When Not to Apply Berquist-Sherman Adjustments

Introduction

Berquist-Sherman adjustments can help make historical loss data more comparable when claim-handling or reserving practices have changed. But an adjustment is not automatically an improvement. If raw development is already stable and the conditions expected to continue are represented in the data, adjustment may add noise without solving a forecasting problem. If operational changes cannot be isolated or measured, an adjustment may instead create false precision.

The decision is therefore not simply whether a change in claims operations occurred. It is whether the change materially affects the development being used, whether its effect can be estimated from suitable data, and whether the adjusted basis is appropriate for the conditions expected in the future. This decision framework is aligned with the CAS Exam 5 (Basic Ratemaking and Estimated Claim Liabilities) syllabus.

Definition: A Berquist-Sherman adjustment modifies historical paid or incurred data to address identified operational effects, such as changes in settlement speed or case-reserve adequacy. An adjustment is supportable only when the relevant effect can be distinguished from other influences, measured with adequate data, and applied consistently with the intended projection basis.

When Raw Development May Be the Better Basis

Raw development is a reasonable basis when the observed pattern is sufficiently consistent across comparable periods and the claims processes represented in the data are expected to remain relevant to the projection. “Stable” does not mean that every factor is identical. It means that observed variation has no material, credible pattern that requires correction for the purpose at hand.

A simplified multiplicative model helps explain why consistent operations may be left embedded in raw development. Let $C_{i,j}$ be cumulative losses for accident period $i$ at development age $j$. Suppose, as a simplifying assumption, that expected cumulative losses can be represented by

C_{i,j}=U_iG_jH_j,

where $U_i$ represents the ultimate level for accident period $i$, $G_j$ represents a development pattern, and $H_j$ represents a common operational effect at age $j$. This model assumes the operational pattern is the same across the accident periods being compared; it does not account for changing claim mix or other period-specific influences.

The age-to-age factor under this model is

\frac{C_{i,j+1}}{C_{i,j}} = \frac{G_{j+1}}{G_j} \frac{H_{j+1}}{H_j}.

The factors include the operational pattern, but if that pattern is consistent across accident periods and is expected to continue, it may be relevant to the projection rather than a distortion that must be removed. An adjustment could still be appropriate if the future basis is expected to differ. The key is that stable observed development alone does not prove an adjustment is never needed; it means the case for adjusting must come from a material, measurable difference between the historical and intended future basis.

Practical test: Before adjusting, ask whether raw development shows a credible operational distortion, whether the distortion can be quantified separately from mix and other changes, and whether the adjusted data better represent the future conditions being projected. If one of these questions cannot be answered, retain the raw result as a benchmark and document why an adjustment is not made.

Worked Example: Stable Development With No Identified Distortion

A hypothetical insurer reviews four comparable accident periods at the same development age. The observed paid age-to-age factors are 1.19, 1.20, 1.21, and 1.20. Claims handling is reported to have remained consistent, and no material change in claim mix is identified. Determine whether these observations, by themselves, support a Berquist-Sherman adjustment.

Step 1: Calculate the simple average. The sum of the four factors is $1.19+1.20+1.21+1.20=4.80$. The arithmetic average is $4.80/4=1.20$.

Step 2: Measure the observed range. The maximum is 1.21 and the minimum is 1.19, so the range is $1.21-1.19=0.02$. The largest absolute deviation from the average is 0.01, or $0.01/1.20=0.00833$, approximately 0.83% of the average.

Step 3: Interpret the evidence. The factors are tightly grouped, and the stated evidence identifies no operational change or mix shift that would explain a systematic distortion. The figures alone therefore do not establish a need to adjust. If the same claims processes are expected to continue, using 1.20 as a raw-development summary is a defensible starting point.

Conclusion and check. The calculated mean, 1.20, lies within the observed range of 1.19 to 1.21. This check confirms the arithmetic. The conclusion is conditional on the periods being comparable and on the process information being reliable; it is not a rule that small variation always makes adjustment inappropriate.

Method and mistake avoided. This is a stability screen, not a formal statistical test. A common mistake is to adjust merely because an adjustment method is available. Here no identified, measurable distortion supports doing so.

When an Operational Change Cannot Be Quantified Reliably

A documented change in claim handling does not, by itself, provide the size or direction of its effect on paid or incurred development. For example, closure rates can indicate a change in claim status, but closure counts and average closed-claim payments do not determine total paid losses. Open claims may already have received payments. Any calculation that uses closure statistics to estimate paid losses must explicitly model those payments on open claims or state an assumption that they are zero.

Other influences can also coincide with a process change: inflation, changes in claim mix, changes in coverage or coding, and changes in how claims are reported. If the data cannot separate these influences, the operational effect is not reliably quantified. In that situation, applying a numerical correction may be less defensible than retaining the raw data and explaining the limitation.

