Normal return to currency loss risk

State the original linear setup

Starting value is 1,000,000 currency units, with no intervening cash flows. Same-horizon simple return is assumed normal with mean 0.01 and standard deviation 0.02. Define loss as L=−Vr.

Transform the mean and dispersion

Mean loss is −1,000,000×0.01=−10,000. Loss dispersion is 1,000,000×0.02=20,000. The negative sign belongs to the mean transformation; a standard deviation is nonnegative.

Apply the two 95% multipliers

Retain the model assumptions

These are tail summaries of the assumed linear normal return law. They are not realised losses or guaranteed future bounds. A normal simple-return law has unbounded support and may be inappropriate where economic constraints or nonlinear pricing matter.