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FRM Part II · FRM Exam Part II · Credit Value at Risk

Two obligors, A and B, each have a one-year default probability of 10%. The joint default probability is 2%. What is the default correlation (the correlation between the default indicator variables)?

The default correlation is 0.111. Covariance is the joint default probability 2% minus the product 1%, giving 0.01, and each default indicator has variance 0.10 times 0.90, which is 0.09. Dividing 0.01 by 0.09 gives about 0.111.

  1. A0.111Correct
  2. B0.200
  3. C0.011
  4. D0.020

Explanation

Cov = P(AB) - P(A)P(B) = 0.02 - 0.01 = 0.01. Variance of each indicator = 0.10 x 0.90 = 0.09. Correlation = 0.01/0.09 = 0.111. The 0.011 distractor divides by 0.9 instead of 0.09; 0.20 confuses the joint probability with correlation.

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