Purpose and Structure of the Actuarial Memorandum
An actuarial memorandum is the narrative guide to a rate filing. It should enable a reviewer to understand what change is proposed, how the analysis supports that proposal, which material assumptions and selections were made, and where the underlying calculations appear. The memorandum does not replace the filing exhibits: it explains how to read them and why the selected results support the filing position.
A well-organized memorandum follows the reasoning of the analysis rather than presenting a list of calculations without context. It first defines the scope and proposed action, then summarizes the data and methods, reports the principal results, explains important assumptions and judgment, and directs the reviewer to relevant exhibits. The description should be concise enough to navigate but specific enough to be independently understood.
A practical sequence is to use clear section headings that correspond to the analysis. The exact headings depend on the filing, but a reviewer should be able to locate the following without searching through unrelated discussion:
- Scope and proposal: the coverage, territory or other applicable scope, effective date, and requested rate change.
- Data and methods: the experience period, data basis, adjustments, and principal analytical methods.
- Selections and assumptions: the selected factors or provisions and the reasons they are appropriate.
- Results and reconciliation: the indicated result, proposed result, and explanation of any material difference.
- Policyholder impacts and support: a summary of material impacts and precise references to the exhibits that support the discussion.
The earlier material on filing scope, data and experience periods, on-leveling, development, trend, exposure and loss bases, credibility, and expense and profit provisions provides the technical building blocks. The memorandum should summarize the selections needed to understand the filing; it should not reproduce every intermediate calculation when a clear exhibit already provides it.
State the Proposal and the Indication Separately
The memorandum should state the requested change directly and identify the premium base to which that change applies. It should also distinguish the proposed change from the indicated change. The indication is a result of the selected analytical methods and assumptions; the proposal is the rate action being requested. They can differ, and the memorandum should explain a material difference rather than treating the two figures as interchangeable.
When indicated premium need and current on-level premium are measured on the same basis, their ratio gives the indicated premium factor. Subtracting one converts that factor to a percentage change. The sign follows from whether the factor is above or below one.
This relationship follows from the definition of a percentage change. If the current premium base is \(P\) and the indicated need is \(N\), the factor required to move from \(P\) to \(N\) is \(N/P\). A factor of \(1\) means no change, a factor above \(1\) means an increase, and a factor below \(1\) means a decrease. Thus the percentage change is the factor minus \(1\), not one minus the factor.
Worked Example: State the Indicated and Proposed Changes
A hypothetical filing has indicated premium need of $6.60 million and current on-level premium of $6.00 million. The company proposes a 6% increase. Assume both premium amounts are on the same exposure and coverage basis, and that the proposal is applied uniformly to the stated current premium base. Calculate the indicated change and proposed premium, then draft a concise memorandum statement.
Method. Divide indicated premium need by current on-level premium, then subtract one to obtain the indicated percentage change:
The indication is a 10% increase. The proposed premium is calculated separately by applying the proposed 6% factor to the current premium base:
A concise memorandum statement could read: “The selected analysis indicates a 10% increase. The company proposes a 6% increase, which would produce $6.36 million of premium on the stated $6.00 million current on-level premium base. The proposal is below the indicated change.” That final sentence identifies the difference without claiming that the indication itself equals the proposal.
Check. The indicated need of $6.60 million is 10% greater than $6.00 million. The proposed amount, $6.36 million, is 6% greater than $6.00 million. The two calculations use their stated factors and bases. The common mistake avoided is to report the proposal as though it were the indicated result.
Summarize Methods and Selections So Results Can Be Traced
A method summary should identify the principal steps and selections, not merely say that the result was calculated “using standard actuarial methods.” State the relevant experience period and data basis; name material adjustments; identify selected factors or assumptions; and refer to the exhibits where a reviewer can inspect their support. If a method relies on a judgmental selection, state what was selected and give the rationale at a level that makes the choice understandable.
A concise summary can be organized in prose or in a compact table. For each material item, connect three pieces: what was done, what was selected, and where it is documented. Avoid both extremes: a bare conclusion with no traceable support, and a repetition of every exhibit cell in the narrative.
Worked Example: Explain Development and Trend Selections
A hypothetical property filing uses $2,000,000 of reported losses from its stated experience period. Assume the selected loss development factor is 1.08 and the selected cumulative trend factor to the projection period is 1.05. The factors apply sequentially to this loss amount, and no other adjustments are included in this illustration. Calculate the developed and trended amount, then describe how the memorandum should summarize it.
Step 1: Apply the selected development factor. The developed amount is:
Step 2: Apply the selected cumulative trend factor to the developed amount.
The combined factor is \(1.08\times1.05=1.134\), and a check gives \(\$2{,}000{,}000\times1.134=\$2{,}268{,}000\). The memorandum might state: “Reported losses of $2.00 million were developed using a selected factor of 1.08 and trended using a selected cumulative factor of 1.05, producing $2.268 million on the stated projected basis. The loss exhibit presents the underlying calculation and selected factors.” In an actual filing, the period, basis, and exhibit reference should be named precisely.
This is a loss calculation, not a complete rate indication: it does not include other required components of the filing analysis. The assumption that the factors apply sequentially matters; reversing the order would produce the same product here, but applying only one factor would not. The common mistake avoided is presenting a developed and trended loss amount as though it alone established the requested rate change.
Explain Assumptions, Proposal Judgment, and Impacts
A memorandum should make material assumptions visible rather than leaving reviewers to infer them from an exhibit. Depending on the filing, these may include the selected experience period, the treatment of loss development and trend, the exposure or premium basis, credibility treatment, or expense and profit provisions. State assumptions that could materially affect the result, and distinguish a selected assumption from an observed fact.
