Why Scenario Rankings Depend on the Decision
A stress scenario does not have one universally correct rank. One scenario may produce the largest modeled loss, another may create the greatest near-term cash strain, and a third may leave the least capital above a required threshold. Which scenario matters most depends on the management decision: protecting solvency, meeting payments, preserving a strategic capability, or satisfying several constraints at once.
The comparison should begin with consistent scenario outputs and a clearly stated decision objective. A ranking is not a replacement for judgment: it is a way to make the consequences and trade-offs visible. In particular, the most severe scenario under one measure need not be the most decision-relevant scenario under another.
For this tutorial, treat scenario outputs as conditional results: they describe what the model produces if the specified scenario occurs. Unless probabilities are supplied and the decision calls for probability-weighted results, do not interpret a larger conditional loss as a more likely event. Scenario plausibility and scenario impact are different questions.
Set Up a Comparable Decision Table
Before ranking alternatives, confirm that their outputs use the same scope, valuation basis, and time horizon. For example, losses should all be measured on the same gross or net basis, capital should refer to the same post-stress date, and liquidity needs should use the same projection period. If a measure is not comparable, show that limitation rather than silently treating the figures as equivalent.
Useful measures commonly include:
- Stress loss: the specified loss measure for the scenario. Larger losses are generally worse, all else equal.
- Liquidity deficit: the amount by which modeled cash obligations exceed available liquid resources at the relevant time. A larger deficit is generally worse.
- Capital surplus: available capital resources less the applicable required capital at the stated measurement date. A smaller surplus is generally worse; a negative surplus indicates a shortfall under that definition.
- Strategic impact: effects such as disruption to a critical service, loss of a market position, or impairment of a business plan. These may be described in ordered categories, but an ordinal rating is not automatically a numerical quantity suitable for arithmetic.
The measures answer different questions. A large modeled loss does not, by itself, establish that the organization will run out of cash. A positive capital surplus does not guarantee that cash is available at the time payments fall due. A favorable result on both measures also may not capture an important strategic disruption.
Worked Example: The “Worst” Scenario Depends on the Measure
A hypothetical insurer compares three one-year enterprise stress scenarios. The model outputs below are stipulated scenario results in millions of dollars. Losses are net of the same assumed recoveries in all scenarios; the liquidity figure is the maximum projected deficit during the year; capital surplus is measured at year-end against the same requirement. Strategic impact uses an ordered scale from 1 (limited) to 4 (severe). These are deterministic conditional stress outputs, not a probability distribution; no interest or mortality assumption is used.
| Scenario | Net loss | Maximum liquidity deficit | Year-end capital surplus | Strategic impact |
|---|---|---|---|---|
| A: regional windstorm | $48 million | $6 million | $24 million | 2 |
| B: claims-system outage | $31 million | $18 million | $37 million | 4 |
| C: concentrated bond downgrade | $42 million | $3 million | $15 million | 1 |
Step 1: Rank by net loss. Larger loss is worse. The values are \(48>42>31\), so the order from worst to least severe by loss is A, C, B.
Step 2: Rank by liquidity deficit. A larger deficit is worse. Since \(18>6>3\), the order is B, A, C. The claims-system outage is not the largest loss, but it creates the greatest modeled cash deficit.
Step 3: Rank by year-end capital surplus. Smaller surplus is worse. Since \(15<24<37\), the order is C, A, B. The bond downgrade is worst on this measure even though its loss is not the largest.
Step 4: Read strategic impact separately. The ordered ratings are B (4), A (2), and C (1), from greatest to least impact. Because these ratings are categories, the difference between 4 and 2 should not be treated as a dollar amount or assumed to equal the difference between 2 and 1.
Conclusion and check. A is worst by loss, B by liquidity and strategic impact, and C by capital surplus. Each order follows the stated direction of the measure, so there is no single ranking that answers every management question. A common mistake would be to call A “the worst scenario” solely because its loss is largest.
Apply Constraints Before Preferences
Some decisions have minimum conditions that alternatives must satisfy before management compares preferences. Examples include a maximum tolerable liquidity deficit, a minimum capital surplus, or a requirement that a critical service remain operable. In that case, first classify each scenario as feasible or infeasible under the stated conditions. Rank the feasible alternatives only after that screening.
This avoids a compensability error: an attractive result on one measure should not automatically offset failure on a hard constraint. If a board requires a minimum capital buffer, a lower loss does not make a scenario acceptable when it breaches that buffer.
