Make Each Solvency Conclusion Traceable
An ORSA result is useful only if a reader can see how the evidence supports the conclusion. A statement such as “capital remains adequate” is difficult to evaluate by itself. The reader needs to know the measure of adequacy, the projection years covered, the scenarios tested, and the assumptions that generated the figures. Clear communication is not a substitute for sound analysis; it makes the analysis inspectable.
For reporting purposes, use consistent definitions and identify them explicitly. In this tutorial, available financial resources means the resources included in the insurer’s internal solvency assessment, and internal capital need means the capital amount against which those resources are assessed. These are internal assessment measures, not a claim that every insurer or jurisdiction uses one prescribed definition.
Here, \(R_t\) is available financial resources at projection time \(t\), and \(K_t\) is internal capital need at that time. A positive surplus indicates resources exceed the stated need; a negative surplus indicates a shortfall on that basis. A ratio above 1.00 indicates resources exceed need. Neither measure, by itself, explains how the values were produced or what uncertainty surrounds them.
Build an Evidence Trail
A reader should be able to follow a short chain from conclusion to calculation: the conclusion names the period, scenario, and measure; a table provides the underlying values; and nearby notes identify the assumptions and limitations needed to interpret them. If the conclusion depends on a minimum projected ratio, for example, show the ratio for each material year rather than only the opening and ending values.
Name the scenario, projection horizon, and measure. Avoid broad claims that do not identify the basis for “adequate.”
Display resources and capital need alongside surplus or coverage. This lets the reader check the arithmetic and see which component drives a change.
Give the valuation date, projection dates, units, scenario description, and material assumptions. Identify the model or data source at a level that allows the result to be located and reviewed.
Explain important model limitations, uncertainty, or scope exclusions that could affect how strongly the conclusion can be relied on.
Tables should support comparisons rather than merely collect numbers. Use the same units, dates, definitions, and rounding across rows being compared. If values are in millions of dollars, say so in the heading. Label a ratio as a percentage or multiple consistently, and distinguish an observed value from a calculated value. Include enough precision to verify displayed calculations, but avoid suggesting that a long decimal is more certain than the underlying projection.
Worked Example: Showing the Weakest Point in a Base Projection
A hypothetical insurer projects its internal solvency position over three years. Amounts are in millions of dollars. The projection assumes no new capital is raised, uses the stated base scenario, and applies the same internal definitions of resources and capital need at every date. Resources at years 0 through 3 are 120, 126, 132, and 138; capital needs are 100, 108, 118, and 132. Calculate surplus and coverage at each date, then state what the table supports.
Method. At each date, subtract capital need from resources and divide resources by capital need. Keep the measures beside their inputs so the result is traceable.
At year 0, surplus is \(120-100=20\), and coverage is \(120/100=1.2000\), or 120.0%. At year 1, surplus is \(126-108=18\), and coverage is \(126/108=1.1667\), or 116.7%. At year 2, surplus is \(132-118=14\), and coverage is \(132/118=1.1186\), or 111.9%. At year 3, surplus is \(138-132=6\), and coverage is \(138/132=1.0455\), or 104.5%.
| Projection year | Resources ($ millions) | Capital need ($ millions) | Surplus ($ millions) | Coverage |
|---|---|---|---|---|
| 0 | 120 | 100 | 20 | 120.0% |
| 1 | 126 | 108 | 18 | 116.7% |
| 2 | 132 | 118 | 14 | 111.9% |
| 3 | 138 | 132 | 6 | 104.5% |
Conclusion and check. On the stated base projection, resources exceed internal need at all four dates, but both surplus and coverage decline. The weakest displayed position is year 3: \(138-132=6\), and \(138/132=1.0455\), which rounds to 104.5%. This supports a conclusion about this projection and its stated basis; it does not establish that the position is robust to adverse scenarios or alternative assumptions.
