Why Premium and Exposure Reports Differ
A policy can be written in one reporting period, provide coverage across several periods, and appear in more than one operational report. For that reason, a written-premium report and an earned-premium report are not expected to match for the same calendar year. Policy counts can differ too: a report of new policies, a report of transactions, and a year-end in-force snapshot answer different questions.
The central monitoring discipline is to align the measure with its date basis. Written premium follows when premium transactions are recorded. Earned premium and earned exposure follow when the associated coverage is provided. A mismatch can create an apparent change in premium per exposure even when the underlying policy terms have not changed.
Time Allocation Under a Pro Rata Convention
For the examples below, assume annual policies, a calendar-year reporting window, and uniform pro rata earning by covered time. A policy-year is one full year of covered exposure. For a policy with full-term premium \(P\), the fraction of premium and exposure assigned to the reporting period is the fraction of the policy term covered in that period. This convention is an accounting allocation; it does not assert that risk is uniform throughout the year.
For a one-year policy, \(m\) covered months correspond to \(m/12\) of a policy-year. If the same pro rata convention applies to premium, the earned premium is \(P(m/12)\). Where policies are earned by exact days instead, the calculation must use the applicable day-count convention consistently. Short-rate cancellations, non-pro-rata earning rules, and exposure bases other than time require their own specified treatment.
The allocation follows directly from the convention: if each equal unit of covered time earns an equal share of the full-term premium, then \(m\) of the policy’s 12 monthly shares earn \(m/12\) of that premium. Exposure is allocated over the same covered time, so \(m\) covered months contribute \(m/12\) policy-year. The formulas therefore use the same time fraction, but premium is measured in dollars and exposure in policy-years.
Worked Example: Calendar-Year Earning Across Three Policy Terms
A hypothetical insurer prepares a calendar-year earned report. Policy A has a $1,200 annual premium and runs from October 1 of the prior year through September 30 of the reporting year. Policy B has a $600 annual premium and runs from July 1 of the prior year through June 30 of the reporting year. Policy C has a $2,400 annual premium and runs from July 1 of the reporting year through June 30 of the next year. Use monthly pro rata earning. There is no interest discounting, mortality assumption, or loss distribution in this deterministic allocation.
Policy A. Its reporting-year coverage is January through September, or 9 months. The earned fraction is \(9/12=0.75\). Therefore:
Policy B. Its reporting-year coverage is January through June, or 6 months. The earned fraction is \(6/12=0.50\). Therefore:
Policy C. Its reporting-year coverage is July through December, or 6 months. The earned fraction is \(6/12=0.50\). Therefore:
Adding the three contributions gives calendar-year earned premium of \(\$900+\$300+\$1{,}200=\$2{,}400.00\) and earned exposure of \(0.75+0.50+0.50=1.75\) policy-years. Policies A and B were written in the prior year; together they contribute \(\$1{,}200.00\) of current-year earned premium and \(1.25\) policy-years. The totals check because each policy’s allocated amount corresponds to precisely its reporting-year covered months.
Method and mistake avoided. Intersect each policy term with the reporting window before calculating the time fraction. Counting only the months after a policy’s effective date within the current year would omit January through September for Policy A and understate both its premium and exposure.
Written Premium, Transactions, and Earned Amounts
Written premium is usually assembled from transaction records within the chosen accounting period. A new policy may create a positive written amount; an endorsement may add or remove premium; and a cancellation may produce a return-premium credit. The exact accounting treatment depends on the reporting rules, so a reconciliation should state whether amounts are gross or net of cancellations and whether it uses transaction posting dates or effective dates.
Earned premium instead assigns the policy premium to covered time. As a result, it can include premium from a policy written before the reporting period, and it can exclude part of premium written during the period when that premium relates to future coverage. An endorsement that changes premium should also be earned over the coverage period to which the additional or return premium applies. It does not automatically create or remove a policy-year of exposure.
