Why Judgment Matters in a Rate Selection
A calculated indication is an output of specified data, assumptions, and methods. A final selection is the actuary’s conclusion about the rate change supported by that analysis. The two may differ, but the difference needs a reason that can be explained and evaluated. “The result feels too high” is not evidence; a verified correction to claim data, or a documented change that the projection does not yet reflect, may be.
Judgment is not a license to replace calculation with preference. It is the disciplined evaluation of whether the inputs, scope, and interpretation behind the calculation are appropriate for the decision. This distinction is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.
The earlier material on assembling and reconciling indications provides the calculation framework. Here, the focus is on deciding whether the evidence warrants changing the calculated result, and on showing that change clearly. Judgment can lead to a different selection, but it can also lead to retaining the calculated indication when a proposed override has no evidential basis.
A Framework for Evaluating an Adjustment
Before changing a selection, identify what the proposed adjustment is meant to address. Then ask whether the evidence is reliable, whether the issue is already reflected in the indication, how much of the book it affects, and how its impact is translated into the rate level. A qualitative concern may deserve discussion without supporting a numerical adjustment.
Record the indication and the data, assumptions, and method that produced it. This establishes the baseline for evaluating a proposed departure.
Specify what the evidence shows, its source, and whether it concerns the data, the model, the proposed business, or an external condition.
Do not adjust for a change that is already incorporated in the loss projection, expense provision, or other inputs.
If evidence applies to one coverage, time period, or segment, do not automatically apply it to the entire book.
Recalculate the indication if the adjustment is quantifiable. If it is not, explain why it does or does not affect the selection and record the uncertainty.
One useful calculation framework makes the reasoning explicit. Let \(L\) be projected losses and loss adjustment expenses per applicable exposure base, and let \(F\) be fixed expenses per that same base. Suppose variable expenses and the target profit and contingency provision together equal a proportion \(q\) of premium. Let \(P_0\) be the current on-level premium for the same projected exposure base. Under these assumptions, the required premium is \((L+F)/(1-q)\), provided \(q<1\). The indicated rate change is the required premium divided by \(P_0\), less one.
The formula follows by balancing premium against the specified costs and provision. If required premium is \(P_{\text{required}}\), then the amount remaining after the proportional provision is \(P_{\text{required}}(1-q)\). That amount must cover losses and fixed expenses, so \(P_{\text{required}}(1-q)=L+F\). Dividing by \(1-q\) gives the stated required premium. The rate-change expression then compares that premium with the current on-level premium for the same exposure base.
This framework applies only when the cost amounts are stated on a consistent base and the combined proportional provision is represented as a fraction of premium. If the profit provision or another component is defined differently, use the appropriate ratemaking equation rather than forcing it into this formula.
Worked Examples
Worked Example: Correcting a Verified Data Issue
A hypothetical product has projected losses and loss adjustment expenses of $500 per exposure base, fixed expenses of $100, and a combined variable expense and profit provision of 25% of premium. Current on-level premium for the same projected exposure base is $800. A claim-file review verifies that a coding issue inflated the projected loss amount by 3%, and that the current indication has not corrected it. Calculate the indication before and after correction, then state the supportable selection.
Method. Use the required-premium equation and correct only the input shown to be wrong. The baseline calculation is
The baseline indicated rate change is \(800/800-1=0\), or 0.0%. The review supports reducing projected losses by 3%: \(500(0.03)=15\), so the corrected loss amount is \(500-15=485\). Fixed expenses and the premium-proportional provision are unchanged.
The corrected indication is a 2.5% decrease. The arithmetic checks: the $780 required premium leaves \(0.75(780)=585\) for costs after the proportional provision, exactly the corrected losses plus fixed expenses, \(485+100=585\). The selection is supported because the claim-file evidence identifies an uncorrected data error.
Common mistake. Subtracting 3 percentage points from the rate indication would confuse a percentage change in projected losses with a percentage-point change in rates. The correction is made to the loss amount first; the rate indication is then recalculated.
Worked Example: Limiting an Adjustment to Its Supported Scope
A hypothetical book has projected losses of $600 per exposure base, fixed expenses of $120, a combined proportional provision of 25%, and current on-level premium of $960. An audited review supports a 10% reduction in projected losses for a segment that represents 25% of the exposure base. The remaining 75% has no identified change. Calculate the appropriately adjusted indication and compare it with applying the adjustment to the whole book.
Method. Apply the reduction only to the affected portion. The unadjusted loss amount consists of \(600(0.75)=450\) for the unaffected portion and \(600(0.25)=150\) for the affected portion. A 10% reduction to the latter is \(150(0.10)=15\). Adjusted losses are therefore \(450+150-15=585\), equivalently \(600[0.75+0.25(0.90)]=585\).
Before the adjustment, required premium is \((600+120)/0.75=720/0.75=960\), giving a 0.0% indication. After the adjustment:
The adjusted indication is a 2.1% decrease, rounded to one decimal place. The check is \(0.75(940)=705\), equal to adjusted losses plus fixed expenses. Applying the 10% reduction to all losses instead would produce \(600(0.90)=540\), required premium \((540+120)/0.75=880\), and a 8.3% decrease. That larger change is not supported by the stated evidence: three-quarters of the exposure base was not affected.
