Why Diagnostic Checks Matter
A filing can contain individually plausible exhibits that do not agree with one another. A paid-loss total may be correct for one valuation date but inconsistent with a later incurred-loss total; a trend factor may be applied for the wrong number of years; or a stated rate indication may not follow from its displayed loss and expense provisions. These are not cosmetic issues. If the supporting exhibits do not form a traceable calculation, a reviewer cannot readily determine what rate change the analysis supports.
A diagnostic check is a controlled comparison: identify the quantity that should agree, align its definition and basis across exhibits, and then recompute or reconcile it. The earlier material on experience periods, on-leveling, development, trend, exposure bases, credibility, and indicated versus proposed changes supplies many of the underlying selections. Here the emphasis is on testing whether those selections and the filing exhibits have been carried through consistently.
A Structured Diagnostic Sequence
Start with the meaning of each number, not just its printed value. For every exhibit total used in a comparison, identify the population or coverage included, the valuation date, the period measured, the dollar unit, and whether the value is paid, incurred, projected, or on-level. Two amounts can differ without either being erroneous if they refer to different scopes or bases. Conversely, numbers that appear close can conceal an important unit or timing error.
State what is being compared: for example, incurred losses for a specified experience period and valuation date, or annual earned premium for a stated policy population.
Check coverage, experience period, valuation date, dollar units, exposure units, and whether amounts are historical or adjusted. Do not reconcile values until their definitions match.
Use a direct relationship, such as incurred losses equals paid losses plus case reserves, or premium equals exposure times average premium when those quantities have matching definitions.
Follow each selected factor from its source through the intermediate values to the stated exhibit result. Confirm the number of applications and the order of operations.
Record the amount and direction of any difference, identify what must be checked, and avoid silently changing a value to force agreement.
Reconciliation Checks
Some relationships are useful because they connect separate exhibits. For a matching population and valuation date, incurred losses are the sum of paid losses and case reserves. If claim counts and average amounts are shown, multiplying the count by the corresponding average should reproduce the total, subject to stated rounding. Similarly, an earned-premium exhibit can be checked against the exposure and average-premium exhibits when the premium basis and exposure definition are the same.
A check must respect the definitions in the filing. Paid losses plus case reserves need not equal a separately presented incurred amount if, for example, the figures have different valuation dates, scopes, or adjustments. That possibility is a reason to investigate the difference, not a reason to label it reconciled. State the observed direction accurately: “the reported subtotal is $5,000 lower” is not interchangeable with “higher by negative $5,000.”
Worked Example: Reconciling an Incurred-Loss Subtotal
In a hypothetical filing, one exhibit reports paid losses of $300,000 and case reserves of $75,000 for the same stated coverage and experience period. A summary exhibit reports incurred losses of $370,000. A claim-detail control total for the same stated scope is $375,000. Determine whether the summary reconciles, and identify the diagnostic follow-up.
Method. First calculate incurred losses from the component amounts, then compare both the summary and the independent control total with that calculation.
Step 1: Calculate the component total.
Step 2: Compare the reported summary. The summary is $370,000, so its difference from the component total is
The reported subtotal is therefore $5,000 lower than paid losses plus case reserves. It is not $5,000 higher.
Step 3: Check the independent control. The claim-detail control is $375,000, equal to the component total:
On the stated matching scope, the components and detail control agree, while the summary does not. The correct disposition is to investigate the summary’s source and confirm scope, valuation date, adjustments, and units. The arithmetic identifies a $5,000 discrepancy but does not establish its cause.
Common mistake avoided: describing the summary as “higher by negative $5,000.” A negative signed difference means the summary is lower; state the direction in words and use the signed difference only as supporting arithmetic.
Units, Periods, and Factor Tracing
Many filing defects arise because a number is carried into a calculation with the wrong unit or time basis. Examples include dollars confused with thousands of dollars, annual exposures confused with monthly exposures, or a one-year trend factor applied to a two-year projection. Label intermediate results with their units. A result such as “$48.67” is incomplete if the reader cannot tell whether it is dollars per vehicle-year, dollars per claim, or a total.
For a constant annual trend rate \(t\) applied over \(n\) years, the corresponding cumulative factor is \((1+t)^n\). This assumes the same annual compounding rate applies in each of the \(n\) intervals. If the period is fractional or the selected trend varies over time, use the appropriate period-specific factors rather than mechanically using this expression.
Worked Example: Checking the Trend Period and Exposure Unit
A hypothetical auto filing reports $1,080,000 of losses for 24,000 earned vehicle-years. The selected annual trend rate is 4%, and the prospective period is two years after the experience level. Calculate the experience loss cost per vehicle-year, the cumulative trend factor, and the trended loss cost. An exhibit instead shows $46.80 per vehicle-year; diagnose the difference.
Step 1: Calculate the historical loss cost. Divide the loss dollars by earned vehicle-years:
Step 2: Apply trend for the full two-year period.
Step 3: Calculate the projected loss cost.
Rounded to the nearest cent only at the final step, the projected loss cost is $48.67 per vehicle-year. The exhibit’s $46.80 is instead
which applies only one year of trend. The discrepancy is consistent with a period-count error, but the filing support should be traced to confirm whether the intended projection is indeed two full years.
