Worked Rate Filing From Indication to Submission

From Experience Data to a Filing Package

A rate filing is more than an indicated percentage. It is a connected argument: the experience base is suitable, selected assumptions produce a prospective cost estimate, the proposed rates are compared with that estimate, and the exhibits and memorandum explain the result. A reader should be able to trace each important number back to data or a stated assumption.

This tutorial develops a compact hypothetical filing from supplied experience through submission-ready support. The calculations are aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus. Actual filing requirements vary by jurisdiction, line, and circumstance; the organization below is a working framework, not a claim that every filing must use identical exhibits or wording.

Definition: A rate indication estimates the premium required for a prospective period under selected loss, expense, and profit assumptions. A proposed rate change is the change the insurer requests to implement. They need not be equal, but any difference should be quantified and explained. A filing package supports both the calculation and the requested action.

For a simple average-premium indication, let $L$ be projected loss and loss adjustment expense (LAE) per exposure, $F$ be fixed expense per exposure, $v$ be the variable expense provision as a proportion of premium, and $q$ be the profit and contingency provision as a proportion of premium. The indicated premium per exposure is

R_{\mathrm{ind}}=\frac{L+F}{1-v-q}.

This form assumes that fixed expense is measured per exposure and that variable expenses and the profit provision are proportional to premium. It requires $v+q<1$; otherwise, the denominator is not positive and the formula does not give a finite positive premium. If a filing uses different expense bases or provisions, the formula must be changed to match those assumptions.

If $R_{\mathrm{current}}$ is the current average premium on the same exposure and premium basis, the indicated rate-level change is

g_{\mathrm{ind}}=\frac{R_{\mathrm{ind}}}{R_{\mathrm{current}}}-1.

For an indicated premium based on a credible blend, $L$ may combine the insurer's projected experience with a selected complement. The method is to state the projected experience cost and complement on the same prospective per-exposure basis, blend them using the selected credibility, and then apply the expense and profit assumptions.

Build the Indication and Preserve Its Audit Trail

A compact calculation should make visible the path from raw experience to prospective costs. A typical sequence is to identify the experience period and exposure base, select development and trend assumptions where needed, calculate prospective loss and LAE costs, apply credibility, and then incorporate expense and profit provisions. Each adjustment should have a stated basis. For example, trend is not a substitute for development: development adjusts experience losses to an ultimate basis, while trend adjusts the resulting costs to the prospective cost level.

Define the data basis.
State the coverage, period, exposure unit, premium basis, and whether losses include LAE. Reconcile totals to their source records before making adjustments.

Select and apply assumptions.
Show development, trend, credibility, and other material selections, including the period or quantity to which each applies.

Calculate the indicated level.
Convert prospective costs to premium using the stated expense and profit provisions, then compare the result with premium at current rates.

Reconcile and assemble.
Show how proposed factors affect premium and policyholders, then check that the exhibits and memorandum agree with the calculation.

Worked Example: Projecting Experience and Calculating an Indication

A hypothetical insurer has 10,000 artisan-liability exposure-years. Reported losses and LAE for the selected experience are $4,000,000. The actuary selects a development factor of 1.10 and annual trend of 4% for two years to the prospective period. The selected credibility for the insurer's projected experience is $Z=0.70$, and the complement is $520 per exposure. Current premium is $6,400,000. Fixed expense is $35 per exposure, variable expense is 18% of premium, and the profit and contingency provision is 4% of premium. Calculate the indication and its change from current rates.

Assumptions and method. Treat the supplied experience totals and selected factors as deterministic filing inputs; no probability distribution is assumed for this calculation. Interest and mortality assumptions are not applicable because no cash flows are discounted and no life-contingent benefits are modeled. Apply development first, then trend the developed losses and LAE by two annual periods. Blend the resulting per-exposure cost with the complement, then use the average-premium indication formula.

Step 1: Develop reported losses and LAE. Applying the selected factor gives

\$4{,}000{,}000 \times 1.10=\$4{,}400{,}000.

Step 2: Trend to the prospective period. The two-year trend factor is $1.04^2=1.0816$. Thus projected losses and LAE are

\$4{,}400{,}000 \times 1.0816=\$4{,}759{,}040.

The projected experience cost per exposure is $\$4{,}759{,}040/10{,}000=\$475.904$.

Step 3: Apply credibility. The credible blend is

L=0.70(\$475.904)+0.30(\$520) =\$333.1328+\$156 =\$489.1328.

Step 4: Calculate indicated premium. The denominator is $1-0.18-0.04=0.78$, and the numerator is $\$489.1328+\$35=\$524.1328$. Therefore,

R_{\mathrm{ind}}=\frac{\$524.1328}{0.78} =\$671.965128\ldots .

