Why Diagnose an Expense Provision?
A selected expense provision is a rate component intended to fund expenses under an expected future portfolio and cost level. A calculation can be internally consistent and still produce an implausible result: it may use a historical ratio without allowing for a change in average premium, spread a policy-level cost across exposure units incorrectly, or ignore a shift in the activity that generates the expense. Diagnosis asks whether the selection is reconcilable to the relevant data and assumptions, not merely whether its arithmetic is correct.
The checks in this tutorial are aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus. They are diagnostic tests, not automatic rules for choosing a provision. Differences between a selection and historical experience can be justified, but the reason should be identifiable and supported.
A Consistent Basis Comes First
Before comparing a selection with historical results, identify which expenses are included, which policies and coverages they relate to, the period measured, the premium basis, and the exposure or activity count. Historical expenses and premium must be comparable in timing and scope. If data have been adjusted to a common cost level, use the adjusted values consistently; if they have not, differences in price level may distort the comparison.
Also separate expenses that behave differently. A premium-proportional expense is commonly assessed as a percentage of premium. A fixed cost may be expressed per policy or exposure. A transaction- or claim-driven expense may be more meaningfully related to transaction or claim counts. Combining these components into one ratio can be useful as a summary, but it can conceal a mismatch between the provision and the cost driver.
For a simple diagnostic model, assume the expense amount \(E\) consists of a fixed amount \(F\) for the portfolio and a variable amount equal to fraction \(v\) of premium \(P\):
If the portfolio has \(N\) exposures and the fixed cost is \(f\) per exposure, then \(F=fN\). Dividing the model by premium gives the expected expense ratio:
This decomposition explains why a historical total expense ratio need not remain constant. The variable component remains \(v\) under the model, but the fixed component’s ratio depends on premium per exposure. When premium per exposure rises and the fixed cost per exposure is unchanged, the fixed expense ratio falls. The equation is not appropriate if the expense does not follow the assumed fixed-plus-premium-proportional pattern; in that case, identify a more suitable driver or use a more suitable model.
Worked Example: Reconciling a Historical Expense Ratio
A hypothetical portfolio has 15,000 earned exposure-years and $7,000,000 of earned premium. At a common cost level, it incurred $1,050,000 of commissions, $210,000 of premium-based assessments, and $900,000 of fixed operating expense. A proposed selection uses an 18% variable provision and $60 per exposure for fixed expense. For the prospective period, assume there are 15,000 exposure-years and $500 of premium per exposure. Test the selection against the historical experience.
Method and assumptions. Treat commissions and assessments as premium-proportional expenses, and operating expense as fixed per exposure. Assume the prospective cost level and expense definitions are consistent with the historical figures, and assume the proposed fixed cost remains $60 per exposure.
Step 1: Calculate the historical variable ratio. The two premium-based expenses total:
Therefore, the historical variable expense ratio is:
Step 2: Calculate fixed expense per exposure.
The selected variable percentage and fixed amount therefore match the historical components on their respective bases.
Step 3: Evaluate the prospective total ratio. Prospective premium is \(15{,}000\times \$500=\$7{,}500{,}000\). The variable expense is \(0.18\times \$7{,}500{,}000=\$1{,}350{,}000\), and fixed expense is \(15{,}000\times \$60=\$900{,}000\). Total expense is \(\$2{,}250{,}000\), giving:
As a check, the historical total was \(\$1{,}260{,}000+\$900{,}000=\$2{,}160{,}000\), or \(\$2{,}160{,}000/\$7{,}000{,}000=30.8571\%\). The prospective ratio is lower because the same fixed cost per exposure is divided by higher premium per exposure.
Common mistake. Carrying the historical total ratio of 30.8571% forward unchanged would ignore the change in premium per exposure. The component calculation supports 30% under the stated assumptions. This does not establish that the selection is right if, for example, fixed costs or the mix of expenses have changed; it shows the assumptions needed to reconcile it.
Test the Provision Against Its Cost Driver
A provision should be tested using the unit that most directly explains the expense. If processing costs are incurred per policy, compare the selected amount with cost per policy and forecast policy counts. If handling costs are incurred per claim, compare cost per claim and forecast claim counts. Per-exposure comparisons are still informative, but the number of policies or claims per exposure can change.
A useful diagnostic sequence is to translate both the historical experience and selection to a common basis. For example, if a cost is expected to remain constant per policy, estimate prospective cost by multiplying cost per policy by prospective policies. Then divide by prospective exposure count if the rate provision is stated per exposure. Comparing those results reveals how changes in policies per exposure affect the selected amount.
Determine whether the expense is primarily proportional to premium, fixed per policy or exposure, or driven by another activity.
Match the expense scope, period, cost level, denominator, and portfolio being evaluated.
Apply the selected cost assumption to expected premium, exposures, policies, claims, or other relevant units.
Quantify the difference from the proposed selection and determine whether a documented change explains it.
Worked Example: Testing a Policy-Driven Cost Per Exposure
A hypothetical service operation incurred $720,000 of costs for 12,000 policies, representing 18,000 exposure-years. Historical amounts have already been adjusted to the prospective cost level. The proposed provision is $42 per exposure-year. The forecast is 15,000 policies and 20,000 exposure-years. Assume the service cost remains constant per policy and the expense scope is unchanged. Is the proposed amount consistent with that assumption?
