Assumption Registers and Change Logs

Why Assumptions Need Their Own Records

A ratemaking result depends not only on data and calculations, but also on choices that may not be directly observed: a trend rate, a development factor, an expense provision, or a rule for treating incomplete information. If these choices are undocumented, a reviewer may see a changed indication without knowing what changed, why it changed, who owns the choice, or which results it affected.

An assumption register records the assumptions used in a defined ratemaking process and the information needed to understand and revisit them. A change log records revisions over time, including the reason for each revision and the model outputs affected. These records complement reproducible workflows and version control: a saved model version can establish which files were run, while the register and log explain the meaning and consequences of the assumptions used.

Definition: An assumption is a selected value, rule, or condition used in analysis where the value or rule is not fully determined by the observed data alone. An assumption register is a structured record of those choices and their supporting context. A change log is a chronological record of revisions that links each change to its rationale, implementation, and affected outputs.

What a Useful Register Records

A register should let a knowledgeable reader answer five questions: What is assumed? Why is it reasonable? What evidence supports it? Who is accountable for maintaining it? How uncertain is it, and when should it be reviewed? The exact fields depend on the use, but a practical record usually includes:

Identity and scope: a unique assumption ID, a concise name, the product or analysis it applies to, and the relevant period or segment.
Specification: the selected value, unit, effective date, and a precise description of how it enters the calculation.
Rationale and evidence: why the choice was made, what data or analysis supports it, and the evidence period or source version.
Ownership: the role responsible for the assumption and for ensuring that it is reconsidered when conditions change.
Uncertainty and limitations: a range, scenario, or qualitative description of uncertainty, along with limitations in the available evidence.
Review controls: the last review date, next review date or triggering event, and the status of the review.

An assumption is not the same thing as an observed data value. For example, the amount of reported loss in a specified extract is a data result; a selected future trend rate applied to that loss is an assumption. A method, such as the formula used to calculate a premium, is also not itself necessarily an assumption, although the method may contain assumptions that should be recorded. This distinction matters because the evidence, owner, and review trigger may differ.

Uncertainty should be described in a way that is useful rather than merely asserted. If a single selected value is used, the register can also state a plausible alternative or range and explain what evidence is missing. The range is not automatically a confidence interval; it may instead be a documented scenario range. State which interpretation applies, and do not imply statistical precision that the evidence does not support.

Connecting an Assumption to an Output

A log entry is incomplete if it says only that an assumption changed. It should identify the prior and revised values, when the change takes effect, why it was made, who authorized or recorded it under the applicable process, and which run and output measures were affected. Record enough information to compare like with like: the data snapshot, model or calculation version, and other assumptions should be held constant when measuring the impact of one change.

For a deterministic annual trend assumption $g$, the projected amount after $n$ annual periods is found by applying the rate once per period. If $C_0$ is the current amount, then each step satisfies $C_t=C_{t-1}(1+g)$. Repeated substitution gives $C_n=C_0(1+g)^n$. Thus, changing $g$ changes the output through every compounded period, not just through a one-time addition of the rate difference. This is why a change log should preserve the period count and units as well as the old and new rates.

C_1=C_0(1+g),\quad C_2=C_0(1+g)^2,\quad \ldots,\quad C_n=C_0(1+g)^n

When multiple assumptions change at once, the total output difference is still useful, but it does not by itself identify each assumption’s separate contribution. If the purpose is to explain individual effects, change one assumption at a time against a stated baseline, or use a clearly specified attribution method. Document interactions where the effect of one assumption depends on another. Never label a total difference as the isolated impact of one revision when other inputs also changed.

Worked Example: Logging a Trend Revision

A hypothetical property rating analysis uses a current loss cost of $500 per exposure and projects it two years. The selected annual trend changes from 4% to 5%. The analysis contains 1,200 exposures. Calculate the change in projected aggregate loss cost and specify the essential log information. Treat the calculation as deterministic: no interest, mortality, or probability distribution is assumed.

Method. Apply annual compound trend to the same current loss cost for the same two-year period, first with the old assumption and then with the revised assumption.

