Why Explain a Reserve Change?
A reserve comparison gives two amounts and their net difference. It does not, by itself, explain why the selected liability changed. The movement may reflect updated claim information, revised assumptions, a different estimation method, or a changed selection judgment. If those causes are combined into one unexplained amount, a reviewer cannot tell which evidence or decision produced the result.
A structured bridge makes the comparison traceable. It starts with the prior selected reserve, changes one component at a time, and records the reserve after each change. The final step must equal the current selected reserve. A bridge is an attribution under a stated sequence of comparisons; it is not proof that each change has one uniquely measurable cause.
For clarity, let \(R(D,A,M,J)\) denote the selected reserve under data \(D\), assumptions \(A\), method \(M\), and selection judgment \(J\). The notation is a bookkeeping device: the data are the information available for the estimate; assumptions are the parameters or conditions used in estimating unpaid claims; the method is the estimation approach; and judgment is the documented choice or adjustment used to reach the selected amount. Judgment should be described specifically, not used as an unexamined label for every difference.
A comparison is meaningful only if the two endpoints use a consistent basis. State the valuation dates, reserve scope, currency and units, and whether the amounts are gross, ceded, or net. Keep the covered claim population and other relevant boundaries clear. If a basis or scope differs, identify that difference explicitly rather than silently attributing it to an assumption or method.
The Sequential Bridge
One practical convention is to update components in a declared order: data first, then assumptions, method, and selection judgment. At each step, change only the named component. Other choices remain at their earlier values until their turn. This convention produces a reproducible bridge, although another order can produce different component amounts when the effects interact.
Record the prior and current selected reserves, with matching scope, valuation basis, and units.
State which component changes at each step. Do not change data, assumptions, method, and judgment all at once.
Use the new value for the component being changed and retain the current values of all other components.
Sum the step changes and confirm that the result equals the current selected reserve less the prior selected reserve. Document any remaining difference rather than forcing it into a category.
Write the estimates along a four-step path as \(R_0\), \(R_1\), \(R_2\), \(R_3\), and \(R_4\), starting with the prior estimate and ending with the current one. The attributed changes are \(R_1-R_0\), \(R_2-R_1\), \(R_3-R_2\), and \(R_4-R_3\). Their sum is the total movement because each intermediate estimate cancels when the differences are added:
This telescoping identity is the essential reconciliation check. It does not guarantee that the categories are well chosen; that depends on the comparisons used at each step. A sound bridge therefore includes both the arithmetic and a clear account of what changed in each comparison.
Worked Example: A Four-Component Reserve Bridge
A hypothetical insurer reports a selected unpaid claim reserve of $12.0 million at the prior valuation date and $14.0 million at the current valuation date. The comparison has the same reserve scope and reporting basis. The analyst uses a fixed sequence: update data, then assumptions, then method, then selection judgment. The reserve recalculations, in millions of dollars, are:
Starting point. With prior data, prior assumptions, the prior method, and prior judgment, the selected reserve is \(R_0=\$12.0\) million.
Data change. Replace only the prior data with the current data. Keep the prior assumptions, method, and judgment. The recalculated reserve is \(R_1=\$13.5\) million. The data effect is \(13.5-12.0=\$1.5\) million.
Assumption change. Keep the current data, and replace only the prior assumptions with the current assumptions. The recalculated reserve is \(R_2=\$14.3\) million. The assumption effect is \(14.3-13.5=\$0.8\) million.
Method change. Keep current data and assumptions, and replace only the prior method with the current method. The recalculated reserve is \(R_3=\$13.7\) million. The method effect is \(13.7-14.3=-\$0.6\) million.
Judgment change. Apply the current selection judgment, with current data, assumptions, and method unchanged. The current selected reserve is \(R_4=\$14.0\) million. The judgment effect is \(14.0-13.7=\$0.3\) million.
Reconciliation. The component effects sum to \(1.5+0.8-0.6+0.3=\$2.0\) million. The endpoint difference is \(14.0-12.0=\$2.0\) million, so the bridge reconciles. The method change reduced the estimate; the other three changes increased it.
