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

A bank's historical-simulation 99% VaR, based on 500 daily observations, has a standard error of 0.40% of portfolio value. Risk management wants the standard error at the same confidence level reduced to 0.10%. Assuming the shape of the return distribution is unchanged and observations are independent, approximately how many observations are required?

About 8,000 observations are needed. Standard error scales with 1/sqrt(n), so reducing it fourfold from 0.40% to 0.10% requires sixteen times the data: 500 x 16 = 8,000. Quadrupling the sample to 2,000 would only halve the standard error.

  1. A8,000Correct
  2. B2,000
  3. C4,000
  4. D1,000

Explanation

The quantile standard error is proportional to 1/sqrt(n). Cutting it from 0.40% to 0.10% is a factor of 4, so sqrt(n) must rise by 4 and n by 16. The required n is 500 x 16 = 8,000. The 2,000 option multiplies n by only 4, confusing the factor on se with the factor on n.

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