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FRM Part I · FRM Exam Part I · Sample Moments

X and Y are standardized variables that follow a bivariate normal distribution with correlation 0.60. For this distribution, the coskewness is zero and the cokurtosis k(X,X,Y,Y) = E[X^2 Y^2] equals 1 + 2ρ^2. What is k(X,X,Y,Y)?

The cokurtosis is 1.72. For a bivariate normal with standardized variables, E[X²Y²] equals 1 plus twice the squared correlation, so 1 + 2(0.36) = 1.72. Using 1.00 ignores correlation, and 3.00 is univariate kurtosis.

  1. A1.36
  2. B1.72Correct
  3. C1.00
  4. D3.00

Explanation

With ρ = 0.60, ρ^2 = 0.36, so k = 1 + 2(0.36) = 1.72. Using 1 + ρ^2 gives 1.36, which drops the factor of 2. The value 1.00 applies only when ρ = 0, and 3.00 is the univariate normal kurtosis, not this cross measure.

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