Why Document the Selection?
A rate selection is supported not only by a final percentage but also by the assumptions and judgments that produced it. A useful record lets another actuary trace the selected change to its inputs, understand which alternatives were considered, and see how sensitive the result is to uncertain assumptions. It also distinguishes a calculated indication from a professional judgment made after reviewing that indication.
This tutorial focuses on documenting that reasoning. It does not prescribe a particular selection method. The earlier material on sensitivity analysis, scenario analysis, and communicating the selected rate change provides tools and context; the task here is to preserve their assumptions and conclusions in a clear, reproducible record.
A record should allow a reviewer to answer four questions: What was assumed? What reasonable alternatives were considered? How did those alternatives change the result? Why was the final selection considered appropriate? A list of percentages without those connections is not an adequate explanation.
What a Useful Record Contains
For each material assumption, record its value or definition, its source or basis, and its role in the analysis. Sources may include the experience period, external information, operational constraints, or a documented actuarial judgment. If the assumption is a judgment rather than a directly observed fact, say so. A precise description matters: “trend is 6%” is less informative than “annual loss trend is 6%, selected from the stated experience review, and applied over the defined projection period.”
A practical record commonly includes the following elements:
- Baseline: the selected values and methods used to produce the central indication, including the relevant data period and any material adjustments.
- Alternatives: plausible choices that were tested, with a short explanation of why they were considered relevant.
- Results: the indication under the baseline and each alternative, stated in consistent units.
- Judgments: the rationale for choosing among evidence or for selecting a rate change different from the central indication.
- Limitations: material uncertainty, data constraints, or assumptions that may not be captured by the sensitivity calculations.
- Reproducibility: enough detail about calculations, dates, and inputs that a qualified reviewer can follow the analysis.
The record should distinguish observations from decisions. For example, “the indication is 8.0% under the baseline assumptions” is a modeled result. “The selected change is 7.0% because of the stated implementation constraint” is a selection judgment. Combining the two into “the rate is 7.0%” hides the difference and makes later review harder.
| Record item | Useful description | Commonly inadequate description |
|---|---|---|
| Assumption | Value, definition, period, and where it enters the analysis | A value with no context |
| Alternative | A plausible competing value or method and why it was tested | An unexplained list of possible values |
| Sensitivity | Change in the result relative to the same baseline | A range with no indication of what changed |
| Judgment | Decision, rationale, and evidence considered | A conclusion stated as though it were a calculation |
How to Summarize Sensitivity Results
For a baseline assumption set \(A_0\), let the corresponding indicated rate change be \(R_0\). If one assumption is replaced by an alternative \(A_1\), let the resulting indication be \(R_1\). Report the sensitivity as the change from baseline:
The subtraction is important: it puts the alternative in context and makes the direction and size of the effect explicit. When rate changes are expressed as percentages, report \(\Delta R\) in percentage points. For example, moving from an 8.0% indication to a 6.5% indication is a decrease of 1.5 percentage points, not a decrease of 1.5%.
This comparison has a direct justification. The baseline indication already reflects every assumption held fixed in the analysis. If only one assumption changes, subtracting \(R_0\) from \(R_1\) removes the common baseline result and isolates the modeled difference associated with that change. If multiple assumptions change at once, the difference describes the combined scenario, not the individual effect of any one assumption. Interactions may also mean that separate one-way effects cannot simply be added.
A sensitivity range is not automatically a probability interval, a forecast range, or a guarantee that the actual result will fall within its endpoints. It shows how the modeled indication responds to the tested assumptions. Document the tested alternatives and any important uncertainties that were not tested.
Worked Documentation Examples
Worked Example: Recording a One-Way Assumption Sensitivity
A hypothetical commercial property program has a baseline indicated rate change of 8.0%, using an annual loss trend assumption of 6%. The analysis reports a 5.5% indication at 5% trend and a 10.5% indication at 7% trend. The selected rate change is 7.0%. Prepare a concise record of the trend sensitivity and distinguish the indication from the selection.
