Matching Premiums to Class Experience

Why Premium Matching Matters

Class experience is useful only when the premium denominator describes the same insured risk as the experience numerator. If losses are organized by coverage, period, and classification cell, premium should be organized on those same bases. A mismatch can distort a later loss ratio or loss cost comparison even when every amount in the source records is individually correct.

The practical task is to identify the premium earned for the relevant exposure during the experience period, assign each portion to the class that applied while it was earned, and include only the coverage being analyzed. This tutorial focuses on that data construction and its checks, rather than on how to allocate losses or calculate classification relativities.

Definition: A matched earned premium is premium earned for the same coverage, experience period, and classification basis as the experience being studied. A classification cell is defined by the classification attributes in the analysis, such as territory and vehicle use. Premium earned while a risk belongs to one cell is assigned to that cell; a later class change does not retroactively change the earlier assignment.

Time, Coverage, and Class Must All Match

Written premium records the premium associated with policies or transactions written during a period. Earned premium recognizes premium over the time insurance coverage is provided. Consequently, written premium for a calendar year is not generally the same as premium earned during that year: policies can begin before the year, end after it, or change during it.

For a policy segment with premium $P$ earned uniformly over a term of $T$ days, the premium earned during an overlapping interval of $d$ days is $P(d/T)$. A segment is a portion of a policy term for which the relevant coverage, premium rate, and classification assignment are constant. Split a policy at an effective date when any of those attributes change, then calculate and assign the earned premium for each segment separately.

EP_{\text{segment, period}} = P_{\text{segment}} \frac{d_{\text{overlap}}}{T_{\text{segment}}}

Here, $P_{\text{segment}}$ is the premium for the entire segment term, and $d_{\text{overlap}}$ is the part of that term inside the experience period. This straight-line method assumes uniform earning over time. Where a valid earning pattern is seasonal or otherwise nonuniform, use the applicable earning basis instead of assuming that each day earns the same amount.

Why Straight-Line Apportionment Works

Under uniform earning, each day of a segment earns the same fraction of its total premium. With total premium $P$ over $T$ days, the amount earned per day is $P/T$. If the experience period contains $d$ days of that segment, it contains $d$ equal daily amounts. Adding those amounts gives $d(P/T)$, which is the apportionment formula.

\underbrace{\frac{P}{T}+\frac{P}{T}+\cdots+\frac{P}{T}}_{d\ \text{days}} = d\frac{P}{T} = P\frac{d}{T}

The formula works only after the segment has been defined correctly. Applying it to an entire policy term despite a midterm class or premium change can assign premium to the wrong cell. Likewise, correct time apportionment cannot fix a coverage mismatch: a package premium is not automatically a valid premium denominator for a single-coverage analysis.

Worked Example: Assigning Premium After a Midterm Class Change

A hypothetical policy covers one vehicle from January 1 through December 31, 2025. The initial annual premium is $1,200, and the vehicle is assigned to class A from January 1 through April 30. An endorsement effective May 1 changes the class to B and changes the annualized premium to $1,800 for the remaining eight months. Find the earned premium by class for all of 2025 and through September 30. Assume uniform monthly earning.

Method. Split the policy at the endorsement date. The initial monthly premium is $ \$1{,}200/12=\$100 $. The revised annualized premium is $ \$1{,}800 $, or $ \$1{,}800/12=\$150 $ per month. Assign each period to the class in force during that period.

Full calendar year. Class A applies for four months, so its earned premium is $4\times \$100=\$400$. Class B applies for eight months, so its earned premium is $8\times \$150=\$1{,}200$. The total is $\$400+\$1{,}200=\$1{,}600$.

Through September 30. Class A has still earned $\$400$. Class B has earned for May through September, or five months: $5\times \$150=\$750$. Cumulative earned premium is $\$400+\$750=\$1{,}150$. Three months remain, so unearned premium is $3\times \$150=\$450$. The check is $\$1{,}150+\$450=\$1{,}600$, the total written premium after the endorsement: the original $\$1{,}200$ plus an $\$400$ adjustment for the eight remaining months.

Common mistake avoided. Assigning the entire revised annualized amount of $\$1{,}800$ to class B and then adding $\$400$ for class A gives $\$2{,}200$. That double counts the first four months. The corrected calculation assigns only the revised rate for the eight months when class B was actually in force.

Constructing a Matched Premium Total

A reliable aggregation starts with the experience basis, not the premium file’s available totals. Specify the dates, coverage, and classification dimensions first. Then identify policy segments that overlap the period and calculate the earned premium for each qualifying segment. Retain the class assignment in force during that segment, and exclude premium for other coverages unless the analysis explicitly includes them.

Define the target.
State the experience period, coverage, and classification attributes to be analyzed.

Identify overlapping policy segments.
Include only segments with covered time inside the target period. Split at effective dates for class, coverage, or premium changes.

Earn and assign premium.
Apply the appropriate earning basis to the overlap, then assign the result to the cell that applied during that overlap.

Reconcile.
Sum the cells and compare with the total premium for the same coverage, period, and classification scope. Investigate differences rather than forcing a match.

Worked Example: Matching Coverage and Calendar-Year Experience

A hypothetical analyst studies liability experience in calendar year 2025. Policy 1 has liability coverage with annual premium of $2,400 for October 1, 2024 through September 30, 2025, and is class C1 throughout. Policy 2 has liability coverage with an annualized premium of $3,600 from July 1 through September 30, 2025, assigned to C2; an October 1 endorsement changes it to C3 and an annualized premium of $4,800. Find 2025 liability earned premium by class, assuming uniform monthly earning. Any property premium is outside the study.

