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Normal loss value at risk

For a normal loss law, VaRc=μL+σL Φ⁻¹(c).

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Define the loss-side law

Assume L=μL+σL Z with Z standard normal and σL>0. Positive loss means loss and negative loss means gain. Confidence c refers to the cumulative loss percentile, not a lower return-tail probability.

Restore location and scale

VaRc=μL+σLzc,zc=Φ−1(c)\mathrm{VaR}_c=\mu_L+\sigma_L z_c,\qquad z_c=\Phi^{-1}(c)

μL and σL share the original loss unit.

Check the original zero-mean case

At c=95%, μL=0 and σL=10, model VaR is 16.448536 loss units. Using variance 100 instead of standard deviation 10 would produce the wrong quantity and unit.

State the law rather than inferring it

Knowing a mean and variance alone does not establish a normal loss distribution. The calculator supports three stated confidence levels and the zero-dispersion constant limit; it does not estimate parameters or reprice positions.

Further references