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CAS Exam 8 · Rate Regulation and Filings · Tutorial 912 of 989

Responding to Regulatory Objections

Build clear, traceable responses to regulatory objections and show how a revised assumption flows through a rate indication.

Intermediate 10 min read

What You'll Learn

  • Organize an objection response around the regulator’s specific concern and the evidence needed to address it
  • Make calculations reproducible by stating data, methods, assumptions, and units
  • Quantify how a changed trend or catastrophe assumption affects required premium
  • Reconcile an overall rate impact using premium-weighted policyholder changes
  • Distinguish an assumption revision from a presentation correction
  • Identify common response errors, including unsupported conclusions and inconsistent denominators

What a Useful Objection Response Must Do

A regulatory objection identifies a concern about a filing’s data, method, assumption, presentation, or compliance with applicable requirements. A useful response does more than repeat the filing’s conclusion. It makes the issue explicit, supplies evidence that another reviewer can reproduce, explains whether anything has changed, and shows the effect of that change on the filing.

The response should be concise enough to answer the question directly, but complete enough that the regulator does not have to infer how a result was obtained. If an assumption is unchanged, explain why the support remains appropriate. If an assumption is revised, identify the old and new values and trace the revision through the relevant calculation. If an exhibit was wrong, correct it and reconcile the corrected exhibit to the filing’s other totals.

Definition: A regulatory objection response is a documented answer to a regulator’s stated concern. A complete response (1) restates the issue accurately, (2) provides reproducible evidence or calculations, (3) explains any unchanged or revised assumption, and (4) quantifies the effect on the indicated or proposed rates and any affected exhibits.

Keep the response aligned with the scope of the objection. A question about the projection period calls for evidence about the selected period and the resulting projected losses, not an unrelated defense of every filing assumption. Likewise, if a regulator asks how policyholder impacts were averaged, show the weighting basis and the arithmetic behind the reported average.

A practical response sequence is:

1
Restate the concern.
Describe the specific assumption, calculation, exhibit, or explanation at issue. Do not answer a different or broader question.
2
Show the support.
Identify the data period, units, selections, method, and calculation needed to reproduce the result. Distinguish observed values from selected assumptions.
3
State the disposition.
Say whether the filing’s treatment is retained, revised, or corrected. Explain the actuarial reason for that disposition without overstating what the evidence establishes.
4
Quantify and reconcile the effect.
Show the old and new results on a consistent basis, identify affected exhibits, and confirm how revised totals reconcile to the filing.

Make the Calculation Reproducible

A calculation is reproducible when a reviewer can identify its inputs, follow each operation, and obtain the stated result. In practice, name the relevant data and period, give units, show the formula, and retain enough intermediate values to expose where an assumption enters. Avoid unexplained labels such as “adjusted loss” when the adjustment can be stated explicitly.

When a response revises the indicated premium, state the premium formula and its assumptions. For example, suppose projected losses are \(L\), fixed expenses are \(F\), variable expenses are a fraction \(v\) of premium, and the target profit provision is a fraction \(p\) of premium. Under this simplifying setup, required premium \(P\) satisfies the following equation.

$$ P=L+F+vP+pP $$

The premium includes projected losses and fixed expenses, while variable expenses and the profit provision are calculated as percentages of premium. Collecting the premium terms gives:

$$ P(1-v-p)=L+F \qquad\Longrightarrow\qquad P=\frac{L+F}{1-v-p} $$

This expression applies only when the stated expense and profit provisions are defined as fractions of premium and the same definitions are used consistently. If the filing uses a different expense treatment, the response must use that treatment instead; the formula is not a substitute for checking the filing’s actual methodology.

Worked Example: Responding to a Trend Objection

A hypothetical filing projects $1,000,000 of losses for two years using a 5% annual trend. The regulator asks why the filing did not use a 4% annual trend. After reviewing the support, the actuary revises the selection to 4%. Fixed expenses are $100,000, variable expenses are 15% of premium, the profit provision is 5% of premium, and the current premium base is $1,400,000. Quantify the effect on required premium and indicated rate change.

Method. Restate the objection as a question about the selected annual trend, calculate both projections over the same two-year period, and apply the same premium formula to each. This avoids comparing values that use different time periods or denominators.

