Historical simulation

What it means

Estimating VaR by revaluing the current portfolio using actual historical changes in risk factors.

The exam angle

Assumes no distribution and captures real fat tails, but can only produce losses that have already happened. A quiet lookback window understates risk.

Where it appears in the syllabus

• Market Risk Measurement & ManagementFRM Part II · exam weight 20% · VaR and ES estimation, backtesting, EVT, GARCH, copulas, FRTB.
• Quantitative MethodsCFA Level I · exam weight 11–14% · Returns and benchmarks, time value, distributions, portfolio maths, regression.

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

• CorrelationCovariance divided by the product of the two standard deviations, giving a unit-free number between −1 and +1.
• KurtosisThe weight of a distribution’s tails.
• Monte Carlo simulationEstimating a distribution of outcomes by repeatedly drawing random inputs from assumed distributions and recomputing…
• Standard deviationThe square root of variance, in the same units as the data.
• BacktestingComparing realised losses with the VaR forecasts that preceded them, to check that breaches occur about as often as…
• Basis riskThe risk that a hedge and the exposure it hedges do not move together, leaving a residual.