Worked Example: Reconciling a Transaction Report to a Calendar-Year Earned Report
A hypothetical insurer reports the following for one calendar year, using monthly pro rata earning and full-term annual premiums. Policy P1 runs January 1 through December 31, has a $1,200 premium, and is written on January 1. Policy P2 runs October 1 of the prior year through September 30 of the reporting year and has a $1,200 premium. Policy P3 runs July 1 of the reporting year through June 30 of the next year, has a $2,400 premium, and is written on July 1. On April 1, an endorsement to P1 adds $120 of premium for coverage from April through December. Assume the endorsement amount applies uniformly across those nine months. There is no interest discounting, mortality assumption, or loss distribution.
Step 1: Calculate written premium. P1 and P3 are the two new policies written in the year. The endorsement is a third premium transaction. Thus written premium is:
The written policy count is 2 if it means distinct new policies issued. The premium transaction count is 3: two policy writings and one endorsement. P2 was written before the reporting year, so it contributes no current-year written premium in this example.
Step 2: Calculate earned premium. P1’s original premium earns for all 12 months, so it contributes \(\$1{,}200(12/12)=\$1{,}200.00\). P2 earns for January through September, or 9 months, so it contributes \(\$1{,}200(9/12)=\$900.00\). P3 earns for July through December, or 6 months, so it contributes \(\$2{,}400(6/12)=\$1{,}200.00\). The endorsement applies to April through December, or 9 months, so it contributes \(\$120(9/9)=\$120.00\) if the stated $120 is the premium for that nine-month coverage period.
On that interpretation, total earned premium is \(\$1{,}200+\$900+\$1{,}200+\$120=\$3{,}420.00\). The endorsement’s full premium is earned because all nine months to which it applies fall inside the reporting year.
Step 3: Calculate earned exposure. P1 contributes \(12/12=1.00\) policy-year, P2 contributes \(9/12=0.75\), and P3 contributes \(6/12=0.50\). The endorsement changes premium but not insured time, so it adds no exposure. Total earned exposure is \(1.00+0.75+0.50=2.25\) policy-years.
As a check, earned premium per earned exposure is \(\$3{,}420/2.25=\$1{,}520.00\) per policy-year. This summary uses earned amounts and should not be calculated by dividing written premium by the earned exposure. The written amount is \(\$3{,}720\), which is \(\$300\) greater than earned premium because it includes P3’s premium for January through June of the next year, while earned premium includes $900 from the prior-year-written P2.
Method and mistake avoided. Keep transaction timing, coverage timing, and endorsement coverage scope distinct. A common error is to earn the endorsement over the full policy year even though its $120 premium applies only to April through December, or to add exposure merely because an endorsement creates another transaction.
Reconcile Counts and Denominators Before Comparing Results
Every reported count needs a definition and a date basis. New-business count might include policies first issued during a period; transaction count can include renewals, endorsements, cancellations, and rewrites; an in-force count is a snapshot on a specified date. Earned exposure is different again: it accumulates covered time across the observation window. A year-end count of policies cannot usually stand in for policy-years earned over the year.
| Measure | What it counts or assigns | Typical date basis |
|---|---|---|
| New-policy count | Distinct policies meeting a defined new-business rule | Issue or effective date, as specified |
| Transaction count | Recorded policy changes or financial transactions | Posting or transaction date |
| In-force count | Policies active at a stated point in time | Snapshot date |
| Written premium | Premium recorded under the selected accounting basis | Transaction or accounting period |
| Earned premium and exposure | Premium and insured time assigned to coverage provided | Coverage within the observation window |
Worked Example: Quantifying a Denominator Error
A hypothetical book has 40 annual policies effective January 1, each with a $1,200 annual premium, and 60 annual policies effective April 1, each with a $1,500 annual premium. All remain in force through December 31. The monitoring window is January through December, and earning is monthly pro rata. There is no interest discounting, mortality assumption, or loss distribution.