At 5%, the two-year trend factor is \(1.05^2=1.1025\). The original projected losses are:

$$ \$1{,}000{,}000(1.1025)=\$1{,}102{,}500 $$

At 4%, the factor is \(1.04^2=1.0816\), so the revised projected losses are:

$$ \$1{,}000{,}000(1.0816)=\$1{,}081{,}600 $$

The loss projection decreases by \(\$1{,}102{,}500-\$1{,}081{,}600=\$20{,}900\). The premium denominator is \(1-0.15-0.05=0.80\). Thus the original required premium is:

$$ \frac{\$1{,}102{,}500+\$100{,}000}{0.80} =\frac{\$1{,}202{,}500}{0.80} =\$1{,}503{,}125 $$

The revised required premium is:

$$ \frac{\$1{,}081{,}600+\$100{,}000}{0.80} =\frac{\$1{,}181{,}600}{0.80} =\$1{,}477{,}000 $$

The required premium therefore decreases by \(\$1{,}503{,}125-\$1{,}477{,}000=\$26{,}125\). Relative to the stated current premium base, the original rate change is \(\$103{,}125/\$1{,}400{,}000=7.37\%\), and the revised rate change is \(\$77{,}000/\$1{,}400{,}000=5.50\%\), rounded to two decimal places. The revision reduces the indicated change by 1.87 percentage points. The calculation checks: the premium reduction is \(\$20{,}900/0.80=\$26{,}125\), matching the difference between the two required premiums.

A complete response would also briefly identify the support for the revised selection and state which filing exhibits are updated. The arithmetic quantifies the effect; it does not by itself establish why 4% is the appropriate assumption.

Explain the Disposition, Not Just the Answer

The response should separate three situations that are easy to blur together. First, the assumption may remain unchanged because the evidence supports it; explain the evidence and why it addresses the objection. Second, the assumption may be revised because further review supports a different selection; show the revised value and its consequences. Third, the assumption may be unchanged but the response or exhibit may need clarification or correction. In that case, say what was corrected and whether the correction changes the indicated result.

Avoid claiming that a result is “reasonable” without describing the basis for that conclusion. If relevant, identify the experience period, data limitations, selection procedure, and sensitivity of the result to plausible alternatives. A sensitivity calculation can show the size of an effect, but it should not be presented as proof that one assumption is correct.

Worked Example: Revising a Catastrophe Load

A hypothetical filing includes a catastrophe provision based on expected annual event counts of 0.020 for events with average loss of $2,000,000 and 0.010 for events with average loss of $5,000,000. A regulator asks for support for the first event-count assumption. In response to the review, the actuary revises that count to 0.015; the second count is unchanged. Projected non-catastrophe losses are $900,000, fixed expenses are $60,000, variable expenses are 18% of premium, and the profit provision is 2% of premium. Calculate the original and revised required premiums, and quantify the effect.

Method. Calculate the expected annual catastrophe loss as event count times average loss for each event type, then add it to non-catastrophe losses. This calculation assumes the counts are expected annual frequencies on the same exposure basis as the projected losses and the stated average losses are appropriate for that basis.

The original catastrophe provision is:

$$ (0.020)(\$2{,}000{,}000)+(0.010)(\$5{,}000{,}000) =\$40{,}000+\$50{,}000 =\$90{,}000 $$

After revising the first expected count, the provision is:

$$ (0.015)(\$2{,}000{,}000)+(0.010)(\$5{,}000{,}000) =\$30{,}000+\$50{,}000 =\$80{,}000 $$

The premium denominator is \(1-0.18-0.02=0.80\). With the original provision, projected losses are \(\$900{,}000+\$90{,}000=\$990{,}000\), so required premium is:

$$ \frac{\$990{,}000+\$60{,}000}{0.80} =\$1{,}312{,}500 $$

With the revised provision, projected losses are \(\$900{,}000+\$80{,}000=\$980{,}000\), giving:

$$ \frac{\$980{,}000+\$60{,}000}{0.80} =\$1{,}300{,}000 $$

The revised required premium is \(\$12{,}500\) lower, a decrease of \(\$12{,}500/\$1{,}312{,}500=0.95\%\) relative to the original required premium, rounded to two decimal places. As a check, the catastrophe provision fell by \(\$10{,}000\); dividing that decrease by \(0.80\) gives the same \(\$12{,}500\) premium effect.

A response should identify the evidence behind the revised event-count assumption and update the catastrophe provision and premium exhibits. The common mistake is to report only the \(\$10{,}000\) decrease in expected loss as the premium effect. Under the stated formula, the corresponding premium decrease is \(\$10{,}000/0.80=\$12{,}500\).

Reconcile Rate Impacts on a Consistent Basis

A response about policyholder impacts should identify what is being averaged. If the filing reports an overall premium-weighted change, the weights are the old premiums for the groups being compared, provided those premiums are measured on a consistent basis. The aggregate change is the change in total premium divided by the old total premium. An unweighted average of group percentage changes answers a different question.

Worked Example: Correcting an Average Rate Impact

A hypothetical filing reports rate changes for three groups. Their current premiums are $100,000, $60,000, and $40,000, and their respective changes are +10%, −5%, and +20%. A regulator asks how the filing calculated its overall average change. Calculate the aggregate premium-weighted change and compare it with the unweighted average.

