Value at Risk

One number for tomorrow’s loss, and what it leaves out

Value at risk states the loss a portfolio is not expected to exceed over a given horizon at a given confidence — a 99% one-day VaR of $1.4m says that on 99 days in 100 the loss should be smaller than that. It is the standard aggregate risk measure across every asset class, the basis of firm-wide limits, and it says nothing whatsoever about the size of the loss on the hundredth day. Everything difficult about it follows from that last sentence.

Open in the app · Risk & the Greeks · advanced

Risk & the Greeks is part of the OTC Learn subscription. Everything the app shipped with — 36 products across six asset classes — stays free.

What the lesson covers

1. What it is
2. How it is computed
3. Expected shortfall
4. Backtesting
5. Risks to watch

Key terms

• Value at risk — The loss not expected to be exceeded over a stated horizon at a stated confidence level.
• Confidence level — The quantile the measure is read at, commonly 97.5% or 99%.
• Historical simulation — Computing VaR by applying a window of past market moves to today’s portfolio.
• Expected shortfall — The average loss given that the threshold is breached — the mean of the tail rather than its edge.
• Backtesting exception — A day whose clean P&L loss exceeded the VaR the model predicted for it.
• Procyclicality — The tendency of risk measures to rise together in a sell-off, forcing simultaneous deleveraging.

In practice

VaR sits at the top of the risk report at every bank and most funds, aggregating across desks and asset classes into one figure the board sees. Its limits are as well known as the measure, which is why it is always paired with stress scenarios — and why the interesting question in a risk meeting is usually about the assumptions rather than the number.

Read next

• P&L Attribution — Yesterday’s profit, accounted for line by line
• DV01 and Rate Risk — What one basis point is worth
• XVA and Counterparty Risk — Why the same swap is never quite the same price twice

In the app, Value at Risk carries a five-step lesson, a worked example and a bank of twelve questions drawn differently every sitting.

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Educational content only. Nothing here is financial advice, an offer to trade, or a recommendation to buy or sell any instrument.