Why Policy Dates Matter
An experience period may be defined by calendar dates, while policies begin and end on many different dates. A policy effective date tells you when coverage begins; it does not, by itself, tell you how much of that policy’s exposure or premium belongs to a particular experience period. To make that assignment, compare the policy’s coverage dates with the experience-period boundaries.
Losses require a separate date check. For an experience basis that assigns losses by occurrence date, include a loss when its occurrence date falls within the period and the loss is covered by the policy. Do not assume that the date a policy begins, the date premium is written, or the date a claim is reported is the date that assigns the loss to the experience period.
For the calculations in this tutorial, dates are represented by half-open intervals: a period includes its start date and excludes its end date. Thus a calendar year 2025 is \([ \text{Jan 1, 2025}, \text{Jan 1, 2026})\). A policy effective Jan 1 begins coverage that day; a policy expiring Jan 1 has no coverage on that expiration date. This convention avoids counting a boundary date in two adjacent periods.
Finding the Overlap
Suppose a policy has effective date \(e\) and term length \(T\). Its coverage interval is \([e,e+T)\). Let the experience period be \([a,b)\). The overlap starts at the later of the two start dates and ends at the earlier of the two end dates. If the end is not later than the start, there is no overlap.
Here \(D_{\text{overlap}}\) is measured in the same time units as \(T\). Under a uniform, pro-rata earning assumption, the fraction of the policy term assigned to the experience period is:
If the policy has a constant exposure unit throughout the term, its earned exposure is that unit multiplied by \(f_{\text{earned}}\). If its full-term premium is \(P\), and premium earns uniformly over the term, its earned premium is \(P f_{\text{earned}}\). These calculations assume the exposure and premium are earned evenly through time. They need adjustment when the exposure changes, the policy is cancelled or endorsed, or the applicable earning pattern is not uniform.
The reason for the fraction is direct: under uniform earning, each equal-length part of a policy term earns the same share of the total. If 3 months of a 12-month policy term lie in the experience period, that period receives \(3/12\) of the policy’s full-term exposure and premium. For a portfolio, calculate the overlap policy by policy and add the results; different effective dates generally produce different earned fractions.
Worked Date Mapping
Worked Example: A Policy Spanning Part of a Calendar Year
A hypothetical annual policy is effective April 1, 2024, with a full-term premium of $1,200 and one unit of exposure for the full year. Calculate its earned exposure and earned premium in calendar year 2024. The policy has covered losses of $6,000 from an occurrence on June 1, 2024, and $3,000 from an occurrence on February 1, 2025. Which loss falls in the calendar-year experience period?
Method and assumptions. Use calendar year 2024 as \([\text{Jan 1, 2024},\text{Jan 1, 2025})\). The policy runs from April 1, 2024, to April 1, 2025. Assume uniform pro-rata earning and constant exposure. This is a deterministic date calculation; no interest rate, mortality assumption, or probability distribution is used.
1. Find the overlap. The overlap begins April 1, 2024, and ends January 1, 2025. That is 9 months of the 12-month policy term.
2. Calculate the earned fraction and exposure.
3. Calculate earned premium.
4. Assign losses by occurrence date. June 1, 2024, is within calendar year 2024, and the policy covers that date, so the $6,000 loss is in the period. February 1, 2025, is outside calendar year 2024, so the $3,000 loss is not in that calendar-year experience, even though the same policy covers it.
Check. Nine of the policy’s 12 coverage months lie in 2024, and \(9/12\) of its premium is $900. The loss assignment follows occurrence dates, not the premium-earning fraction. The common mistake is to include the February loss because the policy was effective during 2024; the correction is to test the loss occurrence date against the defined experience period.
Worked Example: Adding Earned Experience for Staggered Policies
A hypothetical insurer has four annual policies, each with a full-term premium of $1,200 and one exposure unit. Their effective dates are January 1, April 1, July 1, and October 1, 2025. Calculate total earned exposure and earned premium in calendar year 2025. Covered losses occur on February 15 for $2,000, May 20 for $4,000, August 10 for $1,000, and November 12 for $3,000. Find the calendar-year loss total.
Method and assumptions. Use \([\text{Jan 1, 2025},\text{Jan 1, 2026})\) as the experience period. Each policy term is 12 months; exposure and premium earn uniformly. Treat each loss date as an occurrence date and assume the corresponding policy covers it. This is deterministic; no interest rate, mortality assumption, or probability distribution is used.
1. Calculate each overlap. The January policy has 12 months in the period. The April policy has 9 months, the July policy has 6 months, and the October policy has 3 months. The respective earned fractions are \(12/12\), \(9/12\), \(6/12\), and \(3/12\).
2. Add earned exposure.
3. Add earned premium.
4. Add losses by occurrence date. All four dates fall in calendar year 2025, so the loss total is:
Check. The earned fractions sum to 30 months, or \(30/12=2.50\) annual exposure units, and the earned premium is \(2.50\) times $1,200. Do not count four full exposure units simply because four policies had effective dates in 2025: the later policies earned only part of their terms in the calendar year.
