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

A risk manager needs two correlated standard normal variables with correlation 0.80 from independent standard normals Z1 and Z2. Using the Cholesky approach, X1 = Z1 and X2 = 0.80·Z1 + k·Z2. Given Z1 = 1.0 and Z2 = -0.5, what is X2?

X2 equals 0.50. Unit variance requires k = sqrt(1 - 0.64) = 0.6, so X2 = 0.8 × 1.0 + 0.6 × (-0.5) = 0.8 - 0.3 = 0.50.

  1. A0.50
  2. B0.80
  3. C0.20Correct
  4. D0.60

Explanation

For unit variance of X2, 0.8² + k² = 1, so k = 0.6. Then X2 = 0.8(1.0) + 0.6(-0.5) = 0.8 - 0.3 = 0.50. Using k = 0.2 or omitting the Z2 term would give wrong values; only 0.50 follows from the data.

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