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Read a location shift
Holding dispersion and confidence fixed, adding 5 loss units to μL adds 5 to both VaR and ES. The distribution shifts horizontally without changing its spread. A negative mean is a gain location under this loss convention.
Read a dispersion change
At 95% confidence, adding 5 units to σL adds about 8.224268 to VaR and 10.313564 to ES. The difference arises from the quantile and tail-mean multipliers. It is not a change in confidence probability.
Keep both parameters in the same loss unit
| Change | VaR effect | ES effect |
|---|---|---|
| ΔμL | ΔμL | ΔμL |
| ΔσL | z ΔσL | φ(z)/(1−c) ΔσL |
Avoid turning sensitivity into validation
These are sensitivities of the declared normal model. They do not prove that changing a real asset changes only one parameter or leaves the model shape stable. Keep the assumption record with the comparison.