Reading a Filing Through a Reviewer’s Lens
A filing can contain extensive exhibits and still leave important questions unanswered. A reviewer’s task is not simply to check whether a calculation can be reproduced. The reviewer also asks whether the data, assumptions, and selections are described clearly enough to understand the result, and whether changes between exhibits have an explained path.
A useful review follows the indication from its inputs to its conclusion. For example, a reviewer may trace earned premium and loss experience through on-leveling, development, trend, credibility, and the proposed rate change. Earlier material on rate indications and filing exhibits supplies the underlying calculations. Here, the focus is on interpreting what those calculations imply about the support provided and identifying where a question is likely to be needed.
A reviewer should distinguish three different situations. A calculation may be arithmetically incorrect; a calculation may be reproducible but rely on a selection whose rationale is not explained; or a selection may be explained but rely on data whose limitations and potential effects are not discussed. These are different review issues and call for different questions.
| Review issue | What the reviewer observes | What needs clarification |
|---|---|---|
| Calculation or reconciliation | A result does not follow from the displayed inputs, or exhibits do not reconcile. | The arithmetic, definitions, or bridge between amounts. |
| Assumption or selection | A factor is stated, but its basis or alternatives are not described. | The rationale, supporting analysis, and sensitivity to alternatives. |
| Data limitation | Experience is incomplete, sparse, revised, or otherwise constrained. | The limitation’s scope, treatment, and potential effect on the result. |
A Practical Review Sequence
A disciplined sequence helps prevent a reviewer from jumping to a conclusion based on one unexplained number. First, establish what each exhibit measures and how it connects to the indication. Then test whether the stated calculation follows from the stated inputs. Finally, consider whether the selected inputs and methods have enough support for the conclusion drawn.
Confirm the period, population, coverage, exposure basis, and dollar basis represented by each amount. Similar labels do not guarantee that two exhibits use the same basis.
Follow displayed inputs through the indicated calculation and compare the result with the amount carried into the next exhibit. Separate a real discrepancy from a difference caused by rounding or a stated change of basis.
Identify selected development, trend, credibility, or other factors. Ask whether the filing explains the data considered, the reason for the selection, and any important alternatives.
Look for incomplete or excluded data, revised methods, changes to assumptions, and differences between indicated and proposed results. Determine whether the filing quantifies or explains their effects.
The purpose of this sequence is not to demand a separate essay for every judgment. It is to make sure a material judgment is identifiable and its role in the result is understandable. A short, well-supported explanation may be more useful than a lengthy exhibit that does not show how its contents informed the selection.
Reconciling Aggregate Rate Changes
Class-level percentage changes should be combined using current premium weights if the question is the aggregate change in total premium at the current mix of business. The weights are not necessarily the shares of policies, exposures, or customers: they are the shares of current premium.
Why the formula holds. The proposed premium for class \(j\) is \(P_j(1+r_j)\). Summing over classes gives proposed total premium \(\sum_j P_j(1+r_j)=\sum_j P_j+\sum_j P_jr_j\). Subtracting current total premium \(\sum_jP_j\) leaves the dollar change \(\sum_jP_jr_j\). Dividing that change by current total premium gives the displayed aggregate percentage change.
Worked Example: Checking a Class-Level Rate Reconciliation
A hypothetical insurer files changes of +6% for Class A and −4% for Class B. Class A has 300 policies with current annual premium of $2,000 per policy; Class B has 700 policies with current annual premium of $1,000 per policy. The filing states that the aggregate change is +0.8%. Check that statement. Assume the listed policy counts and premiums are the complete current mix, and each class change applies uniformly to its current premium. No interest, mortality, or probability distribution model is used.
Method. Recompute current premium by class, apply each percentage change to its own premium, and divide the total dollar change by total current premium.
Class A current premium is \(300\times \$2{,}000=\$600{,}000\). Its proposed dollar change is \(0.06\times \$600{,}000=\$36{,}000\).