Method. Compare each alternative indication with the baseline indication, changing only the trend assumption. Then record the selected change separately and describe its relationship to the baseline indication.
At 5% trend, the change from baseline is \(5.5\%-8.0\%=-2.5\) percentage points. At 7% trend, it is \(10.5\%-8.0\%=+2.5\) percentage points. The tested trend alternatives therefore produce indications from 5.5% to 10.5%, around the 8.0% baseline.
The selected change is 7.0%, which is \(7.0\%-8.0\%=-1.0\) percentage point below the baseline indication. That difference is a selection decision to be explained by its supporting rationale; it is not another trend sensitivity result.
Example record: “Baseline indication: 8.0%, using 6% annual loss trend. Holding other assumptions fixed, the indication is 5.5% at 5% trend and 10.5% at 7% trend, or 2.5 percentage points below and above baseline, respectively. The selected change is 7.0%, 1.0 percentage point below the baseline indication. The selection rationale is documented separately from the modeled trend sensitivity.”
Check. The alternative indications are centered on 8.0%: each is 2.5 percentage points away in the stated direction. The selected change is correctly distinguished from both alternatives. The common mistake avoided is describing the 7.0% selection as if it were the indication produced by the 6% trend assumption.
Worked Example: Documenting Weighted Evidence and an Alternative Weighting
A hypothetical specialty insurer has two indication estimates: 6.0% from one analysis and 10.0% from another. For the baseline, the actuary assigns weights of 70% and 30%, respectively. An alternative weighting of 50% and 50% is also tested. Calculate both weighted indications and state what the record should say.
Method. For each weighting, multiply each estimate by its assigned weight and add the weighted values. The weights for each calculation must sum to 100%.
The baseline calculation is \(0.70(6.0\%)+0.30(10.0\%)=4.2\%+3.0\%=7.2\%\). The weights sum to \(0.70+0.30=1.00\), so the calculation is properly normalized.
Under equal weighting, the result is \(0.50(6.0\%)+0.50(10.0\%)=3.0\%+5.0\%=8.0\%\). Relative to the baseline, this is \(8.0\%-7.2\%=+0.8\) percentage points.
Example record: “The baseline combined indication is 7.2%, weighting the 6.0% estimate at 70% and the 10.0% estimate at 30%. Equal weighting produces 8.0%, an increase of 0.8 percentage points. The record should state why the baseline gives more weight to the first estimate, including the relevant differences in reliability or applicability. The equal-weight result is an alternative, not the selected baseline.”
Check. Both sets of weights sum to 100%, and the alternative is higher because it places more weight on the higher estimate. The common mistake avoided is reporting a weighted result without documenting why the weights were chosen; arithmetic alone does not justify the judgment.
Worked Example: Recording a Two-Assumption Scenario Grid
A hypothetical liability program has a baseline indication of 8.0% at 6% annual loss trend and a 19% expense provision. A sensitivity analysis estimates that changing trend to 5% lowers the indication by 2.5 percentage points, while changing it to 7% raises the indication by 2.5 points. Changing the expense provision to 18% lowers the indication by 1.2 points, while changing it to 20% raises the indication by 1.2 points. Assume the effects are additive for this grid. Calculate and document the four corner scenarios.
Method. Begin with the 8.0% baseline and add the stated effect for each of the two assumptions. Because the problem specifies additive effects, the combined scenario effect is the sum of the two individual effects.
