Skip to content

FRM Part II · FRM Exam Part II · Estimating Market Risk Measures: An Introduction and Overview

A bank's risk report shows a point estimate of expected shortfall (ES) from historical simulation but no measure of its precision. A reviewer asks how best to quantify the estimation error. Which approach is most consistent with standard practice for estimating standard errors of risk measures?

Bootstrapping is the appropriate approach: resample the return data many times, recompute ES for each resample, and use the dispersion of those estimates as the standard error. Dividing by a square root of time, using the VaR-ES gap, or quoting return volatility does not measure the estimator's sampling error.

  1. AUse bootstrap resampling of the return data to build a distribution of ES estimates and derive a standard errorCorrect
  2. BDivide the ES estimate by the square root of the number of days in the holding period
  3. CAssume the standard error equals the difference between VaR and ES
  4. DReport the standard deviation of the portfolio returns as the ES standard error

Explanation

Bootstrapping repeatedly resamples the observed data, recomputes ES each time, and uses the spread of those estimates as the standard error, which works even when no simple formula exists. The other options conflate unrelated quantities such as the holding-period scaling, the VaR-ES gap, or return volatility, none of which measure sampling error of the estimator.

Did you get it right without looking?

One question tells you little. A timed set on Estimating Market Risk Measures: An Introduction and Overview shows your real accuracy, how long you take and where you lose marks.

Practise Estimating Market Risk Measures: An Introduction and OverviewFree diagnostic mock

More Estimating Market Risk Measures: An Introduction and Overview questions