Policy 1. Its term overlaps 2025 from January through September, or nine months. Its earned liability premium in the period is $9/12\times \$2{,}400=\$1{,}800$, all assigned to C1.

Policy 2, July through September. The monthly premium at the C2 rate is $\$3{,}600/12=\$300$. Three months earn $3\times \$300=\$900$, assigned to C2.

Policy 2, October through December. The monthly premium at the C3 rate is $\$4{,}800/12=\$400$. Three months earn $3\times \$400=\$1{,}200$, assigned to C3.

The matched calendar-year liability totals are therefore C1: $\$1{,}800$, C2: $\$900$, and C3: $\$1{,}200$. The overall total is $\$1{,}800+\$900+\$1{,}200=\$3{,}900$. This total includes only liability premium earned in 2025 and assigns each part to the class in force while earned.

Common mistake avoided. Using the full annual premium for Policy 1 would include its October through December 2024 coverage. Using Policy 2’s full annualized premiums would also include time outside 2025 and could misassign the endorsement period. The overlap calculations avoid both errors.

Reconciliation and Audit Checks

Reconciliation is a control on construction, not a substitute for matching. A total can reconcile to a policy system and still be wrong for the analysis if it includes another coverage, another period, or a class assignment that does not apply to the earned time. Useful checks include:

Period check: confirm that each included premium portion corresponds to covered time in the stated experience period.
Coverage check: confirm that the premium represents the coverage being studied. Do not include a package’s unrelated coverage premium merely because it appears on the same policy.
Class check: compare effective dates and class codes with the policy record. Divide the earned amount at a midterm class change rather than applying the current class to the whole term.
Total check: add the cell totals and compare them with an independently calculated total for the same population, coverage, and period.
Transaction check: account for endorsements, cancellations, and corrections without counting both an original amount and its replacement as separate earned premium.

For example, an analyst studying collision experience should not use a combined collision-and-comprehensive premium as the collision denominator without a justified coverage-specific basis. If a source record contains only a bundled amount, the analyst needs a defensible way to obtain the matching coverage premium; assigning the whole bundle to one coverage silently changes the question being answered.

In a rate-level analysis, matching the earned premium to the underlying experience and adjusting premium to a common rate level are distinct tasks. First establish the relevant premium population and its coverage, period, and classification. Apply any needed on-level adjustment on the appropriate basis afterward; an adjustment does not correct an initial coverage or class mismatch.

Common Exam Trap: Using the Policy Effective Year

A frequent error is to include all premium from policies effective during the experience year, as if policy effective year and earned-premium year were interchangeable. They are not. A policy written during the year may earn premium in later periods, while a policy written earlier may earn premium during the year under study. Another common error is to use the current classification for all historical premium instead of respecting the class effective dates.

Worked Example: Reconciling Written Premium to a Calendar-Year Total

A hypothetical analyst needs calendar-year 2025 collision earned premium by class. Three policies have no midterm changes: Policy A is class A, covers January 1 through December 31, 2025, and has $1,200 collision premium; Policy B is class A, covers October 1, 2024 through September 30, 2025, and has $1,800 collision premium; Policy C is class B, covers July 1, 2025 through June 30, 2026, and has $2,400 collision premium. Ignore any other coverage. Calculate matched earned premium by class and compare it with the sum of the three full-term premiums.

Policy A. The full 12-month term is in 2025, so class A earns $\$1{,}200$.

Policy B. Nine of its 12 months, January through September 2025, are in the target period. Class A earns $9/12\times \$1{,}800=\$1{,}350$.

Policy C. Six of its 12 months, July through December 2025, are in the target period. Class B earns $6/12\times \$2{,}400=\$1{,}200$.

The matched totals are class A: $\$1{,}200+\$1{,}350=\$2{,}550$, and class B: $\$1{,}200$. The overall calendar-year total is $\$2{,}550+\$1{,}200=\$3{,}750$. By contrast, the three full-term premiums sum to $\$1{,}200+\$1{,}800+\$2{,}400=\$5{,}400$. That written-term total includes premium earned outside 2025, so it is not the target-period denominator.

Common mistake avoided. Treating the $5,400 full-term sum as 2025 earned premium confuses policy-term premium with calendar-year earned premium. The overlap method produces $3,750 and assigns that amount to the applicable classes.

Key takeaway: Aggregate only the premium earned for the target coverage during the target period, and assign it to the classification cell in force over that earned time. Check the resulting cells against a total constructed on exactly the same basis.

Check Your Understanding

For each problem, identify the relevant overlap and keep coverage and class assignment aligned with the stated experience.

A hypothetical policy has a $1,800 annual premium, covers January through December 2025, and remains in class D throughout. How much is earned during April through September 2025 under uniform monthly earning? (Answer: $900.)
A policy has a $2,400 annual premium for a July 1, 2025–June 30, 2026 term and stays in class E. Find its calendar-year 2025 earned premium under uniform monthly earning. (Answer: $1,200.)
A hypothetical package policy has $1,500 annual liability premium and $900 annual property premium for a full 2025 term. A study includes liability only. What premium belongs in the 2025 liability total? (Answer: $1,500.)
A policy has annualized premium of $1,200 from January through August 2025 in class A. Effective September 1, its annualized premium becomes $1,800 and its class becomes B. Find full-year 2025 earned premium by class under uniform monthly earning. (Answer: Class A $800; class B $600; total $1,400.)
A collision policy earns $600 annualized premium in class F from January through August 2025, then changes to class G with $900 annualized collision premium for September through December. Find calendar-year collision earned premium by class. (Answer: Class F $400; class G $300; total $700.)

What You'll Learn