Old projected cost per exposure. The two annual factors are $1.04$ and $1.04$:

500(1.04)^2=500(1.0816)=\$540.80

Revised projected cost per exposure. The two annual factors are $1.05$ and $1.05$:

500(1.05)^2=500(1.1025)=\$551.25

The change per exposure is $\$551.25-\$540.80=\$10.45$. Multiplying by 1,200 exposures gives an old aggregate of $1{,}200(\$540.80)=\$648{,}960$, a revised aggregate of $1{,}200(\$551.25)=\$661{,}500$, and a difference of $\$661{,}500-\$648{,}960=\$12{,}540$. The aggregate change also checks as $1{,}200(\$10.45)=\$12{,}540$.

A useful log entry would identify the trend assumption ID, the old and revised rates, the two-year projection horizon, the reason and evidence for the revision, the accountable owner, and the review date. It would also identify the unchanged loss-cost basis, exposure count, calculation version, and output measure. The result is a $12,540 increase in this specified aggregate output, not a claim that every output in the ratemaking process changes by that amount.

Common mistake avoided: using only one year of trend, or multiplying the two-year per-exposure difference by a different exposure count. The calculation explicitly uses two compounding periods and the stated 1,200 exposures.

Worked Example: Recording a Development-Factor Change

For a hypothetical book, an immature loss amount of $800,000 is projected using a selected development factor. The factor changes from 1.20 to 1.25 after a review of the available development evidence. The resulting projected loss is an input to a later ratemaking calculation. Find the output change and state what the log must preserve. All amounts are deterministic; no interest or probability distribution is used.

Method. Multiply the same immature loss amount by each selected factor, then compare the resulting projected losses.

With the old factor, the projected loss is $800{,}000(1.20)=\$960{,}000$. With the revised factor, it is $800{,}000(1.25)=\$1{,}000{,}000$. The change is $\$1{,}000{,}000-\$960{,}000=\$40{,}000$, an increase.

The log should state that the changed assumption is the selected development factor, with old value 1.20 and revised value 1.25. It should identify the loss basis as $800,000, the applicable maturity and period, the evidence considered, the reason for selecting the revised factor, the owner, and a future review date or trigger. It should link the change to the particular calculation run and projected-loss output. If the data extract or any other assumption also changed between runs, that must be recorded: otherwise, the $40,000 difference cannot be attributed solely to the factor revision.

Check. The factor increased by $1.25-1.20=0.05$, so the projected loss increases by $800{,}000(0.05)=\$40{,}000$, matching the direct calculation.

Common mistake avoided: describing the change as a five percent increase in the projected loss. The factor rose by 0.05 in absolute terms, but its relative increase is $0.05/1.20=0.0417$, or about 4.17%. The output change is $40,000, which is also $40{,}000/960{,}000=0.0417$ of the old projected loss.

Worked Example: Separating an Expense Assumption from Its Output

A hypothetical rating calculation uses a loss cost of $480 per exposure, a fixed expense provision of $18 per exposure, and variable expenses equal to 20% of total premium. The fixed expense assumption is revised to $21; the loss cost and variable expense percentage do not change. Calculate the old and revised premiums per exposure, and describe the change-log comparison. All inputs are deterministic; no interest, mortality, or probability distribution is used.

Method. Let $P$ be premium per exposure and $F$ the fixed expense. The expense relationship is $P=L+F+0.20P$, because variable expense is 20% of total premium. Rearranging gives $0.80P=L+F$, so $P=(L+F)/0.80$.

With $L=\$480$ and $F=\$18$, the old premium is:

P_{\text{old}}=\frac{480+18}{0.80}=\frac{498}{0.80}=\$622.50

With the revised fixed expense $F=\$21$, the revised premium is:

P_{\text{new}}=\frac{480+21}{0.80}=\frac{501}{0.80}=\$626.25

The premium change is $\$626.25-\$622.50=\$3.75$ per exposure. As a check, the fixed expense increased by $3, and the premium increases by $\$3/0.80=\$3.75$, because the variable-expense share applies to the total premium.

The log should link the fixed-expense assumption’s old and new values to both premium outputs and record that the loss cost, variable expense percentage, and calculation method were held constant. It should also record the rationale and supporting evidence for the new provision, the accountable owner, uncertainty or limitations, and the review date.

