Worked Workshop: Build an Experience Rating Plan

Building a Plan as One Connected Design

An experience rating plan is not just a formula applied to past losses. It is a set of linked choices: which insured unit is rated, what makes it eligible, which years and losses are reviewed, how exposure is measured, what expected-loss benchmark is used, and which part of prospective premium can change. A mismatch among these choices can make a mathematically correct calculation produce an unsound adjustment.

This workshop builds a hypothetical plan for a portfolio of commercial vehicle liability policies. The figures and rules are illustrative, not descriptions of an actual insurer or market. The design process is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.

Definition: An experience rating plan uses an insured risk's experience over a specified period, compared with an expected-loss benchmark for that risk, to adjust a defined portion of its prospective premium. A complete plan specifies the risk unit, eligibility rules, experience period, exposure basis, loss valuation and benchmark, adjustable premium base, and adjustment boundaries.

Set the Design Before Calculating

For the hypothetical vehicle liability plan, suppose the intended risk unit is one insured account under common ownership, with the account's covered vehicles and policies treated together only when their coverage and experience can be matched consistently. The plan rates this liability coverage alone. A separate coverage would need its own appropriately matched experience and benchmark rather than being combined automatically.

The plan's illustrative eligibility rule is that an account must have at least three complete policy years of usable, comparable experience and at least 100 vehicle-years of exposure over those years. An account failing either test does not receive this experience adjustment; it remains on its otherwise applicable manual premium until eligible. These thresholds are design choices, not universal standards.

The experience period is the three most recent completed policy years. Losses are evaluated at a fixed valuation date six months after the end of the third year. For this example, assume the reported losses have been adjusted to the same prospective cost level as the benchmark and are sufficiently mature for the plan's chosen valuation method. In practice, a plan must specify how development, trend, and other adjustments are handled, and must apply its chosen method consistently.

Exposure is measured in vehicle-years: one covered vehicle for one year contributes one vehicle-year, with partial-year exposure prorated by time covered. The expected-loss rate is $480 per vehicle-year. Assume this rate applies to the same liability coverage, risk population, and prospective cost level as the experience losses. The plan sets a fixed credibility weight $Z=0.60$ for an eligible account. Finally, it adjusts only the prospective loss-sensitive premium component; specified fixed charges and other non-adjustable components are excluded.

Plan specification: Before using a rating formula, record the unit being rated, the eligibility test, the experience and valuation periods, the exposure basis, the expected-loss basis, the premium component subject to adjustment, and the plan's minimum and maximum factors. Each item must describe the same coverage and risk.

From Experience to an Adjustment

Let $L$ denote the plan's eligible actual losses after any prescribed adjustments, and let $E$ denote expected losses for the same exposure and coverage. A simple credibility-weighted experience factor is

F_{\mathrm{raw}}=1+Z\left(\frac{L}{E}-1\right).

This form makes the plan's benchmark explicit. If actual losses equal expected losses, the factor is 1. If actual losses exceed expected losses, the factor rises when $Z>0$; if they are below expected losses, it falls. The credibility weight limits how strongly the observed experience changes the factor. This is a specified plan formula for the workshop, not a claim that every experience rating plan uses the same formula.

Why the Credibility-Weighted Formula Has This Form

The formula can be understood as blending the observed loss ratio with the neutral benchmark factor of 1. Under the plan assumption that $Z$ is the weight assigned to the account's observed experience, write the blended factor as $Z$ times the observed ratio plus $1-Z$ times the benchmark factor:

F_{\mathrm{raw}} =Z\frac{L}{E}+(1-Z)(1) =Z\frac{L}{E}+1-Z =1+Z\left(\frac{L}{E}-1\right).

Thus, the formula shrinks the observed loss ratio toward 1. When $Z=0$, the factor is 1 regardless of the observed losses; when $Z=1$, the factor equals $L/E$. This justification relies on interpreting $Z$ as the plan's assigned weight and on having a meaningful, positive expected-loss benchmark. It does not establish that a particular value of $Z$ is appropriate for every risk; that value must come from the plan's design.

Worked Example: Assemble and Calculate the Account Factor

A hypothetical eligible account has 400, 450, and 500 vehicle-years in the three experience years. Its adjusted liability losses for the period total $702,000. Use the plan specifications above: an expected-loss rate of $480 per vehicle-year and $Z=0.60$. The account's prospective premium consists of a $1,200,000 adjustable loss-sensitive component and $300,000 of non-adjustable components. The plan's factor boundaries are 0.85 and 1.20. Calculate its factor and prospective total premium.

Method. First aggregate the matched exposure, then calculate expected losses, the raw factor, the bounded factor, and the premium. The account has three complete years and exceeds the 100 vehicle-year minimum, so it qualifies.

Total exposure is $400+450+500=1,350$ vehicle-years. Expected losses are $1,350\times \$480=\$648,000$. The actual-to-expected ratio is $\$702,000/\$648,000=1.083333\ldots$.

Using the unrounded ratio, the raw factor is $1+0.60(702,000/648,000-1)=1+0.60(0.083333\ldots)=1.05$. This is within the plan boundaries, so the final factor is 1.05.

The adjusted loss-sensitive premium is $\$1,200,000\times1.05=\$1,260,000$. Add the non-adjustable $300,000: prospective total premium is $\$1,260,000+\$300,000=\$1,560,000$.

Check. The adjustment adds $60,000 to the adjustable component, which is 5% of $1,200,000. The fixed component is unchanged. The total, $1,560,000, is therefore consistent with the factor's application to only the specified premium base. The common mistake avoided is applying the factor to the entire $1,500,000.

