Backtesting

What it means

Comparing realised losses with the VaR forecasts that preceded them, to check that breaches occur about as often as the confidence level implies.

The exam angle

Basel’s traffic light approach escalates the capital multiplier as exceptions accumulate. Too few breaches signals an over-conservative model, not a good one.

Where it appears in the syllabus

• Market Risk Measurement & ManagementFRM Part II · exam weight 20% · VaR and ES estimation, backtesting, EVT, GARCH, copulas, FRTB.
• Foundations of Risk ManagementFRM Part I · exam weight 20% · Risk taxonomy, governance, CAPM, multifactor models, financial disasters.

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

• Coherent risk measureA risk measure satisfying monotonicity, subadditivity, positive homogeneity and translation invariance.
• 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…
• Stress testingRevaluing a portfolio under severe but plausible scenarios, rather than under the distribution of ordinary days.
• Value at RiskThe loss that will not be exceeded over a stated horizon with a stated confidence — for example, a 1-day 99% VaR of…
• Basis riskThe risk that a hedge and the exposure it hedges do not move together, leaving a residual.
• Carry tradeBorrowing in a low interest rate currency to invest in a high interest rate one, profiting if the exchange rate does…