Class B current premium is \(700\times \$1{,}000=\$700{,}000\). Its proposed dollar change is \(-0.04\times \$700{,}000=-\$28{,}000\).
Total current premium is \(\$600{,}000+\$700{,}000=\$1{,}300{,}000\). Total dollar change is \(\$36{,}000-\$28{,}000=\$8{,}000\). Therefore, $$ r_{\mathrm{agg}}=\frac{\$8{,}000}{\$1{,}300{,}000}=0.006153846\ldots\approx +0.6154\%. $$ The proposed total is \(\$1{,}300{,}000+\$8{,}000=\$1{,}308{,}000\), which independently gives \(\$1{,}308{,}000/\$1{,}300{,}000-1=0.006153846\ldots\). The filing’s +0.8% does not reconcile to these inputs.
Reviewer question. Ask for the premium weights and calculation supporting the stated aggregate change, and request a reconciliation to the displayed class-level changes. Common mistake avoided: weighting the changes by policy count. The current premium shares are \(600/1{,}300=6/13\) and \(700/1{,}300=7/13\), not the policy shares of 30% and 70%.
Reviewing a Trend Selection
A trend exhibit should make the selected annual rate, the period over which it is applied, and the compounding convention understandable. A numerical factor alone does not establish whether the factor corresponds to the stated rate and period. If the factor differs from a simple recalculation, a reviewer should first check the time units and whether the filing uses compound or simple application.
Worked Example: Checking a Trend Projection Period
A hypothetical filing projects a loss amount of $2,000,000 using a selected annual trend rate of 5% over 1.5 years. It displays a projected amount of approximately $2,152,000. Assume 5% is an effective annual compound rate, the projection period is exactly 1.5 years, and the starting amount is on the stated base date. No interest rate separate from the specified trend, mortality, or loss distribution model is used.
Method. Apply the annual trend multiplicatively over the fractional-year period. The factor is \((1+0.05)^{1.5}\), not \(1+0.05\times1.5\).
First, \(1.05^{1.5}=1.05\sqrt{1.05}\). Since \(\sqrt{1.05}\approx1.0246951\), the factor is approximately \(1.05\times1.0246951=1.0759298\). The projected amount is therefore $$ \$2{,}000{,}000\times1.0759298 =\$2{,}151{,}859.6\text{ (approximately)}. $$ Rounded to the nearest thousand dollars, this is \(\$2{,}152{,}000\), consistent with the filing’s displayed amount at that precision.
Reviewer question. If the exhibit does not show its factor or projection dates, ask it to identify the annual rate, base and target dates, time conversion, and compounding convention. Common mistake avoided: applying a 5% annual rate for 1.5 years as a simple 7.5% increase. That alternative gives \(\$2{,}000{,}000(1+0.05\times1.5)=\$2{,}150{,}000\), which does not use the stipulated compound convention.
Even when the arithmetic checks, a reviewer may still need to understand the selection. Relevant support can include the experience reviewed, the period represented by the data, the observed pattern, and the reason the selected rate and projection period are appropriate for the filing’s stated purpose. A reviewer should avoid assuming that a mechanically reproducible factor is automatically justified.
Selections, Data Limitations, and Changes
A selection is a judgment about which value or method to use from available evidence. The filing should make the selected value visible and explain, at a level appropriate to its materiality, how the evidence led to it. A reviewer may ask what alternatives were considered, whether experience was unusually volatile, and whether the selected value has a meaningful effect on the indicated result.
Data limitations need similar specificity. “Data are limited” is not enough to show what is limited. The reader needs to know, for example, which periods or records are affected, how much experience is involved, what treatment was applied, and whether the limitation could materially affect the result. A limitation does not by itself establish that an indication is wrong; it identifies uncertainty or a constraint that should be described and evaluated.
