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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 trading portfolio using historical simulation and wants to judge how precise the estimate is. Holding the confidence level fixed, which change will most directly reduce the standard error of the VaR estimate?

Increasing the number of historical observations reduces the standard error of a VaR estimate, since quantile estimates become more precise with larger samples. Raising the confidence level does the opposite by moving into the sparser tail, while changing holding period or asset mix alters the VaR level rather than its sampling precision.

  1. AIncreasing the number of historical observations in the sampleCorrect
  2. BShortening the holding period from ten days to one day while keeping the same sample
  3. CReplacing the portfolio's equity positions with bonds
  4. DMoving from a 95% to a 99% confidence level

Explanation

The standard error of a quantile estimate falls as the sample size grows, because more observations give more information about the tail. Moving to 99% pushes the quantile into a sparser region and raises the standard error. Changing the holding period or asset mix changes the VaR itself, not the sampling precision at a given sample size.

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