Quant · Core
Value at Risk
VaR is a quantile of the P&L distribution over a horizon — a number that says ‘we lose more than this only p percent of the time,’ until the tail arrives.
Definition
A 1-day 99% VaR of $10mm means the model’s 1% left quantile is −$10mm. Historical, parametric, and Monte Carlo VaR disagree. VaR is not the worst loss and is not coherent (subadditivity can fail).
Why it matters
Limits, regulatory capital, and desk dashboards still use it. 2008 was a VaR regime-break, not a 5σ surprise in the old distribution.
Case
A credit book with tight 99% VaR that was short a jump. The 99.9% day was several VaRs. The quantile was the wrong object.
How to read it
Horizon, percentile, and method. Then expected shortfall and a stress. VaR without ES is a speedometer without a cliff.
No query has been run yet. Which is tragically normal for most knowledge systems, but we are trying to evolve past decorative databases.