972\) for April–September, and \(\$486\) for October–December, totaling \(\$1{,}908\). The correct total is \(\$1{,}836\), because the original term remains at its original premium through September 30.
Worked Example: Several Effective Dates and Two Rate Changes
A hypothetical insurer writes one 12-month policy on the first day of each month from June through November 2025. Premium is earned uniformly by month. The annual premium is $1,200 before July 1, increases to $1,320 on July 1, and increases again to $1,386 on October 1. Each rate applies to policies effective on or after its date. For the experience period June 1 through November 30, 2025, calculate earned premium by rate level.
Method and date map. The period includes six months, June through November. The June policy is at the $1,200 level. The July, August, and September policies are at the $1,320 level. The October and November policies are at the $1,386 level. For each policy, count only the months within both its term and the experience period.
| Policy effective date | Annual premium | Months in experience period | Earned premium |
|---|---|---|---|
| June 1, 2025 | $1,200 | 6 | $1,200 × 6/12 = $600 |
| July 1, 2025 | $1,320 | 5 | $1,320 × 5/12 = $550 |
| August 1, 2025 | $1,320 | 4 | $1,320 × 4/12 = $440 |
| September 1, 2025 | $1,320 | 3 | $1,320 × 3/12 = $330 |
| October 1, 2025 | $1,386 | 2 | $1,386 × 2/12 = $231 |
| November 1, 2025 | $1,386 | 1 | $1,386 × 1/12 = $115.50 |
At the first level, earned premium is \(\$600\). At the second level, it is \(\$550+\$440+\$330=\$1{,}320\). At the third level, it is \(\$231+\$115.50=\$346.50\). The total is \(\$600+\$1{,}320+\$346.50=\$2{,}266.50\). Summing the six policy-row amounts gives the same \(\$2{,}266.50\), confirming the allocation. The different month counts arise because each later policy starts later in the experience period; they do not change which rate level applies to that policy.
Common Boundary and Rate-Level Traps
- Confusing a rate date with a policy start date. A rate change date identifies when a new rate may apply under the rules; it does not by itself change every in-force policy’s premium.
- Using the policy’s full premium as earned premium. Include only the portion earned during the experience period. A policy can be written in one period and have part of its premium earned in another.
- Assigning rate level from the experience-period date. Assign it from the policy’s applicable effective or renewal date, according to the stated rule.
- Double-counting an endpoint. Use a consistent convention, such as including the start and excluding the end, for both policy terms and experience periods.
- Mixing prorating bases. Do not use monthly proration for one policy and daily proration for another unless the data or stated method requires it. Use the specified earning basis consistently.
The objective is not merely to list rate changes that occurred during an experience period. It is to identify which policy terms earned premium in that period and the rate level attached to each term. Once that mapping is correct, the resulting rate-level premium totals can be used in the on-leveling calculation.
Check Your Understanding
For each problem, map the dates before calculating; assume uniform monthly earning for 12-month policies unless stated otherwise.
- A hypothetical policy effective May 1, 2026 has an annual premium of $1,500. Another effective October 1, 2026 has an annual premium of $1,800. Both remain in force for 12 months, and calendar 2026 is the experience period. What is their combined earned premium in 2026? (Answer: $1,450)
- A policy effective September 1, 2025 has an annual premium of $2,400 and renews September 1, 2026. A 5% increase is effective January 1, 2026, but applies only at renewal. Find its earned premium in calendar 2026. (Answer: $2,440)
- A rate increase takes effect October 1, 2025 and applies to policies effective on or after that date. One policy is effective August 1 at an annual premium of $1,000; another is effective November 1 at an annual premium of $1,100. Find their combined earned premium from October 1, 2025 through March 31, 2026. (Answer: $958.33)
- Policies are effective May 1, August 1, and October 1, 2025, with annual premiums of $1,000, $1,120, and $1,120, respectively. The increase to $1,120 applies to policies effective on or after August 1. Find total earned premium from May 1 through October 31, 2025. (Answer: $873.33)
- A policy begins November 1, 2024 at an annual premium of $2,400. It renews April 1, 2025, when a 10% increase applies. Find earned premium from November 1, 2024 through April 30, 2025, including the first month of the renewal term. (Answer: $1,220)