Why Earned Premium Timing Matters
An annual policy does not usually begin and end with a calendar year. A policy effective partway through the year earns only the portion of its premium corresponding to coverage provided during that year. This creates an important distinction: the date premium is earned is not necessarily the date that determines its rate level. For a policy with a fixed annual rate, the rate level is generally determined by the policy’s effective date, even when some of its premium is earned in a later calendar year.
For ratemaking, earned premium must be assigned to the period it represents and then adjusted from the rate levels actually charged to the selected prospective rate level. Losses may also need an adjustment to the prospective cost level, but the loss adjustment and premium adjustment have different purposes. A trend adjustment changes the cost level of losses; an on-level adjustment restates premium to a consistent rate level.
Assigning Earned Premium to Policy Terms
Assume each policy has a fixed annual premium, coverage is earned uniformly over the policy term, and there are no midterm endorsements, cancellations, or other premium adjustments. For an annual policy with premium \(P\), if \(m\) months of its term fall within the experience period, the premium earned in that period is \(P(m/12)\). For terms that begin or end within a month, use the applicable fraction of the term if the data support that level of precision.
The rate level assigned to the earned amount follows the policy term, not simply the calendar date on which the coverage is earned. For example, premium earned in January on a policy that began the previous July generally reflects the rate applicable when that policy was issued. A later rate change does not, by itself, reprice the remaining months of an already-issued fixed-rate policy.
Worked Example: Earning Premium Across Two Calendar Years
A hypothetical insurer writes a 12-month policy effective September 1, 2023, with annual premium $1,200 at rate level 1.00. It writes a second 12-month policy effective July 1, 2024, with annual premium $1,320 at rate level 1.10. Calculate calendar-year 2024 earned premium by rate level, then on-level it to rate level 1.10.
Method and assumption. Use pro rata earning over each policy’s 12-month term. The first policy provides coverage in calendar year 2024 from January through August, or 8 months. The second provides coverage from July through December, or 6 months.
First policy. Its 2024 earned premium is \(1{,}200(8/12)=800\). It remains at rate level 1.00 because that is the level applicable to its policy term.
Second policy. Its 2024 earned premium is \(1{,}320(6/12)=660\). It is at rate level 1.10.
Total calendar-year 2024 earned premium is \(800+660=1{,}460\). To restate the first policy’s earned premium to level 1.10, multiply by \(1.10/1.00\). The second policy is already at the target level.
The aggregate on-level factor is \(1{,}540/1{,}460=1.0548\), rounded to four decimal places. Check: the adjusted total exceeds the actual total because the $800 earned at level 1.00 was increased to level 1.10; the $660 already at the target level was unchanged. A common mistake is to apply level 1.10 only to premium earned after July 1. That would incorrectly reassign the first policy’s January–August premium, whose policy term was priced at level 1.00.
On-Leveling Earned Premium to a Target
Represent rate levels as indices relative to a common base. If a policy term was written at level \(R_j\) and the target level is \(R_T\), the premium adjustment factor is \(R_T/R_j\). This factor converts premium at the old level to the premium that the same underlying exposure would produce at the target level, assuming premium is proportional to the rate level and the coverage and rating basis are otherwise unchanged.
where \(P_{E,j}\) is earned premium from policy terms at rate level \(R_j\), and \(F_{\text{on-level}}\) is the aggregate factor for the experience period. The factor is weighted by actual earned premium. A simple average of the rate-level factors is not generally appropriate because the amounts of earned premium at each level can differ.
Worked Example: Aggregating Earned Premium at Three Rate Levels
A hypothetical book has calendar-year earned premium of $24,000 at rate level 0.96, $36,000 at level 1.00, and $20,000 at level 1.08. Calculate the total premium on-leveled to 1.08 and the aggregate on-level factor.
Method. Convert each earned-premium component to level 1.08 by multiplying by the target level divided by its own level.
For the level 0.96 component, the factor is \(1.08/0.96=1.125\), so adjusted premium is \(24{,}000(1.125)=27{,}000\). For the level 1.00 component, the factor is \(1.08/1.00=1.08\), so adjusted premium is \(36{,}000(1.08)=38{,}880\). For the level 1.08 component, the factor is 1.00, so adjusted premium is $20,000.
Actual earned premium is \(24{,}000+36{,}000+20{,}000=80{,}000\). On-level earned premium is \(27{,}000+38{,}880+20{,}000=85{,}880\). Therefore the aggregate factor is \(85{,}880/80{,}000=1.0735\), rounded to four decimal places.
Check and exam trap. The converted components all equal or exceed their actual amounts because each source level is at or below the target. Taking the unweighted mean of the three conversion factors, \((1.125+1.08+1.00)/3=1.0683\), would be wrong: the earned-premium amounts at the three levels are not equal. Weighting each factor by its earned premium gives the correct aggregate result.