Worked Example: Examining a Credibility Selection and Limited Experience
A hypothetical filing reports an experience-based amount of $80,000 and a complement amount of $70,000. It selects credibility \(Z=0.60\) and reports a combined amount of $76,000. The filing also states that one quarter of the most recent year’s exposure records was unavailable when the analysis was prepared, but does not say how much of the experience amount came from that year. Assume the stated linear credibility formula applies, both amounts are on the same basis and period, and the unavailable records are not otherwise included. No interest, mortality, or probability distribution model is used for this arithmetic.
Method. Reproduce the stated credibility combination, then identify what the arithmetic can and cannot verify.
Under the stated formula, the combined amount is \(Z\) times the experience amount plus \(1-Z\) times the complement. The complement weight is \(1-0.60=0.40\). The weighted experience amount is \(0.60\times\$80{,}000=\$48{,}000\), and the weighted complement is \(0.40\times\$70{,}000=\$28{,}000\). Their sum is \(\$48{,}000+\$28{,}000=\$76{,}000\), so the displayed combination is arithmetically correct.
The calculation does not establish that \(Z=0.60\) is supported, nor does it show the effect of the missing exposure records. A focused reviewer question would request the basis for the selected credibility and a description or quantification of the missing records’ effect on the experience and resulting amount. Common mistake avoided: treating a correct weighted average as evidence that its credibility selection and underlying data are adequately supported.
Changes from one exhibit or filing period to another deserve particular attention. A change may be reasonable because the data, method, or business mix changed, but the reader needs a bridge. A useful review asks what changed, why it changed, and how much of the final result is attributable to it. Where several changes occur together, a reconciliation can prevent a reviewer from attributing an overall movement to the wrong factor.
Writing Focused Review Questions
A good question is specific, neutral, and answerable. It should point to the evidence that prompted it, rather than presuming misconduct or assuming that an unexplained selection is necessarily unreasonable. It should also ask for information that would help the reviewer evaluate the filing.
- Point to the location: identify the exhibit, period, or factor.
- State the observation: describe the unreconciled amount, unstated basis, or limitation.
- Request useful support: ask for the calculation, definition, data summary, rationale, or sensitivity needed to understand it.
- Keep the scope proportionate: focus first on items that could materially affect the indication or policyholder impacts.
For example, “Please explain the trend selection” is broad. A more useful question identifies the exhibit and requests the annual rate, projection dates, and the analysis supporting the selected rate. Similarly, when two totals differ, first establish whether they use the same period, premium or exposure basis, and level of adjustment. A difference in definitions should not be mislabeled as an arithmetic error.
Check Your Understanding
For each hypothetical situation, identify the review issue and determine the requested calculation or information.
- A filing reports +3% for a group with $900,000 current premium and −2% for a group with $600,000 current premium. Calculate the aggregate change at the current mix and identify the appropriate weight basis. (Answer: \((0.03\times900{,}000-0.02\times600{,}000)/1{,}500{,}000=0.01\), or +1.0%; use current premium weights.)
- A filing trends $1,200,000 for two years at a selected effective annual rate of 4%. Calculate the projected amount, rounded to the nearest dollar. (Answer: \(1{,}200{,}000(1.04)^2=\$1{,}297{,}920\); ask for support for the selected rate if its basis is not shown.)
- A filing combines an experience amount of $50,000 and a complement of $65,000 using \(Z=0.40\), and reports $59,000. Verify the amount and state one additional review issue if the filing gives no basis for \(Z\). (Answer: \(0.40(50{,}000)+0.60(65{,}000)=\$59{,}000\); request the basis or supporting analysis for the selected credibility.)
- A displayed factor is 1.0612 for an annual compound trend rate of 3% over two years. Recalculate the factor and state what the reviewer should ask. (Answer: \(1.03^2=1.0609\); ask for the dates, rate, period conversion, and calculation behind 1.0612.)
- A filing excludes $120,000 of losses from a stated $1,000,000 loss total, but does not describe the excluded records. Identify two items a focused review question should request. (Answer: ask which records and periods the $120,000 represents, and how its exclusion affects the analysis and indicated result.)