Worked Example: Screen for Feasibility, Then Rank
A hypothetical property insurer is choosing which of three annual stresses to use for a management action review. The supplied model outputs are in millions of dollars, use a common net-loss basis, and refer to the same one-year horizon. Management requires a maximum liquidity deficit no greater than $10 million, year-end capital surplus of at least $20 million, and strategic impact no greater than 3 on the scale from 1 (limited) to 4 (severe). The scenario results are deterministic conditional outputs; no probability distribution, interest rate, or mortality assumption is involved.
| Scenario | Net loss | Liquidity deficit | Capital surplus | Strategic impact |
|---|---|---|---|---|
| D: hail-season accumulation | $38 million | $8 million | $28 million | 2 |
| E: broker-platform interruption | $26 million | $14 million | $40 million | 3 |
| F: regional flood event | $45 million | $5 million | $22 million | 1 |
Step 1: Test scenario D. Its liquidity deficit satisfies \(8\leq10\), its capital surplus satisfies \(28\geq20\), and its strategic rating satisfies \(2\leq3\). D is feasible.
Step 2: Test scenario E. Its liquidity deficit is \(14>10\), so E fails the liquidity constraint. Its capital surplus and strategic rating meet their limits, but meeting two of three conditions does not remove the failed hard constraint. E is infeasible.
Step 3: Test scenario F. Its liquidity deficit satisfies \(5\leq10\), its capital surplus satisfies \(22\geq20\), and its strategic rating satisfies \(1\leq3\). F is feasible.
Step 4: Rank the feasible scenarios under the stated objective. If the objective is to minimize net loss among feasible alternatives, D has a $38 million loss and F has a $45 million loss, so D ranks ahead of F. If management instead prioritizes liquidity resilience, F ranks ahead because its $5 million deficit is below D’s $8 million deficit. The feasibility result does not change; the preference ranking does.
Conclusion and check. E has the smallest loss, but it is not an eligible choice under the stated liquidity limit. A common mistake is to rank all scenarios by loss first and select E without applying the constraint. The correct sequence is to test every condition, exclude failures when the conditions are binding, and then rank the feasible alternatives using the actual objective.
Use Pareto Comparisons to Identify Trade-Offs
When there are several measures and no single measure is designated as primary, a useful first step is to look for Pareto dominance. For measures where smaller is preferred, such as loss and liquidity deficit, a scenario is better when its value is no greater. For capital surplus, larger is preferred. A scenario dominates another if it is at least as good on every included measure and strictly better on at least one.
This rule follows directly from the meaning of “no worse on any included objective.” If A has lower loss, a smaller liquidity deficit, and a greater capital surplus than B, then choosing B cannot improve any of those objectives and worsens at least one. But if A has a lower loss while B has greater capital surplus, the evidence does not establish a universal preference. Management must state which objective has priority or supply another decision rule.
Here \(L\) denotes loss, \(Q\) denotes liquidity deficit, and \(H\) denotes capital surplus; at least one of the inequalities must be strict. Strategic categories can also be compared by their stated order, but their numerical labels should not be added to dollar measures as if they were cardinal quantities.
Worked Example: Find the Non-Dominated Scenarios
A hypothetical mutual insurer compares four conditional stress scenarios for a common planning horizon. All monetary outputs are in millions of dollars, use the same net-loss and capital definitions, and are deterministic model outputs rather than draws from a distribution. Strategic impact is an ordinal scale from 1 (limited) to 4 (severe). No interest or mortality assumption is used.
| Scenario | Net loss | Liquidity deficit | Capital surplus | Strategic impact |
|---|---|---|---|---|
| J: supplier disruption | $35 million | $7 million | $18 million | 2 |
| K: investment-spread shock | $40 million | $4 million | $25 million | 1 |
| M: regional claims surge | $32 million | $9 million | $16 million | 3 |
| N: severe data-center outage | $42 million | $10 million | $14 million | 4 |
Step 1: Compare J with N. J has lower loss (\(35<42\)), a smaller liquidity deficit (\(7<10\)), greater capital surplus (\(18>14\)), and a lower strategic rating (\(2<4\)). Thus J is better on all four ordered comparisons and dominates N.
Step 2: Compare K with N. K has lower loss (\(40<42\)), a smaller deficit (\(4<10\)), greater surplus (\(25>14\)), and a lower strategic rating (\(1<4\)). K also dominates N.
Step 3: Compare M with N. M has lower loss (\(32<42\)), a smaller deficit (\(9<10\)), greater surplus (\(16>14\)), and a lower strategic rating (\(3<4\)). M also dominates N. Therefore N can be removed from the set of non-dominated alternatives under these measures.