At 5% trend and 18% expense provision, the indication is \(8.0\%-2.5\%-1.2=4.3\%\). At 5% trend and 20% expense provision, it is \(8.0\%-2.5\%+1.2=6.7\%\). At 7% trend and 18% expense provision, it is \(8.0\%+2.5\%-1.2=9.3\%\). At 7% trend and 20% expense provision, it is \(8.0\%+2.5\%+1.2=11.7\%\).
| Annual loss trend | 18% expense provision | 20% expense provision |
|---|---|---|
| 5% | 4.3% | 6.7% |
| 7% | 9.3% | 11.7% |
Example record: “The 8.0% baseline uses 6% trend and a 19% expense provision. Under the stated additive sensitivity assumption, the four combined scenarios range from 4.3% to 11.7%. These are tested scenario indications, not a probability range. The grid assumes no interaction beyond the stated additive effects.”
Check. The low-low scenario is below baseline by \(2.5+1.2=3.7\) points, giving 4.3%; the high-high scenario is above baseline by 3.7 points, giving 11.7%. The common mistake avoided is calling the 4.3% to 11.7% range a confidence interval or adding effects without stating the assumption that makes the addition appropriate.
Make Judgments and Limitations Traceable
A professional judgment should identify the decision, the evidence considered, and the reason for preferring one choice over another. If the selected rate change differs from a central indication, document the size and direction of the difference and the rationale. Avoid wording that makes a judgment sound mechanically determined when it was not.
A concise record does not need to reproduce every working paper. It should, however, point to the relevant analysis and preserve enough information to understand the selection. For example, it may state that a sensitivity table contains the full results while summarizing the key tested values and range in the record itself.
State limitations in specific terms. “There is uncertainty” is too general to guide a reviewer. More useful wording identifies the uncertainty, its possible relevance, and whether it was tested. If an alternative was not tested, do not imply that it was covered by the reported sensitivity range.
Identify the central assumptions, methods, and indication that the alternatives will be compared with.
For each test, name the assumption or assumptions changed and the reason the alternative is relevant.
Show each result and its difference from baseline, using percentage points for changes between rate indications.
Separate the selected change from the modeled indication and state the rationale and limitations.
Common Documentation Traps
- Changing the baseline without saying so. Sensitivities are interpretable only when the comparison baseline is clear.
- Confusing percent with percentage points. A move from 8% to 6% is a 2-percentage-point decrease; relative to 8%, it is a 25% decrease.
- Combining changes but attributing the result to one input. A scenario changing trend and expenses measures their combined effect under the tested assumptions.
- Presenting a judgment as a fact. Identify which values are observed, which are modeled, and which are selected by judgment.
- Overstating a tested range. A range from a few scenarios describes those scenarios, not every possible outcome.
- Leaving out the reason for weights or alternatives. A calculation can be reproduced while its most important judgment remains unexplained.
Check Your Understanding
For each problem, calculate the requested result and distinguish it from any selection judgment.
- A hypothetical program has a 9.4% baseline indication. An alternative assumption produces a 7.9% indication. What is the change from baseline in percentage points? (Answer: \(-1.5\) percentage points.)
- Two indication estimates are 5.0% and 11.0%. The baseline weights are 60% and 40%, respectively. What is the weighted baseline indication, and what would equal weighting produce? (Answer: Baseline 7.4%; equal-weight alternative 8.0%, or \(+0.6\) percentage points.)
- A 4.5% trend assumption produces a 7.2% indication. A sensitivity indicates that each 1-percentage-point increase in trend raises the modeled indication by 1.8 percentage points. What indication corresponds to a 6.5% trend under this stated linear sensitivity, and what change from baseline should be recorded? (Answer: 10.8%, or \(+3.6\) percentage points.)
- A 6.0% baseline indication changes by \(-1.4\) points under a low-trend alternative and by \(+0.9\) points under a low-expense alternative. If the effects are explicitly assumed additive, what is the combined indication? What must the record say about the result? (Answer: 5.5%; label it a combined scenario and state the additive-effect assumption.)
- A baseline indication is 8.5%, while the selected change is 7.5%. Name two items the selection record should include beyond those percentages. (Answer: The 1.0-percentage-point difference from baseline and the rationale for the judgment; it should also identify the baseline assumptions and relevant limitations or alternatives.)