Reconciling Indicated and Proposed Rate Changes

Why Reconcile the Indication and the Proposal?

A rate indication estimates the overall change needed to meet the selected actuarial assumptions and target. A proposed change is the adjustment actually put forward for implementation. The two may differ: a company may choose a smaller, larger, or phased change in light of business judgment or practical constraints. The comparison should make the difference clear without changing the underlying actuarial indication to match the proposal.

This distinction matters because an indicated change is a measure of the actuarial result, whereas a proposed change is a decision informed by that result. A proposal may reflect operational timing, customer impact, competitive considerations, or other documented constraints. Such considerations explain the proposal; they do not, by themselves, alter the indication. Filing requirements and permissible considerations vary by jurisdiction, so a reconciliation should not imply that any particular reason is automatically acceptable.

Definition: The indicated rate change, denoted $I$, is the percentage change from the current rate level to the actuarially indicated rate level on the stated basis. The proposed rate change, denoted $P$, is the percentage change being proposed relative to that same current rate level and for the stated scope and effective period. A complete comparison uses a consistent basis for both figures.

Measuring the Difference

When both changes are stated as percentages of the same current rate level, the simple gap is $I-P$, measured in percentage points. If $I$ is positive and $P<I$, the proposal is below the indication by that amount. A separate relative measure is the portion of the indication not reflected in the proposal, $(I-P)/I$. These measures answer different questions: percentage points describe the difference on the rate-change scale, while the relative measure describes the gap as a fraction of the indication.

\text{Gap in percentage points}=I-P, \qquad \text{relative shortfall}=\frac{I-P}{I}\quad (I\ne 0).

The relative shortfall is meaningful only with care. It is not a second rate change. If the indication is zero, the ratio is undefined; if the indication is negative, the ratio may be unintuitive. In those cases, report the signed percentage-point difference and explain the direction rather than relying on a relative-shortfall percentage.

A further distinction is between an overall change and class-level changes. If different classes have different proposed adjustments, their simple arithmetic average generally does not give the overall premium change. The aggregate depends on the amount of current premium in each class.

Assumptions for premium weighting: Let $B_j$ be the current base premium for class $j$, and let $c_j$ be its proposed percentage change expressed as a decimal. If the calculation holds the base premium mix fixed, the aggregate proposed change is the base-premium-weighted average of the class changes. It is not a forecast of future premium if exposures, mix, coverage, or policyholder behavior change.

P_{\mathrm{agg}} = \frac{\sum_j B_j(1+c_j)-\sum_j B_j}{\sum_j B_j} = \frac{\sum_j B_jc_j}{\sum_j B_j}.

Why the Weighted Formula Holds

The aggregate formula follows by calculating proposed premium and comparing it with current premium. Under the fixed-base assumption, class $j$'s proposed premium is $B_j(1+c_j)$. Summing across classes gives total proposed premium. Subtracting total current premium leaves the dollar increase; dividing that increase by total current premium expresses it as a percentage. Expanding the numerator gives the weighted formula:

\begin{aligned} \text{Proposed premium}-\text{current premium} &=\sum_j B_j(1+c_j)-\sum_j B_j\\ &=\sum_j B_jc_j,\\ P_{\mathrm{agg}} &=\frac{\sum_j B_jc_j}{\sum_j B_j}. \end{aligned}

This is why a class with more current premium contributes more to the aggregate result. The formula assumes the same base premium amounts are used to measure both the current and proposed levels. If the filing uses a different exposure basis or premium mix, the weights must be appropriate to that stated basis.

Worked Example: Quantifying an Overall Shortfall

For a hypothetical personal-lines filing, the indicated overall change is $12.5\%$, while the proposed change is $8.0\%$. Both are measured from the same current rate level and apply to the same scope and effective period. Determine the gap in percentage points and the relative shortfall. This is a deterministic comparison of stated rate changes; no interest, mortality, or probability distribution is assumed.

Method. Subtract the proposed change from the indication to obtain the percentage-point gap:

12.5\%-8.0\%=4.5\text{ percentage points}.

The proposal therefore implements 8.0 percentage points of the indicated 12.5-point change. To express the unimplemented portion relative to the indication, divide the gap by the indication:

\frac{12.5\%-8.0\%}{12.5\%} = \frac{4.5}{12.5} = 0.36 = 36\%.