Method and common mistake avoided. This is a sequential one-component-at-a-time bridge. A common mistake is to describe all $2.0 million as “data deterioration” because the reserve increased. That claim is not supported: the bridge attributes only $1.5 million to data, and shows that method selection offset $0.6 million. The method effect is conditional on the data and assumptions already having been updated in this stated order.
Interactions and Order Dependence
A component’s effect can depend on the values of other components. For example, a data revision may produce one reserve change under an older assumption and a different change under a revised assumption. This interaction means there is not always a single order-independent answer to “how much was due to data?” The endpoint difference remains fixed, but the allocation among bridge steps may vary.
The appropriate response is to define and disclose the bridge order, not to imply that the allocation is uniquely determined. If a different order is important to the interpretation, calculate that alternative as a separate bridge. Do not add the component effects from different bridge orders together: they are alternative allocations of the same total change.
Worked Example: How the Bridge Order Changes Attribution
A hypothetical portfolio has two changing components, data and assumptions. Method and selection judgment are fixed. The four recalculated reserves, in millions of dollars, are: prior data with prior assumptions, $10 million; current data with prior assumptions, $12 million; prior data with current assumptions, $11 million; and current data with current assumptions, $14 million.
Data-first bridge. Start at $10 million. Update data while keeping prior assumptions: the reserve becomes $12 million, so the data step is \(12-10=\$2\) million. Then update assumptions using current data: the reserve becomes $14 million, so the assumption step is \(14-12=\$2\) million. The total is \(2+2=\$4\) million, matching \(14-10=\$4\) million.
Assumptions-first bridge. Start again at $10 million. Update assumptions while keeping prior data: the reserve becomes $11 million, so the assumption step is \(11-10=\$1\) million. Then update data using current assumptions: the reserve becomes $14 million, so the data step is \(14-11=\$3\) million. The total is again \(1+3=\$4\) million.
Why the allocations differ. With prior assumptions, the data change is $2 million; with current assumptions, it is $3 million. With prior data, the assumption change is $1 million; with current data, it is $2 million. The extra $1 million is an interaction reflected in whichever component is changed second. Both paths reach the same $14 million endpoint.
Common mistake avoided. Adding the data-only change of $2 million and the assumptions-only change of $1 million gives $3 million, not the actual $4 million endpoint difference. Those two comparisons each hold the other component at its prior value, so their effects cannot simply be added when they interact. A sequential path includes the interaction in its second step and reconciles exactly.
Distinguishing the Four Components
The labels in a bridge are useful only when the change assigned to each one is defined precisely. A data update is a change in information supplied to an otherwise unchanged estimate. Examples can include corrected claim records or newly available claim status information. An assumption update changes a parameter or condition used in the estimate while holding the data and method fixed. A method update changes the estimation procedure while applying it to the specified data and assumptions. A judgment update changes the documented selection or adjustment after the other specified components are held fixed.
These categories can be difficult to separate in practice. For instance, a revised assumption may have been prompted by newly observed claim information. In the bridge, the new information can be assigned to the data step and the subsequent parameter change to the assumption step, provided the calculations actually isolate them. State the convention and avoid counting the same evidence twice.
A selection judgment should not be a plug used to make the bridge balance. If the modeled result changes from one step to another, show that result. If an actuary then selects an amount above or below the model indication, show the selection adjustment and explain its basis. If a difference remains after all specified comparisons, report it as unreconciled pending investigation.
Worked Example: Separating a Method Change From Selection Judgment
A hypothetical insurer compares two selected reserves, in millions of dollars, on a consistent basis. At the prior valuation, the selected reserve is $20.0 million. The analyst’s documented sequential recalculations are: $22.4 million after updating data only; $21.3 million after updating assumptions only in addition; $22.0 million after changing the method only in addition; and $21.5 million after applying the current selection judgment. Find each attributed change and verify the total.
Data effect. The first recalculation changes the reserve from $20.0 million to $22.4 million. Thus \(22.4-20.0=\$2.4\) million.
Assumption effect. The next recalculation changes it from $22.4 million to $21.3 million. Thus \(21.3-22.4=-\$1.1\) million.
