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FRM Part II · FRM Exam Part II · Non-parametric Approaches

An analyst runs a bootstrap on a historical sample of 1,000 daily losses. In each of 200 bootstrap iterations, she draws 1,000 observations with replacement and records the 95% VaR. The average of the 200 VaR estimates is USD 4.10 million, and the standard deviation of those estimates is USD 0.30 million. Using the bootstrap standard error and a normal approximation, what is the approximate 95% confidence interval for VaR (use 1.96)?

The bootstrap standard error equals the standard deviation of the resampled VaR estimates, USD 0.30 million. Multiplying by 1.96 gives about 0.59, so the 95% interval is 4.10 plus or minus 0.59, roughly USD 3.51 million to USD 4.69 million.

  1. AUSD 3.51 million to USD 4.69 millionCorrect
  2. BUSD 3.80 million to USD 4.40 million
  3. CUSD 3.81 million to USD 4.39 million
  4. DUSD 3.51 million to USD 4.40 million

Explanation

The bootstrap standard error is the standard deviation of the bootstrap VaR estimates, 0.30. The margin is 1.96 x 0.30 = 0.588. The interval is 4.10 +/- 0.588, i.e. 3.512 to 4.688, about 3.51 to 4.69. Using 1 standard error (3.80 to 4.40) understates the interval width.

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