Choosing the Experience Period and Target Level

Why Period Selection Comes First

An on-level calculation answers a specific question: what would premium from the selected experience period have been at the selected target rate level? The calculation is only meaningful when those two periods are defined clearly. A factor based on the wrong dates can be arithmetically correct and still adjust premium inappropriately.

The premium experience period is the span of earned exposure whose premium is being adjusted. The target period is the span for which the indicated premium is intended to represent the rate level. The periods need not have the same dates. They do need to correspond to the intended analysis: the historical premium and exposure must be measured on the stated experience basis, and the target level must reflect the intended prospective period.

Definition: A rate level is an index of premium rates relative to a chosen base level. An average earned rate level for an experience period is the average of the rate-level indices applicable to the exposures earned in that period, weighted by earned exposure. The target rate level is the corresponding level, or average level, for the target period. The on-level factor is the target rate level divided by the average earned rate level for the experience period, provided the exposure basis and underlying mix are comparable.

For example, if a rate change becomes effective partway through a calendar year, a calendar-year earned-premium experience period can include exposure earned at both the old and new levels. Its average level depends on how much exposure was earned under each level. It is not necessarily the level in force at year-end, nor is it generally an average weighted by the dollars of premium.

Define the Periods on the Same Basis

Before calculating a factor, state the premium measure and its dates. Earned premium for a calendar year, written premium for a policy year, and premium associated with accident-year losses do not automatically represent the same exposure period. The period choice should follow the data being adjusted and the intended use of the result.

For this tutorial, suppose the rate level at time $t$, relative to a common base, is $R(t)$, and earned exposure is distributed over the period. The experience average $L_E$ is the exposure-weighted average of $R(t)$ over the experience period. The target average $L_T$ is defined in the same way over the target period, using its exposure distribution. When a single target level applies throughout the target period, $L_T$ is simply that level.

\text{On-level factor}=\frac{L_T}{L_E}

This formula adjusts premium to the target level. It does not decide which dates belong in either period; that is a separate modeling choice. If exposure mix or exposure units differ materially between the two periods, a single factor may not be adequate without further standardization.

Why the Factor Has This Form

The ratio follows from comparing premium at the historical average level with premium at the target level for the same amount of exposure. Assume a common base premium per exposure unit, denoted by $b$, and let total experience-period earned exposure be $e$. If the experience average rate level is $L_E$, the corresponding premium is $b e L_E$. At the target level, premium for that same exposure would be $b e L_T$. Therefore:

\frac{\text{target-level premium}}{\text{experience premium}} = \frac{b e L_T}{b e L_E} = \frac{L_T}{L_E}

The base premium $b$ and exposure $e$ cancel. This justification depends on comparing the same exposure basis at rate levels measured against the same base. If the selected experience period does not match the premium being adjusted, or if the target level does not describe the intended target period, the cancellation does not repair the mismatch.

Worked Applications

Worked Example: Equal Exposure Shares Are Not Equal Premium Shares

A hypothetical insurer measures earned premium for a six-month experience period. During the first three months, the applicable rate level is 1.100; during the next three months, it is 1.045. Earned exposure is 500 units in each half. The target level is 1.100. The base premium is $100 per exposure unit. Find the experience average level, on-level factor, and adjusted premium.

Method. Weight each rate level by earned exposure. Equal exposure in the two halves means equal exposure weights, even though the premium dollars produced at the two levels differ.

The experience-period earned premium is $100 per exposure unit multiplied by exposure and rate level in each half:

500(100)(1.100)=\$55{,}000,\qquad 500(100)(1.045)=\$52{,}250

Total earned premium is $\$55{,}000+\$52{,}250=\$107{,}250$. Total exposure is $500+500=1{,}000$ units. The average earned rate level is:

L_E=\frac{500(1.100)+500(1.045)}{1{,}000} =\frac{550+522.5}{1{,}000} =1.0725

The target level is $L_T=1.100$, so the factor is:

\frac{1.100}{1.0725}=1.025641\ldots

Applying the factor gives $\$107{,}250(1.100/1.0725)=\$110{,}000$, which also equals $1{,}000(100)(1.100)$, the premium for the same exposure at the target level. The check confirms the calculation.

The premium shares are not equal: $\$55{,}000/\$107{,}250\approx51.28\%$ and $\$52{,}250/\$107{,}250\approx48.72\%$. Common mistake: calling the two premium shares 50% each because the exposure shares are equal. The correction is to weight the rate levels by exposure, as above, or to calculate the average level from the actual premium and exposure amounts.

Worked Example: Matching the Experience Period to Earned Exposure

A hypothetical portfolio has calendar-year 2025 earned exposure split equally between two rate levels: 1.00 and 1.20. Its base premium is $1,000 per exposure unit, and total calendar-year exposure is 1,000 units. The target level is 1.20. A separate policy-year summary has 20% of exposure at 1.00 and 80% at 1.20. Calculate the appropriate factor for the calendar-year experience and show the effect of using the policy-year distribution instead.