When the proposed change differs from the indicated change, describe the difference accurately and explain the basis for the proposal. Do not imply that a judgment or constraint changed the underlying indication unless the analytical method itself was changed. Similarly, use impact summaries carefully: the average percentage change per policy and the aggregate premium change need not be the same because policies can have different premium weights.
Worked Example: Distinguish Policy-Count and Premium-Weighted Impacts
A hypothetical filing changes rates for two groups. Group A has 600 policies with average current annual premium of $800 per policy and a proposed 5% increase. Group B has 400 policies with average current annual premium of $1,200 per policy and a proposed 2% decrease. Assume these counts and average premiums represent the same measurement period and that the proposed percentages apply to each group’s current premium. Calculate both the policy-count-weighted average change and the aggregate premium change.
Policy-count-weighted average. Weight each group’s percentage change by its policy count:
Aggregate premium change. First calculate current premium by group:
Total current premium is \(\$480{,}000+\$480{,}000=\$960{,}000\). The proposed premium for Group A is \(\$480{,}000\times1.05=\$504{,}000\). For Group B it is \(\$480{,}000\times0.98=\$470{,}400\). Total proposed premium is \(\$504{,}000+\$470{,}400=\$974{,}400\). Therefore the aggregate premium change is:
The memorandum should not label these as the same measure. It could state that the policy-count-weighted average change is 2.2%, while the aggregate premium change on the stated current premium base is 1.5%. The check is that both groups have equal current premium, so the aggregate change is the average of 5% and negative 2%, or 1.5%. The common mistake avoided is weighting only by policy count when reporting an aggregate premium effect.
Connect Narrative Claims to Filing Exhibits
Exhibit references should be specific and consistent. If the filing uses numbered or lettered exhibits, cite the applicable identifier and, where useful, the relevant section or page. A reviewer should be able to move from a statement in the memorandum to the supporting calculation without guessing which table is intended. For example, a statement about experience data should point to the earned premium and exposure support; a statement about developed losses should point to the loss and loss adjustment expense support; and a statement about distributional effects should point to the policyholder rate impact support.
The memorandum should state the relationship between exhibits rather than merely listing them. If a selected result is summarized in the narrative, identify the exhibit that supports the method and the exhibit that supports the resulting impact, where those are different. Use the same terminology, period labels, units, and selected values across the narrative and exhibits. A mismatch in naming or units can make a technically sound calculation difficult to review.
State the filing scope, effective date, proposed change, and premium or exposure basis used to describe it.
Name the data period, principal methods, material adjustments, and selected assumptions.
Separate the indicated change, proposed change, and policyholder impact measures; explain material differences.
Attach precise references to the exhibits that document each material statement or calculation.
Confirm that figures, signs, units, periods, and terminology agree between the memorandum and exhibits.
Common Memorandum Errors
A frequent sign error is to confuse a factor below one with an increase. For example, if indicated premium need is $7.20 million and current on-level premium is $8.00 million, the indicated factor is \(\$7.20/\$8.00=0.90\). The indicated change is \(0.90-1=-0.10\), or a 10% decrease—not a 10% increase. If a separate proposal is a 3% increase, proposed premium on that $8.00 million base is \(\$8.00\times1.03=\$8.24\) million. The indicated decrease and proposed increase are different results and must be labeled separately.
- Omitting the base. A percentage change is hard to interpret unless the memorandum says what premium, exposure, or policy population it applies to.
- Presenting a selection as a fact. Identify selected assumptions and explain their relevance rather than implying they were directly observed.
- Overstating a partial result. A developed and trended loss amount is not, by itself, a full rate indication.
- Using vague exhibit references. “See supporting exhibits” is less useful than naming the exhibit and the calculation it supports.
- Mixing impact measures. A policy-count-weighted average change is not necessarily the aggregate premium change.
- Leaving a proposal-indication difference unexplained. State both figures and describe the basis for selecting the proposal.
The goal is not to make the memorandum lengthy. It is to make each important statement understandable, reproducible from the filing support, and appropriately qualified. A clear narrative helps a reviewer distinguish what the analysis calculates, what the actuary selects, and what the filing proposes. This organizational discipline is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus.
Check Your Understanding
For each situation, identify the relevant memorandum statement or calculation. Keep the indicated result, proposal, and impact measure distinct.
- A hypothetical filing has indicated premium need of $11.40 million and current on-level premium of $12.00 million. The proposal is a 2% increase on that current base. What are the indicated change and proposed premium? (Answer: 5% indicated decrease; proposed premium is $12.24 million.)
- A proposed change applies to 1,200 policies at +4% and 800 policies at −1%. Each policy is to receive equal weight for the requested policy-count average. What average change should the memorandum report? (Answer: 2.0% policy-count-weighted average increase.)
- A hypothetical loss exhibit shows $4.00 million of losses before trend. The selected cumulative trend factor is 1.1025, and no other adjustment is included. What trended loss amount should the memorandum summarize, and what limitation should it state? (Answer: $4.41 million; it is a trended loss amount, not by itself a complete rate indication.)
- Indicated premium need is $6.30 million and current on-level premium is $7.00 million. The proposal is a 4% decrease on the current base. Calculate both the indicated change and proposed premium. (Answer: 10% indicated decrease; proposed premium is $6.72 million.)
- A filing uses Exhibit B for methods and selected factors, Exhibit C for the proposed premium impact, and Exhibit D for policyholder-level changes. Which exhibits should the memorandum cite when summarizing the selections and the impacts, and what distinction should it preserve? (Answer: Cite Exhibit B for methods and selections, Exhibit C for proposed premium impact, and Exhibit D for policyholder-level changes; distinguish the indicated result from the proposal and distinguish aggregate premium impact from policyholder-level changes.)