The 40 January policies each contribute 12 months of exposure and the full $1,200 premium. Their totals are \(40(12/12)=40\) policy-years and \(40(\$1{,}200)=\$48{,}000.00\) earned premium.
The 60 April policies each contribute 9 months of exposure and \(9/12\) of their annual premium. Their totals are \(60(9/12)=45\) policy-years and \(60(\$1{,}500)(9/12)=\$67{,}500.00\) earned premium.
Thus earned exposure is \(40+45=85\) policy-years and earned premium is \(\$48{,}000+\$67{,}500=\$115{,}500.00\). The earned-premium-per-earned-exposure ratio is \(\$115{,}500/85=\$1{,}358.82\) per policy-year, rounded to cents.
All 100 policies are in force at year-end, but 100 is not the earned-exposure denominator. Dividing \(\$115{,}500\) by the year-end count gives \(\$1{,}155.00\) per policy, which is 15% below the correctly time-weighted ratio: \(1{,}155/1{,}358.8235=0.85\). The difference arises because the 60 April policies each contribute only 0.75 policy-year during the window.
Method and mistake avoided. Sum covered time, not policy snapshots, for an exposure denominator. The calculation is internally checked by the total: 40 full policy-years plus 45 partial policy-years equals 85, not 100. The resulting ratio is a descriptive premium-per-exposure measure; by itself it is not a conclusion about rate adequacy.
Practical Reconciliation Checks
A useful reconciliation starts by fixing the observation window and the measurement basis. Then trace each amount to the policy or transaction that generated it. For policies spanning the start or end of the window, allocate only the intersecting covered time. For premium changes, document the effective coverage period and whether the amount is additional premium or a return premium. Finally, check that the exposure unit and premium basis are compatible before calculating a ratio.
Specify the period, transaction-date or effective-date basis, gross or net premium basis, policy-count rule, and exposure unit.
Sum policy writings, endorsements, cancellations, and other included transactions, retaining the sign and accounting treatment of each item.
For each policy and premium change, determine the covered time that overlaps the observation period and apply the stated earning convention.
Keep transaction counts, distinct-policy counts, point-in-time in-force counts, earned premium, and earned exposure as separate measures until their definitions are aligned.
These checks are useful when operational, finance, and actuarial reports do not agree. A difference may be legitimate because the reports use different dates or units; it may also reveal a missing transaction, a misapplied endorsement period, or an exposure denominator that does not match the premium numerator. A transparent reconciliation makes those possibilities distinguishable and supports monitoring aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
Check Your Understanding
Use monthly pro rata earning for these hypothetical cases unless stated otherwise. Each problem is deterministic; no interest, mortality, or loss-distribution assumption is needed.
- A policy written in the prior year runs from October 1 through September 30 and has a $1,800 annual premium. For a calendar-year report, calculate earned premium and earned exposure. (Answer: $1,350.00 and 0.75 policy-year.)
- A policy written in the prior year runs from April 1 through March 31 and has a $2,400 annual premium. Calculate its earned premium and exposure in the current calendar year. (Answer: $600.00 and 0.25 policy-year.)
- During a calendar year, 25 annual policies with $960 premium each are effective January 1, and 15 annual policies with $1,200 premium each are effective October 1. Calculate total earned premium and exposure for the year. (Answer: $28,500.00 and 28.75 policy-years.)
- Twelve annual policies with a $1,500 premium each are written on October 1. The reporting window is the calendar year containing that October 1. Find the written premium for that year and the earned premium and exposure for the calendar year. (Answer: $18,000.00 written premium; $4,500.00 earned premium; 3.00 policy-years.)
- In a reporting period, an insurer records 30 new annual policies at $900 each, 10 endorsements adding $120 each, and 4 cancellation credits of $300 each. Under a net transaction basis, find written premium, new-policy count, and transaction count. (Answer: $27,000.00 written premium; 30 new policies; 44 transactions.)