Value at Risk (VaR)

Value at Risk answers: what is the loss that only α% of days should exceed? A 95% one-day VaR of −2.1% means that, historically, one day in twenty lost more than 2.1%. It is a quantile of the return distribution — simple to state, easy to compare, and required vocabulary in institutional risk.

Its known flaw is that it says nothing about how bad the exceedances are: two books with identical VaR can hide very different disasters beyond the threshold. That is what expected shortfall exists for, and why the two are best read together.