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Read the original conversion
For fixed starting value 1,000,000, a normal return with mean 1% and dispersion 2% produces mean loss −10,000 and dispersion 20,000. Using −z95 directly in the upper loss formula would select the opposite side of the loss law.
Use the stated loss-side confidence
The 95% loss quantile is −10,000+20,000×z95≈22,897.072539. Equivalently, the lower 5% return quantile is 0.01−0.02×z95; applying −V to that return yields the same loss amount.
Retain the direction record
| Modeled quantity | Adverse tail |
|---|---|
| Positive return | Lower return tail |
| Positive loss | Upper loss tail |
| Transformation L=−Vr | Reverses order for V>0 |
Do not fix a sign by taking an absolute value
An absolute-value repair can hide a mistaken tail direction or remove a legitimate negative loss summary. Establish the sign convention and the linear transformation before interpreting the number.