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Merging identical loss outcomes

Combining probabilities at an identical loss amount preserves the quantile and selected-tail average.

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Read mutually exclusive scenario records

Suppose two separate scenarios both produce loss −10, with probabilities 10% and 20%. Other losses are 0 with 40%, 10 with 25%, and 50 with 5%. The two −10 scenarios are mutually exclusive records in this stipulated model.

Group by economic loss amount

Original split versus grouped record
LossSplit probability recordsGrouped probability
−1010% and 20%30%
040%40%
1025%25%
505%5%

Recompute at 90% confidence

The cumulative distribution remains 30/70/95/100 percent. VaR remains 10 and the selected worst 10% average remains 30. The public tool groups identical loss amounts before displaying the allocation table.

Do not merge different economic outcomes

Different loss amounts cannot be combined by adding probabilities and keeping one arbitrary loss. Joint events also need their joint probabilities; scenario records must not be treated as mutually exclusive merely because they have different names.

Further references