Why Reconcile Totals?
A ratemaking dataset is useful only if its inputs can be traced to the records and business scope they are intended to represent. A dataset can have plausible averages and still omit exposure, include out-of-scope losses, or use a different valuation basis from its source extract. Reconciliation compares key totals across those stages so that differences are visible before they affect indications or model results.
The measures are related, but they are not interchangeable. A policy count describes a defined set of policies or policy terms. Earned exposure measures the amount of risk time represented. Claim count describes claims under a specified counting rule. Loss amount depends on the chosen loss basis, such as paid or incurred, gross or net, and the valuation date. Each total needs its own definition and control.
A valid comparison starts with consistent definitions. For each control, identify the population, time period, product and coverage scope, unit of measure, and any relevant valuation or accounting basis. Also specify the data grain: for example, one row per policy term, policy-month, coverage, or claim. Counts at different grains do not have the same meaning.
| Control | Definition to specify | Typical unit |
|---|---|---|
| Policy count | Whether counting policies, policy terms, or another defined unit; applicable in-force or written scope | Count |
| Earned exposure | Exposure basis, earning period, coverage scope, and unit conversion | Policy-years, car-years, or another exposure unit |
| Claim count | Whether counting claim occurrences, claim records, or another defined claim unit; applicable loss period | Count |
| Loss amount | Paid or incurred basis, gross or net basis, included components, currency, and valuation date | Dollars or stated scaled units |
Set the Reconciliation Basis
Before calculating differences, write down what the source extract and model dataset are each meant to contain. A common comparison basis might specify policies with a particular coverage in force during a defined earning period, claims assigned to a stated accident period, and losses valued at a stated date. A source extract can legitimately contain more records than a model dataset if a documented eligibility rule excludes part of that source population. The task is to quantify and explain the bridge, not to assume every total must be identical.
For a measure \(T\), define the signed difference as model minus source:
When the source total is nonzero, a relative difference can help summarize scale:
A percentage difference does not explain a variance, and it can be misleading when the source total is zero or very small. Retain both the absolute difference and its explanation. For material totals, reconcile by useful dimensions such as period, product, coverage, or territory before relying on an overall agreement: offsetting differences in separate groups can cancel in the aggregate.
Build a Bridge from Source to Model
A bridge identifies the controlled changes between totals. For an additive measure, the bridge can be written as a starting total plus documented additions and minus documented exclusions. This form follows directly from partitioning the starting population into retained and excluded components. If \(S\) is the source total, \(E\) is the total for documented exclusions, and \(A\) is the total for documented additions, then the resulting total is:
The equation is useful only when the components are defined on the same basis. For example, a policy count cannot be bridged to exposure by subtracting a count from an exposure total. Likewise, a gross incurred loss total cannot be compared directly with a net paid total without separately identifying the basis changes.
State the population, period, grain, unit, and accounting or valuation basis for each control.
Summarize policy count, exposure, claim count, and loss amount separately at each data stage.
Calculate signed differences, then compare by relevant dimensions to determine where they arise.
Show each bridge component, recompute the ending total, and record any unresolved variance for investigation.
Worked Reconciliations
Worked Example: Bridging an Eligible Policy Population
A hypothetical source extract contains four policy terms for a one-year earning period. Their earned exposures are 12, 9, 6, and 3 policy-months, respectively. The source controls show 4 policy terms, 5 claims, and $18,000 of loss. The rating dataset excludes the second policy term under a documented product-eligibility rule. That term contributes 9 policy-months, 1 claim, and $3,000 of loss. Reconcile each control, expressing exposure in policy-years.
Method. Apply the same documented eligibility exclusion separately to each additive measure. Convert exposure from policy-months to policy-years by dividing by 12.
Policy count. The source has 4 policy terms. Excluding the one ineligible term gives \(4-1=3\) policy terms in the model dataset.
Earned exposure. The source exposure is \(12+9+6+3=30\) policy-months. Excluding 9 months leaves \(30-9=21\) policy-months. Converting gives \(21/12=1.75\) policy-years. As a check, the excluded term contributes \(9/12=0.75\) policy-years, so \(30/12-0.75=2.50-0.75=1.75\) policy-years.
