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FRM Part I · FRM Exam Part I · Calculating and Applying VaR

When simulating correlated risk factors for a Monte Carlo VaR of a portfolio with two assets, which step correctly introduces the desired correlation into independent standard normal draws?

Apply the Cholesky decomposition of the covariance or correlation matrix to the independent standard normal draws. Multiplying the draw vector by the lower triangular factor yields correlated variables with the desired covariance structure, which is the standard method in Monte Carlo VaR.

  1. AMultiply the independent draws by the correlation matrix elementwise
  2. BApply the Cholesky decomposition of the covariance (or correlation) matrix to the vector of independent drawsCorrect
  3. CSort each set of draws independently from smallest to largest
  4. DAdd the correlation coefficient to each draw

Explanation

Cholesky decomposition factors the matrix as LL', and multiplying independent standard normal vectors by L produces draws with the target covariance structure. Elementwise multiplication or adding the coefficient does not give the correct covariance. Sorting each set independently would destroy pairing and push correlation toward one.

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