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Scaling discrete tail losses by square root of time

A finite scenario distribution does not establish a square-root-of-time scaling rule on its own.

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Read what the inputs actually provide

The tool takes a supplied same-horizon loss distribution. Its probabilities and loss values do not describe how separate periods depend on each other, how positions change or how losses accumulate. Selecting a longer reporting horizon therefore needs additional assumptions.

Distinguish a dispersion rule from a tail model

Under particular independent/increment assumptions, a variance calculation can lead to square-root scaling of standard deviation. That does not automatically establish how a finite loss quantile, a mean component or nonlinear exposures scale across periods.

Collect the missing horizon information

Horizon-extension questions
FieldQuestion
DependenceHow do period outcomes relate?
AggregationAdditive losses, compounded returns or repricing?
ExposureStatic holdings or changing positions?
DistributionWhich multi-period loss law?
MeasureWhich confidence and quantile rule?

Keep the tool within its scope

Construct or obtain the appropriate multi-period loss record, label its source and then calculate its summaries. The public tool performs no horizon scaling and supplies no calibrated market distribution.

Further references