On-Leveling a Rate Change When Policyholders Renew Early
A regional personal auto carrier is preparing its 2026 rate indication. Policy year 2023 earned premium is $48.0M on 60,000 exposure units; PY2024 is $51.0M on 63,000 units, both at historical rate levels. A +9.0% rate change took effect July 1, 2024, with no other program changes. The analyst assumed writings are uniform through the year and used parallelogram on-level factors of 1.090 for PY2023 and 1.040 for PY2024 (1.090 / 1.048). Peer review surfaced one fact: marketing ran a 'lock in your rate' campaign, and about 70% of the policies that would normally have renewed between April and September 2024 instead renewed early in March 2024 at old rates. Incurred loss and LAE is $21.0M for PY2023 and $23.0M for PY2024; selected trend factors to the prospective period are 1.18 and 1.10 respectively. Fixed expense is $32 per exposure unit, variable expense is 17% of premium, and the profit and contingency provision is 4%. Current average earned premium is $560.
1. Recompute the PY2024 average rate level and on-level factor once the early-renewal campaign is recognized. State the direction and approximate size of the bias in the indication.
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Uniform-writings benchmark. With annual policies and a July 1 change, half of PY2024 writings sit at 1.000 and half at 1.090, so the average rate level is 0.5(1.000) + 0.5(1.090) = 1.045 and the on-level factor is 1.090 / 1.045 = 1.0431. The analyst's 1.040 is materially the same.
Campaign effect. April through September is six months of writings, or 50% of the year. Moving 70% of those renewals into March moves 0.50 x 0.70 = 35% of annual writings from the post-change period to the pre-change period. Pre-change share = 0.50 + 0.35 = 0.85; post-change share = 0.15.
Average rate level = 0.85(1.000) + 0.15(1.090) = 1.0135. On-level factor = 1.090 / 1.0135 = 1.0756.
Bias. 1.0756 / 1.0431 - 1 = 3.1%. Because more business than assumed is sitting at old rates, restating PY2024 losses to the current level requires a larger factor than the analyst used. His on-level losses, and therefore the indicated change, are biased low by roughly three percent of the PY2024 loss provision.
2. Beyond the on-level factor itself, what else does the early-renewal campaign distort, and how should the actuary fix it?
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Three further distortions, and each one matters independently of the factor error:
Average accident date. Early renewal does not just shift the applicable rate level, it moves earned exposure and losses earlier in calendar time. The PY2024 average accident date is earlier than the midpoint assumed under uniform writings, so the trend period to the prospective period is longer than 1.10 implies. The trend factor is understated.
Exposure timing. The 63,000 PY2024 exposure units include business pulled forward out of PY2025. PY2025 exposure will be correspondingly light, so any year-over-year exposure or pure premium comparison is contaminated, and the 63,000 denominator overstates PY2024's true underlying volume.
The comparison base. The $560 current average earned premium is an earned figure that still carries old-rate policies and pulled-forward business. It should be replaced with the average premium at current rate level taken from the rate manual, not from earned premium.
Fix. Extension of exposures at the policy level: multiply each policy's written premium and expected loss dollars by the factor from that policy's own effective date to the current level, using the actual count of policies by effective month rather than a uniform assumption. At a minimum, build the written-exposure distribution by month and use exposure-weighted average accident dates for the trend, and restate the comparison premium base to current rate level.
3. Compute the indicated change on both the analyst's basis and the corrected basis, and advise the company on what to file.
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Corrected basis.
- PY2023: 21.0 x 1.090 x 1.18 = $27.01M
- PY2024: 23.0 x 1.0756 x 1.10 = $27.21M
- Total 54.22M / 123,000 = $440.8 per exposure unit
- Indicated average rate = (440.8 + 32) / (1 - 0.17 - 0.04) = 472.8 / 0.79 = $598.5
- Indicated change = 598.5 / 560 - 1 = +6.9%
Analyst's basis. PY2024 = 23.0 x 1.043 x 1.10 = $26.39M; total 53.40M / 123,000 = $434.1; rate = (434.1 + 32) / 0.79 = $590.0, or +5.4%. The early-renewal bias alone is worth about 1.5 points of rate.
Recommendation. File on the corrected basis, since the corrected factor is supported by the actual effective-date distribution and the campaign is documented, and disclose the method. Before filing, confirm two things. First, verify the $560 base against the rate manual; if it too is understated, the indication moves again. Second, ask whether the lock-in program will run again in 2026. If it will, a portion of the 2026 average rate level will also sit below the filed level and part of the +6.9% is a one-time catch-up rather than a permanent need. That distinction belongs in the filing memorandum, not in the arithmetic.