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FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches

Two independent standard normal variables Z1 and Z2 are drawn in a Monte Carlo simulation. To simulate correlated shocks with correlation 0.60, an analyst sets X1 = Z1 and X2 = 0.60 Z1 + k Z2. What value of k makes X2 have unit variance?

The value is 0.80. For X2 to have unit variance, 0.60 squared plus k squared must equal one, so k squared is 0.64 and k is 0.80. This is the Cholesky-style construction, and it also preserves correlation of 0.60 with X1.

  1. A0.40
  2. B0.64
  3. C0.80Correct
  4. D0.84

Explanation

Var(X2) = 0.36 + k^2 = 1, so k^2 = 0.64 and k = 0.80. Check: Corr(X1,X2) = 0.60 because Cov = 0.60. Using 0.40 (1 - rho) or 0.64 (k^2 without the root) are common mistakes.

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