Step 4: Compare J, K, and M. K has the best liquidity deficit, capital surplus, and strategic rating among these three, but its $40 million loss exceeds J’s $35 million and M’s $32 million. M has the lowest loss, but its liquidity deficit and strategic rating are worse than J’s and its capital surplus is lower. J also trades off against K and M. No one of J, K, and M is at least as good as the others on every measure.
Conclusion and check. The non-dominated set is J, K, and M; N is dominated. A loss-minimization objective favors M, while a capital or liquidity objective favors K. The analysis does not claim that the three non-dominated scenarios are equally desirable. It shows that further preferences or constraints are needed to distinguish them.
Make the Decision Rule Explicit
A defensible comparison records both the results and the rule used to interpret them. The rule may be a single priority measure, a set of binding constraints followed by a priority measure, or a multi-criteria approach agreed by decision-makers. Whatever the form, state it before announcing a winner. If the objective changes, rerank the alternatives rather than presenting an old ranking as universal.
Confirm common definitions, net or gross basis, measurement date, and horizon for the measures being compared.
State whether outputs are conditional scenario results or probability-weighted estimates. Do not infer likelihood from the size of a stress result.
Identify alternatives that fail required liquidity, capital, or operational conditions before considering preferences.
Show the measure’s preferred direction and the resulting order. If objectives conflict, report the trade-off or non-dominated set.
Describe which scenarios move up or down when management changes its priority, and identify any judgment that the outputs do not resolve.
Common Mistakes in Scenario Comparisons
- Using “worst” without naming a measure. Replace it with “largest modeled loss,” “greatest liquidity deficit,” or another precise description.
- Confusing scenario impact with likelihood. A severe conditional outcome is not automatically a probable outcome. Use probabilities only when they are available and appropriate to the decision.
- Comparing inconsistent quantities. A gross loss for one scenario and a net loss for another do not support a fair ranking without an explicit reconciliation.
- Letting a hard constraint become a soft preference. If a minimum capital level is binding, failure cannot be erased by a favorable result elsewhere unless management explicitly changes the constraint.
- Adding ordinal ratings to money. A strategic rating can support ordering and discussion, but its labels do not have dollar units or necessarily equal spacing.
- Reporting one ranking when measures conflict. Show the separate orders or the non-dominated alternatives, then state what additional preference would resolve the choice.
Scenario comparisons are most useful when they expose these conflicts rather than hide them. This decision-focused approach is aligned with the CAS Exam 9 (Risk Management for Actuaries) syllabus: interpret risk results in context, make assumptions visible, and connect a ranking to the management objective it is intended to serve.
Check Your Understanding
For each original scenario problem, state the relevant comparison rule before selecting or ranking alternatives.
- A hypothetical insurer reports two one-year stress outputs, all in millions of dollars: scenario R has loss 27, liquidity deficit 11, and capital surplus 34; scenario S has loss 33, liquidity deficit 6, and capital surplus 29. Which scenario ranks worse by loss, which by liquidity deficit, and which by capital surplus? (Answer: R by loss; R by liquidity deficit; S by capital surplus.)
- A hypothetical health insurer requires a liquidity deficit no greater than $8 million and a capital surplus of at least $16 million. Scenario T has deficit $7 million and surplus $15 million; scenario U has deficit $9 million and surplus $24 million. Which scenarios meet both conditions? (Answer: Neither; T fails the capital condition and U fails the liquidity condition.)
- For a hypothetical three-year planning stress, scenario V has loss $19 million, liquidity deficit $5 million, and capital surplus $21 million. Scenario W has loss $22 million, deficit $4 million, and surplus $25 million. Does either dominate the other using loss, deficit, and surplus? (Answer: Neither; V has the lower loss, while W has the smaller deficit and greater surplus.)
- A hypothetical reinsurer compares scenario X with loss $41 million, liquidity deficit $12 million, and capital surplus $18 million, against scenario Y with loss $37 million, deficit $9 million, and surplus $20 million. Which scenario dominates, assuming lower loss and deficit and higher surplus are preferred? (Answer: Y dominates X on all three measures.)
- Two hypothetical scenarios have the same one-year loss of $30 million. Scenario Z has a maximum quarterly liquidity deficit of $13 million and year-end capital surplus of $26 million; scenario AA has a deficit of $8 million and surplus of $19 million. Which scenario is preferable under a liquidity-first objective, and which under a capital-surplus-first objective? (Answer: AA under the liquidity-first objective; Z under the capital-surplus-first objective.)