Value at Risk

What it means

The loss that will not be exceeded over a stated horizon with a stated confidence — for example, a 1-day 99% VaR of £1m means losses should exceed £1m on about one day in a hundred.

The exam angle

Says nothing about how bad the breach is when it happens, and is not subadditive, so the VaR of a combined book can exceed the sum of its parts. Both failings motivate expected shortfall.

Where it appears in the syllabus

• Foundations of Risk ManagementFRM Part I · exam weight 20% · Risk taxonomy, governance, CAPM, multifactor models, financial disasters.
• Market Risk Measurement & ManagementFRM Part II · exam weight 20% · VaR and ES estimation, backtesting, EVT, GARCH, copulas, FRTB.
• Portfolio ConstructionCFA Level I · exam weight 8–12% · Risk and return, the CAPM, IPS construction, behavioural biases.

See it worked through

• Value at Risk: the square-root-of-time ruleScale a one-day VaR to ten days with a worked example, and see where the rule breaks.

There is also a short video: watch it on YouTube.

Related terms

• BacktestingComparing realised losses with the VaR forecasts that preceded them, to check that breaches occur about as often as…
• BetaThe sensitivity of an asset’s return to the market’s return — its share of systematic risk.
• Capital asset pricing modelA model stating that an asset’s expected return equals the risk-free rate plus beta times the equity risk premium.
• Coherent risk measureA risk measure satisfying monotonicity, subadditivity, positive homogeneity and translation invariance.
• DiversificationCombining imperfectly correlated assets so that portfolio risk falls below the weighted average of the individual risks.
• Expected shortfallThe average loss in the cases where the VaR threshold is breached — the expected size of a bad day, given that it is a…