Claim count. The source has 5 claims. Removing the 1 claim associated with the excluded term gives \(5-1=4\) claims.
Loss amount. The source loss is $18,000. Removing $3,000 gives \($18{,}000-$3{,}000=$15{,}000\).
Check. The model controls are 3 policy terms, 1.75 policy-years, 4 claims, and $15,000. Each matches the source total less the corresponding documented exclusion. The common mistake is to subtract a policy count from exposure or to compare 21 policy-months directly with a model total expressed in policy-years; keep each measure separate and convert units before comparing.
Worked Example: Reconciling Loss Basis and Recoveries
A hypothetical claim extract contains three claims at the same valuation date. Claim A has $8,000 paid and a $2,000 case reserve; claim B has $5,000 paid and no case reserve; claim C has $4,000 paid and a $6,000 case reserve. The source reports gross incurred loss. The model dataset reports net incurred loss after $1,500 of recoveries. Reconcile the loss totals and explain why the paid total is not the appropriate source control for this comparison.
Method and assumption. For this example, gross incurred loss at the stated valuation date equals paid loss plus case reserve for each claim. The model’s net incurred basis subtracts the stated recoveries from gross incurred loss. No other loss components or adjustments are included.
Paid control. Total paid loss is \(8{,}000+5{,}000+4{,}000=$17{,}000\).
Case-reserve control. Total case reserves are \(2{,}000+0+6{,}000=$8{,}000\).
Source gross incurred control. Gross incurred loss is paid plus case reserves: \($17{,}000+$8{,}000=$25{,}000\). Equivalently, the claim-level amounts are \(8{,}000+2{,}000=$10{,}000\), \(5{,}000+0=$5{,}000\), and \(4{,}000+6{,}000=$10{,}000\), which sum to $25,000.
Bridge to model net incurred. Subtract the $1,500 of recoveries from gross incurred: \($25{,}000-$1{,}500=$23{,}500\). The model total is therefore $23,500, a difference of \($23{,}500-$25{,}000=-$1{,}500\) from the gross incurred source control, exactly explained by recoveries.
Check and trap. The source paid total is $17,000, not the comparable gross incurred control. Comparing model net incurred of $23,500 directly with paid loss would produce an apparent difference of $6,500. That difference combines the $8,000 case reserve with the $1,500 recovery adjustment in opposite directions: \($23{,}500-$17{,}000=$6{,}500\). It is not a valid reconciliation of the specified bases. The appropriate bridge starts at $25,000 gross incurred and subtracts $1,500.
Worked Example: Detecting an Exposure-Unit Variance
A hypothetical portfolio has source exposure controls of 360 car-months in Territory North and 240 car-months in Territory South. Source claim counts are 18 and 12, and source losses are $45,000 and $30,000, respectively. The model dataset expresses exposure in car-years: it reports 30 in North and 19.5 in South. Its claim counts and losses agree with the source by territory. Reconcile exposure and quantify the effect of the unexplained variance on the overall loss cost.
Method. Convert source car-months to car-years by dividing by 12, then compare like units. Use loss cost, defined here as loss amount divided by earned exposure, only as a diagnostic of the exposure difference.
Convert source exposure. North has \(360/12=30\) car-years. South has \(240/12=20\) car-years. Total source exposure is \(30+20=50\) car-years.
Compare with model exposure. The model total is \(30+19.5=49.5\) car-years. Its signed difference is \(49.5-50=-0.5\) car-year. The entire territory-level variance is in South: \(19.5-20=-0.5\) car-year, equal to 6 car-months. Claim counts reconcile to \(18+12=30\), and losses reconcile to \($45{,}000+$30{,}000=$75{,}000\).
Calculate diagnostic loss costs. On the source controls, overall loss cost is \($75{,}000/50=$1{,}500\) per car-year. On the model exposure control, it is \($75{,}000/49.5=$1{,}515.1515\ldots\) per car-year, or $1,515.15 to the nearest cent. The model result is higher because the same loss amount is divided by less exposure. The 0.5 car-year difference is \(0.5/50=0.01\), or 1% of source exposure.
