Skip to content

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

A risk analyst wants a standard error and confidence interval for a 99% expected shortfall estimated from 750 historical returns, without assuming a parametric distribution. Which procedure correctly applies the bootstrap?

The correct procedure resamples the 750 returns with replacement many times, computes ES on each resample, and uses the spread of those estimates for the standard error and confidence interval. Sampling without replacement would just reproduce the original sample, and the other approaches are parametric or invalid.

  1. ADraw many samples of 750 returns with replacement from the historical data, compute ES for each, and use the dispersion of these estimates to get the standard error and intervalCorrect
  2. BDraw many samples of 750 returns without replacement from the data, compute ES for each, and use their dispersion for the standard error
  3. CFit a normal distribution to the data, then use its analytical quantile formula to compute the standard error of ES
  4. DCompute ES once from the full sample and divide by the square root of 750 to obtain the standard error

Explanation

The bootstrap resamples the observed data with replacement to create many pseudo-samples of the same size, computes the statistic on each, and uses the empirical distribution of those estimates for the standard error and confidence interval. Sampling without replacement 750 from 750 reproduces the original sample every time, giving zero dispersion. The other options impose a parametric model or an invalid shortcut.

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