Statistics

Value at Risk

Also known as: VaR

The loss threshold that will not be exceeded with a given probability over a given horizon.

A 99% one-day VaR of 1 million means a 1% chance of losing more than that in a day.

Two serious criticisms, both worth raising.

It says nothing about how bad the tail is beyond the threshold - two portfolios with identical VaR can have wildly different losses in the worst 1%. Expected shortfall (average loss beyond VaR) fixes this.

It is not subadditive, so the VaR of a combined portfolio can exceed the sum of its parts - which violates the intuition that diversification cannot increase risk, and disqualifies it as a coherent risk measure.

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