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

A risk analyst estimates the 95% VaR of a portfolio from 1,000 daily historical P&L observations and wants to report how precise the estimate is. Holding the confidence level fixed, which change would most directly reduce the standard error of the VaR estimate?

Increasing the number of observations reduces the standard error of a VaR estimate, because quantile estimators become more precise as the sample grows, roughly with the inverse square root of sample size. Changes in presentation or rounding do not affect sampling error.

  1. AUsing a larger sample of observationsCorrect
  2. BReducing the holding period assumption only in the report
  3. CSwitching the quoted VaR from a loss figure to a percentage figure
  4. DRounding the VaR estimate to the nearest thousand

Explanation

The standard error of a quantile estimate falls as the sample size rises, roughly in proportion to 1/sqrt(n). Changing units, rounding or relabeling does not change the sampling uncertainty of the underlying estimate.

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