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Interpreting a 99.9% Confidence Level as a 1-in-1,000-Year Event

Article Quant Q&A · Author: eemrunn
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Summary

The document asks how a 99.9% confidence level used in a Basel context corresponds to an event described as occurring once in a thousand years, and how to express a rarer event such as one in ten thousand years. It raises the distinction between a probability threshold and a return-period interpretation, but provides no answer or derivation.

Under a simple model with a fixed annual exceedance probability, a 0.1% annual probability corresponds to an average return period of 1,000 years; a 0.01% annual probability corresponds to 10,000 years, or a 99.99% non-exceedance level. These interpretations rely on the stated probability being annual and stable over time. A return period is an average frequency, not a schedule, and the document itself does not discuss dependence, changing risks, or Basel’s specific modeling assumptions.

Key ideas

  • A 99.9% non-exceedance level leaves a 0.1% exceedance probability for the relevant period.
  • If the probability is annual and stable, a 0.1% annual exceedance probability implies a 1,000-year average return period.
  • A 10,000-year average return period corresponds to a 0.01% annual exceedance probability under the same assumptions.
  • Return periods describe average probabilities and do not predict when an event will occur.
  • The source poses the question but does not provide its own derivation or answer.

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Risk managementStatistics
Full text
# Derivation of the 99.9% CI to a 1 in a 1000 year event


# Derivation of the 99.9% CI to a 1 in a 1000 year event












Keen to understand how BASEL derived the 1 in a 1000 year event from the CI 99.9%:

The confidence level is fixed at 99.9% (0.999) (i.e. a bank is expected to suffer losses that exceeds its capital on average, once in a thousand years).

Anyone know how? I am interested to calculate scenarios based on events that can occur in, lets say, 1 in 10,000 years. What should be the CI be?

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