Check. The proposal is $64\%$ of the indication because $8.0/12.5=0.64$, and $64\%+36\%=100\%$. The proposal is 4.5 percentage points below the indicated change, a relative shortfall of $36\%$. The relative shortfall is not a 36-point rate change.

Common mistake avoided. Subtracting $8.0/12.5$ from 1 and reporting $36\%$ as the percentage-point gap confuses a relative measure with a rate-change difference. The correct gap is 4.5 percentage points; $36\%$ describes that gap relative to the indication.

Reconciling Class-Level Changes

A filing may show class indications and class proposals that differ from one another. The overall comparison should use the same base premium weights for each set of changes. This allows the reviewer to distinguish two questions: how large is the proposed overall change, and how does it compare with the indicated overall change? A class proposal can be above its class indication even when the overall proposal is below the overall indication, or vice versa.

Worked Example: Aggregating Class Proposals

A hypothetical insurer has three rating classes with current annual base premiums of $2,000,000, $1,200,000, and $800,000. The class indications are $8\%$, $15\%$, and $20\%$; the proposed class changes are $6\%$, $10\%$, and $15\%$. Assume the base premium mix remains fixed for this comparison. Find the indicated and proposed overall changes and their gap. These are deterministic premium calculations; no interest, mortality, or probability distribution is assumed.

Step 1: Find total current premium.

B_{\mathrm{total}} = \$2{,}000{,}000+\$1{,}200{,}000+\$800{,}000 = \$4{,}000{,}000.

The corresponding weights are $2{,}000{,}000/4{,}000{,}000=0.50$, $1{,}200{,}000/4{,}000{,}000=0.30$, and $800{,}000/4{,}000{,}000=0.20$.

Step 2: Aggregate the indicated changes. The indicated dollar increases by class are $0.08(\$2{,}000{,}000)=\$160{,}000$, $0.15(\$1{,}200{,}000)=\$180{,}000$, and $0.20(\$800{,}000)=\$160{,}000$. Total indicated increase is $\$500{,}000$, so:

I_{\mathrm{agg}} = \frac{\$500{,}000}{\$4{,}000{,}000} = 12.5\%.

The weighted calculation gives the same result: $0.50(8\%)+0.30(15\%)+0.20(20\%)=4.0\%+4.5\%+4.0\%=12.5\%$.

Step 3: Aggregate the proposed changes. The proposed dollar increases are $0.06(\$2{,}000{,}000)=\$120{,}000$, $0.10(\$1{,}200{,}000)=\$120{,}000$, and $0.15(\$800{,}000)=\$120{,}000$. Total proposed increase is $\$360{,}000$, giving:

P_{\mathrm{agg}} = \frac{\$360{,}000}{\$4{,}000{,}000} = 9.0\%.

Step 4: Reconcile. The overall proposal is $12.5\%-9.0\%=3.5$ percentage points below the indication. Relative to the indication, the shortfall is $3.5/12.5=28\%$.

Check. The weighted proposal is $0.50(6\%)+0.30(10\%)+0.20(15\%)=3.0\%+3.0\%+3.0\%=9.0\%$, consistent with the dollar calculation. A simple average of the three class proposals, $10.3\%$ when rounded to one decimal, would be wrong because it gives every class equal weight.

Common mistake avoided. Averaging class percentages without considering class premium gives the wrong overall result. Use base-premium weights when the intended comparison is the aggregate change in premium on the stated current mix.

Explaining a Proposal Below or Above the Indication

A useful reconciliation identifies the numerical difference and then explains why the proposal differs. The explanation should be specific enough to connect the decision to the proposed amount or timing. Depending on the filing circumstances and applicable requirements, relevant considerations may include implementation capacity, customer impact, uncertainty in assumptions, competitive strategy, or a deliberate transition plan. These are possible explanations, not universal permissions or substitutes for the indicated result.

A transparent comparison can state the selected indication, the proposed change, the common scope and basis, the measured gap, and the reason for the departure. Where a constraint has a numerical effect, quantify it. For example, distinguish a constraint that limits the first effective-date change from a change to the ultimate target. Avoid wording that implies an indication has been reduced merely because a smaller proposal is preferred.

