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Parametric VaR

Value at risk computed from a volatility estimate and an assumed distribution, usually the normal one - fast to calculate and reliably too small.

The formula is blunt: VaR = portfolio value x volatility x z-score. For a $200,000 book with 1.2% daily volatility at 95% confidence, VaR = 200,000 x 0.012 x 1.645 = $3,948.

Its speed is why it persists and its assumption is why it misleads. Assuming normality directly denies fat-tails, so the estimate is too low precisely in the region that matters, and the error grows as you push confidence higher: at 99% or 99.9% the normal model is not slightly wrong, it is wrong by multiples. For a book with options, the delta-normal version also ignores gamma, so it misprices the very non-linearity the portfolio contains.

If you use it, use it as a relative gauge - has risk doubled since last month? - rather than as an absolute loss estimate. The absolute number is a comfortable fiction.

Related: value-at-risk, fat-tails, historical-var, portfolio-volatility

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