Common mistake. Treating a segment-specific finding as a book-wide finding overstates its impact. The adjustment must reflect both the size of the affected segment and the change within it.
Worked Example: Rejecting an Unsupported Preference
A hypothetical indication uses projected losses of $629, fixed expenses of $100, a combined proportional provision of 25%, and current on-level premium of $900. A manager asks for a 4% rate increase because that level is preferred commercially. No new data, documented constraint, or model issue is offered. Calculate the indication and explain how judgment should be applied.
Method. First calculate the result supported by the stated inputs:
The calculated indication is an 8.0% increase. The arithmetic checks because \(0.75(972)=729\), equal to losses plus fixed expenses. The request for 4% does not identify evidence that changes the expected costs, a flaw in the method, or another actuarial basis for revising the indication. Therefore, on the information given, the supportable actuarial selection remains an 8.0% increase. A commercial preference may be considered separately in a business decision, but it should not be presented as an evidence-based actuarial adjustment.
Common mistake. Calling a requested cap “judgment” does not make it evidence-based. If relevant evidence or a documented constraint becomes available, evaluate it explicitly and show how it affects the selection; do not silently replace the calculated result.
What Makes a Judgment Defensible?
A defensible selection explains the difference, if any, between the indication and the selected rate change. It should be possible for another actuary to identify the evidence considered, understand the adjustment, and reproduce its numerical effect. Useful documentation separates measured facts from assumptions and professional conclusions.
| Defensible judgment | Unsupported preference |
|---|---|
| Identifies the evidence, its source, and the issue it addresses | Relies on statements such as “the result is too large” without supporting information |
| Checks whether the evidence is already reflected in the indication | Adjusts for a change that is already included in the assumptions |
| Applies a quantified effect to the portion of the book it affects | Applies a segment-specific effect to the whole book without justification |
| Shows the calculation and the resulting selected rate change | Reports a final number without explaining how it relates to the indication |
| States limitations and uncertainty where the evidence is incomplete | Describes an uncertain opinion as if it were a measured fact |
The strength of a judgment depends on more than whether it is plausible. Consider the quality and relevance of the evidence, whether it relates to the rate period and population being priced, and whether another part of the indication already captures the same effect. If those checks do not support a numerical change, the actuary can record the concern, explain its limitations, and retain the calculated result.
Common Exam Traps
- Confusing the indication with the selection. State which figure is calculated and which is ultimately selected.
- Changing the result without changing or qualifying a basis. A final number needs an explainable connection to the analysis.
- Applying an adjustment twice. First check whether the evidence is already included in the projected costs or provisions.
- Ignoring scope. A finding for one segment does not automatically apply to all segments.
- Mixing percentage changes and percentage points. Adjust the relevant cost input, then recalculate the premium requirement and rate change.
- Overstating certainty. If an effect cannot be quantified reliably, describe the uncertainty rather than presenting an unsupported precise adjustment.
Check Your Understanding
For each problem, distinguish the calculated indication from any judgmental adjustment and check that the adjustment matches the stated evidence.
- A hypothetical book has losses of $440, fixed expenses of $80, a combined proportional provision of 30%, and current on-level premium of $800. A verified correction has already been incorporated in the $440 loss amount. Calculate the indicated rate change and state whether applying the correction again is justified. (Answer: Required premium \(=(440+80)/0.70=\$742.86\); indicated change \(=742.86/800-1=-7.1\%\) to one decimal place. Do not apply the correction again.)
- Losses are $700, fixed expenses are $150, the combined proportional provision is 25%, and current premium is $1,100. Verified evidence supports a 5% loss reduction for 40% of the exposure base only. Calculate the adjusted indication. (Answer: Adjusted losses \(=700[0.60+0.40(0.95)]=686\); required premium \(=(686+150)/0.75=\$1,114.67\); indicated increase \(=1.3\%\) to one decimal place.)
- A calculated indication is based on losses of $555, fixed expenses of $90, a 25% proportional provision, and current premium of $800. A manager requests a 3% cap but provides no evidence or documented constraint. Calculate the indication and state the actuarial conclusion on the stated facts. (Answer: Required premium \(=(555+90)/0.75=\$860\); indicated increase \(=7.5\%\). Retain 7.5% as the supported actuarial selection on the information given.)
- Losses are $500, fixed expenses are $100, the combined proportional provision is 25%, and current premium is $800. A verified coding correction reduces losses by 2% in a segment representing 30% of exposure; no other segment is affected. Calculate the adjusted indication. (Answer: Adjusted losses \(=500[0.70+0.30(0.98)]=497\); required premium \(=(497+100)/0.75=\$796\); indicated change \(=796/800-1=-0.5\%\).)
- A hypothetical indication has losses of $600, fixed expenses of $120, a 25% proportional provision, and current premium of $900. A stakeholder proposes a 4% increase based only on preference. Calculate the indicated change and say whether the preference supports an actuarial adjustment. (Answer: Required premium \(=(600+120)/0.75=\$960\); indicated increase \(=6.7\%\) to one decimal place. Preference alone does not support changing the actuarial selection.)