Scaling Normal VaR from 95% to 99% Confidence

Summary

The document addresses how to estimate a higher-confidence Value-at-Risk from an existing VaR estimate when returns are assumed to follow a normal distribution and the confidence level is one-tailed. Its method is to rescale the original estimate by the ratio of the standard normal quantiles associated with the new and original confidence levels. In practical terms, this converts the VaR at the lower confidence threshold to the corresponding tail threshold at the higher one.

The response provides a compact calculation rule but no worked numerical result, supporting data, or discussion of alternative distributions. The estimate depends entirely on the normality assumption and on interpreting both confidence levels consistently as one-tailed. It does not address whether the underlying VaR model is calibrated well, how to estimate the original VaR, or how fat tails and changing market conditions could affect the result.

Key ideas

• Under a normal-return assumption, VaR at a new confidence level can be scaled using standard normal quantiles.
• The scaling factor is the quantile for the target confidence level divided by the quantile for the original level.
• The method assumes one-tailed confidence levels and does not account for departures from normality.

Tags

# Calculating the Value-at-Risk when changing the confidence level


# Calculating the Value-at-Risk when changing the confidence level












If I have a VaR estimate at a 95% confidence interval is 10, how do I calculate the approximate level of the VaR if the confidence level was raised to 99%, assuming a one-tailed normal distribution?

## Answer by Dimitri Vulis (score 3, accepted)

https://quant.stackexchange.com/a/59949

If you assume that everything is normally distributed, then you just divide by normsinv(95%) and multiply by normsinv(99%).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.