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FRM Part I · FRM Exam Part I · Simulation and Bootstrapping

A risk manager simulates 10,000 independent one-day portfolio losses and estimates the mean loss as 2.0 with sample standard deviation 15.0. Using a normal approximation, what is the approximate 95% confidence interval (z = 1.96) for the true mean loss?

The 95% confidence interval is roughly 1.71 to 2.29. The standard error is 15 divided by 100, or 0.15, and the margin is 1.96 times 0.15, about 0.294, added to and subtracted from the mean of 2.0.

  1. A1.71 to 2.29Correct
  2. B0.53 to 3.47
  3. C-27.4 to 31.4
  4. D1.41 to 2.59

Explanation

Standard error = 15/sqrt(10,000) = 0.15. Margin = 1.96 x 0.15 = 0.294. Interval = 2.0 +/- 0.294 = 1.71 to 2.29. The -27.4 to 31.4 option uses s rather than the standard error, and 0.53 to 3.47 uses a standard error of 0.75.

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