Worked Example: Partial Policies at Both Period Boundaries
A hypothetical experience period is July 1, 2024, through June 30, 2025, represented as \([\text{Jul 1, 2024},\text{Jul 1, 2025})\). Three annual policies have these terms: April 1, 2024, with premium $2,400; October 1, 2024, with premium $1,800; and April 1, 2025, with premium $1,200. Each has one exposure unit for its full 12-month term. Calculate total earned exposure and earned premium. Covered losses occurred on September 20, December 3, and June 30, with amounts $4,000, $2,500, and $1,000, respectively. A further covered loss of $9,000 occurred on July 1, 2025. Identify the losses in the experience period.
Method and assumptions. Use the stated half-open period, 12-month policy terms, and uniform pro-rata earning. Assume the policies cover the stated losses. This is deterministic; no interest rate, mortality assumption, or probability distribution is used.
1. Find each overlap. The policy effective April 1, 2024, overlaps the experience period from July 1, 2024, through April 1, 2025: 9 months. The October 1, 2024, policy overlaps from October 1, 2024, through July 1, 2025: 9 months. The April 1, 2025, policy overlaps from April 1 through July 1, 2025: 3 months.
2. Calculate the exposure. Each policy has one full-term exposure unit, so the total is:
3. Calculate earned premium policy by policy.
4. Check occurrence dates. September 20, December 3, and June 30 fall within the period, so their losses total \(\$4{,}000+\$2{,}500+\$1{,}000=\$7{,}500\). July 1, 2025, is the excluded end date, so the $9,000 loss is outside this period. Its policy may still be in force, but that does not change the experience-period boundary.
Check. The overlap lengths total 21 months, which is \(21/12=1.75\) annual exposure units. The common mistake is to include the July 1 occurrence because it is adjacent to June 30; the correction is to apply the stated end-date convention consistently.
Dates to Keep Separate
A reliable mapping keeps three questions distinct. First, which part of each policy term overlaps the experience period? This determines earned exposure and, under the stated earning convention, earned premium. Second, which loss occurrence dates fall inside the period? This determines the losses assigned to an occurrence-date experience basis. Third, was each loss covered on its occurrence date? A loss outside the policy term is not made covered merely because some other part of that policy earned in the period.
| Item | Date or interval to check | Role in the mapping |
|---|---|---|
| Policy exposure | Policy effective and expiration dates | Defines the coverage interval whose overlap is measured |
| Earned premium | Policy term and experience-period boundaries | Assigns the appropriate premium portion under the earning convention |
| Occurrence-date loss | Date of occurrence and experience-period boundaries | Determines whether the loss date falls in the period |
| Coverage check | Policy coverage on the occurrence date | Confirms that the policy covers the loss being assigned |
A written premium amount and an earned premium amount are not interchangeable. A full-term premium can be written near a policy’s effective date while being earned over time. Similarly, a policy can contribute earned premium to a period even when it began before that period. The overlap calculation handles both cases without using the effective date as a substitute for the experience-period dates.
Use the stated earning convention and time unit. Month-based pro-rata calculations are convenient when the data and convention use equal months or month boundaries. If the applicable convention earns by day, calculate overlap and term using days instead; do not combine a day-count numerator with a month-count denominator. Changes in exposure, cancellations, and policy endorsements may also require a more detailed schedule than a single uniform fraction.
Check Your Understanding
For each problem, use uniform pro-rata earning and the half-open interval convention unless stated otherwise. These are deterministic calculations; no interest, mortality, or probability model is required.
- A hypothetical annual policy effective November 1, 2024, has a full-term premium of $960. What exposure fraction and earned premium belong to calendar year 2025? (Answer: \(10/12=0.8333\) of the term; $800 earned premium.)
- Three annual policies, each with a $1,500 full-term premium and one exposure unit, are effective January 1, May 1, and September 1, 2025. Calculate their combined earned exposure and earned premium in calendar year 2025. (Answer: 2.00 exposure units and $3,000.)
- A policy effective July 1, 2025, has a 12-month term and a full-term premium of $2,400. For the period October 1, 2025, through March 31, 2026, how much exposure and premium are earned? Are covered occurrences on October 1 and April 1 both in the period? (Answer: \(6/12=0.50\) exposure units and $1,200; October 1 is included and April 1 is excluded.)
- A hypothetical experience period is January 1 through June 30, 2026. Annual policies effective October 1, 2025, January 1, 2026, and May 1, 2026, have full-term premiums of $1,800, $1,200, and $2,400, respectively, and one exposure unit each. Find total earned exposure and premium. (Answer: \(14/12=1.1667\) exposure units and $1,900 earned premium.)
- Calendar year 2026 is the experience period. Three covered losses occur on December 31, 2025, January 1, 2026, and December 31, 2026, with amounts $2,000, $3,000, and $4,000. Which losses belong to the 2026 occurrence-date experience, and what is their total? (Answer: the January 1 and December 31, 2026, losses; $7,000.)