Current premium per exposure is $\$6{,}400{,}000/10{,}000=\$640$. The indicated change is

\frac{\$671.965128\ldots}{\$640}-1 =0.0499455\ldots .

Result and check. Rounded only at the end, the indicated premium is $671.97 per exposure and the indicated change is +4.99%. At the indicated level, total premium is approximately $\$671.965128\ldots \times 10{,}000=\$6{,}719{,}651.28$, which is about $\$319{,}651.28$ above current premium. Dividing this increase by $\$6{,}400{,}000$ gives the same 4.99% change after rounding. The method avoids the common mistake of applying trend to reported losses without first applying the selected development factor.

Reconcile the Indication With the Proposed Rates

A filing should distinguish the indicated overall rate-level change from the requested change. If the proposal is phased, capped, or otherwise differs from the indication, calculate the requested premium effect on an explicit base. Do not average class percentage changes without weights: the relevant weights for an overall premium impact are the current premiums, unless the filing's stated calculation uses a different appropriate base.

A reconciliation can state the current premium at current rates, indicated premium, proposed premium, and the dollar and percentage differences. If the requested change reflects a practical constraint or a staged implementation, identify that as the reason for the difference and explain how the proposal is supported. Do not describe a proposal as fully implementing the indication if the arithmetic shows otherwise.

Worked Example: Reconciling a Class-Level Proposal

A hypothetical insurer has current premium of $3,000,000 in Class A and $2,000,000 in Class B. Its overall indication is +16%, but the proposed changes are +8% for Class A and +13% for Class B as a first-stage request. Calculate the overall proposed change and quantify the difference from the indication.

Assumptions and method. Treat current class premiums as the exposure weights and assume the proposed factors apply uniformly within each class. The premium and rate calculations are deterministic; no distribution, interest rate, or mortality assumption is used. Compare the premium-weighted proposal with the indicated overall target.

Step 1: Calculate indicated premium. Current premium is $\$3{,}000{,}000+\$2{,}000{,}000=\$5{,}000{,}000$. An overall indication of 16% implies

\$5{,}000{,}000(1.16)=\$5{,}800{,}000.

Step 2: Calculate proposed premium by class.

\begin{aligned} \text{Class A proposed premium}&=\$3{,}000{,}000(1.08)=\$3{,}240{,}000,\\ \text{Class B proposed premium}&=\$2{,}000{,}000(1.13)=\$2{,}260{,}000. \end{aligned}

The proposed total is $\$3{,}240{,}000+\$2{,}260{,}000=\$5{,}500{,}000$. Its overall change is $(\$5{,}500{,}000/\$5{,}000{,}000)-1=10\%$. Equivalently, the premium-weighted calculation is $0.60(8\%)+0.40(13\%)=10\%$.

Step 3: Quantify the reconciliation. The proposal is 6 percentage points below the indicated change. Its premium is $\$5{,}800{,}000-\$5{,}500{,}000=\$300{,}000$ below the indicated premium. Relative to the indicated premium, the proposal is $\$300{,}000/\$5{,}800{,}000=5.1724\%$ lower.

Result and check. The requested overall change is +10%, not +16%, and the indicated-premium gap is $300,000. The method avoids the mistake of taking the unweighted mean of the class changes, which would be $(8\%+13\%)/2=10.5\%$ and would not reflect the different current premium volumes. The filing should state why the first-stage proposal differs from the indication and should not imply that the 10% request fully achieves the 16% indicated level.

Connect the Exhibits and Memorandum

Supporting exhibits should be designed as a connected set rather than as isolated tables. The earned-premium and exposure exhibit establishes the base used in the analysis. The loss and LAE exhibit should make the relevant experience totals and prospective adjustments traceable. The policyholder-impact exhibit should show how the proposed factors translate into premium changes. The memorandum should summarize the choices, results, and reconciliation without contradicting those exhibits.

For each exhibit, label the period, units, and premium or loss basis. State whether the figures are historical, adjusted, or prospective. Where a total is carried from one exhibit into another, check that it agrees exactly or explain any rounding difference. A useful filing check is to recompute the overall proposed impact from the detailed class or policy records, then compare it with the headline change.

Worked Example: Checking Exhibit Totals and Rounding

A hypothetical insurer has 4,000 exposure-years. Its earned premium at current rates is $2,400,000. Projected prospective losses and LAE are $1,440,000, fixed expense is $120,000 in total, variable expenses are 18% of premium, and the profit and contingency provision is 5% of premium. A proposed factor reduces Class A rates by 10% and Class B rates by 25%. Class A has 3,000 exposures at a current average premium of $500; Class B has 1,000 exposures at a current average premium of $900. Calculate the indicated premium and check the proposed-premium exhibit against it.