Check and conclusion. North reconciles exactly; South is short 0.5 car-year; claims and losses reconcile. The exposure difference remains unexplained by the stated facts, so the analyst should not silently adjust the model total or treat the ratios as proof of a cause. Record the six-month variance for investigation. The common trap is comparing 600 source car-months directly with 49.5 model car-years, or treating agreement in claims and losses as evidence that exposure must also agree.
Use Ratios as Checks, Not Replacements
Once exposure, claim count, and loss amount are on aligned bases, simple ratios can help reveal whether a variance has a plausible effect on the model inputs. Claim frequency is claim count divided by earned exposure; average severity is loss amount divided by claim count when the claim count is positive; and loss cost is loss amount divided by earned exposure. These relationships imply that loss cost equals frequency multiplied by severity when all three quantities use the same scope and loss basis:
The claim count cancels algebraically, which justifies the identity. If the count is zero, severity is undefined, so this factorization cannot be used; loss cost may still be calculated when exposure is positive. These ratios are diagnostics, not independent controls. Matching a ratio does not establish that the underlying totals reconcile: for example, proportionate changes to loss and exposure can leave loss cost unchanged.
Common Reconciliation Traps
- Comparing unlike units. Convert months to years, or other exposure units, before calculating a variance.
- Mixing grains. A count of policy terms is not automatically comparable with a count of coverage rows. State what is being counted.
- Mixing loss bases. Paid and incurred, or gross and net, are different controls. Identify reserves and recoveries explicitly when they form part of the bridge.
- Relying only on an overall total. Differences by period or segment can offset. Compare meaningful subtotals as well as the grand total.
- Calling an unexplained difference immaterial without evidence. Quantify it, apply the relevant review threshold if one is established, and retain its status and disposition.
- Using a ratio to conceal a total variance. Reconcile counts, exposure, and loss amounts themselves; a plausible frequency or loss cost does not replace those controls.
Why the Controls Matter
Reconciled control totals make data transformations reviewable. They help an actuary distinguish an expected scope change from an unintended mismatch and show whether a variance affects policy volume, exposure, claim experience, or loss cost. The supporting record should state the measure and scope, source and model totals, signed and relative differences where meaningful, bridge components, unit conversions, and any unresolved items. That evidence supports reproducible analysis and a clear explanation of which data were used.
This discipline is aligned with the CAS Exam 8 (Advanced Ratemaking) syllabus: the exam candidate should be able to reason carefully about the data feeding a ratemaking analysis, not merely calculate a final indicated value.
Check Your Understanding
For each problem, align the basis before calculating. Answers are shown for checking after the question.
- A source extract has 6 policy terms and 48 policy-months of exposure. A documented eligibility rule excludes 2 terms contributing 18 policy-months. How many terms and policy-years remain in the model population? (Answer: 4 terms and 2.5 policy-years.)
- A source has $31,000 gross incurred loss, including $7,000 in case reserves. The model reports net incurred after $2,000 of recoveries. What is the model loss total, and what is the bridge difference from source? (Answer: $29,000; model minus source is −$2,000.)
- Source exposure is 420 equipment-months; model exposure is 34 equipment-years. Convert the source total and calculate the model-minus-source difference in equipment-years. (Answer: 35 equipment-years; −1 equipment-year.)
- A source control has 24 claims, 40 earned units of exposure, and $60,000 of loss. The model has the same claims and loss but 38 earned units. Calculate source and model frequency and loss cost. (Answer: source frequency 0.6000, model frequency 0.6316; source loss cost $1,500.00 per unit, model loss cost $1,578.95 per unit.)
- A source reports $12,000 paid loss and $3,000 case reserves. The model reports $14,000 net incurred after recoveries. Assuming no other adjustments, how much recovery bridges source gross incurred to model net incurred? (Answer: source gross incurred is $15,000; recoveries are $1,000.)