Worked Example: Closure Rates Do Not Determine Total Paid

Two hypothetical cohorts each contain 100 reported claims. In the earlier cohort, 60 claims are closed; the closed claims have $2,400,000 paid in total, and open claims have $800,000 paid in total. In the later cohort, 75 claims are closed; the closed claims have $3,000,000 paid in total, and open claims have $1,500,000 paid in total. In both cohorts, claims handling changed during the observation period, and the available records do not separate that change from changes in claim mix. Compare the observed amounts and assess whether closure rates alone support a paid-loss adjustment.

Step 1: Calculate closure rates. The earlier rate is $60/100=60\%$. The later rate is $75/100=75\%$. The observed increase is 15 percentage points.

Step 2: Calculate average paid amounts by status. Earlier closed-claim average paid is $$2{,}400{,}000/60=$40{,}000$; earlier open-claim average paid is $$800{,}000/40=$20{,}000$. Later closed-claim average paid is $$3{,}000{,}000/75=$40{,}000$; later open-claim average paid is $$1{,}500{,}000/25=$60{,}000$.

Step 3: Calculate total paid and paid per reported claim. Earlier total paid is $$2{,}400{,}000+$800{,}000=$3{,}200{,}000$, or $$3{,}200{,}000/100=$32{,}000$ per reported claim. Later total paid is $$3{,}000{,}000+$1{,}500{,}000=$4{,}500{,}000$, or $$4{,}500{,}000/100=$45{,}000$ per reported claim.

Step 4: Check the tempting calculation. Multiplying the number of claims by the closure rate and average payment for closed claims gives $100(0.60)($40{,}000)=$2{,}400{,}000$ for the earlier cohort and $100(0.75)($40{,}000)=$3{,}000{,}000$ for the later cohort. These amounts equal closed-claim payments only. They omit the respective $800,000 and $1,500,000 paid on open claims, so they are not total paid losses.

Conclusion and check. The totals reconcile: earlier paid losses are $2,400,000 on closed claims plus $800,000 on open claims, and later paid losses are $3,000,000 plus $1,500,000. Although the closed-claim average is $40,000 in both cohorts, total paid per reported claim differs. Closure rates and closed-claim payments alone cannot explain that difference or isolate the effect of claims handling.

Method and mistake avoided. This is a status-specific reconciliation. The common mistake is to assume all payments arise from claims already closed. That assumption is not given here and is contradicted by the open-claim payment data. Because claim mix and operational effects cannot be separated, the closure-rate change does not support a reliable numerical adjustment on its own.

Claim Mix and Data Limitations

Aggregate statistics can change even when the experience within each claim group does not. If the proportions of simple and complex claims vary across periods, an overall closure rate or paid pattern may move because the weights changed. A single aggregate adjustment can then attribute a mix effect to operations.

Data limitations create a related problem. A credible adjustment may require consistent definitions of claim status, development age, paid amounts, incurred amounts, and relevant claim groupings. Missing or inconsistent fields, changes in coding, incomplete histories, or too few observations within important groups can prevent a meaningful comparison. More detailed segmentation is not automatically better: if the segments become too sparse, the estimates may be unstable.

Worked Example: An Aggregate Closure Change Caused by Mix

A hypothetical portfolio has two claim groups: routine and complex. In the earlier period, 80 of 100 claims are routine, of which 64 are closed; 20 are complex, of which 6 are closed. In the later period, 40 of 100 claims are routine, of which 32 are closed; 60 are complex, of which 18 are closed. Assume the group definitions and closure measurement are consistent. Determine whether the aggregate closure change indicates a change in closure performance within groups.

Step 1: Calculate group-specific closure rates in the earlier period. Routine claims: $64/80=80\%$. Complex claims: $6/20=30\%$. The overall closure rate is $(64+6)/100=70\%$.

Step 2: Calculate group-specific closure rates in the later period. Routine claims: $32/40=80\%$. Complex claims: $18/60=30\%$. The overall closure rate is $(32+18)/100=50\%$.

Step 3: Compare the group results and the weights. Within each group, the closure rate is unchanged. But routine claims fall from $80/100=80\%$ of the earlier portfolio to $40/100=40\%$ of the later portfolio. Complex claims rise from 20% to 60%.

Step 4: Verify the aggregate rates using the weights. Earlier: $0.80(0.80)+0.20(0.30)=0.64+0.06=0.70$, or 70%. Later: $0.40(0.80)+0.60(0.30)=0.32+0.18=0.50$, or 50%.

Conclusion and check. The aggregate closure rate falls by $70\%-50\%=20$ percentage points, even though neither group’s closure rate changes. The weighted calculations reproduce both observed aggregate rates, confirming that the changed mix fully explains this example’s aggregate movement.