Common mistake avoided: Reporting only the year-3 ratio could hide the direction and timing of deterioration. Showing the intervening values makes clear that the position weakens each year, even though resources rise.
Compare Scenarios on the Same Basis
A scenario comparison is informative only when the compared figures use a common measurement basis. Set out the same projection dates and measures for each scenario. Explain what changes between scenarios, and do not describe a difference as an effect of one assumption if several assumptions changed together. Reporting both surplus and coverage can help: the former shows the dollar margin, while the latter scales resources to the size of the need.
A useful comparison states the direction and size of the change, not merely that the adverse result is “worse.” When comparing ratios, distinguish a percentage-point change from a relative percentage change. For example, a decline from 120% to 110% is 10 percentage points; relative to the initial 120%, it is an \(10/120=8.33\%\) decline.
Worked Example: Quantifying a Scenario Deterioration
A hypothetical insurer compares its base projection with an adverse claims scenario. At year 3, base resources are $138 million and base internal capital need is $132 million. Under the adverse scenario, resources are $126 million and need is $139 million. The dates, valuation basis, and definitions are identical. Calculate both scenarios’ surplus and coverage, and quantify the change from base to adverse.
Method. Calculate each scenario’s measures from its own resource and need values, then subtract base results from adverse results. This avoids comparing a ratio from one basis with a surplus from another.
For the base scenario, surplus is \(138-132=6\) million and coverage is \(138/132=1.0455\), or 104.5%. For the adverse scenario, surplus is \(126-139=-13\) million and coverage is \(126/139=0.9065\), or 90.6%.
The surplus change is \(-13-6=-19\) million. The coverage change is \(90.6\%-104.5\%=-13.9\) percentage points, using the displayed rounded ratios. Using unrounded ratios, the change is \(0.9065-1.0455=-0.1390\), or approximately \(-13.90\) percentage points. The adverse scenario therefore changes the position from a $6 million surplus to a $13 million shortfall on this internal basis.
Check. The resource change is \(126-138=-12\) million, and the capital-need change is \(139-132=7\) million. Together they reduce surplus by \(-12-7=-19\) million, matching the direct surplus comparison.
Common mistake avoided: Calling the 13.9 percentage-point coverage decline a 13.9% relative decline confuses two different comparisons. Relative to the unrounded base coverage, the decline is approximately \(0.1390/1.0455=13.30\%\); the percentage-point change is about 13.90 points.
Make Assumptions and Uncertainty Visible
A solvency projection is conditional on its assumptions, model structure, and data. A concise report should identify the assumptions that materially affect the conclusion rather than burying them in a general technical appendix. Depending on the assessment, relevant items may include the valuation date, projection horizon, economic environment, loss assumptions, management actions included, and important exclusions. The report should distinguish assumptions used in the central projection from assumptions changed in a sensitivity or scenario.
Uncertainty communication is more useful when it explains the consequence for the conclusion. State which assumptions were varied, whether they were varied individually or together, and how the reported measures changed. A sensitivity result is not automatically a probability statement, and a set of individually varied assumptions does not by itself quantify every possible combined outcome. Avoid implying that a range is a confidence interval unless it was constructed and interpreted as one.
Worked Example: Reporting an Assumption Sensitivity Without Overstating It
At year 3, a hypothetical insurer’s central projection has resources of $138 million and internal capital need of $132 million. The assessment tests claims inflation and reinvestment yield. A claims-inflation sensitivity gives resources of $134 million and need of $137 million. A lower-yield sensitivity gives resources of $135 million and need of $133 million. A combined scenario gives resources of $130 million and need of $139 million. All figures are in millions, use the same projection date and definitions, and are deterministic scenario outputs; no probabilities are assigned. Calculate the surplus for each case and describe the evidence.
Method. Calculate \(R-K\) separately for the central projection, each one-at-a-time sensitivity, and the combined scenario. Then compare each surplus with the central surplus.