Keep the indicated result visible as the actuarial benchmark.
Identify whether the proposal differs in amount, timing, or both.
State the base premium or other weighting basis for any aggregate class comparison.
Explain material judgment or implementation constraints and their effect on the proposal.
Do not describe a temporary phase-in as though it were the full indicated change.

Phase-In Plans and Compounding

When changes are applied at successive renewal periods, their cumulative effect is multiplicative. If the first change is $r_1$ and the second is $r_2$, both measured as percentage changes from the rate level immediately before that step, the cumulative change from the original level is $(1+r_1)(1+r_2)-1$. Adding the percentages is only an approximation and is not exact when the adjustments compound.

Worked Example: Measuring a Two-Step Phase-In

A hypothetical filing indicates an $18\%$ change from the current rate level. The proposal applies a $7\%$ increase at the first renewal and plans a second increase so that the cumulative rate change reaches the indicated $18\%$ target. Assume both changes apply successively to the then-current rate level, with no other rate changes. This is deterministic rate arithmetic; no interest, mortality, or probability distribution is assumed.

Step 1: Set the cumulative target. Let $x$ be the second renewal change. Starting from a rate level of 1.00, the first step gives $1.00(1.07)=1.07$. To reach an $18\%$ cumulative increase, the final level must be $1.18$:

$$ 1.07(1+x)=1.18. $$

Step 2: Solve for the second change.

1+x=\frac{1.18}{1.07}=1.102803738\ldots, \qquad x=0.102803738\ldots=10.2804\%.

The second-step increase is therefore $10.2804\%$, rounded to four decimal places. It is larger than the first $7\%$ step because it applies to the already increased rate level.

Check. $1.07(1.102803738\ldots)=1.18$, so the cumulative increase is $18\%$. If instead the proposal applied $7\%$ in each of two periods, the cumulative change would be $1.07^2-1=0.1449=14.49\%$, which remains 3.51 percentage points below the target.

Common mistake avoided. Adding $7\%$ and $10.2804\%$ gives $17.2804\%$, not the cumulative change. Each percentage applies to a different starting rate level; multiply the factors to test the total.

Common Reconciliation Traps

Mixing bases. Comparing a proposed change for one effective period or scope with an indication for another can produce a meaningless gap. State the basis and align it before subtracting.
Confusing percentage points with percent. A move from $12\%$ indicated to $9\%$ proposed is a 3-point gap and a $25\%$ relative shortfall, not a 3% relative difference.
Using unweighted class averages. An overall premium change generally reflects the starting premium distribution, not the number of classes.
Adding phased changes. Successive percentage changes compound. Multiply their rate-level factors.
Recasting the indication as the proposal. A constrained proposal does not change what the indicated result was. Report both and explain the reconciliation.

Key takeaway: Reconciliation has three separate tasks: preserve the actuarial indication as the benchmark, calculate the proposed change on a consistent basis, and explain the amount or timing difference. Use percentage points for the direct gap, appropriate weights for class aggregation, and compounded factors for a phase-in.

Check Your Understanding

For each problem, compare changes on the stated basis and keep percentage-point differences distinct from relative measures.

A hypothetical filing has an indicated change of $11.4\%$ and a proposed change of $8.9\%$, both from the same current rate level. What are the gap in percentage points and the relative shortfall? (Answer: 2.5 percentage points; 21.9% relative shortfall.)
Three classes have current base premiums of $400,000, $350,000, and $250,000. Their proposed changes are $4\%$, $10\%$, and $16\%$. Assuming a fixed base mix, calculate the aggregate proposed change. If the aggregate indication is $12\%$, how far below it is the proposal? (Answer: 9.1% proposed overall; 2.9 percentage points below the indication.)
Two classes account for $70\%$ and $30\%$ of current base premium. Their proposed changes are $5\%$ and $15\%$, respectively. What is the aggregate change, assuming fixed weights? (Answer: 8.0%.)
A proposal applies a $5\%$ increase first and a second increase at the next renewal. What second-step change reaches a cumulative $16\%$ increase from the original rate level? (Answer: $10.4762\%$, rounded to four decimal places.)
A hypothetical insurer has $2,400,000 of current base premium, an indicated change of $9.0\%$, and a proposed change of $6.3\%$. Under a fixed-premium comparison, calculate the proposed dollar increase, the indicated dollar increase, and the dollar gap. (Answer: proposed increase $151,200; indicated increase $216,000; gap $64,800.)

What You'll Learn