Method. Use the earned-exposure distribution for the calendar-year premium being adjusted. The policy-year summary has different period boundaries and therefore a different distribution of exposure across rate levels.

For the calendar-year experience, each rate level applies to $0.50(1{,}000)=500$ exposure units. Earned premium is:

500(1{,}000)(1.00)+500(1{,}000)(1.20) =\$500{,}000+\$600{,}000 =\$1{,}100{,}000

The calendar-year average level is $0.50(1.00)+0.50(1.20)=1.10$. Thus the appropriate factor to reach 1.20 is $1.20/1.10=1.090909\ldots$. The adjusted premium is $\$1{,}100{,}000(1.20/1.10)=\$1{,}200{,}000$. This equals $1{,}000$ units at $1,000 per unit and level 1.20.

If the policy-year distribution is substituted, its average level is $0.20(1.00)+0.80(1.20)=1.16$, giving a factor of $1.20/1.16=1.034483\ldots$. Applying that factor to the calendar-year premium gives approximately $\$1{,}137{,}931$, not $\$1{,}200{,}000$. The difference arises because a distribution from a different period was used. Common mistake: treating “policy year” and “calendar year” as interchangeable labels. The period basis must match the earned exposure underlying the premium being adjusted.

Worked Example: The Target Level Is an Average Over the Target Period

A hypothetical insurer uses calendar-year 2024 earned premium as its experience. All exposure in that year is at level 1.00. For calendar-year 2025, the level is 1.00 for January through June and 1.08 for July through December. Assume exposure is earned uniformly across both years and the base premium is $250 per exposure unit. There are 1,000 units in each year. Find the appropriate target average, factor, and on-level premium.

Method. The target is calendar-year 2025, not merely the rate level in force at the end of 2025. With uniform earning, the two six-month portions have equal exposure.

The 2024 experience premium is $1{,}000(250)(1.00)=\$250{,}000$, and its average level is $L_E=1.00$. The 2025 target average is:

$$ L_T=0.50(1.00)+0.50(1.08)=1.04 $$

Therefore, the factor is $1.04/1.00=1.04$, and the adjusted 2024 premium is $\$250{,}000(1.04)=\$260{,}000$. Direct calculation gives the same target-period amount: $1{,}000(250)(1.04)=\$260{,}000$.

Using the latest level, 1.08, as the target would produce $\$270{,}000$, overstating the premium for the stated full-year target by $\$10{,}000$. Common mistake: using an end-of-period rate level when the target is a period containing more than one level. The target average must reflect the target-period exposure distribution.

A Practical Period-Selection Check

A disciplined period definition helps prevent a valid formula from answering the wrong question. State the dates and basis before calculating the factor, then verify the adjusted premium against the intended target.

Name the premium experience period.
Specify whether the premium is earned or written and give its exact start and end dates.

Identify exposure by rate level.
Use exposure earned during those dates to determine the historical average level. Do not substitute premium shares for exposure shares.

Define the target period.
State the dates the indicated premium is intended to represent, including any rate changes within that span.

Calculate and check the factor.
Divide the target average level by the experience average level, apply it to the matched premium, and check that the result represents the same exposure at the target level.

This check matters whenever losses and premium are summarized on different period bases. For instance, losses grouped by calendar year do not by themselves establish that a policy-year premium summary is the matching denominator. The analyst must determine whether the premium being adjusted actually represents the exposure associated with the selected experience period. If the boundary mismatch changes the exposure distribution across rate levels, it can change the factor materially.

Key takeaway: On-leveling is not simply “apply the latest rate change.” Define the experience and target periods first, average rate levels over the exposure earned in each period, and use a factor only when the premium, exposure, and period definitions are consistent.

Check Your Understanding

For each problem, identify the period basis before calculating. Answers use unrounded inputs and give factors to four decimal places.

A hypothetical experience period has four months at level 1.00 and eight months at level 1.09, with exposure earned uniformly. The target level is 1.09. Find the experience average level and factor. (Answer: $L_E=1.0600$; factor $=1.0283$.)
Calendar-year earned exposure is split equally between levels 1.02 and 1.06. The target level is 1.06. Find the average experience level and on-level factor. (Answer: $L_E=1.0400$; factor $=1.0192$.)
All experience premium is at level 1.00. The target calendar year has nine months at 1.03 and three months at 1.07, with uniform exposure. Find the target average and factor. (Answer: $L_T=1.0400$; factor $=1.0400$.)
A calendar-year experience has 30% of earned exposure at level 1.00 and 70% at level 1.10. The target is 1.10. Calculate the average experience level and factor; explain why using the latest level as the experience average would be wrong. (Answer: $L_E=1.0700$; factor $=1.0280$; the experience includes exposure at both levels.)
Calendar-year earned exposure is 40% at level 1.00 and 60% at level 1.15; target level is 1.15. A policy-year summary instead has 20% at 1.00 and 80% at 1.15. Calculate both candidate factors and identify the one appropriate for calendar-year earned premium. (Answer: calendar-year factor $=1.0550$; policy-year factor $=1.0268$; use the calendar-year factor.)

What You'll Learn