Central surplus is \(138-132=6\) million. The claims-inflation surplus is \(134-137=-3\) million, a change of \(-3-6=-9\) million from central. The lower-yield surplus is \(135-133=2\) million, a change of \(2-6=-4\) million. The combined-scenario surplus is \(130-139=-9\) million, a change of \(-9-6=-15\) million.
The two individual sensitivities indicate that each tested change weakens the central surplus; the claims-inflation sensitivity produces a shortfall of $3 million. The combined scenario produces a $9 million shortfall. It is not valid to infer the combined result by simply adding the standalone surplus changes: \(-9+(-4)=-13\) million, whereas the actual combined change is \(-15\) million. In this hypothetical set of outputs, the combined scenario is $2 million more adverse than that simple sum. The results do not, by themselves, establish the cause of that difference or the likelihood of any scenario.
Check. The combined scenario’s resource change is \(130-138=-8\) million and its need change is \(139-132=7\) million. Thus its surplus changes by \(-8-7=-15\) million, matching the direct calculation. The central surplus of $6 million less $15 million also gives the combined shortfall of $9 million.
Common mistake avoided: Treating one-at-a-time sensitivities as additive can misstate the combined outcome. Report the combined scenario as its own model result, and label the sensitivity outputs as deterministic tests rather than probabilities.
Present Evidence So It Can Be Reviewed
A clear exhibit generally needs more than a table of numbers. Its title should identify the scenario and projection basis; column headings should state units and dates; and a nearby note should identify material assumptions and any important scope limitation. If figures have been rounded, use consistent rounding and ensure the displayed arithmetic still supports the narrative. If rounding creates a small apparent discrepancy, disclose that the displayed values are rounded rather than silently altering a result.
The narrative should direct attention to the decision-relevant feature of the evidence without substituting interpretation for results. For example, say which projected year has the lowest coverage, whether the surplus becomes negative under a named scenario, and which assumptions are material to that observation. Avoid selective endpoints when an intervening year is worse, and avoid presenting only a ratio when a change in the numerator or denominator materially explains the result.
A practical review asks whether a reader can answer these questions from the report:
- What conclusion is being made, and over what horizon?
- Which resources, capital need, and derived measure support it?
- Are the compared scenarios measured on the same basis?
- Which assumptions materially drive the result, and how were they varied?
- What limitations or uncertainty qualify the conclusion?
Check Your Understanding
For each hypothetical case, calculate the requested measure and consider what conclusion the evidence supports.
- A projection reports resources of $154 million and internal capital need of $140 million at year 2. Calculate surplus and coverage as a percentage. (Answer: Surplus = $14 million; coverage = 110.0%.)
- A base scenario has resources of $160 million and need of $150 million. An adverse scenario has resources of $151 million and need of $158 million, on the same date and basis. Calculate both surpluses and the adverse-minus-base change. (Answer: Base surplus = $10 million; adverse surplus = \(-$7\) million; change = \(-$17\) million.)
- Coverage declines from 125% to 115%. State the change in percentage points and the relative percentage decline from the initial coverage. (Answer: Decline = 10 percentage points; relative decline = \(10/125=8.00\%\).)
- A central projection has resources of $92 million and need of $88 million. A single assumption sensitivity has resources of $89 million and need of $91 million. Calculate the two surpluses and the change, and state whether the sensitivity produces a shortfall. (Answer: Central surplus = $4 million; sensitivity surplus = \(-$2\) million; change = \(-$6\) million; the sensitivity produces a $2 million shortfall.)
- A central result has resources of $210 million and need of $200 million. Two separate sensitivities each reduce the surplus by $5 million. A combined scenario reports resources of $198 million and need of $197 million. Calculate the combined surplus and explain why adding the standalone changes is not a valid substitute for the combined result. (Answer: Combined surplus = $1 million; the standalone changes imply a $0 surplus only under an unverified additivity assumption, so the combined scenario must be reported from its own output.)