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Interpreting normal loss VaR and expected shortfall

The default quantile and selected-tail average use different standard normal coefficients.

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Read the original record

The default is a declared normal loss law with mean 0 and dispersion 10, in one hypothetical horizon and common loss unit. Confidence is 95%. No observed exposure or data source is implied.

Interpret each quantity

Default normal-model outputs
QuantityValueInterpretation
VaR16.448536Upper loss quantile
ES20.627128Average of worst 5%
Quantile coefficient1.644854Standard normal cumulative crossing
Tail coefficient2.062713Standard normal selected-tail average
Selected probability5%Complement of confidence

Make a controlled parameter comparison

Changing the mean shifts both loss summaries equally. Changing dispersion scales them by different coefficients. Changing confidence changes the selected quantile and tail mass. Retain a new assumption record for each comparison.

Keep standardized and original coordinates distinct

The density’s x coordinate is z, not the original loss amount. Convert a coordinate to loss using μL+σL z. The graph’s endpoints are display choices rather than maximum losses. A zero-dispersion input uses a constant limit instead of that standardization.

Further references