Method and assumptions. Estimate the prospective expense using cost per policy, because the scenario specifies that the service operation’s cost is policy-driven. Convert that amount to a per-exposure basis only after projecting the policy count.
Step 1: Calculate historical cost per policy.
Historical cost per exposure-year is \(\$720{,}000/18{,}000=\$40\), but that figure reflects the historical ratio of policies to exposure-years.
Step 2: Project cost using the policy driver.
The projected cost per exposure-year is:
Step 3: Compare with the selection. The proposed $42 per exposure-year funds \(20{,}000\times \$42=\$840{,}000\). Relative to the projected $900,000, the implied shortfall is \(\$900{,}000-\$840{,}000=\$60{,}000\), or $3 per exposure-year.
Common mistake. Applying the historical $40 per exposure-year gives only \(20{,}000\times \$40=\$800{,}000\), understating projected costs by $100,000. The policy-to-exposure ratio rises from \(12{,}000/18{,}000=0.6667\) policies per exposure-year to \(15{,}000/20{,}000=0.75\). With unchanged cost per policy, the higher ratio increases cost per exposure-year. The proposed $42 requires further investigation under the stated assumptions; a documented productivity improvement or different cost behavior could change the conclusion.
Portfolio Change Can Make a Historical Ratio Misleading
Historical experience is evidence, not a guarantee of future expense. A portfolio can change in size, average premium, policy structure, transaction frequency, claim frequency, or class mix. Each change can affect which denominator is informative and whether a historical unit cost remains applicable. For example, a higher expected number of claims per exposure can increase a claim-driven handling provision even if the cost per claim is unchanged.
The following example isolates that effect. It assumes the expense is proportional to claim count and that cost per claim is stable. If the expense also includes a fixed component or varies with claim complexity, claim count alone may not be sufficient; the difference should prompt a more detailed analysis rather than a mechanical adjustment.
Worked Example: Checking a Claim-Driven Provision After a Frequency Change
A hypothetical coverage incurred $600,000 of claim-handling expense for 4,000 claims across 20,000 exposure-years. For the projected period, the expected volume is 5,000 claims across 20,000 exposure-years. A proposed provision is $30 per exposure-year. Assume all amounts are at the same cost level and handling expense is $150 per claim, with no separate fixed component. Test the selection.
Method and assumptions. Use claims as the cost driver, as specified. Assume unchanged handling cost per claim and use the forecast claim count rather than carrying forward the historical expense per exposure-year.
Step 1: Verify historical cost per claim and frequency.
Step 2: Project total expense.
For 20,000 exposure-years, the implied provision is:
Step 3: Compare with the proposed provision. The $30 selection provides \(20{,}000\times \$30=\$600{,}000\), which is \(\$750{,}000-\$600{,}000=\$150{,}000\) below the cost projected under the assumptions. The claim frequency increases from 0.20 to \(5{,}000/20{,}000=0.25\) claims per exposure-year.
Common mistake. Using the historical $30 per exposure-year as if it were a stable unit cost would miss the increased claim frequency. The calculation does not prove the selection is inadequate if the forecast claim count or $150 unit cost is unsupported; it identifies the assumptions that must be reconciled.
What an Implausible Result Signals
A substantial difference between a selection and a diagnostic benchmark is a reason to ask questions, not necessarily a reason to reject the selection. Investigate whether the comparison uses the same expense scope and premium or exposure definition; whether expenses have been adjusted to a common cost level; and whether the forecast reflects changes in portfolio mix, policy counts, or activity levels. Review whether a fixed cost has been treated as a percentage, whether a variable expense has been treated as fixed, and whether the same expense is included in more than one provision.
Conversely, a close match does not prove the provision is appropriate. Two errors can offset each other, or a historical average can conceal substantial variation. A useful selection should have a traceable rationale: the relevant historical data, the assumed cost driver, the projected activity, and an explanation for material departures from the benchmark.
Check Your Understanding
For each hypothetical situation, identify the relevant diagnostic and calculate the requested result. Assume stated cost levels and expense scopes are comparable unless a question says otherwise.
- A portfolio has $4,800,000 premium, $720,000 of premium-proportional expenses, and $360,000 of fixed expense across 12,000 exposures. Calculate the variable ratio, fixed cost per exposure, and historical total expense ratio. (Answer: 15%; $30 per exposure; 22.5%)
- A policy-driven expense is $540,000 for 9,000 policies and 15,000 exposure-years. The forecast is 10,000 policies and 16,000 exposure-years. Assuming constant cost per policy, calculate projected expense per exposure-year. (Answer: $37.50 per exposure-year)
- Claim-handling expense is $420,000 for 2,800 claims. A forecast has 3,600 claims and 18,000 exposure-years. Assuming constant cost per claim and no fixed component, calculate the implied expense per exposure-year. (Answer: $30 per exposure-year)
- A fixed expense is $48 per exposure and a variable expense is 16% of premium. If prospective premium is $600 per exposure, calculate the combined expense ratio. (Answer: 24%)
- Historical claim frequency is 0.18 claims per exposure-year at $125 handling cost per claim. Forecast frequency is 0.24 claims per exposure-year over 25,000 exposure-years. At the same cost per claim, calculate projected total handling expense and cost per exposure-year. (Answer: $750,000 total; $30 per exposure-year)