FRM Part II · FRM Exam Part II · Financial Correlation Modeling - Bottom-Up Approaches
In a one-factor Gaussian copula, each firm's latent variable is x_i = sqrt(rho)*M + sqrt(1-rho)*Z_i, with M and Z_i independent standard normals. If rho = 0.36, what is the correlation between the latent variables of any two firms?
The pairwise correlation equals 0.36. Both latent variables load on the common factor with sqrt(rho), so their covariance is rho, and with unit variances this is the correlation. The 0.60 figure is only the factor loading, not the pairwise correlation.
- A0.60
- B0.36Correct
- C0.13
- D0.64
Explanation
Cov(x_i,x_j) = sqrt(rho)*sqrt(rho)*Var(M) = rho = 0.36, and each variance is 1, so correlation is 0.36. The distractor 0.60 is sqrt(rho), the loading, wrongly used as the pairwise correlation. 0.64 is 1-rho, the idiosyncratic weight.
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