Value at Risk (VaR)

Suppose you want a single sentence that captures how bad a bad day could be for your investments. You might say: 'I am 99% sure I won't lose more than $50,000 over the next year.' That $50,000 figure is Value at Risk. It answers the everyday question 'on a really unlucky but not freakish day, how much could I be down?' by drawing a line at a chosen confidence level and reporting the loss you would not expect to exceed.

Precisely, VaR is a quantile of the loss distribution. Pick a confidence level, say 99.5%, and a time horizon, say one year. Line up every possible outcome from best to worst. The 99.5% VaR is the loss figure such that only a 0.5% chance — one year in two hundred — of doing worse remains. If your one-year, 99.5% VaR is 100 million, then there is just a 0.5% probability of losing more than 100 million over the year. Note what it is NOT saying: it does not tell you how bad things get on that worst 0.5% of days, only where the cut-off sits.

VaR became the lingua franca of risk because it is intuitive, comparable across desks, and underpins capital rules — Solvency II's headline capital requirement is essentially a one-year 99.5% VaR. But it has a famous and dangerous blind spot: it says nothing about the size of losses beyond the cut-off. Two portfolios can share the same VaR while one has a modest tail and the other can lose ten times more in the rare event. Worse, VaR is not always a 'coherent' measure — combining two portfolios can occasionally make total VaR larger than the sum, wrongly punishing diversification. For these reasons many actuaries prefer Tail VaR / expected shortfall, which averages the losses in the tail rather than stopping at its edge.