Method and mistake avoided. This is a stratified comparison. Treating the ratio $70\%/50\%=1.4$ as an operational adjustment multiplier would be misleading: the group-specific rates show no within-group change to correct. If only aggregate data were available, the mix explanation could not be verified, and a numerical operational adjustment would not be justified by these closure figures alone.

A Decision Process for Not Adjusting

A decision not to adjust should be reasoned and documented, not based on convenience. The following sequence keeps the decision tied to the purpose and quality of the data.

Define the projection basis.
State what conditions the selected development is intended to represent, including the relevant claim-handling and reserving environment.

Review raw development.
Compare comparable periods and ages. Look for a material, consistent pattern rather than treating every difference as evidence of distortion.

Test whether an operational effect is identifiable.
Check whether the change can be separated from mix, inflation, coding, coverage, and data-definition changes.

Assess measurement quality.
Verify that the required status, payment, reserve, and timing information is sufficiently complete and comparable for the proposed adjustment.

Choose and explain the basis.
If raw development is stable and relevant, or if an adjustment is not reliably measurable, retain raw data as appropriate and state the limitations. Do not present an unsupported estimate as a precise correction.

Common Exam Traps and Professional Implications

“A process changed, so an adjustment is required.” A change matters only if it materially affects the measured development and its effect can be estimated for the intended projection.
Confusing closure statistics with paid amounts. Closure status does not show whether an open claim has been paid. Do not infer total paid losses from closed-claim amounts unless a model for open-claim payments is specified.
Ignoring changing claim weights. Aggregate movement may reflect a shift between groups rather than a change within groups. Compare groups where data support it.
Adjusting unstable or inconsistent data. An adjustment cannot repair missing histories, incompatible definitions, or too few observations. It can amplify those weaknesses.
Treating a decision not to adjust as a claim that no change occurred. The defensible conclusion may instead be that the change is known but its effect cannot be separated or quantified reliably.

Key takeaway: Do not adjust merely because a Berquist-Sherman method is available or an operational change is suspected. Use an adjustment only when the effect is relevant, identifiable, measurable, and appropriate for the projection. Stable raw development or inadequate data can make a documented decision not to adjust more credible than a precise-looking but unsupported correction.

Check Your Understanding

For each problem, decide what the data support and show the essential calculations.

A hypothetical portfolio has four comparable age-to-age factors: 1.16, 1.17, 1.18, and 1.17. Claims procedures are reported unchanged, and no material mix shift is identified. Calculate the mean and range, then state whether these figures alone establish a need for adjustment. (Answer: Mean $=(1.16+1.17+1.18+1.17)/4=4.68/4=1.17$; range $=1.18-1.16=0.02$. The observations are tightly grouped and do not alone establish a need for adjustment if the stated comparability and process assumptions hold.)
A cohort has 80 claims, of which 40 are closed. Closed claims have $1,200,000 paid, and open claims have $300,000 paid. Find total paid and explain the error in estimating it as $Nqm$, where $m$ is the average paid per closed claim. (Answer: $m=$1{,}200{,}000/40=$30{,}000$; $Nqm=80(0.50)($30{,}000)=$1{,}200{,}000$, which omits open-claim payments. Total paid is $$1{,}200{,}000+$300{,}000=$1{,}500{,}000$.)
In an earlier period, group A has 100 claims and 75 closed, while group B has 100 claims and 20 closed. In a later period, group A has 40 claims and 30 closed, while group B has 160 claims and 32 closed. Calculate each group’s closure rates and both aggregate rates. Does the aggregate change establish a within-group operational change? (Answer: Group A is 75% in both periods; group B is 20% in both. Earlier aggregate is $(75+20)/200=47.5\%$; later aggregate is $(30+32)/200=31\%$. No; the group-specific rates are unchanged, while the portfolio mix shifts toward group B.)
A claims system was replaced during one accident period. The aggregate paid triangle is complete, but status definitions changed and there is no claim-level history linking old and new codes. What can be concluded about applying a paid settlement adjustment? Name two limitations that should be documented. (Answer: The aggregate evidence does not support a reliable quantified adjustment by itself. Document that status definitions are not comparable and that claim-level histories cannot link or validate the classifications; other coincident changes may also be inseparable.)
Four periods have raw factors of 1.30, 1.29, 1.31, and 1.30. The insurer has also announced that future claims will be handled under a materially different process, but no data quantify how the new process affects development. What is the appropriate conclusion about raw and adjusted indications? (Answer: The raw factors are stable, with mean $5.20/4=1.30$ and range $1.31-1.29=0.02$, but the future process differs. The stable raw pattern does not establish that it represents the future basis; without a measurable effect, do not claim a precise adjustment. Retain the raw indication as a benchmark, explain the limitation, and seek other support for the future projection.)

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