Exposure and Losses Must Match

A sound benchmark is calculated on the same coverage and exposure basis as the experience being rated. For this plan, vehicle-years are appropriate only if the expected-loss rate is stated per vehicle-year and both the actual losses and the exposure refer to the same liability coverage. The exposure period must also match the loss period. Midterm additions and removals therefore affect the exposure total; using only the number of vehicles at the policy's start or end can misstate expected losses.

The next example isolates that exposure calculation. It assumes a single policy year, constant coverage for each vehicle while insured, and no separate adjustment needed to align the provided loss and expected-loss amounts.

Worked Example: Measure Exposure After Midterm Changes

A hypothetical fleet begins a policy year with 100 covered vehicles. At the start of month 5, 20 vehicles are added. At the start of month 11, 8 vehicles are removed. Assume the policy covers each group continuously for its stated months, the expected-loss rate is $480 per vehicle-year, the eligible actual losses are $56,448, and $Z=0.50$. Find the exposure, expected losses, and raw experience factor.

Method. Divide the year into the three periods with different vehicle counts. The initial 100 vehicles are covered for four months, 120 vehicles for the next six months, and 112 vehicles for the final two months.

The exposure is $100(4/12)+120(6/12)+112(2/12)=33\frac{1}{3}+60+18\frac{2}{3}=112$ vehicle-years.

Expected losses are $112\times \$480=\$53,760$. The actual-to-expected ratio is $\$56,448/\$53,760=1.05$. The raw factor is $1+0.50(1.05-1)=1+0.025=1.025$.

Check. Since actual losses are 5% above expected losses and the plan assigns half weight to experience, the factor is 2.5% above 1. The common mistake avoided is counting only the initial 100 vehicles or using the year-end count of 112 for all 12 months.

Boundaries and the Premium Base

A plan may cap the factor to limit the effect of one period's experience. If the minimum is $F_{\min}$ and the maximum is $F_{\max}$, apply the boundary after calculating the raw factor:

F_{\mathrm{final}}=\min\left(F_{\max},\max(F_{\min},F_{\mathrm{raw}})\right).

The boundaries do not change the experience data or the raw factor; they constrain the factor ultimately applied. The plan must also define which premium components that final factor affects. Applying it to a manual premium that includes fixed charges, taxes, or other components not intended to vary would alter more than the stated plan design.

Worked Example: Apply a Maximum and Separate Fixed Charges

A hypothetical eligible account has expected losses of $60,000 and adjusted actual losses of $90,000. Its plan uses $Z=0.70$, with a minimum factor of 0.90 and maximum factor of 1.25. Its prospective premium comprises a $240,000 adjustable component and $60,000 of non-adjustable charges. Calculate the final factor and total premium.

Method. Calculate the raw factor first, then apply the boundaries, then adjust only the designated premium component.

The loss ratio is $\$90,000/\$60,000=1.50$. Thus, $F_{\mathrm{raw}}=1+0.70(1.50-1)=1+0.35=1.35$. This exceeds the maximum of 1.25, so $F_{\mathrm{final}}=1.25$.

The adjustable component becomes $\$240,000\times1.25=\$300,000$. Adding the unchanged $60,000 gives a prospective total premium of $\$360,000$.

Check. The final adjustment increases the adjustable component by $60,000, or 25%, and leaves the fixed charges unchanged. The common mistake avoided is using the raw 1.35 factor without the maximum, which would produce an unauthorized adjustable premium of $324,000.

Design Checks Before Applying the Plan

A plan's rules should be stated clearly enough that two analysts using the same account data would identify the same experience and produce the same adjustment. Before calculating, verify the following:

Risk unit and eligibility: The account definition and qualifying thresholds are explicit. If the risk is ineligible, the plan states what applies instead of implying that a short history should be rated as though it were complete.
Period and valuation: The experience years and loss valuation date are fixed. Losses are treated under the stated valuation method and brought to a consistent cost level when required by the plan.
Exposure and benchmark: The exposure measure, expected-loss rate, and actual losses refer to the same coverage and period. A rate per vehicle-year cannot be multiplied by a different unit without a justified conversion.
Premium base and boundaries: The plan identifies the premium portion that can change and applies the stated minimum and maximum to the raw factor before calculating premium.

These checks matter because the calculation is only as credible as the alignment of its inputs. For example, a correct loss ratio based on one coverage cannot be used with a benchmark for another, and a correctly calculated factor can still produce an incorrect premium if applied to the wrong base.

Key takeaway: Design the plan as a matched chain: eligible risk unit, experience period, valuation basis, exposure, expected-loss benchmark, and adjustable premium. Calculate the factor only after those elements agree, then apply the plan's boundaries and premium-base rule.

Check Your Understanding

Work each problem using the stated hypothetical plan assumptions. Apply boundaries only when specified.

A plan has 240 exposure units, an expected-loss rate of $325 per unit, actual losses of $85,800, and $Z=0.40$. Find expected losses and the raw factor. (Answer: Expected losses $78,000; raw factor 1.040.)
A fleet has 72 vehicles for the first three months and 96 for the remaining nine months. At $620 per vehicle-year, calculate exposure and expected losses. (Answer: 90 vehicle-years; $55,800.)
For expected losses of $100,000, actual losses of $110,000, and $Z=0.75$, calculate the raw factor. If the plan's boundaries are 0.90 and 1.06, what factor applies? (Answer: Raw factor 1.075; applied factor 1.06.)
A final factor of 0.92 applies to a $480,000 adjustable premium component. A separate $120,000 component is expressly non-adjustable. Find the total after adjustment. (Answer: $561,600.)
A hypothetical plan requires at least two complete experience years and 40 exposure units. An account has two complete years but only 39 units. Is it eligible under this rule? (Answer: No; it fails the 40-unit minimum.)

What You'll Learn