Common mistake avoided: applying the annual trend rate once merely because the stated rate is annual. The number of compounding intervals must match the time from the experience level to the projection level.
Recomputing the Indicated Change
A final diagnostic is to independently reproduce the stated indication from the displayed projected losses, fixed expenses, variable expense provision, and profit provision. The following relationship applies when variable expenses and the profit provision are each expressed as a proportion of premium, fixed expenses are stated as dollars, and projected losses and expenses are on compatible bases. The denominator must be positive. The calculation is not appropriate without modification if the filing defines provisions on a different basis.
Justification. Required premium must cover the projected losses and fixed expenses, as well as variable expenses \(vP\) and the profit provision \(qP\), both of which vary with premium. Moving those two premium-proportional terms to the left gives \(P-vP-qP=L+F\). Factoring out \(P\) yields \(P(1-v-q)=L+F\), and division by the positive denominator gives the stated formula. If current on-level premium is \(P_0\), the uniform indicated rate change is \(P/P_0-1\), provided the comparison uses the same exposure and premium basis.
Worked Example: Testing Whether the Indication Follows from Its Selections
A hypothetical filing has current on-level premium of $1,000,000. Its selected projected losses and loss adjustment expenses are obtained by applying a 1.05 trend factor to a $600,000 base. Fixed expenses are $100,000, variable expenses are 15% of premium, and the profit provision is 5% of premium. Recalculate the required premium and indicated change, then verify the result.
Step 1: Reproduce projected losses and loss adjustment expenses.
Step 2: Calculate the premium denominator. The variable expense and profit proportions total \(0.15+0.05=0.20\), so
Step 3: Calculate required premium.
Step 4: Calculate the indicated rate change.
The selections support a decrease of 8.75%, or a uniform factor of 0.9125. To check the premium equation, variable expenses are \(0.15\times\$912{,}500=\$136{,}875\), and the profit provision is \(0.05\times\$912{,}500=\$45{,}625\). Therefore,
Common mistake avoided: adding the variable expense and profit percentages to the numerator or dividing by \(1+v+q\). They are proportions of the required premium, so they belong on the premium side of the equation and lead to the denominator \(1-v-q\).
How to Report a Diagnostic Finding
A useful diagnostic report is concise but specific. Name the two values, state the observed difference and its direction, and identify the checks needed to determine its cause. For example: “The summary incurred-loss amount is $5,000 lower than paid losses plus case reserves. Confirm that both amounts use the same valuation date, claim scope, adjustment treatment, and dollar units.” This communicates what is known without asserting an unsupported explanation.
When an exhibit fails to reproduce, trace the calculation from inputs to output rather than changing the displayed answer until it matches. Verify the source value, sign, unit conversion, period count, factor order, and rounding point. Recalculate with unrounded intermediate values where possible; round only at the stated reporting precision. If the discrepancy remains, the filing support should identify the corrected value or explain the legitimate basis difference.
- Compare like with like: matching coverage, period, valuation date, and adjustment basis are essential to a reconciliation.
- Keep units visible: distinguish dollars from thousands of dollars and total amounts from per-exposure measures.
- Trace time factors: confirm the number of trend intervals and the direction of adjustment.
- Recompute the endpoint: test that selected inputs reproduce the stated indication, not just an intermediate exhibit.
- Describe the evidence accurately: a discrepancy is a finding to resolve, not permission to infer its cause.
Check Your Understanding
For each hypothetical filing situation, identify the relevant check and calculate the requested result. Answers are included for self-checking.
- An exhibit lists paid losses of $420,000 and case reserves of $80,000 for a stated matching scope and valuation date. A summary incurred-loss amount is $495,000. By how much, and in which direction, does the summary differ from paid losses plus case reserves? (Answer: The reported subtotal is $5,000 lower.)
- A filing reports $240,000 of losses over 8,000 earned exposure units. The annual trend rate is 5%, and the prospective period is two years. Find the historical loss cost and the trended loss cost per exposure unit, rounding the latter to cents. (Answer: $30.00 historical; $33.08 trended, using a factor of 1.1025.)
- A rating exhibit starts with a $500 base rate and applies a territory factor of 1.20 and a limit factor of 0.90. A summary reports a selected rate of $550. Recalculate the selected rate and state the amount and direction of the discrepancy. (Answer: The factors produce $540; the reported rate is $10 higher.)
- Current on-level premium is $2,000,000. Projected losses and loss adjustment expenses are $1,300,000, fixed expenses are $150,000, variable expenses are 12% of premium, and the profit provision is 3% of premium. Calculate required premium and the indicated percentage change. (Answer: Required premium is $1,705,882.35; the indicated change is a 14.7059% decrease.)
- A premium exhibit reports $840,000 of earned premium for 700 exposures. A separate exhibit reports an average premium of $100 per exposure per month for the same population and period. Annualize the monthly amount, calculate the implied annual total, and identify the reconciliation difference. (Answer: $1,200 per exposure per year; implied total $840,000; difference $0.)