Keeping Premium and Loss Adjustments Consistent
Once earned premium has been assigned to its policy-term rate levels, it can be compared with losses only after the intended period and adjustments have been made explicit. For example, if losses are to be trended to a stated prospective cost level and premium is to be on-leveled to a stated prospective rate level, the adjusted loss ratio is the trended losses divided by on-level earned premium. Apply the loss trend to losses, not again to premium. The rate-level conversion belongs on premium, not on losses.
The following calculation assumes that the loss trend factor is supplied, that losses and earned premium are the intended matching experience, and that the selected target rate level is appropriate for the prospective analysis. It does not determine which trend period is appropriate; that depends on the loss period and prospective period being represented.
Worked Example: Combining the Adjustments in a Loss Ratio
A hypothetical calendar-year analysis has $1,260,000 of losses and earned premium of $400,000 at rate level 1.00 plus $600,000 at rate level 1.10. The target premium level is 1.10, and the selected loss trend factor to the prospective cost level is 1.08. Calculate the adjusted loss ratio.
Step 1: On-level premium. The $400,000 at level 1.00 becomes \(400{,}000(1.10/1.00)=440{,}000\). The $600,000 at level 1.10 remains \(600{,}000(1.10/1.10)=600{,}000\). Thus on-level earned premium is \(440{,}000+600{,}000=1{,}040{,}000\).
Step 2: Trend losses. Apply the supplied loss trend factor once: \(1{,}260{,}000(1.08)=1{,}360{,}800\).
Step 3: Divide adjusted losses by adjusted premium.
The result is rounded to two decimal places as a percentage. Check: the premium adjustment is 4% overall because the $400,000 at level 1.00 increases by 10%, while the rest is already at target; \(1{,}040{,}000/1{,}000{,}000=1.04\). The losses increase by 8%. A common error is to multiply the premium by the 1.08 loss trend as well. That would change the denominator for a cost trend that applies to losses, not rates, and would no longer represent the stated rate-level adjustment.
A Practical Timing Sequence
A reliable calculation starts with the coverage represented, rather than with a calendar-year total alone. Trace each premium component to its policy term, determine how much of that term is earned in the experience period, and retain the rate level associated with that term. Then adjust the resulting earned-premium amounts to the chosen target. Keep a separate record of the loss period and the cost-level adjustment applied to losses.
Specify the dates represented by the earned premium and associated losses. Do not assume that a calendar-year total consists only of policies effective during that calendar year.
For each policy term, determine the coverage falling within the experience period. Use pro rata earning only when uniform earning over the term is a suitable assumption.
Use the level applicable to the policy term generating the premium, rather than the level in force on the date that portion is earned.
Multiply each earned-premium component by target level divided by its applicable level, then sum the adjusted components.
Apply the selected loss-cost adjustment to the losses and compare those losses with the on-level premium. Confirm that the resulting comparison represents the intended periods.
Assumptions and Common Pitfalls
The calculations above rely on a fixed rate level over each policy term, uniform pro rata earning, and a rate-level index that adequately represents the premium change. Actual premium records may require adjustments for cancellations, endorsements, audit premium, seasonal exposure, or other features that alter how or when premium is earned. If those features are present, use the corresponding premium and earning data rather than forcing the simplified annual-policy calculation.
- Using the earning date to assign the rate level. A policy’s premium can be earned after its effective date while still reflecting the rate level applicable to that policy term.
- Counting a full annual premium in one calendar year. A calendar year usually contains only part of the premium for policies that begin or end during that year.
- Averaging rate-level factors without weights. Aggregate on-leveling must reflect how much earned premium is at each source level.
- Applying trend to premium as well as losses. A loss-cost trend does not change the rate level embedded in earned premium.
- Ignoring what the losses represent. A mathematically correct premium adjustment does not fix a comparison whose losses and premium represent incompatible experience periods.
Check Your Understanding
For each problem, assume pro rata earning unless stated otherwise. Work through the timing before calculating the adjusted amount.
- A 12-month policy effective January 1 has annual premium $960 at level 1.00. What is its calendar-year earned premium on-leveled to 1.08? (Answer: $1,036.80)
- A policy effective October 1, 2023, has annual premium $1,200 at level 1.00. It has no midterm changes. Calculate its calendar-year 2024 earned premium, then on-level that amount to 1.10. (Answer: $990.00)
- A book has earned premium $40,000 at level 1.00 and $60,000 at level 1.15. Calculate on-level earned premium at target level 1.15 and the aggregate factor. (Answer: $106,000; factor 1.0600)
- Losses are $720,000, with a supplied trend factor of 1.05. Earned premium is $200,000 at level 1.00 and $300,000 at level 1.10. Calculate the loss ratio using losses trended by 1.05 and premium on-leveled to 1.10. (Answer: 145.38%)
- A policy effective April 1, 2024, has annual premium $1,500 at level 1.00; a second policy effective October 1, 2024, has annual premium $1,760 at level 1.10. Find their combined calendar-year 2024 earned premium on-leveled to 1.10. If calendar-year losses are $1,600 and the supplied loss trend factor is 1.08, find the adjusted loss ratio. (Answer: $1,677.50 on-level earned premium; 103.01% adjusted loss ratio)