Method effect. The method step changes it from $21.3 million to $22.0 million. Thus \(22.0-21.3=\$0.7\) million.
Judgment effect. The selection step changes it from $22.0 million to $21.5 million. Thus \(21.5-22.0=-\$0.5\) million.
Reconciliation. The bridge effects sum to \(2.4-1.1+0.7-0.5=\$1.5\) million. The endpoint movement is \(21.5-20.0=\$1.5\) million. The bridge reconciles. In this example, it would be incorrect to call the $0.7 million method effect a selection adjustment: the method was changed before the separate $0.5 million judgment step.
Method and common mistake avoided. This is a sequential component reconciliation. It distinguishes the method’s effect from the later selection overlay. A common mistake is to use “judgment” as a residual without identifying an actual selection decision. Here the judgment amount is explicitly the difference between the method-step estimate and the final selected estimate.
Reviewing and Reporting the Bridge
A reviewer should be able to reproduce the endpoints and each intermediate amount. A compact bridge table can show the component, the estimate before and after that step, the change, and a short description of the evidence or decision. Report amounts in consistent units, with signs that make increases and decreases clear. For estimates stated in thousands, for example, do not combine a component reported in thousands with an endpoint reported in dollars without conversion.
| Bridge item | What to report |
|---|---|
| Prior selected reserve | Amount, valuation date, scope, and reporting basis |
| Data | Information changed and the recalculated amount with other components fixed |
| Assumptions | Assumptions changed and the next recalculated amount |
| Method | Estimation procedure changed and the resulting amount |
| Selection judgment | Documented selection or adjustment and the final selected amount |
| Reconciliation | Sum of component changes compared with the endpoint difference |
A bridge is an explanation of an estimate comparison, not a guarantee that the estimate is correct. Its value is that it makes the mechanics, choices, and unresolved questions visible. That supports review, repeatability, and clearer communication than reporting a net change alone.
Check Your Understanding
For each problem, use the stated comparison order and verify the endpoint reconciliation.
- A hypothetical reserve rises from $8.0 million to $9.2 million. In a data-first bridge, the data update moves the estimate to $8.7 million, and the assumption update moves it to $9.0 million. The method change moves it to $9.4 million. What judgment effect is required to reach the current selected reserve? (Answer: \(-\$0.2\) million)
- For a two-component comparison, the reserve is $15 million under prior data and prior assumptions, $17 million under current data and prior assumptions, $16 million under prior data and current assumptions, and $19 million under current data and current assumptions. In a data-first bridge, what are the data and assumption effects? (Answer: data \(+\$2\) million; assumptions \(+\$2\) million)
- A selected reserve is $30 million. Updating data alone gives $31.2 million; updating assumptions next gives $30.8 million; changing method next gives $31.5 million; and applying selection judgment gives $31.0 million. State the four component effects and confirm the total movement. (Answer: data \(+\$1.2\) million; assumptions \(-\$0.4\) million; method \(+\$0.7\) million; judgment \(-\$0.5\) million; total \(+\$1.0\) million)
- In a two-component bridge, the estimate under prior data and prior assumptions is $40 million. Under current data and prior assumptions it is $43 million; under prior data and current assumptions it is $42 million; under current data and current assumptions it is $46 million. If assumptions are updated first and data second, what are the two step effects, and how much larger is the combined endpoint change than the sum of the two single-component changes from the prior state? (Answer: assumptions \(+\$2\) million; data \(+\$4\) million; endpoint change \(+\$6\) million, which is \( \$1\) million larger than the \( \$5\) million sum of the single-component changes)
- A bridge reports a prior selected reserve of $25 million and a current selected reserve of $27.4 million. Its stated sequential effects are data \(+\$1.8\) million, assumptions \(+\$0.9\) million, method \(-\$0.6\) million, and judgment \(+\$0.5\) million. Does the bridge reconcile, and if not, what is the unreconciled difference between the component sum and endpoint movement? (Answer: No; component sum \(+\$2.6\) million versus endpoint movement \(+\$2.4\) million, so the component sum exceeds the endpoint movement by $0.2 million)