Assumptions and method. The prospective losses and LAE and the expense selections are supplied on the stated bases. Treat the class exposures and average premiums as exact and the proposed class factors as rounded to whole percentage points for this illustration. The calculations are deterministic; no loss distribution, interest rate, or mortality assumption is used. Calculate the indication using per-exposure amounts, then independently total the proposed class premiums.

Step 1: Check the current-premium base. The class totals are $3{,}000(\$500)=\$1{,}500{,}000$ and $1{,}000(\$900)=\$900{,}000$. Together they equal the stated $\$2{,}400{,}000$.

Step 2: Calculate the indicated premium. Projected loss and LAE cost per exposure is $\$1{,}440{,}000/4{,}000=\$360$. Fixed expense per exposure is $\$120{,}000/4{,}000=\$30$. The variable expense and profit provisions sum to $0.18+0.05=0.23$, so the denominator is $1-0.23=0.77$. Thus

R_{\mathrm{ind}}=\frac{\$360+\$30}{0.77} =\$506.493506\ldots\text{ per exposure}.

Total indicated premium is $\$506.493506\ldots \times 4{,}000=\$2{,}025{,}974.03$, rounded to cents. Compared with current premium, the indicated change is $(\$2{,}025{,}974.03/\$2{,}400{,}000)-1=-15.5844\%$.

Step 3: Calculate the proposed-premium exhibit. Class A's proposed premium is $\$1{,}500{,}000(0.90)=\$1{,}350{,}000$. Class B's proposed premium is $\$900{,}000(0.75)=\$675{,}000$. The proposed total is $\$2{,}025{,}000$, a reduction of $\$375{,}000$ from current premium. Its overall change is $-\$375{,}000/\$2{,}400{,}000=-15.625\%$.

Result and check. The proposed total is $\$2{,}025{,}000$, which is $\$974.03$ below the indicated premium. The difference is consistent with the stipulated whole-percentage-point rounding of class factors; the indicated change is approximately -15.58%, while the proposal produces -15.63%. The method avoids treating a small rounding residual as evidence that the exhibits agree exactly. The memorandum should identify the rounded proposal and report the resulting overall change rather than copy the unrounded indicated percentage as the proposal.

Final Review Before Submission

A concise memorandum can follow the same logic as the calculation: identify the data and exposure basis; summarize material adjustments and selected assumptions; state the indicated change; state the proposed change; and explain any difference between them. It should refer to supporting exhibits in a way that lets a reviewer locate the underlying figures. Do not bury an important assumption in a table heading or use a narrative description that conflicts with the calculation.

Before finalizing a package, check arithmetic, units, and labels. In particular, confirm that:

the exposure base used to calculate per-exposure costs matches the exposure exhibit;
losses and LAE are consistently included or excluded across the data and calculations;
development, trend, and credibility are applied to the intended amounts and periods;
the indicated premium uses expense provisions on the bases stated;
the proposed premium total can be reproduced from the proposed factors and current premium base; and
the memorandum distinguishes the indicated result from the requested action.

A sound filing package is internally reproducible: a reviewer can start with the stated experience, follow the adjustments, recalculate the indication, and verify the proposed premium impact. That audit trail is the practical value of organizing a rate filing from indication to submission.

Check Your Understanding

Work each problem using the stated bases, then compare your result with the answer.

A hypothetical book has 5,000 exposures and reported losses and LAE of $2,000,000. Apply a development factor of 1.00 and annual trend of 0% for one year. Credibility is 60%, the complement is $430 per exposure, fixed expense is $20 per exposure, variable expense is 20% of premium, profit is 5% of premium, and current premium is $500 per exposure. Calculate the indicated premium and rate change. (Answer: $576.00 per exposure; +15.20%.)
Current premium is $4,000,000 in two classes: 60% is in Class A and 40% is in Class B. Proposed changes are +5% and +15%, respectively. Calculate the overall proposed change and proposed premium. (Answer: +9.00%; $4,360,000.)
A proposed filing affects 2,500 exposures with current premium of $1,500,000. The proposed uniform change is +8%. Calculate proposed premium and the dollar increase. (Answer: $1,620,000; $120,000.)
Reported losses and LAE are $900,000, the selected development factor is 1.20, annual trend is 5% for two years, and there are 2,000 exposures. Calculate the prospective loss and LAE cost per exposure. (Answer: $595.35 per exposure.)
Projected loss and LAE cost is $510 per exposure, fixed expense is $40 per exposure, variable expense is 22% of premium, profit is 3% of premium, and current premium is $700 per exposure. Calculate the indicated premium and rate change. (Answer: $733.33 per exposure; +4.76%.)

What You'll Learn