Method. Apply each percentage change to that group’s current premium, add the resulting premiums, and compare the new total with the old total. This directly reproduces the aggregate percentage change.

The group premiums after the changes are:

$$ \$100{,}000(1.10)=\$110{,}000,\quad \$60{,}000(0.95)=\$57{,}000,\quad \$40{,}000(1.20)=\$48{,}000 $$

The old total premium is \(\$100{,}000+\$60{,}000+\$40{,}000=\$200{,}000\). The new total is \(\$110{,}000+\$57{,}000+\$48{,}000=\$215{,}000\), an increase of \(\$15{,}000\). Therefore, the premium-weighted change is:

$$ \frac{\$215{,}000-\$200{,}000}{\$200{,}000} =\frac{\$15{,}000}{\$200{,}000} =0.075 =7.50\% $$

The unweighted arithmetic average is \((10\%-5\%+20\%)/3=8.33\%\), rounded to two decimal places. It is not the aggregate premium change because it gives each group equal weight regardless of premium size. The check is that the premium-weighted calculation uses the same \(\$200{,}000\) old-premium total used to form the group weights.

Common mistake and correction. Reporting 8.33% as the overall premium impact confuses the unweighted mean of group changes with the change in total premium. The response should state which measure the filing intends to report and, for an aggregate premium impact, show the total-premium calculation above.

Common Response Traps

  • Answering a nearby question. Restate the actual concern before presenting the analysis. A detailed explanation of a different selection does not resolve the objection.
  • Leaving out units or periods. A trend rate without its annual period, or a loss amount without its exposure basis, is difficult to reproduce and may be misapplied.
  • Showing a new result without a bridge. State the old value, new value, changed input, and resulting difference. Keep the calculation on a consistent basis.
  • Using the wrong denominator. A rate change should be divided by the stated base premium, not by the new premium, unless the filing specifically defines a different measure.
  • Calling a correction an assumption change. A display or arithmetic correction may leave the underlying selection unchanged; describe the distinction and confirm whether totals change.
  • Failing to propagate a revision. A changed assumption may affect multiple linked exhibits. Identify and reconcile those exhibits rather than updating only the paragraph that prompted the objection.
  • Overstating what the calculation proves. Arithmetic verifies the consequence of an assumption. Separate that verification from the evidence supporting the assumption itself.
Key takeaway: A strong objection response is specific, reproducible, and reconciled. It identifies the concern, shows the evidence and calculation, explains whether the filing’s treatment changes, and quantifies the effect using consistent definitions and denominators.

Check Your Understanding

For each hypothetical filing situation, determine the requested result and check that your calculation uses the stated basis.

  1. A filing projects $500,000 of losses for two years at 3% annual trend. A review results in a revised selection of 2%. Calculate both projected loss amounts and the decrease in projected losses. (Answer: $530,450 originally; $520,200 revised; decrease of $10,250.)
  2. A catastrophe provision uses expected annual event counts of 0.015 at $1,200,000 average loss and 0.005 at $4,000,000 average loss. Fixed expenses are $45,000, variable expenses are 16% of premium, and profit is 2% of premium. Calculate the catastrophe provision and its incremental required-premium effect over a filing with no catastrophe provision. (Answer: catastrophe provision $38,000; incremental required premium \(\$38{,}000/0.82=\$46{,}341.46\), rounded to the nearest cent.)
  3. Two groups have current premiums of $80,000 and $120,000 and rate changes of +12.5% and −2.5%, respectively. Calculate the new total premium and the aggregate premium-weighted change. (Answer: new total premium $207,000; aggregate change \(\$7{,}000/\$200{,}000=3.50\%\).)
  4. A filing has projected losses of $720,000 and fixed expenses of $30,000, with variable expenses of 20% and profit of 5% of premium. A revised loss selection reduces projected losses by 5%. Calculate the old and revised required premiums and their changes relative to a current premium base of $980,000. (Answer: old required premium \(\$750{,}000/0.75=\$1{,}000{,}000\), or +2.04%; revised losses $684,000 and revised required premium \(\$714{,}000/0.75=\$952{,}000\), or −2.86%.)
  5. A response reports an overall impact by taking the simple average of three group changes: +8%, +4%, and −6%. The groups’ current premiums are $50,000, $150,000, and $100,000. Calculate the simple average and the aggregate premium-weighted impact, and state which represents the change in total premium. (Answer: simple average 2.00%; new premiums $54,000, $156,000, and $94,000, totaling $304,000 versus $300,000 old premium; aggregate change is +1.33%, which represents the change in total premium.)

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