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Value at risk

The loss level a portfolio should not exceed over a set horizon at a set confidence - for example, 5% of capital over one day, 95% of the time.

A VaR statement has three parts: horizon, confidence and amount. A one-day 95% VaR of $8,000 means that on 19 days out of 20 the loss should be smaller than $8,000. It says precisely nothing about the twentieth day.

That silence is the standard criticism, and it is the right one. VaR gives the threshold, not the magnitude beyond it, so two portfolios with identical VaR can have wildly different tails - one loses $9,000 on a bad day, the other loses everything. conditional-var exists to answer the question VaR refuses to.

It comes in three flavours with different assumptions: historical-var, parametric-var and monte-carlo-var. All three are estimated from the past, all three understate risk when correlation-breakdown hits, and all three were prominently in place at institutions that blew up. Useful as a dashboard gauge, dangerous as a limit you trust.

Related: historical-var, parametric-var, monte-carlo-var, conditional-var

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