Common mistake avoided: adding the fixed expense outside the variable-expense gross-up. The expression $18+480/0.80$ would treat the fixed provision as exempt from variable expense, contrary to the stated condition that variable expense is 20% of total premium.

Maintaining a Change Log That Can Be Reperformed

A concise, controlled log can be maintained as a table or structured record. Each revision should have a unique entry and a clear relationship to the corresponding register item. A practical sequence is:

Identify the assumption and baseline.
Record its ID, scope, prior value, effective period, and the run or calculation against which the change will be compared.

Explain the revision.
Record the new value, reason, evidence considered, owner, and any limitations or uncertainty that affect interpretation.

Make a controlled comparison.
Hold the data, method, other assumptions, and relevant units constant when estimating the change attributable to this assumption.

Link the results.
Identify the run, input and model versions, affected output measure, old and new output, and calculated difference.

Set the next review.
Record the review date or a concrete trigger, such as receipt of additional experience or a change in the applicable rating period.

A reviewer should be able to follow the link from a register entry to a log entry, then to the relevant input versions and output comparison. When an assumption is reviewed and retained, record that outcome too, including the review date and evidence considered. A register with only changed assumptions can conceal choices that were reconsidered but left unchanged.

Record element	Question it answers	Example of a useful entry
Rationale and evidence	Why was this value selected?	State the evidence period, source, and reason for the selection.
Owner and review date	Who maintains it, and when is it reconsidered?	Name an accountable role and a date or specific review trigger.
Uncertainty	What limitations or alternatives remain?	Describe a plausible range or scenario and its basis.
Output linkage	What changed in the calculation?	Identify the run, output measure, old result, revised result, and difference.

Common Traps and Practical Checks

Vague evidence: “industry practice” or “actuarial judgment” alone does not show the evidence considered. Record the source, period, and specific rationale, while distinguishing judgment from measured evidence.
No accountable owner: a team name may not identify who ensures that an assumption is reviewed. Assign a responsible role, even if several people contribute.
Uncertainty omitted: a selected point value does not mean the value is known with certainty. Note meaningful limitations and alternatives without presenting a scenario range as a statistical interval unless it is one.
Impact overstated: if data, code, or several assumptions changed together, the total output difference is not automatically the effect of one assumption. Record the other changes or perform a controlled comparison.
Units or periods lost: a 5% annual trend for two years is not the same calculation as a 5% total change or a one-year trend. Preserve units, effective dates, and period counts.
Old entries overwritten: replacing an old value without retaining its history prevents a reader from reconstructing what was previously used. Keep a dated sequence of revisions consistent with the established version-control process.

Key takeaway: A useful assumption record explains the choice; a useful change log explains what changed and links that change to a reproducible comparison of affected outputs. Rationale, evidence, ownership, uncertainty, review timing, and output linkage are all necessary parts of that record.

Check Your Understanding

For each problem, distinguish the assumption record from the output calculation and check that the units and comparison are consistent.

A hypothetical analysis projects a $350 loss cost for two years. Annual trend changes from 3% to 4%, and there are 600 exposures. Find the change in projected aggregate loss cost. (Answer: $4,347 increase.)
A selected development factor changes from 1.15 to 1.18 and is applied to $2,400,000 of unchanged immature losses. Find the projected-loss change. (Answer: $72,000 increase.)
List four items, beyond the new numerical value, that should be recorded when an assumption is revised. (Answer: Any four of rationale, supporting evidence and its period or source, accountable owner, uncertainty or limitation, effective date, review date or trigger, prior value, and affected run and outputs.)
A premium calculation has a $620 loss cost, a $25 fixed expense, and variable expenses equal to 22% of total premium. The fixed expense changes to $30. Find the old and revised premiums and the change per exposure. (Answer: Old $826.92; revised $833.33; increase $6.41 per exposure, rounded to cents.)
A $400 current loss cost is projected for two years using annual trend revised from 3% to 4%, for 1,000 exposures. Calculate the aggregate change and state one condition needed to attribute it solely to the trend revision. (Answer: $8,280 increase; the data, exposure count, calculation method, and other assumptions must be held constant, or any other changes must be separately identified.)

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