I have been working with a group which references a 99.97% 10-day VaR figure.

They calculate this value via a 99% 1-day historical simulation over 500 days and then scale it under the assumption of a normal distribution, i.e. $scale = \frac{\Phi^{-1}(0.9997)}{\Phi^{-1}(0.99)}$, and also accounting for time, $scale2 = \sqrt{10}$.

So a \$100, 99% 1-day VaR becomes a \$466, 99.97% 10-day VaR.

I have two questions:

What is the significance (possibly in regulatory capital requirements) of the 99.97% confidence level? A google search has this figure appearing too much for it to be an arbitrarily chosen value.

Is this method quite poor or standard practice? While there might not be enough data to bootstrap the higher confidence level, is the assumption of normality particularly weak in the tails giving rise to significant underestimate?

Bonus points for considered alternatives..


The 99.97% confidence is somtimes referred to as corresponding to the 1-year probability of default of 3 bps for AA-rated entities. (Here for example https://papers.ssrn.com/sol3/papers.cfm?abstract_id=963233 ) The normal approximation works better for general securities portfolios than for credit portfolios and might thus be seen as good enough from a regulatory perspective.

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