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

A firm uses historical simulation with a 500-day window to estimate 1-day 99% VaR. A risk officer wants the VaR estimate to be more precise at the 99% level without changing the confidence level. Which action most directly reduces the sampling error of the estimate?

Lengthening the window reduces sampling error because more observations fall in the tail beyond the 99% quantile. With 500 days only about five observations determine VaR; shortening the window would worsen precision, and horizon scaling does not address it.

  1. AShortening the window to 100 days so only recent data is used
  2. BLengthening the window so more observations lie in the tailCorrect
  3. CMultiplying the VaR by the square root of 10
  4. DReplacing the loss quantile with the median loss

Explanation

The 99% estimate relies on very few tail observations (5 of 500). A longer window increases the number of tail observations, reducing sampling error, though it may slow responsiveness. A 100-day window leaves only 1 tail observation. Square-root-of-time scaling changes the horizon, not precision.

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