On this page
Inspect the original model
Mean loss is zero and standard deviation 10 loss units, so variance is 100 squared loss units. Inserting 100 into μ+zσ gives 164.485363 numerically, but that substitutes the wrong risk object and unit.
Restore the correct dispersion
Use σ=10 to obtain 95% VaR 16.448536 and ES 20.627128 loss units. A variance input needs a square root before it can be used as dispersion in these equations.
Check the sum’s compatibility
| Term | Unit |
|---|---|
| Mean loss μ | Loss units |
| z or normal tail multiplier | Dimensionless |
| Standard deviation σ | Loss units |
| Variance σ² | Squared loss units |
Keep estimator labels with the data
A data source might report variance, volatility percentage or currency dispersion. Identify and convert the actual quantity rather than relying on a column labeled risk. The calculator expects mean loss and loss standard deviation in the same unit.