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Treating VaR as a worst-case loss

A percentile threshold does not make larger losses impossible.

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Inspect the original threshold

At 90% confidence in the original model, VaR is 10 loss units. The 50-unit loss still carries 5% probability. Calling 10 the most that can be lost contradicts the stated distribution itself.

Report the relevant quantities

Original quantities
QuantityResult
Lower 90% loss quantile10
Probability strictly above it5%
90% expected shortfall30
Largest listed loss50

Avoid replacing one bound with another

The largest listed loss is only the end of this finite record. An observed maximum does not rule out future events outside the sample. A stress case can explore an adverse scenario, but a chosen case is not proof of every possible loss.

Keep the model in the statement

Describe the threshold of the supplied distribution at its stated confidence and horizon. Preserve the tail evidence rather than converting a percentile into a guarantee.

Further references